NISTIR 6055

NIST Construction Automation Program

Report No. 3

Electromagnetic Signal Attenuation

in Construction Materials

Building and Fire Research Laboratory

Gaithersburg, Maryland 20899

United States Department of Commerce

Technology Administration

National Institute of Standards and Technology
NISTIR 6055

NIST Construction Automation Program

Report No. 3

Electromagnetic Signal Attenuation

in Construction Materials

William C. Stone

October 1997

Building and Fire Research Laboratory

National Institute of Standards and Technology

Gaithersburg, Maryland 20899

U.S. Department of Commerce

William M. Daley, Secretary

Technology Administration

Gary R. Bachula, Acting Under Secretary for Technology

National Institute of Standards and Technology

Robert E. Hebner, Acting Director

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

O2@@@@6K ?

W2@@@@@@@@6XgW2@@@@@@@@6K ? O2@@@@@@he?W&@@@@@@@@@@)X?f7@@@@@@@@@@@@? ?

W2@@@@@@@@@@@@he?7@@@@@@@@@@@@1?f@@@@@@@@@@@@@? ?

7@@@@@@@@@@@@@heJ@@@@(M??I'@@@@Lf@@@@@@@@@@@@5? ? @@6Xe3@@@@@@@@@@0M?he7@@@(YfV'@@@1f@@@@@?fI(Y?hf?O@K ?

@@@1eV4@@@@@@@@ @@@@H?f?N@@@@f@@@@@? O2@@@@@6K? ?

@@@@gI'@@@@ @@@@h@@@@f@@@@@? ?@@@@@@@@@@6X? ? @@@@6Xf@@@@L?f?N@@@@ @@@@h@@@@f@@@@@@@@@6X?heJ@@@@@@@@@@@1? ?

@@@@@)X?e3@@@1?g@@@@ @@@@h@@@@e?J@@@@@@@@@@1?h?W&@@@@@@@@@@@@L ?

?O)Xf@@@@@@)XeN@@@@Lg@@@@ @@@@h@@@@e?7@@@@@@@@@@@?h?7@@@@fI'@@@1 ? ?O2@@)X?e3@@@@@@)X??@@@@1g@@@@L?hf@@@@L?g@@@@e?@@@@@@@@@@@@?hJ@@@@5f?N@@@@L? ?

O2@@@@@@,?eN@@@@@@@)X?@@@@@g@@@@1?hf@@@@)Xg@@@@e?@@@@@ 7@@@@Hg3@@@,?eW2@@@@@@@6X? ?

O2@@@@@@@(Y?e?@@@@@@@@)X@@@@@g3@@@@?hf3@@@@)K??O2@@@@5e?@@@@@ @@@@@?gV4@0Y??W&@@@@@@@@@)X ?

W2@@@@@@@@0Yf?3@@@@@@@@@@@@@@L?fN@@@@LhfV'@@@@@@@@@@@@@He?@@@@@ @@@@@?hfW&@@@@@@@@@@@)X? ?

7@@@@@@0M?g?N@@@@X?@@@@@@@@1?f?@@@@1hf?V'@@@@@@@@@@@@?e?@@@@5 @@@@@?hf7@@@@(M?I4@@@@1? ?

@@@@@@hf@@@@1?@@@@@@@@@?f?@@@@@ V4@@@@@@@@(Mf?@@@(Y @@@@@?he?J@@@@(Yf?@@@@? ?

3@@@@@fO2@6X?e3@@@@??I'@@@@@@?f?@@@@@ I4@@@@@0Y?f?@@0Y? @@@@@?fW26Xe?7@@@(Y?f?3@@@L ? ?W26X?eV'@@@@?O2@@@@@,?eN@@@@?eN@@@@@@Lf?@@@@@ 3@@@@?e?O&@@1e?@@@@Hg?N@@@1f?W26X? ?

O&@@1?e?N@@@@@@@@@@@0Y?e?@@@@Le?@@@@@@,gI@M? V'@@@@6?2@@@@@e?@@@@?h@@@@fW&@@)X ?

?@@@@@@Lf@@@@@@@@@(M?f?3@@@1fI'@@0Y ?V'@@@@@@@@@@5e?@@@@?g?J@@@@f7@@@@1 ?

?3@@@@@)X?e3@@@@@@@0Yg?N@@@@f?V+M V'@@@@@@@@(Ye?@@@@?g?7@@@5e?J@@@@@@ ?

?N@@@@@@1?eN@@@@@(Mhe@@@@ ?V4@@@@@@0Y?e?@@@@?g?@@@@HeW&@@@@@@ ?

@@@@@@@Le?3@@@@f?O2@@@e@@@@ ?I4@0Mg?@@@@LgJ@@@@?e7@@@@@@@ ? ?O2@6Xf3@@@@@@1e?N@@@@)K?O2@@@@@ ?3@@@)K?e?O&@@@5??J@@@@@@@@f?O@K ?

@@@@@)X?eN@@@@@@@L?e3@@@@@@@@@@@@5 ?N@@@@@6KO2@@@@@H??7@@@@@@@5e?W2@@@6X ?

@@@@@@)Xe?@@@@@@@)XeN@@@@@@@@@@@0Y @@@@@@@@@@@@@@eJ@@@@@@@@HeW&@@@@@1 ?

@@@@@@@)X??@@@@@@@@1e?@@@@@@@@0M? ?I'@@@@@@@@(M??W&@@@@@@@@??W&@@@@@@@ ?

3@@@@@@@)K?@@@@@@@@@L??3@@@@@0M? V4@@@@@@0Ye?7@@@@@@@@5?W&@@@@@@@5 ?

?W2@@@eV'@@@@@@@@@@@@@V'@@@1??V4@@0M? ?I@MgJ@@@@@@@@@YO&@@@@@@@(Y ? W&@@@@e?N@@@@@@@@@@@@@LN@@@@L 7@@@(Y@@@@@@@@@@@@@(Y?eW26X ?

?W&@@@@5f3@@@@@@@@@@@@1?3@@@, @@@@H?@@@@@@@@@@@@@Hf7@@)K? ?

W&@@@@(YfV'@@@@@@@@@@@@?V'@(Y 3@@5?J@@@@@@(Y@@@@5?e?J@@@@@@ ? ?O&@@@@@H?f?N@@@@W@@@@@@@eV+Y? V40Y?7@@@@@(YJ@@@@H?eW&@@@@@@ ?

?W2@@@@@@@L?g3@@@@<I'@@@@ ?@@@@@(YW&@@@5e?W&@@@@@@5 ?

W&@@@@@@@@1?gN@@@@L?V'@@5 ?3@@@(Y?7@@@(Ye?7@@@@@@@H ? 7@@@@@@@@@@Lg?3@@@1eV40Y ?V4@0Y?J@@@@H?e?@@@@@@@5? ?

3@@@0?'@@@@)X?f?N@@@@L? ?7@@@5e?@@@@@@@@@H? ?

V40MeV'@@@@1?g3@@@,? ?@@@@HeJ@@@@@@@@5fO2@@6X ?

?V'@@@@LgV4@0Y? ?3@@@??W&@@@@@@@@HeW2@@@@@)X? ?

V'@@@)X? ?V+MeW&@@@@X@@@@??O&@@@@@@@1? ?

W2@@6Kh?N@@@@)X 7@@@(R@@@@@W2@@@@@@@@@@? ?

?W&@@@@@6Xh3@@@@)X? @@@(Y?@@@@@@@@@@@@@@@? ?

W&@@@@@@@1hV'@@@@1? @6X? ?W2@ @@0Y?J@@@@@@@@@@@@@@5? ?

?O&@@@@@@@@@h?V'@@@5? @@)K W&@@L? ?7@@@@@@@@@@@@@(Y? ?

@@@@@(MI'@@@heV4@0Y? @@@@6X ?W&@@@@? ?@@@@@@@@@@@@@(YfW2@6X? ?

?J@@@@0YeN@@@@6X? @@@@@)X? W&@@@@H? ?@@@@@0Y@@@@@(Y?e?W&@@@)X ?

W&@@@?fJ@@@@@)K @@@@@@)X ?W&@@@@@L? ?3@@0M?J@@@@(YfO&@@@@@)K? ?

*@@@@?f7@@@@@@@6X 3@@@@@@)X? O&@@@@@@@? ?V+MeW&@@@(Y?eW2@@@@@@@@@@ ?

V'@@@@6Ke@@@@@@@@@)K? N@@@@@@@)K W2@@@@@@@@H? ?W&@@@@He?W&@@@@@@@@@@@L? ?

?V'@@@@@@@@@@@@@@@@@@( ?@@V4@@@@@6X ?W&@@@@@@@@@ ?*@@@@5?eW&@@@@@(?'@@@@)X ?

V'@@@@@@@(M??I'@@@(Y ?@@?e@@@@@)K? O&@@@@@@@@@@ ?V'@@(Y??W&@@@@@@??V'@@@@)X? ?

?V'@@@@@@HfV4@0Y? ?3@?e3@@@@@@6X? O2@@@@@@@@@@@@ V40YeW&@@@@@@@)X?V'@@@@1? ?

V'@@@@@? ?N@LeN@@@@@@@)K W2@@@@@@@@@@@@@@ ?W&@@@@@@@@@)X?V4@@@@? ?

?V'@@@@? @)X??3@@@@@@@@6K ?O&@@@@@@@@@@@@@@5 ?7@@@@(MI'@@@)X??I4@@? ? N@@@@@@? @@)X?V'@@@@@?@@@6K ?W2@@@@@@@@@@X@@@@@H ?@@@@@H??V'@@@)X ?

?3@@@@@L @@@)K?N@@@@@@@@@@@6K O&@@@@@@@@@@V@@@@@@? ?3@@@@L?eV'@@@1 ?

W26Khe?V4@@@@1 3@@@@6X@@@@@@@@W@@@@6X ?W2@@@@@@@@@@@@@@@@X@@@? ?V'@@@)Xe?V'@@5g?O)X ? ?W&@@@@6K?he@@@5 N@@@@@@@@@@@@@@@Y?@@@)K? O&@@@@@@@@@@@@@@@@>@@@@? V'@@@)X?eV40Yf?W2@@)X? ?

?7@@@@@@@@6Kh@@0Y ?@@@W@@@@@@@@@@@@@@@@@@6X? O2@@@@@@@@@@@@@@@@@>@@@@5? ?V'@@@)XheO&@@@@1? ?

?3@@@@@@@@@@@6K? ?3@@@>@@@@@@@@@@@@@@@@@@)K W2@@@@@@@@@@@@@@@@@XV@@@@(Y? V'@@@)X?gW2@@@@@@@L ? ?N@@@@@@@@@@@@@@@6K? ?N@@@@UI4@@@@@@@@@@@@@@@@@6X ?W&@@@@@@@@@@@@@@@0MS@@@@@@H ?N@@@@1?f?O&@@@@@@@@1 ?

3@@@@W@@@@@@@@@@@@ 3@@@)K?I4@@@@@@@@@@@@@@@@)X? W&@@@@@@@@@@@@@@@??O&@@@@@@? 3@@@5?e?W2@@@@@@@@@@@L? ? N@@@@@<?@@@@@@@@@5 N@@@@@6Ke@@@@@@@(?4@@@@@@)X ?W&@@@@(M?I4@@@@@@@W2@@@@@@@@? V4@0Y?eO&@@@@@(M??@@@)X ?

?3@@@@e@@@@@@@@0Y ?@@@@@@@@@@@@@@?@HeI'@@@@@1hO26Kh?7@@@@@Hf?@@@@@@@@@@@@@@@5? W2@@@@@@@?e?3@@@1 ?

?V'@@@@@@@@(M? ?3@@@@?@@@@@@@@@@?e?V'@@@@@L?f@@@@@@@@@@fJ@(Y@@5?eW2@@@@@@@@@@@@@@@@H? ?W&@@@@@@@@1e?N@@@@ ?

V'@@@@@@(Y ?N@@@@@@?W@@@@@@@@@?eN@@@@@1?f@@@@@@@@@@L?e7@HJ@(Y?e7@@@@@@X?@@@@@@@@5 ?7@@@@@@@@@@e?J@@@@L? ?

?N@@@@@(Y? 3@@@@@@@Y??@@@@@5?e?3@@@@@??W2@@@@@@@(M?@1??J@@W&@Hf3@@@@@V@@@@@@@@@@H ?3@@@(M??@@@@6?&@@@@@? ?

3@@@@H V'@@@@@@@@@@@@@@Y?e?V'@@@@?O&@@@@@@@@H??@@L?7@@@@@?fV@@@@@@@@@@@@@@@5? ?N@@0Ye?3@@@@@@@@@@H? ?

?O2@6KgN@@@@L ?N@@@@?W@@@@@@@@@6K?eN@@@@@@@@@X?I4@@e?@@1?@@@@@5??W2@@@@@@@@@@@@@@@@@H? @Mf?N@@@@@@@@@@ ?

?W2@@@@@6Xf?3@@@1 @@@@@@Y?@@@@@@@@@@e?@@@@@@@@@)Xg?3@@?@@?@@H??7@@@@@?@@@@@@@@@@@5 @@@@@@@(M? ?

W&@@@@@@@)X?e?V'@@@ 3@@@@@@@@@@@@@@@@@e?@@@@@@@@@@1g?N@@@@@?@@e?@@@@@@@@@@@@@@@@@@H ?J@@@@@@0Y ? ?W&@@@@@@@@@1?fN@@@ N@@@@@@@@@@@@@@@@@e?@@@@@@@@@@@h@@@@@?@@W2@@@@@@@@@@@@@@@@@@5? W&@@@(M? ?

?7@@@@(?'@@@@?f?@@@ ?3@@@@@@?@@@@@@@@@@@@@@@@(M?e@5h@@?@@@@@@@@@@@e?@@@@@@@@@@(Y? ?O&@@@(Y ?

J@@@@(Y?N@@@@? ?V'@@@@@@@@@@@e@@@@@@@@@He?J@Hh@@?@@@@@@@@@@@@@@@@@@@@@@@@H @@@@@(Y? ?

7@@@(Ye?@@@@? N@@@@@@@@@@@@@@@@@@@@@@?eW&@?h@@?@@@@@@@@@@@@@@@@@@@@@@@5? 3@@@(YfO2@@@@@@@6X? ?

?J@@@@fJ@@@5? ?3@@@@@?@@@@@@@@@@@@@@@??W&@@?e?O@Ke@@?@@@@@@@@@@@@@@@@?@@@@@(Y? V'@(Y?eW2@@@@@@@@@@)X ?

?7@@@@)K?O&@@@H? ?V'@@@@?@@@@@@@@?@@@@@@?O&@@@@@@@@@@@@@@@@@@X@@@@@@@@@@@@@@@@@@H ?V+Yf7@@@@@@@@@@@@)X? ?

?3@@@@@@@@@@@5 V'@@@@@@V'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@V@@@@@@@@@??@@@@@@@5? ?J@@@@@@@@@@@@@@1? ?

?V4@@@@@@@@@@H ?N@@@@@@?N@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@(M?W@@@??@@@@@@(Y? W&@@@(M?e?I'@@@@? ?

?I4@@@@@@@@L 3@@@@@e@@@@@?I'@@@@@@@@@@@@@@0Me@@@@@@@(Y?W&@@@@@@@@@@@H 7@@@@HgV'@@@? ?

?I4@@@@@@)K? N@@@@@@@@@@@@??V'@@@@?hf@@@@@@(Ye7@@@@@@@@@@@5? @@@@5?g?N@@@L ?

?I'@@@@@@6X? ?3@@@@@@@@@@@?eV'@@5?hf@@@@@@H?e@@@@@@@@@@@(Y? ?J@@@@H?g?J@@@@ ?

?W2@@?gV4@@@@@@)X ?V'@@@@@@@@@@@@@e@@H?he@@@@@@@@e@@@@@@@@@@@@@H ?@@@@@h?7@@@H ?

?7@@@?hI'@@@@@, V'@@@@@@@@@@@@W&@5hf@@@@@@@@e@@@@@@@@@@@@5? ?N@@@@L?g?@@@@? ?

J@@@5?h?V4@@@(Y ?N@@@@@@@@@@@@@@@Hhf?I4@@@@@@@@@@@@@@@@@@(Y? @@@@1?g?@@@5? ? 7@@@H??W26X?f?I40Y? 3@@@@@@@@@@@@@@? ?W@@@@@@@@@@@@@@@@(Y 3@@@@?g?@@0Y? ?

@@@5e?7@@1? V'@@@@@@@@@@@@@?he?@@@@(Y@@@@@@@@@@@@@@@H? V'@@@@@@6X ?

?J@@@HeJ@@@5?eW2@@ ?V'@@@@@@@@@@@@?hf@@0Y?@@@@@@@@@@@@@@5 ?V'@@@@@@1 ? W&@@@?e7@@@H??W&@@@ N@@@@@@@@@@@@?heO&@XeJ@@@@@@@@@@@@@@H V4@@@@@5h?O)X ?

7@@@@?e@@@5e?7@@@@ ?3@@@@?@@@@@@?h?'@@@1e7@@@@@@@@?@@@@@? ?I4@0YgO2@@@)X? ? @@@@@?e@@@He?@@@@5 ?V'@@@@@@@@@@?h?V'@@@e@@@@@@@@@@@@@? O2@@@@@@1? ?

?J@@@@@@@@@@@?eJ@@@(Y V'@@@@@(Y@@?heV'@@@@@@@@e@@@@@@5? ?O2@@@@@@@@@@? ?

?'@@@@@@@@@@@?e7@@@H? ?N@@@@@HJ@@Lhe?V4@@@@@@@e@@@@@@H? O2@@@@@@@@@@@@@L ?

?V4@@@@@@@@@@?e@@@@ 3@@@@W&@@1 @@@@@@@@@@@5 W2@@@@@@@@@@@@@@@1 ?

I4@@@@@@@@@@@@@5 V'@@@@@@@@ @@@@@@@@@@(Y 7@@@@@@@@@@(?'@@@@ ?

I4@@@@@@@@@@@H ?N@@@@@@@@L? @@@@@@@@@(Y? @@@@@@@@@@@??N@@@@L? ? ?I4@@@@@@@5? 3@@@@@@@1? @@@@@@@@@H @@@@@?e@@@1e3@@@1? ?

?I4@@@@@H? V'@@@@@@@? @@@@@@@@@? 3@@@@?e@@@@eN@@@@L ?

?I4@@@ ?V4@@@@@@Lf?@@@@?f@@@@@@(M N@@@@?e3@@@L??@@@@1 ? ?O2@@6K? @@?@@1f?@@@5?f@@@@@@H? ?3@@@LeN@@@1??3@@@5 ?

?@@@@@@@@@6K ?J@@?@@5f?@@@H?f3@@@@@L? ?N@@@1e?3@@@??V4@0Y ?

J@@@@@@@@@@@6X ?7@@X@@Hf?3@5gN@@W@@1? @@@@e?V4@@? ?

?W&@@@@@@@@@@@@)X? J@(R@@5?g@Hg?3@@R'@L 3@@@L? ?

?7@@@(M??I4@@@@@)X 7@H?@@H?f?@@Lg?V@@?N@1 N@@@1? ? J@@@@Hf?I'@@@@1 ?J@5e@@W2@@e?N@1f?O2@@@e@@ ?3@@5? ?

7@@@5?gV'@@@@ ?7@He@@@@@@W2@?@@?@@?@@@@@@e3@ ?V40Y? ?

@@@@H?g?N@@@@ ?@@?e@@@@@@@@@?@@?@@?@@@@@@eN@ ?

@@@@L?h@@@@ ?@@?e@@@@@@@@@?@@?@@@@@@@@@eJ@ ?

?J@@@@)Kh@@@@ ?@@Le@@@@@@@@@?@@?@@@@@@@@@e7@L? ?

?7@@@@@@@6K?e?J@@@@ ?@@)X?@@@@@@@@@?@@@@@@@@@@@@e@@)K ? ?3@@@@@@@@@@6KO&@@@5 ?O2@@@@6KO2@@@@@)X@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6X? ?

?V4@@@@@@@@@@@@@@@@H @@@@@@@@@@@@@@@@@@@@@(MI4@@@@@@@@@@@@@@0?4@@@@@@@@@@@@)X ?

?I4@@@@@@@@@@@5? @@(MeI4@@@@@@@@@@@@(Yf@@@@@@@@@@@@fI'@@@@@@@@@@@)X? ? I4@@@@@@@@H? @@g?@@@@@@@@@@@g@@@@@@@@@@@@L?e?V'@@@@@@@@@@@,? ?

I4@@@@ 3@)Kf?@@@@@@@@@@@)Kf@@@@@@@@@@@@)KfV@@@@@@@@@@(Y? ?

V'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@(Y ?

?V4@@@@@@0?4@@@@@@@@@@@@@@@0MI4@@@@@@@@@@@@@0M?I4@@@@0Y? ?

?

? W&?2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?

*@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ? V'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0?4@@@@@@@@@@@@@@@@@@@(?40M?e?I40?4@@@@0Mhf?I4@0Mf?I40?40MgI@M?I40M?I@MI4@@@@@@@@5? ?

?V'@@@X? ?@@@H? ?W@@@(Y? ?

V'@@1? W2@@@@ W&@@(Y ?

?N@@@? ?O&@@@@@hf?O2@@? ?W&@@(Y? ? @@@@6X ?O2@@0M?@@he?O2@@@@? W&@@(Y ?

?I'@@)X? ?W2@@(M?e@@h?O2@@@@@@L ?W&@@(Y? ?

N@@@)X ?7@@@Uf@@g?W2@@@(M?@@@ W&@@(Y ?

?@@@@)X? ?@@?V@@@@@@@g?7@@@0Y?J@@?hfO2@? ?W&@@(Y? ?

?@@@1? ?@@@@@@@@@@@g?@@?e?O&@@1heO2@@@? W&@@(Y ?

?3@@@? ?3@@@0M??@@@g?@@W2@@@@@@@hW2@@@@@? ?W&@@(Y? ? ?V'@@@@? ?V40M?e?@@@g?@@@@@0Y@@@@h7@@@@@@L ?7@@(Y ?

V'@@@? ?@@@g?@@@0Me@@@@h@@@@@@@1 ?@@(Y? ? ?N@@@? ?W2@@@@@@@@@ @@@@h@@@@@@@@ ?@@H ?

@@@? W&@@@@@@@@@@@@@@@?e?@@@@@@@@@h@@@@@@@@L? ?@@? ? @@@? ?W&@(Mf?W@@@@@@@?eJ@@@@@@@@@@@@@@@?J@@e@@@@)K ?@@? ?)X? ?

@@@? O&@@H?fW&@@@@?@5?e7@fI4@@@@@@@@?7@@@@@@@@@@@@@? ?@@? J@1? ?

@@@? O2@@@@g7@@@@@@@H?e@@he?@@@?@@@@@@@@@@@@@@? ?@@? 7@@L ? ?W-X @@@? W2@@@@@@L?f@@@@(?'@f@@gW2@@@@@@X@@?e?@@@@@@@@? ?@@? ?J@@@1 ?

?7@1 @@@? ?O&@@@X?@@)Kf@@@@H?N@f@@f?W&@@@@@@V@@@?e?@@@@@@@@? ?@@? W&@@@@ ?

J@@@L? @@@? ?O2@@(MS@@@@@@@@@@@@@@e?@f@@fO&@@@(Y@@?@@@?eJ@@@@@@@@L ?@@? ?O&@@@@@@@@@@@ ?

7@@@1? @@@? ?W2@@@0YW&@@@@@@@@@@@@@@@@@@L??J@@@@@@@@@@@Y?@@@@@@??O&@@@@??@@1 ?@@? @@@@@@@@@@@@@@@5 ?

?J@@@@@? @@@? O&@@0M?O&@@@@@@@@@@@@@@@@@@@)KO&@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@L? ?@@? @@@@@@@@@@@@@@(Y ?

O&@@@@@@@@@@@? @@@? O2@@(M?W2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@1? ?@@? ?I'@@@@@@@@@@(Y? ?

'@@@@@@@@@@@@@@@@? @@@? W2@@@0Y?O&@@0Y@@@?he?I'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?@@? V'@@@@@@@@@H ?

V4@@@@@@@@@@@@(M @@@? ?O&@@0M?W2@@(M?J@@5?eW26KgN@@@@?h?I@?4@@@@@@@@@@@@@@@@@@@@? ?@@? ?N@@@@@@@@@? ?

I'@@@@@@@@@(Y? @@@? ?O2@@(M??W&@@0Y??7@@H??W&@@@@(f?@@@@? @@@?e?W@@@Xf?@5? ?@@? ?J@@@@@@@@@? ? ?V'@@@@@@@@H @@@? ?W2@@@0YeW&@(M?e?@@5e?*@@@@(Yf?@@@@?f@@6Kg@@@?eW&@@@1f?@H? ?@@? ?7@@@@@@@@@? ?

?@@@@@@@@? @@@? O&@@0Me?O&@0Ye?@@@@?e?V'MI(Y?f?@@@@?e?J@@@@(?f@@@?e*@@@@5f?@ ?@@? ?@@@@@@@@@@? ?

7@@@@@@@@L @@@? W2@@0Me?W2@@?fJ@@@@)K?hf?@@@@?e?7@@@0Y?f@@@?eV4@@0Yf?@L? ?@@? ?@@(M??I4@@? ?

?J@@@@@@@@@1 @@@?hf?O&@(MfW&@@@?f7@@X@@@@@@@@@@@6K?e?@@@@?e?@@?h@@@?hf?@1? ?@@? ?@0Y ?

?7@@(MeI'@@ @@@?he?O2@@0Y?e?W&@(Mg@@>@@@@@@@@@@@@@@6K??@@@@?O2@@@@@6K?f@@@??O2@@@@@@6K??@@L ?@@? ?

?@@(Y?e?V4@ @@@?h?W2@@0M?fO&@(Y?f@@(R@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6Ke@@@@@@@@@@@@@@@@@@@1 ?@@? ? ?@0Y @@@?hO&@@gW2@@0Yf?J@@HJ@@V4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@L? ?@@? ?

@@@?g@@@@@@f?W&@(Mg?7@5?7@5he?I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@1? ?@@? ?

@@@?g@@@@@@@6K?O&@(Y?g?@(Y?@@H ?@@@(Mf?I4@@@@@@@@@@?f@@@?g@@@? ?@@? ?

@@@?g?I'@@@@@@@@@@YgO2@(Y??@@?f?W26X?gJ@@0Y?hfI'@@@?e?J@@@?g3@@L ?@@? ?

@@@?hV4@@@@@@@@@@@@@@@@@@@?e?@@?fW&@@)Xg7@ ?N@@5?eW&@@@?gV'@)X? ?@@? ?

@@@?heI'@@@@@@@@@@@@@@@@@)K??@@?f7@@@@)X?f@@g?O@Kh@@H?e7@@@@@@?f?V'@)X ?@@? ?

@@@?he?V4@@@@@@@@@@@@@@@@@@@@@@?f@@@@@@,?f@@g@@@@@?g@@f@@@@@@5?gV'@)K? ?@@? ? @@@?hf?I'@@@@@@@@@@@@@@@@@@@@?f?W@@@0Y?f@@g@@@@@Lg@@hW@Y?g?V@@@6X? ?@@? ?

@@@? V4@@@@@@@@@@@@@@@@@@@@6?2@@@Y?h@@f?J@@@@@1f?J@@L?e?O@?&@@@@@@@@@@@@@@@)K ?@@? ?

@@@? I'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6K?e@@fO&@@@@@@f?7@@)?2@@@@@@@@@@@@@@@@@@@@@@@6Xhf?@@? ? @@@? ?V4@@@@@@@@@@@@@@@@@@@@@@@eI4@@@6K?@@@@@@@@@@@@@@f?@@@@@@@0Me?@@@@@@@@@@@@@@@@@@)K?he?@@? ?

@@@? ?I4@@@@@@@@@@@@@@@@@@@@@@6K??I4@@@@@@@0Me?I4@@@@@6K?@@@@0M?f?@@@@@@@@@@@@@@@@@@@@6X?h?@@? ?

@@@? ?I'@@@@@@@@@@@@@@@@@@@@@@6K?e@@@@@Xhe@@@@@@@@X?fO2@@@@@@@@@@@@@@@@@@@@@@)?h?@@? ?

@@@? V4@@@@@@@@@@@@@@@@@@@@@@@@6X@@@@@)K?h@@@@@@@@)KeO2@@@@@@@@@@@@@@@@@@@@@@0Mhe?@@? ?

@@@? I'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0Mhf?@@? ?

@@@? ?V'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?@@? ?

@@@? ?O2@@@6XV'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?@@? ?

@@@?f?W2@@@@@@@@@@@@@@@@@@)KV@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?@@? ?

@@@LfO&@@@@@@@@@@@@@@0M?I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6K?he?@@? ?

@@@)K?O2@@@0M?f?@@@@Xf?I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6Kf?@@? ?

@@@@@@@@@0M?g?@@@@)K?g?@@@X?fI4@@@@@@@@0MeI4@@@@@@@@@(M?eI4@@@@@@@@@0M?I4@@@@@@@@@@(MfI4@@@@@@@@@?e?@@? ? @@@@@@0Mg?O2@@@@@@@@6K?eO2@@@@)Khe@@@XhI4@@@@@?gI4@@@@@@h?I'@@@@@H? ?@@? ?

@@@(M?gO2@@@@0MeI'@@@@@@@@@@@@@@6Kh@@@)K?h?@@@@)X?g?W@@@@he?@@@@@h?O2@h?@@? ?

@@@Hf?O2@@@@0M?f?V@@@@@@@@@?e@@@@@@@@@@@@0MI'@@6KfO2@@@@@@)KgO&@@@@@6K?f?O&@@@@@@6K?e?O2@@5h?@@? ?

@@@?eW2@@@@@0M?f?O2@@@@0?4@@@@@@@@@@@@@@@@@?e?V'@@@@@@@@@0MeI'@@@@@@@@@(M??I4@@@@@@@@@@(M??I'@@@@@@@@@(Yh?@@? ?O26X? ? O2@@6X @@@?e7@@@0MgO2@@@@0MfI4@@@@@@@0MI4@@@@?fV@@@@@@@@?f?V@@@@@@@@@Yf?W@@@@@@@@@Yf?@@@@@@@@@Y?fO2@??@@? ?O2@@@@@@@@@1? ?

O2@@@@@@@1 @@@?e@Mg?O2@@@@0M?he?I@MgI4@@@@@@@@(M?I4@@@6K?O2@@@0MI4@@@@6KeO&@@0?4@@@@@@@6?&@@@@@@@@@@@@@@@@@@??@@? ?@@@@@@@@@@@@@@@@@5? ?

?O2@@@@@@@@@@@ @@@?h?@@@@@0M I4@@@@@0Y?fI4@@@@@@0Mf?I'@@@@@@@(Me?I4@@@@@@@@(M?e?I'@@@@@@@(MeJ@@? J@@@@@@@@@@@@@@@@(Y? ? ?W2@@@@@@@@@@@@@ @@@?h?@@@@? @@@?hV@?@@@@@Y?g?@@@@@@YgV@@@@@@@Y??O&@@? 7@@@@@@@@@@@@@@@0Y ?

W&@@@@@@@@@0M? @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? @@@@@@@@@@@@@@ ?

7@@@@@@@0M 3@@@@@@?e@@@5 ?

@@@@ @@@?f?I4@@@@@@@@@@@@@ ?@@@@@@@ ?@@@@@@@@@@@@@0Mf?I'@@? V4@@@@@@@@@@@H ? ?J@@@5 @@@?hf?I4@@@@@@@@6K? ?@@@@@@@L? O@?2@@@@@@@@0M N@@? I'@@@@@@@@@? ?

?@@@@H @@@? I4@@@@@@@@@@6K J@@@@@@@1? ?O2@@@@@@@@@0M ?@@? ?V4@@@@@@@@L ?

?N@@@?he?O2@ @@@? I4@@@@@@@@@@@6K?he?W&@@@@@@@@LhfO2@@@@@@@@@@0M ?@@? I'@@@@@)X? ? @@@Lg?O2@@@@@L? @@@? ?I4@@@@@@@@@@6K?fO&@@@@@@@@@)K?fO2@@@@@@@@@@0M ?@@? ?V4@@@@@)X ?

@@@)K?eO2@@@@@@@@1? @@@?e?@@@@@@@6?@K I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0M O26?2@@@@@@@@@@@f?@@? ?I'@@@@1 ?

3@@@@@@@@@@@@@@@@@@? @@@?e?@@@@@@@@@@@@@@@@@@@@@@@@@@6K?O@K?h@@@@@@@@f@@@@@@@@@@@@@@f?O2@@@@6?2@@@@@@@@@@@@@@@@@@@@@@@@@@f?@@? V'@@@@ ?

N@@@@@@@@@@@@@@@0M @@@?hI4@@0M?I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@L?e@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0M? ?@@? ?V4@@@ ?

?@@@@@@@@@@0M? @@@? I4@0Y@?@@@@@@@@@@@@@@@@@)Ke@@@@@@@@@@@@@@@@@@@@@@@@ ?@@? W2@6K? ?

?I4@@@0M @@@? ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6K? ?@@? ?O&@@@@( ? ?O2@@? @@@? ?O@?2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6K ?@@? @@@@@@(Ye?W-X ?

O2@@@@@? @@@? ?O2@@@@@@@@@@@@@@0M?e@@@@@@@@@@@@@@@@e@@@@@@@@@@@@@@@@@@@??@X?I4@@@@@@@@@@@@@@@6K? ?@@? ?J@@@@@(Y?e?7@)X? ?

O2@@@@@@@? @@@?heO2@@@@@@@@@@@@0Mh?O2@@@@@@@@@@@@0M?@@e3@@@@@@@@@@@@@@@@@@@@@)KgI@?4@@@@@@@@@@@@6KO@K?g?@@? ?7@@@@0Yf?@@@)X ?

?O2@@@@@@@@@@? @@@?e?@@@@@@@@@@@@@@0M?he?O2@@@@@@@@@@@@@@0M?e@@eN@@@@@eI'@@@@@@@@@@@@@@@@6KhfI4@@@@@@@@@@@@f?@@? ?@@@@?g?@@@@1 ?

O2@@@@@@@@@@@@5? @@@?e?@@@@@@@@0M?hf?O2@@@@@@@X@@@@@@@@(M?f@@e?@@@@@e?V4@@@@@@@@@@@@@@@@@@6K? I4@@@@f?@@? ?@@@@?g?3@@@@ ? W2@@@@@@@@@@@@@(Y? @@@? ?O2@@@@@@@@X?V@@@@@@@@(Yg@@e?@@@@@f?I4@@@@@@@@@eI4@@@@@@@6K? ?@@? ?@@@@?g?N@@@@ ? 7@@@@@@@@@@@@@(Y @@@? O2@@@@@@0MeV@@@@@@@@@@0Y?g@@eJ@@@@@g?I4@@@@@@@@6K?eI4@@@@@@6K ?@@? ?@@@@?h@@@@ ?

3@@@@@0M?W@@@@H? @@@? O2@@@@@@0MfO2@@@@@@@@@0M?h@@e7@@@@@h?I4@@@W@@@@@6KfI4@@@@@@6K ?@@? ?@@@@Lh@@@@L? ? V4@0M?eW&@@@5 @@@?hfO2@@@@@@0MgO2@@@0MW@@@(M?he@@e@@@@@@he?I'@@YW@@@@@6KgI4@@@@@@6Khf?@@? ?@@@@)K?f?J@@@@,? ?

?W&@@@(Ye?O26X? @@@?hO2@@@@@@@0M?f?O2@@@@0M?O&@@0Yhf@@e@@@@@@hfV4@@@U?I4@@@6KhI4@@@@@@6Kh?@@? ?3@@@@@6K?eO&@@@(Y? ?

?7@@@(Y??O2@@@1? @@@?fO2@@@@@@@0M?g?O2@@@0MeW2@@(M @@e@@@@@@ I'@)K??I4@@@6KheI4@@@@@@6Kf?@@? ?V'@@@@@@@@@@@@@@H ?

J@@@@YO2@@@@@@@? @@@?e?@@@@@@0M?hW2@@@@0Me?O&@@0Y? @@e3@@@@@ ?V4@@6K??I4@@@@6K?heI4@@@@@?e?@@? V'@@@@@@@@@@@@5? ? ?W&@@@@@@@@@@@@@5? @@@?e?@@0M?he?O&@@@0Me?O2@@0M? @@eN@@@@@ ?I'@@6X?eI4@@@6K?he?I4@@?e?@@? ?V4@@@@@@@@@@(Y? ?

W&@@@@@@@@@@@@@0Y? @@@? O2@@@@0Me?W2@@(M? @@eJ@@@@@ V4@@)Kf?I4@@6K? ?@@? W&K?f?I4@@@@@@@0Y ? 7@@@@@@@@@@@0M @@@? O2@@@0M?fO&@@0Y @@e7@@@@@ I4@@6Kf?I4@@@6K ?@@? 7@@6K?gI4@0M? ?

@@@@@@@@@0M? @@@?he?O2@@@@0M?fW2@@(M @@e@@@@@@ I'@@6Xf?I4@@@6Khf?@@? ?J@@@@@6K? ?

@@@@@@0MhO2@@ @@@?h?O2@@@@0M?f?O&@@0Y? @@e@@@@@@ ?V4@@)K?gI4@@@6K?h?@@? ?'@@@@@@@6K? ?

@@@@0Mg?W2@@@@@ @@@?g?O2@@@0Mg?O2@@0M? @@?J@@@@@@ ?I'@@6X?gI4@@@6K?gJ@@? ?V4@@@@@@@@6K? ?

O&@@@@@@ 3@@?g@@@@0Mg?W2@@(M? @@?@@@@@@@ V4@@)KhI4@@@(g7@@? I4@@@@@@@6K? ? O2@@@@@@@5 N@@?g@@0MhO&@@0Y @@?N@@@@@@ I4@@6XhI40Yg@@@? I4@@@@@@@6X? ?

O2@@@@@@@@0Y ?@@? W2@@(M @@e@@@@@@ I'@)K? @@@? I4@@@@@@)X ?

O2@@@@@@@0M? ?@@L ?O&@@0Y? @@e3@@@@@ ?V4@@6X? @@@? I4@@@@@1 ? W2@@@@@@@(M?e?W26X? ?@@@hf?O2@@(M? @@e?@@@@@ ?I'@)K @@@? W2@@@6X?gI'@@@5 ?

7@@@@@@@0Yf?7@@)X ?@@?he?W2@@@0Y @@e7@@@@@ V4@@6Khf@@@? ?W&@@@@@)Xg?V4@0Y ?

@@@@@0M?g?3@@@1 ?@@1heO&@@(M ?J@@?J@@@@@@ I4@@6Xhe@@@? W&@@@@@@@)X? ?

3@@0M?h?N@@@@L? ?@@@hW2@@@0Y? ?7@@?7@@@@@@ I'@)K?h@@5? 7@@@@@@@@@)K ?

V+M?hf@@@@)X ?@@@g?O&@@0M? ?@@@?3@@@@@@ ?V4@@6X?g@@H? ?J@@@(M??@@@@@@6K? ?

?J@@@@@1 ?@@@g@@@0M? ?@@5?N@@@@@@L? ?I4@1?f?J@@ ?7@@(Ye?@@@@@@@@@6X ? W&@@@@@@L? ?3@@g@0M? ?@@He@@@@@@1? ?I@?f?7@@ J@@@H?eJ@@@@@@@@@@1 ?

?O&@@@@@@@)X ?N@@L? ?@@?e@@@@@@@? ?@@@ ?W&@@@L?e7@@@@@@@@@@5 ? ?O2@@@@@@@@@@1 @@1? ?@@?e@@@@@@@? J@@5 ?7@@@@)Ke@@@(M?I4@@@H ?

?W2@@@@@@@@@@@@@L? 3@@L ?@@?e@@@@@@@? ?W&@@H ?3@@@@@@@@@@@Hf?I@? ?

O&@@@@@@0M?I'@@@,? N@@)X? ?@@?e@@@@@@@? ?7@@5? ?V4@@@@@@@@@5? ?

W2@@@@@@0MfV4@0Y? ?3@@1? ?@@?e@@@@@@@? J@@(Y? ?I4@@@@@@@ ? 7@@@@@(M ?N@@@? ?@@?e@@@@@@@? ?O&@@H @6X?e?I'@@@@@)K ?

3@@@@0Y?heW26X @@@@6X ?@@?e@@@@@@@? ?W2@@@5? ?J@@1?fV4@@@@@@6X ?

V4@0M?he?W&@@)X? ?I'@@)K? ?@@?e@@@@@@@? O&@@@0Y? W&@@@?gI'@@@@@)X? ?

W&@@@@)X V'@@@6X? ?@@?e@@@@@@@? W2@@@(M? ?W&@@@5?g?V4@@@@@,? ?

?W&@@@@@@)X? ?V4@@@)K ?@@?e@@@@@@@? ?O&@@@0Y W&@@@(Y?h?I4@@(Y? ?

O&@@@@@@@@1? ?I'@@@6K ?@@?e@@@@@@@? ?O2@@@(M 7@@@(YeW26Xg?I(Y ? W2@@@@@@@@@@@L V4@@@@6K ?@@?e@@@@@@@? ?O2@@@@0Y? @@@(Y??W&@@1 ?

?W&@@@@@@?I'@@@)X? I4@@@@6K ?@@L?J@@@@@@@? ?O2@@@@0M? @@@@@HeW&@@@5 ?

O&@@@@@@@??V'@@@)X I4@@@@6K ?O2@@@@@@@@)?&@@@@@@@?e?W2@@@6K ?O2@@@@0M? ?J@@@@@??W&@@@(Y ?

?@@@@@@@@@@LeV'@@@1 I4@@@@@6K?g?O2@@@@6K?eO2@@@@@@@@@@@@@@@@@@@@@@@6?&@@@@@@@6K? ?O2@@@@0M? ?'@@@@@?O&@@@(Y?eO2@@ ? J@@@@@@@@@@)X??N@@@@ I4@@@@@6X?eW2@@@@@@@@@@@@@@@@0MgI4@@@@@@@@@@@@@@@0M??I'@@6X?he?O2@@@@0M? ?V'@@@@@@@@@@He?@@@@@ ?

?W&@@@@(MI'@@@)Xe@@@5 ?I4@@@)K?O&@@(M?eI4@@@@@(M?he?I'@X?f?@@@gV4@@)Xh?O2@@@@(M? V'@@@@@@@@5?eJ@@@@5 ?

?&@@@@@HeV'@@@1e?I(Y ?I'@@@@@@@(YgI4@@@H N@1?f?3@@hI'@)X?fW2@@@@@@0Y ?V'@@@@@@@e?W&@@@(Y ? ?@@@@?e?V'@@@g?W&K V4@@@@@@Y?h?@@? ?@@?g@@h?V'@)Xe?O&@@@@0M? W2@6X?eV4@@@@@@)KO&@@@(Y? ?

?3@@@@@?eN@@5gW&@@6X I4@@@@@6K?g?@@? ?@@?fW&@@L?hV'@)KO2@@@@0M? ?W&@@@)XfI'@@@@@@@@@@@H ?

?V'@@@@Le?@0Yf?W&@@@@1 ?I'@@@@6K?f?@@? J@5?e?O&@@@1?h?N@@@@@@@0M? ?7@@@@@)X?e?V'@@@@@@@@@5? ?

V'@@@1heW&@@@@@@ V4@@@@@6K?eJ@@?hf?W&@Y??O2@@@@@@?he@@@@@0M? ?3@@@@@@)XfV'@@@@@@@(Y? ?

?N@@@@h?W&@@@@@@@@6X? ?I4@@@@6KO&@@@@@6KhO&@@@@@@@@@@@@@@6Xf?O2@@@@0M? ?N@@@@@@@)X?e?V'@@@@@(Y ?

3@@@@@gW&@@@@@@@@@@1? ?I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@)K?O2@@@@@0M? 3@@@@@@@)XfV4@@@(Y? ?

V'@@@5f?W&@@@@0MI'@@@@? ?I4@@@@@@@?I4@@@@@@@@@@@@@@@@(M?eI4@@@@@@@@@@@0M? V'@@@@@@@)X?fI40Y ?

?V4@0YfW&@@@@fN@@@@L ?I4@@@@@fI'@@@(MI4@@@@@0Yg?@@@@@@@@0M? ?N@@@@@@@@)X ?

?W&@@@@5f?@@@@1 ?I4@@@@6K??V'@@?f@@@?h?@@@@@0M O2@@6Kf@@@@@@@@@)X? ? W&@@@@0Yf?@@@@@ ?I4@@@@6K?V@@)K?e@@@LgO2@@@@0M ?@@@@@@@6Xe3@@@@@@@@@)X ?

?W&@@@@?g?@@@@5 ?I4@@@@@@@@@@@@@@@@)X?eO2@@@@0M ?@@@@@@@@)K?V@@@@V'@@@@1 ?

?7@@@@@?gJ@@@@H I4@@@@@@@@@@@@@@)KO2@@@@0M ?3@@@@@@@@@@@@@@@LV'@@@@ ?

?3@@@@@?f?W&@@@@? I'@@@@@@eI4@@@@@@@@0M ?V'@@@@@@@@@@@@@@1?V4@@@ ?

?V'@@@@?fO&@@@@5? ?V4@@@@@f?@@@@@0M V'@@@@@@@@@@@@@@L? ?

V'@@@@6KO2@@@@@(Y? ?I4@@@@@@@@@@@0M ?V'@@@@@@@@@@@@@1? ? ?V'@@@@@@@@@@@(Y ?I4@@@@@@@0M O26KhV'@@@@@W@@@@@@@? ?

V'@@@@@@@@@(Y? I4@@0M ?@@@@@6Xg?V'@@@@@R4@@@@5? ?

?V4@@@@@@@0Y ?@@@@@@)K?gV'@@@@L?I4@0Y? ?

?I4@@@0M ?@@@@@@@@6X?f?V'@@@)X ?

?3@@@@@@@@)XgV'@@@)X? ?

O2@@@@6X ?N@@@@@@@@@)X?f?N@@@@,? ?

W2@@@@@@@)X? @@@@@@@@@@)Kg@@@(Y? ? 7@@@@@@@@@)X @@@@X?@@@@@@6Xf?I(Y ?

@@@@@@@@@@@1 @@@@)X@@@@@@@)K? ?

@@@@@Xe@@@@ 3@@@@@@@@@@@@@@6X? ? 3@@@@1e@@@@e?W&K N@@@@@@@@@@@@@@@)? ?

N@@@@@L?3@@@e?7@@@6K? ?3@@@@@@(MI4@@(M ?

?3@@@@)XV'@@e?3@@@@@6K? ?O2@6X ?N@@@@@(Y?eI(Y? ?

W2@6XV'@@@@)XV4@e?V'@@@@@@@6K ?O2@@@@1 @@@@(Y ?

7@@@1?V'@@@@1?gV'@@@@@@@@6X ?O2@@@@@@5 @@@@H? ? @@@@@??V'@@@@Lg?V'@@@@@@@@)X? W2@@@@@@@@0Y 3@@@L? ?

3@@@@?eN@@@@1h?@@@@@@@@@,? 7@@@@@@@0M N@@@,? ?

N@@@@?eJ@@@@@h7@@@@@@@@0Y? @@@@@@(M ?@@(Y? ?

?3@@@@6?&@@@@5g?J@@@@hfW2@6X? 3@@@@@H? ?@0Y ?

?V'@@@@@@@@@@Hg?7@@@@hf7@@@1? ?O2@@@@@6XfN@@@@@eO2@@@? ?

V'@@@@@@@@5?gJ@@@@5he?J@@@@@L ?W2@@@@@@@@)X?e?@@@@@@@@@@@@? ? ?V4@@@@@@0Y?g7@@@@HheW&@@@@@1f?W2@@@6K W&@@@@@@@@@@)Xe?3@@@@@@@@@@5? ? I4@0M?g?J@@@@5?h?W&@@@@@@@f?7@@@@@@@@@@6K ?W&@@@@@@@@@@@@)X??V'@@@@@@@@0Y? ?

?7@@@@H?h?7@@@@@@@@f?3@@@@@@@@@@@@@?eW2@@6KhfO2@@@@6K ?7@@@@(Me?I'@@@)XeN@@@@@@0M? ?

?@@@@5heJ@@@@@@@@@f?V4@@@@@@@@@@@@??W&@@@@@@@@@@@f?@@@@@@@@@6Xhf?@@@@(Y?fN@@@@1e?@@@@@ ? J@@@@Hh?W&@@@@@@@@@h?@@@@@@@@@5??7@@@@@@@@@@@@fJ@@@@@@@@@@1hf?@@@@Hg?@@@@@e?3@@@@L? ?

7@@@5?hW&@@@@e@@@@h?@@@@@eI(Y??@@@@@@@@@@@@5f7@@@@@@@@@@@L?he?@@@@?g?3@@@@e?N@@@@1? ?

3@@@H?h7@@@@@e@@@@h?@@@@@g?@@@@@(?4@@@0Yf@@@@eI'@@@@,?he?@@@@Lg?N@@@@f@@@@@? ? V4@@h?J@@@@@@@@@@@@h?@@@@5g?@@@@@H?he@@@@L??V4@@0Y?he?@@@@1h@@@@f3@@@@? ?

W&@@@@@@@@@@@@h?@@@@Hg?@@@@@hf@@@@)K ?@@@@@g?J@@@@fN@@@@? ?

?W&@@@@@@@@@@@@@hJ@@@@?g?@@@@@@@@@@6X?f@@@@@@@@6K ?3@@@@L?f?7@@@@f?3@@5? ?

?7@@@@(M?I4@@@@@h7@@@@?g?@@@@@@@@@@@1?f@@@@@@@@@@@6X?he?N@@@@)Xf?@@@@5f?V40Y? ? ?@@@@0Y?f@@@@h@@@@@?g?@@@@@@@@@@@@?f?I4@@@@@@@@@1?hf3@@@@)K?O2@@@@(Y ?

I@M?g@@@@h@@@@5?g?@@@@@@@@@@@@?g?I4@@@@@@@@LhfV'@@@@@@@@@@@(Y? ?

@@@@h@@@@H?g?@@@@(M? I4@@@@@1hf?V'@@@@@@@@@(Y ? 3@@@h@@@@h?@@@@?he?W2@6Xf?@@@@@ V4@@@@@@@0Y? ?

V4@@h@@@@hJ@@@@)K?h?*@@@)K?eJ@@@@5 I4@@@0M? ?

@@@5h7@@@@@@@@@@6K?e?N@@@@@6KO&@@@@H ?

@@0Yh3@@@@@@@@@@@@@f3@@@@@@@@@@@5? ?

N@@@@@@@@@@@@5fV'@@@@@@@@@0Y? ?

?@@@@@@@@@@@0Yf?V4@@@@@@0M? ?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?
Other Titles in the NIST

Construction Automation Series

Non-Line-of-Sight Construction Metrology

NISTIR-5825, February1996, 230 pp

Author: William C. Stone

Proceedings of the NIST Construction Automation Workshop

March 30-31, 1995

NISTIR-5856, May 1996, 158 pp.

Editor: William C. Stone

To order any of these, you may contact the National Technical 

Information Service or write NIST directly at 

Construction Automation Group

Building 226/B168

NIST

Gaithersburg, MD 20899

Tel: 301-975-6048

Fax: 301-869-6275

or via email to 

william.stone@nist.gov

lawrence.pfeffer@nist.gov
ABSTRACT

Laboratory studies of electromagnetic (EM) signal propagation through construction

materials were carried out as part of the NIST initiative in Non-Line-of-Sight surveying

technology. From these data it is possible to determine several important material-specific characteristics needed for the design of engineering systems which make use of

EM signal propagation through matter: 1) the power attenuation as a function of the

material thickness and 2) the values of the electrical permittivity and dielectric constants for a particular material as a function of frequency. The latter can be used to calculate the propagation delay time associated with an EM pulse penetrating through a

specified thickness of a given material. This information is essential for error compensation for time-of-flight metrology instrumentation systems. In this report, only the

power attenuation aspects are discussed; dielectric and permittivity constants will be

discussed in a future volume. The materials investigated included brick, masonry

block, eight different concrete mixes, glass, plywood, lumber (spruce-pine-fir), drywall,

reinforced concrete, steel reinforcing bar grids, variations of the plywood and lumber

tests in which the specimens were soaked with water, and composite specimens

involving brick-faced masonry block and brick-faced concrete. For each material, varying thickness specimens were fabricated in order to measure attenuation as a function

of penetration distance. Each specimen was placed in a special test range consisting of

spread spectrum transmission and reception horns spaced 2 meters apart with a metal

RF isolation barrier located midway between the antennas to eliminate multipath signals. The isolation barrier contained a window at its center against which the specimens were fit. Measurements of power loss were taken at 2 MHz intervals from 0.5 to

2 GHz and from 3 to 8 GHz. Frequency power spectra were discretely generated for

each material as a function of thickness and fit with closed-form predictor equations.

Coefficients for the predictor equations are provided.

KEYWORDS: building technology; construction materials; electromagnetic wave

propagation; metrology, non-line-of-sight metrology, signal attenuation, spread spectrum radar, surveying, wireless communications.

iii
Table of Contents

Abstract iii

Table of Contents v

Acknowledgement vii

1.0 Introduction 1

1.1 Background 1

1.2 Approach 2

1.3 Objectives and Scope 3

2.0 Experiment Description 5

2.1 RF Transmission System 5

2.2 Antenna Descriptions 14

2.2.1 “Low” Frequency Bandwidth (0.5 to 2.0 GHz) 15

2.2.2 “High” Frequency Bandwidth (3.0 to 8.0 GHz) 19

2.3 Test Fixtures 21

2.4 Specimen Design 24

2.5 Test Protocol 24

2.6 Post-Processing Procedures 26

3.0 Material Properties and Specimen Geometry 29

3.1 Brick 32

3.2 Masonry Block 37

3.3 Plain Concrete 42

3.4 Reinforced Concrete and Rebar Grid 47

3.5 Glass 49

3.6 Lumber 52

3.7 Plywood 56

3.8 Drywall 59

4.0 Frequency Power Spectra 61

4.1 Brick 63

4.2 Brick-Faced Concrete Wall 69

4.3 Brick-Faced Masonry Block 75

4.4 Plain Concrete: Mixture 1 81

4.5 Plain Concrete: Mixture 2 87

4.6 Plain Concrete: Mixture 3 93

4.7 Plain Concrete: Mixture 99

v
4.8 Plain Concrete: Mixture 5 105

4.9 Plain Concrete: Mixture 6 111

4.10 Plain Concrete: Mixture 7 117

4.11 Plain Concrete: Mixture 8 123

4.12 Masonry Block 129

4.13 Drywall 135

4.14 Glass 141

4.15 Lumber (Dry) 147

4.16 Lumber (Wet) 153

4.17 Plywood (Dry) 159

4.18 Plywood (Wet) 165

4.19 Reinforced Concrete 171

4.20 Rebar Grid 177

5.0 Summary 182

6.0 References 185

Appendix A: MatLab Scripts A.1

vi
Acknowledgement

The author would like to thank several researchers at M.I.T. Lincoln Lab, including

Dennis Blejer, Steven Scarborough, and Carl Frost, for their assistance with this project.

Their patience, and willingness to discuss at the chalk board, and via endless faxes and

email correspondences, fundamental theory and general “rules of thumb” relating to

radar and electromagnetic wave propagation through matter have contributed significantly to the present document. Thanks are also due to Thomas F. Rogers, a distinguished electrical engineer and communications pioneer, for his thoughts on the subject of EM penetration of matter. Lastly, the author thanks NIST technician Erik

Anderson and visiting summer researcher Jose Ortiz for their invaluable assistance in

the laboratory.

Left to Right: NLS Phase 2 Research Team: Carl Frost, Bill Stone, Steve Scarborough, and Dennis Blejer.

vii
1.1 Background

The NIST program in Construction

Automation seeks to develop, integrate,

and implement new technologies which

will permit generalized automation at the

construction job site. Research is presently focused on methods and standards for

closing the information loop from the job

site to a central dynamic, evolving project

database, and returning information from

that database in an on-demand, real-time

format to a wide variety of users at the

construction site. Current research

includes the development of a real-time,

non-line-of-sight surveying system that

can “see through walls;” the development of the National Construction

Automation Test Bed for testing various

automation mechanisms,standards, and

software; the development of kinematic

representation standards for construction

machinery and components; and the

development of standards for wireless

data telemetry packets for transmission

of information from the active job site to

a high bandwidth trunk line which links

the various project participants. 

Each of the above research areas leverage

upon the rapid advance of information

technology and infrastructure that has

occurred during the last decade and is still

continuing. The emergence of high speed

computer communication networks (the

“information superhighway”) and realtime, immersive, computer graphics (vir

tual reality) technologies presage the

imminent ability to manage remote construction sites from central offices; to

automate certain portions of the tasks performed by common construction

machines; and to provide information on

the state of such machines to operators

(on-site or remote) that would greatly

enhance their productivity. 

In order to achieve real automation in the

construction industry, a standard means

of rapidly interfacing any piece of

machinery to a construction-site database

must be developed. The development of

this standard is highly unlikely to be

addressed by the construction industry

itself, where corporate research budgets

are small in the United States. Nor will it

be developed by equipment manufacturers who, left to their own devices, tend to

develop closed, proprietary systems

which by their very nature inhibit the

free exchange of data with other systems

that might be operational at a construction site. In this respect, NIST has been

uniquely positioned, as a neutral entity,

to establish the framework for the integration of construction machinery into

emerging global database standards. The

underpinning to the above technology is

the ability to know the real-time position

of any piece of equipment and component on the construction site. Present

surveying tools suffer from many shortcomings in this regard, the most important of which is that they must operate

under line-of-sight conditions. The

development of a non-line-of-sight surveying system, which can in effect “see

through walls”, represents the pinnacle

1.0 Introduction

1
seamless metal walls distance measurements are feasible (see [1] for further

details). 

1.2: Approach

Although proof-of-concept data obtained

in 1995 was very encouraging, the accuracies obtained were far from those needed to be practical for machine automation

purposes. They were, however, sufficient

for other applications, such as personnel

tracking in unstructured environments.

Typical propagation delay errors when

penetrating a 500 mm thick slab of concrete were on the order of 800 mm. The

measured distance was thus 800 mm

longer than the true distance between the

transmitter and receiver. This error was

not affected by the range between the

transmitter and receiver, thus confirming

that most of the error was attributed to

the slower phase velocity of the signal as

it propagated through the concrete.

Thus, a clear path was identified by

which the phase propagation error could

be compensated. Briefly the approach

involves:

1) The development of empirically based

statistical models of the electromagnetic

characteristics for a large class of construction materials at varying frequencies

of transmission and

2) A method by which a real-time mathematical model of the construction site (in

the form of CAD solid model elements)

can be updated with sufficient robustness

to reflect the as-built condition of the site

and the material specification of the various components.

2

of construction site metrology and has

guided the focus of NIST research in

Non-Line-of-Sight (NLS) metrology.

Tests conducted at NIST from 1994

through 1997 proved the potential of

NLS technology to meet the above objectives [1, 2, 3]. If the technology can be

brought to practical implementation the

implications are profound. Briefly summarized, the technology involves the use

of ultra-wide bandwidth spread spectrum radio signals which are beamed

through non-metallic construction materials as a series of sequential, discrete frequencies. The same approach applies

equally well to an impulse baseband

transmission. A time-domain response is

reconstructed from the frequency power

spectrum and the time of flight from

transmitter to receiver is calculated by

comparing the measured response to a

free-space calibration between two or

more known points. Problems arise,

however, due to reduced propagation

velocities when penetrating solid media.

This leads to a delayed arrival of the

straight-line (true distance) transmission

pulse, thereby producing error in the calculated range relative to free space propagation. 

Other errors arise from scattering (dispersion) of the beam, refraction, and multipath reflections as well as instrumental

error. However, it was demonstrated, by

means of qualitative tests in 1994 [1] and

by extensive quantitative tests in 1996 [2],

that most common construction materials behave as non-conductors and can

therefore be successfully penetrated for

substantial distances, thereby allowing

range measurement. To be more emphatic, unless the building is constructed with
Given this foundation it is possible to

develop a software algorithm which

takes into account the site geometry and

material properties and predicts the

delay in the arrival of the transmitted

pulse due to propagation through engineering materials between the transmitter and receiver. In a more sophisticated

variant of this approach all of the physical phenomena associated with wave

propagation (including scattering, constructive and destructive interference,

reflection, and diffraction) may be taken

into account and the result used to correct the initial measurement. With sufficient local processing power (in the form

of a low power parallel processor array)

such compensations could be made in a

kinematic sense with update rates in

excess of the 10 to 20 Hz commonly associated with real-time machine control.

Work in 1996 and 1997, which forms the

basis of this paper, concentrated on

defining propagation and error characteristics of spread spectrum signal penetration through construction materials as a

function of the type of material (e.g.

glass, concrete, wood etc.), frequency

bandwidth, power, signal-to-noise ratio

(and techniques, both physical and analytical for improving same), and obstacle

geometry.

The resulting experimental data -- which

encompass behavior across 8 GHz of

bandwidth and comprise one of the most

complete sets of information concerning

electromagnetic (EM) attenuation in construction materials -- form the basis for

the development of auto-compensation

algorithms which will account for propagation delays as the signal passes

through different materials. It is the

propagation delay component that

accounts for most of the range error. 

Ongoing research is being directed to

developing a range-error compensation

model based on non-dispersive ray tracing techniques, which heretofore have

largely been used for computer graphics

rendering and intra-building cellular

phone base station coverage simulators.

In this work, CAD models of simulated

construction sites are being developed

and material characteristics, based on the

extensive empirical EM material data

reported herein, are being attached to

entities in the CAD model. This model

will be used to estimate range error in

calculated position determined using the

NLS system. It will thus allow conclusions to be drawn concerning the accuracy achievable through NLS, and its limitations and possibly will identify avenues

for further resolution enhancement. The

more complex phenomenon of EM wave

propagation in dispersive media will be

addressed in future research.

1.3 Objectives and Scope

From the data presented in this report it

is possible to determine several important material-specific characteristics

needed for the design of engineering systems which make use of EM signal propagation through matter: 1) the power

attenuation as a function of the material

thickness and 2) the values of the electrical permittivity and dielectric constants

for a particular material as a function of

frequency. The latter can be used to calculate the propagation delay time associated with an EM pulse penetrating

through a specified thickness of a given

material. This information is essential for

3
error compensation for time-of-flight

metrology instrumentation systems. In

this report, only the power attenuation

aspects are discussed; dielectric and permittivity constants will be discussed in a

future volume.

Because of the unique fashion in which

the spread spectrum signal was constructed -- using discrete 2 MHz continuous wave (CW) response steps -- data

were able to be acquired which represent

the affect on the transmitted signal when

it penetrates and is re-transmitted

beyond a broad samplling of materials

and thicknesses for a very wide range of

frequencies. The bandwidth investigated

extends from 500 MHz through 8 GHz.

Because this amply covers, and extends

both well beyond and below, the frequencies allocated for use in mobile and personal communications equipment, as

well as for certain RF based positioning

equipment (most notably GPS), it was

felt that this data would be of wide use to

engineers designing such communications systems.

As such, efforts have been made to limit

the theory and background derivations

related to non-line-of-sight metrology in

this report. For those interested in further information on the NIST programs

in construction automation, and NLS

metrology in particular, please refer to

[Stone, 1996[1], and Stone, 1996[2]). The

data acquired from the tests described in

Chapter 2 was in the form of calibrated

frequency voltage spectra, that is, complex data in the frequency domain containing both in-phase and quadrature

components of the received signal for

each discrete step in frequency. There are

many ways of presenting these data. For

purposes of illustration and trend we

have included in this report plots of signal attenuation (in dB) relative to free

space propagation as a function of frequency for all of the materials and thicknesses investigated. The manner in

which these were developed is discussed

in Chapter 2. Simplified closed-form

regression equations are provided as a

means of quickly categorizing the

response of a particular material over a

wide range of frequencies.

These power spectra can also be used to

derive empirical values for range error

(propagation delay time), and the material constants of permittivity and conductivity as a function of both frequency and

material thickness. The derivation and

presentation of these latter values will be

discussed in a future paper.

A large amount of data was acquired in

this experimental program. A total of

1220 tests were conducted (610 in the

band between 0.5 and 2.0 GHz and 610 in

the band between 3 to 8 GHz). The frequency domain and time domain data

(resulting from a chirp-Z transform of the

frequency data) comprise approximately

600 megabytes on digital media. Various

post-processing techniques (gating in the

time domain to reduce multipath phenomena, and averaging of the results

both while sampling in the frequency

domain and between ten duplicate tests

conducted at slightly different spatial

positions on the same specimen) were

used to produce the smoothed frequency

spectra provided in this report. The

smoothed data (both time and frequency)

can be compressed into 59 Mbytes.

Requests for digital copies of this data

should be sent to the internet address

listed at the beginning of this document.

4
ing were custom developed by Flam and

Russell, Inc. of Horsham, PA. MIT

Lincoln Lab developed the SAR imaging

system (detailed in Figure 2.1.1) and processing software and cooperated with

NIST researchers on all aspects of the laboratory research. The radar was fieldportable with the electronics and computational hardware based in a mid-size

van. Table 2.1.1 lists characteristics of

this system. The unit is fully polarimetric and operates over two frequency

bands (0.1-2 GHz and 2-18 GHz). 

In order to measure distance through an

obstruction (e.g. a concrete wall), two

separate antennas are used, as shown in

Figures 2.1.2, 2.1.3, and 2.1.5. The receiver

becomes a “roving” unit whose position

is to be determined. For the situation

depicted in Figure 2.1.5 it is important to

recognize that it is the time of flight,

determined by performing a chirp-Z

transform on the in-phase and quadrature components of the received frequency spectrum, that is being measured. 

5

2.1 RF Transmission System

The NLS measurement system was based

on a modification of a an ultra-wideband

synthetic aperature radar. The modification made to the radar used for these

tests was to operate the radar in bistatic

mode and to collect one-way transmission data. The radar used separate transmit and receive antennas that were

directed at each other at a distance of 2 m

[Blejer, 1995 (2)].

In this study the receiving antenna comprised a roving unit that was located on

the opposite side of the material target.

In this sense, it was “cooperatively”

working with the system, receiving the

transmitted signal as opposed to the

reflected signal. The microwave transmission system was based on a HewlettPackard HP8530* network analyzer/

microwave receiver combined with an

HP 83623A frequency synthesizer, HP

8511A frequency converter, and an HP

85330A multiple channel controller. A

486 PC-based computer network performed radar control functions, while

data calibration and data management

were handled with a Pentium PC. 

The wideband pulse modulators used for

hardware gating and the computer software for system control and data process2.0 Experiment Description 

Frequencies 0.5-2 GHz, 2-18 GHz

Bandwidth Antenna limited

Waveform Gated CW

Pulse Width 10 ns to 500 ns

PRF 50 kHz to 5 MHz

Polarization Fully polarimetric

Output Power 20 dBm

Dynamic Range 80 dB

Noise Floor -100 dBm

Table 2.1.1: RF Transmission System

Characteristics

* Any mention of commercial products is for information only; it does not imply recommendation or endorsement by the National Institute of Standards and

Technology nor does it imply that the products mentioned are necessarily the best available for the purpose.
6

Horizontal Polarization

Vertical Polarization

i80486 - 66 MHz

STORAGE DISKS, I/O PORTS

RAM, GPIB BUS, NETBEUI

FR959, WINDOWS, OS

FR-8005

Tx PULSE, Rx PULSE, DELAY

PULSE REPETITION

HP-85330A

MULTI-RS-232 PORT

CONTROLLER

HP-E1364A 16 CHANNEL

FORM “C” SWITCH

MANUAL/COMPUTER

INTERFACE

FREQUENCY BAND AND

POLARIMETRIC CONTROL

ANTENNA HEIGHT READOUT

HP-8530A

MICROWAVE RECEIVER

DISPLAY, IF DETECTOR

PROCESSOR

HP-37204

HPIB BUS EXTENDER

HP-83623A

SYNTHESIZER SWEEPER

FREQUENCY GENERATOR

FR-8205B

TRANSMIT & RECEIVE

MODULATOR 2.0-18 GHZ

FR-81206

1 WATT AMPLIFIER

2.0-18 GHZ

DUAL PENTIUM

MS WINDOWS NT

FR DATAPRO

IMAGE PROCESSOR

FREQUENCY AND POLARIMETRIC

SWITCH

FR-8205B

TRANSMIT & RECEIVE

MODULATOR

0.1 - 2.0 GHZ

HP-8511A

FREQUENCY IF

CONVERTER

HP-27204

HPIB BUS EXTENDER

IF

Internal

HPIB Bus

eference

ignal

 10 MHz

Trigger In

Sweep Out

5 Bits

Tx (transmit)

Rc (receive)

HPIB BUS

Transmit Receive OBSTRUCTION

Horizontal Polarization

Vertical Polarization

Figure 2.1.1: Schematic of the spread spectrum transmission system

used for NLS research.
7

The measured time of flight then converts directly to a straight line distance

between the transmitter and receiver following the equality given by eq (2.1.1).

Equation (2.1.1) can determine only the

straight line distance from the transmitting antenna to the roving antenna. In

order to acquire a unique three dimensional position of the receiver at least

three transmitters are required. The position can then be determined based on

three dimensional triangulation. In such

calculations it is assumed that precision

(mm level) surveys will have been made

to establish the benchmark positions of

the transmitting antennas.

Returning now to the determination of

time of flight, the following simplified

summary will assist in helping to understand the NLS concept. Since accuracy is

of primary concern in the design of a precision surveying instrument it is discussed first. Position update rate is also

of importance for those items requiring

real-time feedback (e.g. automated operation of construction machinery).

However, as will become evident, speed

is primarily controlled by processor

speed, which improves every year.

Therefore, the approach discussed below,

while designed primarily for accuracy,

will nonetheless provide the algorithmic

basis for real-time processing as local

embedded microprocessors become

faster.

Traditional imaging radars and scatterometers [4] make use of a swept frequency for the generation of a response

spectrum. An alternative, discrete

approach [5] was used for the NIST NLS

studies. In this approach, the response of

the system is obtained at individual continuous wave frequencies. The discrete

step size is user-definable, but for the

CONTROL

SYSTEM

FREQUENCY

SOURCE

TRANSMIT

ANTENNA

DOWNCONVERTER

HP8511A

FREQUENCY

CONVERTER

I, Q TRANSMIT

RECEIVE

ANTENNA

DOWNCONVERTER

HP8511A

FREQUENCY

CONVERTER

I, Q RECEIVE

Figure 2.1.3: Simplified schematic of the

receiver system and means for characterizing the received signal.

Figure 2.1.2: Simplified schematic of the

transmission system and means for characterizing the transmitted signal.

x

x

= ⋅

=

×

c t

 straight line distance (m)

c = speed of light in a vacuum, 3 10

dt = time of flight (s)

8

δ

m s /

eq(2.1.1)
8

recover amplitude and phase in the form

of quadrature components.

The in-phase component (or “I” component) is created by multiplying the transmitted signal by a reference signal generated by the mixer oscillator. The input

signal is defined as:

The mixer reference signal, generated at

the same frequency, but different amplitude and phase, is:

The result of multiplying the two signals

is:

NIST tests, 401 points were used for the

0.5 to 2.0 GHz experiments and 801

points for the 3.0 to 8.0 GHz experiments.

This produced a frequency step size of

approximately 3.74 MHz and 6.24 MHz,

respectively. 

Figure 2.1.2 is a schematic of the transmitter subsystem. In the actual system,

the computer directs the HP-83623A to

generate the specified frequency which is

then amplified and sent to the transmission antenna. This same signal is also

tapped to an RF-to-IF converter (HP8511A) where the IF signal is sent to the

network analyzer (HP-8530A) for signal

detection. The magnitude and phase of

the transmitted signal are extracted in a

fashion following that depicted in Figure

2.1.4. This procedure is known as “quadrature” detection and can be thought of

as a mixing operation that translates the

received (tapped) signal to baseband to

“I” Channel

“Q” Channel

“In-Phase”

“Quadrature”

Input Signal

Mixer

Phase Shift 90

(convert to sin signal)

o

Figure 2.1.4: Schematic representation of a down conversion “mixer” used for quadrature detection in both the transmitted and received signals. In the NIST NLS tests, a

common mixer oscillator was used as the reference for both signals.

B ft 1 1 cos( ) 2π φ +

B ft 1 1 sin( ) 2π φ +

B B ft ft 12 1 2 sin( )cos( ) 2 2 πφ πφ + +

B B ft ft 12 1 2 cos( )cos( ) 2 2 πφ πφ + +

B ft 2 2 cos( ) 2π φ +

π

2

B ft 1 1 cos( ) 2π φ +

B ft 2 2 cos( ) 2π φ +

Eq(2.1.2)

Eq(2.1.3)
Eq (2.1.4) can be expanded by means of

standard trigonometric identities to yield:

where the term ω , the circular frequency,

is used interchangeably with the term

2πf. By collecting terms this can be rewritten as Eq(2.1.6):

The first component in Eq(2.1.6) represents the DC signal or “bias” component

and does not depend on frequency. It

does, however, contain information relating to the phase difference between the

input (transmitted) and reference signals. 

In order to extract the first part, the composite signal is typically run through a

low pass filter. The output from the low

pass filter, for the in-phase component is:

where the “I” is used to indicate that this

term characterizes the real or “in-phase”

component of the input signal. In a similar fashion the quadrature (or imaginary)

component of the complex input signal

can be generated by phase shifting the

input signal by π/2 radians. The resulting

“quadrature” signal (after multiplication)

is:

Passing this signal through a low-pass filter yields the “quadrature” (or imaginary) component of the input signal as:

The transmitted signal, at the discrete frequency, f0, can now be completely characterized as:

ST = IT +jQT Eq(2.1.10)

where 

The transmit signal amplitude is:

The same procedure (quadrature detection) is applied to the received signal, as

depicted in Firgure 2.1.3. In this situation

there is an important additional consideration in that, although we are transmitting continuously at the selected discrete

frequency, f0, there may (and and almost

always will) be other components of the

signal, with different phases, resulting

from multipath reflections, refraction and

9

BB t 12 1 2 1 2

1

2

1

2 sin( ) cos( ) φφ ωφφ − + ++ 2 







BB t 12 1 2 1 2

1

2

1

2 cos( ) cos( ) φφ ωφφ − + ++ 2 







B B I 1 2

1 2 2 cos( ) φ φ − ≡

B B1 2

1 2 Q 2 sin( ) φ φ − ≡

B B ft ft 12 1 2 cos( )cos( ) 2 2 πφ πφ + + Eq(2.1.4)

B B

t t

t t

1 2

1 2

1 2

1

2

1

2

cos( ( ))

cos( ( ))

ωφ ωφ

ωφ ωφ

+− +

+

++ +





























Eq (2.1.5)

Eq (2.1.7)

Eq (2.1.9)

j = −1

A IQ TTT = +2 2 Eq (2.1.11)

Eq (2.1.8)
other dispersive phenomena. In order to

reject out-of-band signals, the receiver is

tuned to listen at the specified frequency,

f0, by means of a narrow band pass filter.

The band width typical of the NIST tests

was ± 20 KHz. In the particular implementation described in Figure 2.1.3, the

same mixer reference signal is used for

quadrature detection as that shown in

Figure 2.1.2. The resulting complex

description of the received signal is given

by:

SR = IR +jQR Eq(2.1.12)

At this point it will be useful to switch to

phasor notation to describe the process

by which the attenuation and phase

10

~ Transmit A [Vector with

Amplitude and Phase] at

Single Frequency

Receive B [Vector with

Amplitude and Phase] at

Same Single Frequency

Wall ~

1: Ratio of Transmitted

to Received Signals is a

Measure of their

Amplitude and Phase

Difference

3: Use Free Space

Measurement to

Divide Out the

Hardware System

Response

4: Convert to Time

Domain Using

Fourier Transform

2: Repeat at

Multiple

Frequencies to

Define C as a

Function of

Frequency

Figure 2.1.5: Impulse synthesis approach used in the NIST NLS tests. Composite signal with a bandwidth of 1.5 and 5 GHz, respectively, was achieved by recording the

response for discrete single frequency transmissions. The composite time domain

response was synthesized via chirp-Z transform from the discrete frequency response

spectrum.

 ̃  ̃

 ̃ C B

A RAW

RECEIVE

TRANSMIT

=

Repeat above

to form C ̃

 ̃  ̃

 ̃ C C

C CALIBRATED

RAW

FREESPACE

=

 ̃( )  ̃ Ct Cf e ( ) n

j ft

n

N n = ∑ =

2

0

π
angle are derived. Phasor notation is

based on the equality:

Using this notation, the received signal is:

and the transmitted signal is:

The ratio of the received to transmitted

signals, as depicted in Figure 2.1.5, is:

If we substitute Eqs(2.1.14 and 2.1.15)

into Eq(2.1.16) we obtain:

The amplitude ratio, B/A, in the above

equation represents the attenuation of the

signal as a result of propagation through

a lossy medium. The ratio varies from

0.0 to 1.0 with 1.0 representing transmission in a vacuum (ideal transmission)

and 0.0 representing complete attenuation (absorption and reflection) by the

medium. The phase angle difference in

the exponent is a measure of the time of

flight between the transmitter and receiver, including dispersion-related group

velocity effects as the signal propagates

through engineering materials.

The mechanics needed to perform the

division described in Eq(2.1.16) require

the use of the following definitions,

which make use of Eqs(2.1.13 and 2.1.17):

From Eq(2.1.18) it is apparent that the

values for IR, QR, IT, and QT can be determined via quadrature detection as

expressed in Eqs(2.1.10 and 2.1.12) above.

We can thus proceed directly to write

that the ratio of received to transmitted

signals is given by:

Eq(2.1.19) represents a complex division

of the form [6]:

11

e j jθ = + cos sin θ θ

 ̃ cos

Re

Re

B B ft

al Be

al Be e

B

j ft

j j ft

B

B

= + ( )

= ( ) = ( )

( ) +

( )

2 0

2

2

0

0

π φ

π φ

φ π

 ̃ cos

Re

Re

A A ft

al Ae

al Ae e

A

j ft

j j ft

A

A

= + ( )

= ( ) = ( )

( ) +

( )

2 0

2

2

0

0

π φ

π φ

φ π

 ̃  ̃

 ̃ C B

A

received

transmitted RAW = =

Eq (2.1.13)

Eq (2.1.14)

Eq (2.1.15)

Eq (2.1.16)

 ̃

 ̃

B

A

Be

Ae

= B

A

j

j

B

A =

( ) −

φ

φ

φ φ ej B A

Eq (2.1.17)

 ̃

 ̃

cos sin

cos sin

cos

sin

cos

sin

B

A

I

I

R

T

= +

+

=

=

=

=

B jB

A jA

B

Q jB

A

Q jA

B B

A A

B

R B

A

A A

φ φ

φ φ

φ

φ

φ

φ

Eq (2.1.18)

S

S

I jQ

I jQ

R

T

R R

T T

= = +

+

 ̃

 ̃

B

A Eq (2.1.19)
The solution for the ratio of the received

to transmitted signals, at the discrete frequency, f0, being investigated is:

As shown in Figure 2.1.5, this procedure

is carried out for each discrete frequency

of interest with the ultimate objective of

building a discrete frequency response

spectrum for a given bandwidth of interest. However, the results presented in

Eq(2.1.21) represent uncalibrated, or

“raw” data. There are a number of factors which need to be taken into account.

For free space measurements, the most

important of the corrections involves

deviations in the signal propagation

velocity through the atmosphere. As previously discussed, the objective is to

determine the time of flight of the signal

from the transmitting antenna to the

receiving antenna. The conversion to distance involves the velocity of electromagnetic radiation in the atmosphere, as

given by Eq(2.1.1). Small errors in the

determination of the propagation velocity

can lead to measurable errors in the

straight line distance estimate. Empirical

correction factors have been derived for

propagation of radio waves through the

atmosphere as follows:

where

N= scaled-up refractivity

p= total pressure in millibars

e= partial pressure of water

vapor in millibars

T= absolute temperature in 

degrees Kelvin

cvacuum= speed of light in a

vacuum

In addition there are also errors which

result from the internal electrical nature

of the radar instrument. For example,

the length and efficiency of the coaxial

cables which connect the antennas to the

system and the efficiency with which signals are propagated through the various

electrical subsystems. 

Fortunately, there is an elegant, and simple method for accounting for instrumental error, by means of a calibration procedure [5]. This involves the generation of

12

A

C

a jb

c jd

ac bd j bc ad

a b

ac bd

a b

j bc ad

a b

= +

+

( ) + + − ( )

+

= ( ) +

+

+ ( ) −

+

= 2 2

22 22

Eq (2.1.20)

 ̃  ̃

 ̃ C S

S

B

A

II QQ

I Q j QI IQ

I Q

I jQ

RAW

R

T

RT R T

R R

RT R T

R R

RAW RAW

= ==

( ) +

+

+ ( ) −

+

= +

22 22

N p

T

e

T

c

c

n atmosphere vacuum

= +

=

77 6 373000

2

.

n =1+ N

106

Eq (2.1.21)

Eq (2.1.22)
a point for point discrete response spectrum, using the same techniques outlined

above, but with the important difference

that the setup be a line of sight test over a

known, precision surveyed bench. The

bench consists of two benchmarks whose

positions have been established relative

to one another using standard total station surveying equipment. The resulting

“freespace” response is used to calibrate

the raw data by dividing the raw signal,

at each discrete frequency, by the freespace result, as shown in Figure 2.1.5, following equation 2.1.23:

The freespace signal is defined as

where the notation is the same as previously used to describe the normalized inphase and quadrature components for

the raw signal defined in Eq (2.1.21). The

F subscripts in Eq(2.1.24) denote the freespace calibration. Equation 2.1.23 can

now be re-written as Eq (2.1.25).

For the NLS tests conducted at NIST, the

above calculations were performed in a

post-processing mode since the data

acquisition system was only designed to

write one file at a time. Thus, the freespace response was always acquired

prior to the commencement of any day’s

testing. A second freespace measurement

was made at the end of each day to

determine any changes that might have

occurred during the day. Subsequent to

the freespace measurement, raw experimental data files were created for each

material test following Eq(2.1.21). The

final calibration, following Eq(2.1.25),

was performed as part of an automated

MatLab post-processing script that operated on all data files. The MatLab scripts

13

 ̃  ̃

 ̃ C C

C CALIBRATED

RAW

FREESPACE

=

S C I jQ F FREESPACE F F = =+  ̃ Eq (2.1.24)

Eq (2.1.23)

 ̃  ̃

 ̃ C C

C

I jQ

I jQ

II QQ

I Q

j QI IQ

I Q

I jQ

where

I II QQ

I Q

Q QI IQ

I

CALIBRATED

RAW

FREESPACE

RAW RAW

FREESPACE FREESPACE

RAW FREE RAW FREE

RAW RAW

RAW FREE RAW FREE

RAW RAW

CALIBRATED CALIBRATED

RAW

RT R T

R R RAW

RAW

RT R T

R

= =

+

+ =

( ) +

+

+

( ) −

+

= +

= ( ) +

+





 





= ( ) −

2 2

2 2

2 2

2 2

2 2

2 2

+





 





= ( ) +

+





 





= ( ) −

+





 





Q

I II QQ

I Q

Q QI IQ

I Q

R RAW

FREE

RT R T

R R FREE

FREE

RT R T

R R FREE

Eq (2.1.25)
used for this process are listed in

Appendix A and were written for a PC

running Windows95.

The calibrated response spectra were

stored as a 5 x n matrix, where n was the

number of discrete frequencies sampled.

As previously described, 401 evenly

spaced points were acquired for the 0.5

to.0 GHz tests and 801 points were

acquired for the 3.0 to 8.0 GHz tests. For

each frequency, the I and Q values (ICALIBRATED and QCALIBRATED as per Eq.2.1.25)

are stored in the second and third

columns respectively. The fourth column

contains the derived calibrated, which is

calculated as:

This is a decimal value between 0.0 and

1.0, with 1.0 meaning that there was no

attentuation observed during the test for

which a material specimen was placed

between the transmitter and receiver, relative to the same freespace test. The decimal amplitude may easily be converted

to decibels (dB):

A(dB)=20*log10(A[decimal]) Eq(2.1.27)

In addition, the phase angle (radians) for

the calibrated response signal is stored in

the fifth column in each calibrated data

file. The phase angle is:

In the attenuation versus frequency plots

presented later in the report the frequency (in GHz) is plotted on the x-axis while

both the decimal and dB versions of 

Eq(2.1.26) are plotted on the y-axis.

Efforts have been made to fit simplified

polynomial functions to these curves for

the purposes of characterizing the attenuation characteristics of a broad range of

materials over a wide frequency bandwidth while maintaining a manageable

and compact means for accessing that

data. For those who desire the original

digital record sets, see the earlier instructions regarding request submissions to

NIST.

2.2 Antenna Descriptions

Two antenna geometries were used for

this test program. The first, originally

manufactured by Watkins-Johnson and

now fabricated by Condor Systems, had

a bandwidth of 1.5 GHz between 0.5 and

2.0 GHz. The second, manufactured by

Flam and Russell, had a bandwidth of 5

GHz from 3.0 to 8.0 GHz. Where polarization capability existed, the V-V polarization configuration was employed for

the NIST tests, as initial studies [1] clearly indicated that multipath distortion due

to ground bounce was minimized

through the use of a vertically polarized

plane wave transmission. This polarization setting was not important to the tests

described herein because of the presence

of a multipath shield (see Figure 2.3.1). 

14

φCALIBRATED

CALIBRATED

CALIBRATED

Q

I = 



 



 − tan 1

A

Q

CALIBRATED

CALIBRATED

=

ICALIBRATED +2 2

Eq (2.1.26)

Eq (2.1.28)
2.2.1 “Low” Frequency Bandwidth (0.5

to 2.0 GHz)

A dual-polarized Quad-Ridged Horn

antenna, model WJ-48450 from WatkinsJohnson (Table 2.2.1 and Figures 2.2.1

through 2.2.2), was used for the NIST

experiments. This unit has a frequency

coverage of 0.5-2 GHz. These antennas

provide high-gain directional patterns

over multi-octave bandwidths. Each

pyramical horn has two orthogonally

placed input feeds which provide the

capability for horizontal and vertical

polarization. For the attenuation tests

reported herein, only the vertical polarization was used. A typical implementation is shown in Figure 2.2.3, where

attenuation and distance measurements

are being taken for a composite specimen

consisting of three back-to-back brick

walls.

Typical radiation patterns for the WJ48450 are provided in Figures 2.2.4

through 2.2.7. Figures 2.2.4 and 2.2.5 present the measured magnitude (in dB) as a

function of the azimuth angle (zero

degrees = straight ahead) for the E-plane

and H-plane, respectively, at a reference

frequency of 0.5 GHz, that is, the limiting

lower frequency of the horn. Similar

data are given in Figures 2.2.7 and 2.2.8

for the upper, 2.0 GHz design limit of the

horn.

15

Product Specification AS-48450

Frequency 0.5 to 2.0 GHz

Polarization Simultaneous horizontal and vertical

Gain 6 to 12 dBi

Beamwidth, 3dB(BW) 70° to 25°, nominal

Beam squint (3 dB bisector) 5°, maximum

Cross polarization -15 dB, maximum

Isolation between ports 20 dB, minimum

Maximum input power, each connector 70W CW, 3kW peak

RF connectors Type N female

Impedance 50W reference

VSWR 3:1, maximum

Size 444 mm square,

533 mm long (maximum)

Weight 15 kg

Table 2.2.1: Specifications for0.5 to 2.0 GHz antenna usef for “Low” Bandwidth Tests.

Figure 2.2.1: Quadridged 0.5 to 2.0 GHz .

Vertical polarization, used for NIST tests,

used only the two central vertical ridges.
These figures demonstrate the relatively

broad area illumination provided by this

design. Although signal power is

reduced by approximately one half (3dB)

by an azimuth angle of 30 degrees to

either side of center, considerable signal

strength can still be measured at azimuth

angles of 90-degrees. Because of the relatively different radiation pattern geometry for this antenna, as contrasted with

that for the 3.0 to 8.0 GHz diagonal horn

described below, results presented later

in this report will be antenna specific.

Researchers wishing to draw general conclusions over the entire frequency band

investigated in this report should take

into account both the test geometry (also

described below) as well as these radiation patterns.

2.2.2 “High” Frequency Bandwidth (3.0

to 8.0 GHz)

For tests in the range of 3.0 to 8.0 GHz

FR6400 class range illumination horns

from Flam & Russell, Inc. were used.

These horn antennas produce radiation

patterns with low sidelobe structure,

nearly circularly symmetric beam, and

nominally constant gain and beamwidth. 

16

200

2.3 9.65

82.5

167.1

6.4

.76

76.2

240

521.2

SMA Female

99 304.8 49.28

4x7.1

167.64

14

139.7

200

449

82.6

Figure 2.2.2: Side, Bottom, and End

Views, top to bottom, respectively, for the

WJ-48450, 0.5 to2.0 GHz antenna (Condor

Systems, 1996).

Figure 2.2.3 (Right):

Experimental calibration of a composite wall consisting of

three back-to-back

76 mm brick walls.

The wall sections

measure 1 meter

square. Three millimeter aluminum

panel in background

served as a multipath signal shield.
17

Figure 2.2.4: Typical E-Plane radiation pattern (Magnitude in dBi as a function of

azimuth angle in degrees) for a WJ-48450 horn operating at the lower, 0.5 GHz, limit of

its design spectrum (Condor Systems, 1996).

Figure 2.2.5: Typical H-plane radiation pattern (Magnitude in dBi as a function of

azimuth angle in degrees) for a WJ-48450 horn operating at the lower, 0.5 GHz, limit of

its design spectrum (Condor Systems, 1996).
18

Figure 2.2.6: Typical E-plane radiation pattern (Magnitude in dBi as a function of

azimuth angle in degrees) for a WJ-48450 horn operating at the high, 2.0 GHz, limit of

its design spectrum (Condor Systems, 1996).

Figure 2.2.7: Typical H-plane radiation pattern (Magnitude in dBi as a function of

azimuth angle in degrees) for a WJ-48450 horn operating at the higher, 2.0 GHz, limit

of its design spectrum (Condor Systems, 1996).
The particular model used for the NLS

tests was the FR-6415 3.0 to 8.0 GHz

horn, which was designed to serve as

a source antenna in the measurement

of antenna radiation patterns or as

transmit and receive antennas in the

measurement of radar cross-section

data. These antennas exhibit significantly reduced E-plane sidelobes typically associated with horn antennas.

The FR-6415 incorporates aperature

defocusing to procuce minimal variations in gain and beamwidth over a

frequency range of 2.5:1. Table 2.2.2

lists the pertinent manufacturer’s

specifications for this horn. Dimensions

are given in Figure 2.2.2.1.

Figure 2.2.2.2 shows a typical laboratory

setup involving the FR-6415 in which the

effect of a reinforcing bar grid on time-offlight distance measurement is being conducted. A frequency response spectrum

was generated from 3.0 to 8.0 GHz with

this system. 

Figures 2.2.2.3 and 2.2.2.4 present E-Plane

and H-Plane radiation patterns for the

FR-6415 at an operating frequency of 3.0

GHz. Similar data are presented in

Figures 2.2.2.5 and 2.2.2.6 at 8 GHz.

2.3 Test Fixtures

Because of the large number of test specimens, and the representative full-size

thicknesses used for the various materials, a test set-up was designed that made

use of an indoor laboratory at NIST

equipped with an overhead crane. The

set-up is shown in isometric view in

Figures 2.3.1 and 2.3.2 and in dimen

19

Model Specification FR-6415

Frequency (GHz) 3.0 to 8.0

Gain 1.7 dBi (nominal)

Beamwidth Level 17 degrees nominal

Sidelobe -30 dB nominal

VSWR 2:1 maximum

Isolation 60 dB minimum

Aperture Width 261 mm

Overall Length 627 mm

Weight 4.77 kg

Input SMA Female

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

@@@@@@@@@@@@6K ? @@@@@@@@@@@@@@@? ?

@@@@@@@@@@@@@@@L @@ ?

@@@@@@@@@@@@@@@1 @@ ?

?@@? @@@@@?f?@@@@@ ?@K?g@@ ?

?@@? @@@@@?f?@@@@@ ?@@6K?f@@ ?

?@@?gO@ @@@@@?fJ@@@@@ ?@@@@6K?e@@ ? ?@@?fO2@@ @@@@@?e?O&@@@@5 ?@@@@@@6K?@@ ?

?@@?eO2@@@@ @@@@@@@@@@@@@@(Y O@K?fO@K?O@K? ?O26K?fO@K?O2@@@@@6?2@6?2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?

?@@?O2@@@@@@ ?O@KfO@K?eO@?2@@6?2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?

?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@)X @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0?40?@MI4@@0MI4@0?40?4@@@0M?heI40M ?@@@@@@@0Y@@ ?

?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0?4@@@@@@@0?@MI40Me?I40M??I@Me?I@M @@@@@@@@@@@@@@@)X? ?@@@@@0Me@@ ? ?@@@@@@@@@@@V@M? @@@@@?fI'@@@@1? ?@@@0Mf@@ ?

?@@@?I4@@@@@ @@@@@?f?N@@@@@? ?@0Mg@@ ?

?@@5e?I'@@@ @@@@@?f?J@@@@@? @@ ? ?@@?fV4@@ @@@@@?fO&@@@@@? @@ ?

?@@@ @@@@@@@@@@@@@@@@5? @@ ?

?@@H @@@@@@@@@@@@@@@(Y? @@ ?

?@@? @@@@@@@@@@@@@@0Y @@ ? ?@@? @@@@@@@@@@@@0M @@ ?

?@@? @@ ?

?@@? @@ ? ?@@? @@ ? ?@@L @@ ?

?@@@ @@ ?

?@@H @@ ? ?@@? @@ ?

?@@? @@ ? ?@@? @@ ?

?@@? @@ ? ?@@? @@ ?

?@@? @@ ? ?@@? @@ ?

?@@? @@ ?

?@@? @@ ?

?@@? @@L? ? ?@@? @@1? ?

?@@? @@@? ?

?@@? @@5? ?

?@@? @@H? ? ?@@? @@ ?

?@@? @@ ? ?@@? @@ ?

?@@? @@L? ?

?@@? @@@? ?

?@@? @@ ? ?@@? @@1? ?

?@@? @@5? ?

?@@? @@H? ?

?@@? @@ ?

?@@? @@ ?

?@@? @@ ?

?@@? @@L? ?

?@@? ?@@@ @@@? ?

?@@? ?@@@ @@H? ?

?@@? ?@@? ?@@@ @@ ?

?@@? ?@@? ?@@? ?@@@ @@ ?

?@@? ?@@? ?@@? ?@@@ @@ ? ?@@? ?@@? ?@@? ?@@@ @@ ?

?@@? ?@@? ?@@? ?@@@ @@ ?

?@@? ?@@? ?@@? ?@@@ @@L? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@H? ?

?@@? ?@@? ?@@? ?@@@ @@L? ?

?@@? ?@@? ?@@L ?@@@ @@@? ?

?@@? ?@@? ?@@@ ?@@@ @@ ?

?@@? ?@@? ?@@? ?@@@ @@1? ? ?@@? ?@@? ?@@@ ?@@@ @@@? ?

?@@? ?@@? ?@@H ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@5? ?

?@@? ?@@? ?@@? ?@@@ @@ ?

?@@? ?@@? ?@@? ?@@@ ?@@@@@@@@6K? @@@? ? ?@@? ?@@? ?@@? W2@@@@@6K? ?@@@ ?@@@@@@@@@@@6X @@H? ?

?@@? ?@@? ?@@? ?O&@@@@@@@@6X? ?@@@ ?@@@@@@@@@@@@)X? @@ ?

?@@? @@@@@6X? ?@@? ?@@? @@@@@@@@@@@@)X ?@@@ ?@@@@@@@@@@@@@)X @@ ?

?@@? @@@@@@1? ?@@? ?@@? ?J@@@@@@@@@@@@@1 ?@@@ ?@@@@@eI'@@@@@1 @Kg@@ ?

?@@? ?J@@@@@@@? ?@@? ?@@? ?7@@@@(Me?@@@@@L? ?@6Kf?@@@f?O2@ ?@@@@@e?V'@@@@@ @@6Kf@@L? ? ?@@? ?7@@@@@@@L ?@@? ?@@L J@@@@@H?e?3@@@@1? ?@@@6Ke?@@@e?O2@@@ ?@@@@@fV'@@@@L? @@@@6Xe@@1? ?

?@@? ?@@@@@@@@1 @6K?f?@@? ?@@@fW2@@ 7@@@@5f?N@@@@@? J@@@@@6K?@@@?O2@@@@@ ?@@@@@f?N@@@@1? @@@@@)K?@@@? ?

?@@?fO2@@ ?@@@@@@@@@ @@@6K?e?@@? ?@@?e?O&@@@ @@@@@Hg@@@@@? ?O&@@@@@@@@@@@@@@@@@@@@6K?O2@6?26?2@6KO2@@@6?2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?@@@@@g@@@@@? ?W2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@5? ? ?@@?eO2@@@@ J@@@@@@@@@L? @@@@@6K??@@? ?@@)KO2@@@@@ @@@@@? ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@5 ?@@@@@g@@@@@? ?*@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?

?@@?O2@@@@@@ 7@@@V'@@@@1? @@@@@@@@@@@? ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? @@@@@? ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0Y ?@@@@@g@@@@@? ?V4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0?4@@@@@@@@@@0?'@@@@@@@@@@1? ?

?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6X ?J@@@@?N@@@@@? @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? @@@@@? ?@@@@@0?@MeI@M?fI@MI4@@@0M?I@?@Mg?I@M?I@MI@M? ?@@@@@@0Y@@@V4@@@@@@ ?@@@@@g@@@@@? ?N@@@@@(M?@@5? ? ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@) ?7@@@@e@@@@@? @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?@@@@@@@@@@@@@0Mf?I@M @@@@@? ?@@@@0M??@@@eI4@@@@ ?@@@@@g@@@@@? @@@@0Ye@@H? ?

?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0M?I4@0MI@Mf?I@M ?@@@@5e3@@@@L @@@@@@0M?@@? ?@@??I4@@@@@ @@@@@? ?@@0M?e?@@@fI4@@ ?@@@@@f?J@@@@5? @(M?f@@L? ? ?@@?I4@@@@@@ ?@@@@YeV@@@@1 @@@@0Me?@@? ?@@?e?I'@@@ 3@@@@Lg@@@@@? ?@M?f?@@@gI@ ?@@@@@fW&@@@@H? (Yg@@1? ?

?@@?eI4@@@@ J@@@@@@@@@@@@@L? @@0Mf?@@? ?@@?fV4@@ N@@@@)X?e?J@@@@5? ?@@@ ?@@@@@e?O&@@@@5 @@@? ?

?@@?fI4@@ 7@@@@@@@@@@@@@1? @Mg?@@? ?@@? ?@@@@@)XeW&@@@@H? ?@@@ ?@@@@@@@@@@@@@@H @@@? ?

?@@?gI@ @@@@@@@@@@@@@@@? ?@@? ?@@? ?3@@@@@)KO&@@@@@ ?@@@ ?@@@@@@@@@@@@@5? @@@? ?

?@@? ?J@@@@@@@@@@@@@@@? ?@@? ?@@? ?V'@@@@@@@@@@@@@ ?@@@ ?@@@@@@@@@@@@0Y? @@@? ?

?@@? ?7@@@(M?f@@@@@L ?@@? ?@@? V'@@@@@@@@@(M? ?@@@ ?@@@@@@@@@@0M? @@@? ? ?@@? J@@@@Hg3@@@@1 ?@@? ?@@? ?V4@@@@@@@0Y ?@@@ @@@? ?

?@@? 7@@@@?gN@@@@@ ?@@? ?@@? I4@@0M ?@@@ @@@? ?

?@@? @@@@@?g?@@@@@ ?@@? ?@@? ?@@@ @@@? ? ?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ? ?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ? ?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@5? ?

?@@? ?@@? ?@@? ?@@@ @@ ?

?@@? ?@@? ?@@? ?@@@ @@1? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ?

?@@? ?@@? ?@@? ?@@@ @@@? ? ?@@? ?@5? ?@@? ?@@@ @@@? ?

?@@? ?(Y? ?@@@ @@@? ?

?@@@ @@@? ? ?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ? ?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ? ?@@@ @@@? ? ?@@@ @@@? ?

?@@@ @@@? ? ?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ? ?@@@ @@5? ?

?@@@ @@ ?

?@@@ @@@? ? ?@@@ @@ ?

?@@@ @@1? ? ?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ? ?@@@ @@@? ?

?@@@ @@@? ?

?@@@ @@@? ?

?3@5 @@@? ?

?V+Y @@@? ? ?O@Kf?O@Ke?O2@6?@?2@@@@@@@@@@@@@@@@@@@@6X? ?@6K @@@? ? ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@1? ?@@@@@@6K? @@@? ?

?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?@@@@@@@@@@6K? @@@? ?

?@@@@@@@@@@@@@@@@@@0?4@@@@@@@@@@@@@@@@@@@@0?@MI@M? ?@@(M?I@M?I@M? ?@@? ?@@?eI4@@@@@@6K @@@? ?

@@@? ?@@H ?@@? ?@@?gI4@@@@@@@6K? @@@? ?

?J@@@L ?@@? ?@@? ?@@?heI4@@@@@@@6K? @@@? ? ?7@@@)X? ?@@? ?@@? ?@@? ?I4@@@@@@6K? @@@? ?

J@@@@@1? ?@@? ?@@? ?@@? ?I4@@@@@@@6K @@@? ?

?W&@@@@@@L ?@@?f@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@f?@@? ?@@? ?I4@@@@@@6K? @@@? ?

?7@@@@@@@1 ?@@?f@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@f?@@? ?@@? ?I4@@@@@@@6K @@@? ?

J@@@@@@@@@L? ?@@?f@@@@@@@@@@@@@@@@@@@0?40MI4@@0MeI@?40?4@@@@0M??I@M ?I@M W@@@@@f?@@? ?@@? ?I4@@@@@@@6K @@@? ? @@@@@@@@@@@? ?@@?f@@@@X? ?W&@@@@@f?@@? ?@@? I4@@@@@@@6K? @@@? ?

@@@? ?@@?f@@@@)K ?7@(Y@@@f?@@? ?@@? ?I4@@@@@@@6K @@@? ?

@@@? ?@@?f@@?I'@@? ?@(Y?@@@f?@@? ?@@? I4@@@@@@@6K? @@@? ? @@@? ?@@?f@@eV'@L ?@@(Y??@@@f?@@? ?@@? I4@@@@@@@6K? @@@? ?

@@@? ?@@?f@@e?V')K? J@(Ye?@@@f?@@? ?@@? I4@@@@@@@6K? @@@? ?

@@@? ?@@?f@@fV'@@ ?O&(Y?e?@@@f?@@? ?@@? I4@@@@@@@6K? @@@? ?

@@@? ?@@?f@@f?V'@L? @@(Yf?@@@f?@@? ?@@? I4@@@@@@@6K? @@@? ?

@@@? ?@@?f@@gV')K ?J@(Y?f?@@@f?@@? ?@@? I4@@@@@@@6K? @@@? ?

@@@? ?@@?f@@g?V'@@? O&(Yg?@@@f?@@? ?@@? ?I4@@@@@@@6K @@@? ? @@@? ?@@?f@@hV'@L ?@@(Y?g?@@@f?@@? ?@@? ?I4@@@@@@6K? W2@@@@@@@@@@@@@@@6K? @@@? ?

@@@? ?@@?f@@h?V')K? J@(Yh?@@@f?@@? ?@@? ?I4@@@@@@6K? ?W&@@@@@@@@@@@@@@@@@@6X? @@@? ?

@@@? ?@@?f@@heV'@@ ?O&(Y?h?@@@f?@@? ?@@? ?I4@@@@@@@6K W&@@0Mhe?I4@@@1? @@@? ? @@@? ?@@?f@@he?V'@L? @@(Yhe?@@@f?@@? ?@@? ?I4@@@@@@@6K 7@(M ?@@? @@@? ? @@@? ?@@?f@@hfV')X ?J@(Y?he?@@@f?@@? ?@@? I4@@@@@@6K @@H? ?@@L @@@? ?

@@@? ?@@?f@@hf?V')X? O&(Yhf?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@1 @@@? ? @@@? ?@@?f@@ V')X ?@@(Y?hf?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V')K? J@(Y ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V'@@ ?W&(Y? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V'@L? W&(Y ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@5 @@@? ?

@@@? ?@@?f@@ V')K ?W&@H? ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@? @@@? ?

@@@? ?@@?f@@ ?V'@@? W&@@ ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@1 @@@? ?

@@@? ?@@?f@@ V'@L ?W&(M? ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V')X? W&@H ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V')X ?W&@@? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@hO@KO@?f?@@@g@6?@?@K?O26?@?26?2@@@@@@@@@@@6?2@@6X @@@? ?

@@@? ?@@?f@@ ?V')X? W&(M ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@g@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@1 @@@? ? @@@? ?@@?f@@ V')K ?W&(Y? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@g@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@? ?

@@@? ?@@?f@@ ?V'@@? W&(Y ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V'@L ?W&@H? ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V')X? W&@5 ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V')X ?W&@0Y ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V')X? W&@? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V')K ?W&@5? ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V'@@? W&@0Y? ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ N@@L ?W&@ ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?@@)X? W&@5 ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ I')X ?W&@0Y ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ? @@@? ?@@?f@@ ?V')X? W&@? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V')K ?W&@5? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V'@@? W&@0Y? ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ N@@L ?W&@ ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@ @@@? ? @@@? ?@@?f@@ ?@@)X? W&@5 ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ I')X ?W&@(Y ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@ @@@? ? @@@? ?@@?f@@ ?N@)X? W&@(Y? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ @@)K ?W&@(Y ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?I'@@? W&@0Y? ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V'@L ?W&@ ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V')X? W&@5 ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V')X ?W&@0Y ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?N@)X? W&@? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ @@)K ?W&@5? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?I'@@? W&@0Y? ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ N@@L ?W&@ ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?@@)K? W&@5 ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ I'@@ ?W&@0Y ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V'@L? W&@? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V')K ?W&@5? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ? @@@? ?@@?f@@ ?V'@@? W&@0Y? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V'@L ?W&@ ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V')X? W&@5 ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V')X ?W&@0Y ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@ @@@? ? @@@? ?@@?f@@ ?V')X? W&@? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V')K ?W&@5? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ? @@@? ?@@?f@@ ?V'@@? W&@0Y? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ V'@L ?W&@ ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V')K? W&@5 ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@ @@@? ? @@@? ?@@?f@@ V'@@ ?W&@0Y ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@ @@@? ?

@@@? ?@@?f@@ ?V'@L? W&@? ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@W2@@@@@@@@6K @@@? ? @@@? ?@@?f@@ V')X ?W&@5? ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@@@@@@@@@@@@@6X @@@? ?

@@@? ?@@?f@@ ?V')X? W&@0Y? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@@@@@@@@@@@@@@1 @@@? ?

@@@? ?@@?f@@ V')X ?W&@ ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@ @@@? ?

@@@? ?@@?f@@ ?V')K? W&@5 ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@hf@@ @@@? ?

@@@? ?@@?f@@ V'@@ ?W&@0Y ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@hf@@ @@@? ?

@@@? ?@@?f@@ ?V'@L? W&@? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@ @@@? ? @@@? ?@@?f@@ V')K ?W&@5? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@ @@@? ?

@@@? ?@@?f@@ ?V'@@? W&@0Y? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@@@6X @@@? ?

@@@? ?@@?f@@ V'@L ?W&@ ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@@@@)K? @@@? ?

@@@? ?@@?f@@ ?V')X? W&@5 ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@V4@@@@ @@@? ?

@@@? ?@@?f@@ V')X ?W&@0Y ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@eI'@@L? @@@? ?

@@@? ?@@?f@@ ?V')X? W&@? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@e?N@@1? @@@? ?

@@@? ?@@?f@@ V')K ?W&@5? ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@hf@@f3@@? @@@? ?

@@@? ?@@?f@@ ?V'@@? W&@0Y? ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@hf@@fV@@? @@@? ? @@@? ?@@?f@@ V'@L ?W&@ ?@@@f?@@? ?@@? I4@@@@@@@6K? W&K?O26KO@?26K?O2@6?2@@@@@@@@@@@@@6Xg@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@? ?

@@@? ?@@?f@@ ?V')K? W&@5 ?@@@f?@@? ?@@? I4@@@@@@@6K? 7@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@,g@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@5 @@@? ?

@@@? ?@@?f@@ V'@@ ?W&@0Y ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0Yg@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@0MI@?40MI@M?I@?(Y @@@? ?

@@@? ?@@?f@@ ?V'@L? W&@? ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@hf@@f@@@? @@@? ?

@@@? ?@@?f@@ V')K ?W&@5? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@e?J@@5? @@@? ?

@@@? ?@@?f@@ ?V'@@? W&@0Y? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@eO&@(Y? @@@? ? @@@? ?@@?f@@ V'@L ?W&@ ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@W2@@(Y @@@? ?

@@@? ?@@?f@@ ?V')K? W&@5 ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@@@@(Y? @@@? ?

@@@? ?@@?f@@ V'@@ ?W&@0Y ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@@@0Y @@@? ?

@@@? ?@@?f@@ ?V'@L? W&@? ?@@@f?@@? ?@@? ?I4@@@@@@@@6K? @@ ?@@@hf@@ @@@? ?

@@@? ?@@?f@@ V')K ?W&@5? ?@@@f?@@? ?@@? ?I4@@@@@@@@6K? @@ ?@@@hf@@ @@@? ? @@@? ?@@?f@@ ?V'@6X W&@(Y? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@ @@@? ? @@@? ?@@?f@@ V'@1 ?W&@(Y ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@ @@@? ?

@@@? ?@@?f@@ ?V'@ W&@(Y? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@ @@@? ? @@5? ?@@?f@@ V'@6X? ?W&@0Y ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@ @@@? ?

@@ ?@@?f@@ ?V'@1? W&@? ?@@@f?@@? ?@@? I4@@@@@@@@6K @@ ?@@@hf@@ @@@? ?

@@1? ?@@?f@@ V'@? ?W&@5? ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@hf@@ @@@? ?

@@@? ?@@?f@@ ?V'@6X W&@0Y? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@ @@@? ?

?@@?f@@ V'@1 ?W&@ ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@ @@@? ?

?@@?f@@ ?V'@ W&@5 ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@ @@@? ? ?@@?f@@ V'@6X? ?W&@0Y ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@L? @@@? ?

?@@?f@@ ?V'@)X W&@? ?@@@f?@@? ?@@? I4@@@@@@6K @@ ?@@@hf@@)K W2@@@@@@@@@@6K @@@? ?

?@@?f@@ V'@)X? ?W&@5? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@@@@6X? ?W&@@@@@@@@@@@@@@? ?

?@@?f@@ ?V'@)X W&@0Y? ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@@@@@)X ?7@(M?g?I'@@? ?

?@@?f@@ V'@)X? ?W&@ ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@?I'@@1 ?@@HheN@@? ? ?@@?f@@ ?V'@)X W&@5 ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@eV'@@L? ?@@?he?@@? ?

?@@?f@@ V'@)X? ?W&@0Y ?@@@f?@@? ?@@? ?I4@@@@@@6K? @@ ?@@@hf@@e?V'@1? ?@@?he?@@? ?

?@@?f@@ ?V'@1? W&(M ?@@@f?@@? ?@@? I4@@@@@@@6K? @@ ?@@@hf@@fN@@? ?@@?he?@@? ? ?@@?f@@ V'@? ?W&@H? ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@f?@@? ?@@?he?@@@@@@@@@@@@@6K ?

?@@?f@@ ?V'@6X W&@@ ?@@@f?@@? ?@@? ?I4@@@@@@@6K @@ ?@@@hf@@f?@@? ?@@?he?@@@@@@@@@@@@@@@6X ?

?@@?f@@ V'@)K? ?O&@ ?@@@f?@@? ?@@? ?I4@@@@@@@6Khe@@ ?@@@hf@@f?@@? ?@@?he?@@@@@@@@@@@@@@@@1 ?

?@@?f@@ ?V'@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@5 ?@@@f?@@? ?@@? ?I4@@@@@@@6Kg@@ ?@@@hf@@fJ@@? ?@@?he?@@?he?@@@ ?

?@@?f@@ N@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@H ?@@@f?@@? ?@@? ?I4@@@@@@@@6K?@@ ?@@@hf@@f7@5? ?@@?he?@@?he?@@@ ?

?@@?f@@ ?@@(M? @@@? ?@@@f?@@? ?@@? I4@@@@@@@@ ?@@@hf@@e?J@@H? ?@@?he?@@?he?@@@ ? ?@@?f@@ ?@@H @@@? ?@@@f?@@? ?@@? I4@@@@ ?@@@hf@@eO&@5 ?@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@(Y ?@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@(Y? ?@@?he?@@?he?@@@ ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@Y ?@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@@@@@@@@6K? ?@@?he?@@?he?@@@ ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@@@@@@@@@@@@@@@@@@@@@@@6K ?@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@heI4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6K ?@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6K J@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@6K ?O&@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?he?@@?he?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ I4@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?he?@@?he?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?I'@@?he?@@?he?@@@ @@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ N@@?he?@@?he?@@@ @@@? ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?@@?he?@@?he?@@@ @@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?@@?he?@@?he?@@@ @@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?@@?he?@@?he?@@@ @@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@6X ?@@?he?@@?he?@@@ @@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@)X? ?@@?he?@@?he?@@@ @@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@)X ?@@?he?@@?he?@@@ @@@? ? ?@@@@@6X ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@eI'@)X? ?@@?he?@@?he?@@@ @@@? ?

?@@@@@@1 ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@e?N@@1? ?@@?he?@@?he?@@@ @@@? ?

J@@@@@@@ ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@f3@@? ?@@?he?@@?he?@@@ @@@? ? 7@@@@@@@ ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@fN@@? ?@@?he?@@?he?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?

@@@@@@@@L? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@f?@@? ?@@@@@@@@@@@@@@@@?he?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?

?J@@@@@@@@1? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@f?@@? ?@@@@@@@@@@@@@@@@?he?@@@ @@@? ?

?7@@@@@@@@@? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@f?@@? ?@@(M?g?I'@@?he?@@@ @@@? ?

?@@@@V'@@@@L ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@fJ@@? ?@@HheN@@?he?@@@h?O@K @@@? ?

?@@@@?N@@@@1 ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@e?W&@5? ?@@?he?@@?he?@@@g?W2@@@6Xhf@@@? ?

J@@@5??@@@@@L? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@eW&@@H? ?@@?he?@@?he?@@@gW&@@@@@1hf@@@? ?

7@@@H??@@@@@1? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@?O&@@5 ?@@?he?@@?he?@@@g7@@?e@@L?he@@@? ?

?J@@@@e?@@@@@@? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@0Y ?@@?he?@@?he?@@@g@@@?e@@1?he@@@? ?

?7@@@@@@@@@@@@@? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@0M ?@@?he?@@?he?@@@g@@@@@@@@@?he@@@? ?

?@@@@@@@@@@@@@@L ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@(M ?@@?he?@@?he?@@@g@@@@@@@@@?he@@@? ?

J@@@@@@@@@@@@@@1 ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@H? ?@@?he?@@?he?@@@g@@(Me@@@?he@@@? ?

7@@@@@@@@@@@@@@@ ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?@@?he?@@?he?@@@g@@H?e@@@?he@@@? ? @@@@g?@@@@@ ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?@@?he?@@?he?@@@g@@L?e@@@?he@@@? ?

@@@@g?3@@@@L? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?@@?he?@@?he?@@@g@@)Ke@@5?he@@@? ?

?J@@@5g?N@@@@1? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ O@?@?26KfO@?2@@@@@@@@6?2@@6?2@@@@@@6?2@@@@@@@@@@?he?@@?he?@@@g3@@@@@@@H?he@@@? ?

?@@@0Yh@@@@@? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?O2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?he?@@?he?@@@gV4@@@@@@hf@@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ O2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?he?@@?he?@@@hI4@0M?hf@@@? ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?O2@@@@@@@@@@@@@@@@@@@@@@@@@@@0M ?@@?he?@@?he?@@@ @@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@ ?O2@@@@@@@@@@@@@@@@@@@@@@@@@@@@0M? ?@@?he?@@?he?@@@ @@@? ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@hfO@?2@@@@@@@@@@@@@@@@@@@@@@@@@@0M ?@@?he?@@?he?@@@ @@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0M? ?@@?he?@@?he?@@@ ?J@@@? ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@@@@@@@@@@@0M ?@@?he?@@?he?@@@ O@KO26K?O&@@@? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@ ?@@?he?@@?he?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@5? ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? @@ ?@@@hf@@@@@@ ?@@?he?@@?he?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0Y? ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? ?J@@ ?@@@hf@@@@@@@@ ?@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? O&@@ ?@@@hf@@eI'@@L? ?@@?he?@@?he?@@@ ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? ?O2@@@@@@@ ?@@@hf@@e?N@@1? ?@@?he?@@?he?@@@ ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? ?O2@@@@@@@@@@@ ?@@@hf@@f3@@? ?@@?he?@@Lhe?@@5 ?

?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? O2@@@@@@0Mf@@ ?@@@hf@@fN@@? ?@@?he?@@)K?h?@@H ? ?@@?f@@ ?@@? @@@? ?@@@f?@@? ?@@? ?O2@@@@@@@0Mh@@ ?@@@hf@@f?@@? ?@@?he?@@@@@@@@@@@@@@@5? ?

?@@?f@@ ?@@L @@@? ?@@@f?@@? ?@@? ?O2@@@@@@@0Mhf@@ ?@@@hf@@f?@@? ?@@?he?@@@@@@@@@@@@@@0Y? ? ?@@?f@@ ?@@)?@K??O@K?O2@6?@?@KO2@@6KO26KeO@K?O2@@@@@@@@@@@@@@@@@@@@@? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@fJ@@? ?@@?he?@@? ? ?@@?f@@ J@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@L ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@f7@@? ?@@?he?@@? ? ?@@?f@@ ?W&@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@e?J@@5? ?@@?he?@@? ?

?@@?f@@ W&@(M? ?I'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@eO&@@H? ?@@?he?@@? ?

?@@?f@@ ?W&@0Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@W2@@@@ ?@@?he?@@? ?

?@@?f@@ W&@? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@@@@(M? ?3@@@@@@@@@@@@@@5? ?

?@@?f@@ ?W&@5? V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@@@0Y ?V4@@@@@@@@@@@@0Y? ?

?@@?f@@ W&@0Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@(M ?

?@@?f@@ ?W&@ V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@H? ?

?@@?f@@ W&@5 ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@ ?

?@@?f@@ ?W&@0Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@ ?

?@@?f@@ W&@? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@ ?

?@@?f@@ ?W&@5? V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@ ?

?@@?f@@ W&@0Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@ ?

?@@?f@@ ?W&@ V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@ ?

?@@?f@@ W&@5 ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@ ? ?@@?f@@ ?W&@0Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@ ?

@@@? ?@@?f@@ W&@? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@ ?

@@@? ?@@?f@@ ?W&@5? V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@L? ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@)K ?

@@5? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@@@6X ?

@@H? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@@@@)K? ?

@@L? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@?I'@@@ ? @@1? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@eV'@@L? ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@hf@@e?V'@1? ? @@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@he?J@@f?@@? ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@g@KO@?&@@@@6?&@@@6KO@K?g?O@K ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@g@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?

@@@? ?@@?f@@ ?W&@0Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@g@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ? @@@? ?@@?f@@ W&@? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@hf@@fW@@? ?

@@@? ?@@?f@@ ?W&@5? V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@f7@@? ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@hf@@e?J@@5? ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@eO&@(Y? ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@@@@@(Y ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@hf@@@@@(Y? ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@@@0Y ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@ ?

@@@? ?@@?f@@ W&@0Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@ ?

@@@? ?@@?f@@ ?W&@ V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@ ?

@@@? ?@@?f@@ W&@5 ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@hf@@ ?

@@@? ?@@?f@@ ?W&@0Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@hf@@ ?

@@@? ?@@?f@@ W&@? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@@@@@@@@@@@@@@@ ?

@@@? ?@@?f@@ ?W&@5? V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@@@@@@@@@@@@0M? ? @@@? ?@@?f@@ W&@0Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@V40M ?

@@@? ?@@?f@@ ?W&@ V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@5 ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ? @@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ? @@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ? @@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ? @@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ? @@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@0M @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@g@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@g@@g@@@@@@@?f?@@@g@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ? @@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ? @@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ? @@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?e?J@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?e?@@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ? @@@? ?@@?e?N@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? ?O2@@@@@@@0M @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?f@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? @@ ?@@@ ?

@@@? ?@@?e?J@@ ?W&@(Y V'@)X? ?@@@f?@@? ?@@? ?O2@@@@@@0M? @@L? ?@@5 ?

@@@? ?@@?e?@@@ W&@(Y? ?V'@)X ?@@@f?@@? ?@@? O2@@@@@@@0M? 3@)X J@@H ? @@@? ?@@?e?N@@ ?W&@(Y V'@)X?hf?@@@f?@@? ?@@? O2@@@@@@@0M? V'@)K?hf?O&@5? ?

@@@? ?@@?f@@ W&@(Y? ?V'@)Xhf?@@@f?@@? ?@@? O2@@@@@@@0M? ?V'@@@@@@@@@@@@@@@@@@(Y? ?

@@@? ?@@?f@@hf?W&@(Y V'@)X?he?@@@f?@@? ?@@? O2@@@@@@@0M? V4@@@@@@@@@@@@@@@@0Y ?

@@@? ?@@?f@@hfW&@(Y? ?V'@)Xhe?@@@f?@@? ?@@? O2@@@@@@@0M? ?

@@@? ?@@?f@@he?W&@(Y V'@)X?h?@@@f?@@? ?@@? O2@@@@@@@0M? ?

@@@? ?@@?f@@heW&@(Y? ?V'@)Xh?@@@f?@@? ?@@? O2@@@@@@@0M? ?

@@@? ?@@?f@@h?W&@(Y V'@)X?g?@@@f?@@? ?@@? O2@@@@@@@0M? ?

@@@? ?@@?f@@hW&@(Y? ?V'@)Xg?@@@f?@@? ?@@? O2@@@@@@@0M? ? @@@? ?@@?f@@g?W&@(Y V'@)X?f?@@@f?@@? ?@@? O2@@@@@@0M ?

@@@? ?@@?f@@gW&@(Y? ?V'@)Xf?@@@f?@@? ?@@? O2@@@@@@@0M? ?

@@@? ?@@?f@@f?W&@(Y V'@)X?e?@@@f?@@? ?@@? O2@@@@@@@0M? ? @@@? ?@@?f@@fW&@(Y? ?V'@)Xe?@@@f?@@? ?@@? ?O2@@@@@@@0M ?

@@@? ?@@?f@@e?W&@(Y V'@)X??@@@f?@@? ?@@? O2@@@@@@0M ? @@@? ?@@?f@@eW&@(Y? ?V'@)X?@@@f?@@? ?@@? O2@@@@@@@0M? ?

@@@? ?@@?f@@?W&@(Y V'@)X@@@f?@@? ?@@? ?O2@@@@@@@0M ?

@@@? ?@@?f@@W&@(Y? ?V'@@@@@f?@@? ?@@? O2@@@@@@0M ?

@@@? ?@@?f@@@@@H V@@@@@f?@@? ?@@? O2@@@@@@@@0M ?

@@@@@@@@@@ ?@@?f@@@@@? O@K?eO@?@KO26?2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@f?@@? ?@@? ?O2@@@@@@@0M ?

N@@@@@@@@@ ?@@?f@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@5f?@@? ?@@? ?O2@@@@@@@0M ?

?3@@@@@@@5 ?@@?f@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0Yf?@@? ?@@? O2@@@@@@@0M? ?

?V'@@@@@@H ?@@? ?@@? ?@@?hf?O2@@@@@@@0M ? N@@@@@5? ?@@? ?@@? ?@@?heO2@@@@@@0M ?

?3@@@(Y? ?@@? ?@@? ?@@?gO2@@@@@@@0M? ?

?N@@@H ?@@? ?@@? ?@@??O2@@@@@@@0M ?

@@@? ?@@? O@K? ?O@KgO26KeO@?2@@@6?@KO26?2@@@@6?2@@@6?2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@? ?@@@@@@@@@0M ?

O26KO26?@KO@?2@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@5? ?@@@@@0M ? ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@0?40Y? ?@0M ?

?@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ ?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

?

627

261 279 310

261

Table 2.2.2: Characteristics of Flam & Russell

FR-6415 Diagonal Range Illumination Horn

Figure 2.2.2.1: Dimensions of FR-6415 Diagonal Range Illumination Horn. All dimensions are in millimeters.
20

-30

-25

-20

-15

-10

-5

0

5

-40 -20 0 20 40

FR-6415 Diagonal Horn

3 GHz E-Plane Response

Magnitude (dBi)

Azimuth (degrees)

Figure 2.2.2.2: Flam & Russell Diagonal Range Illumination Horn (3.0 to 8.0 GHz) in

use with concrete reinforcement grid specimen.

-50

-40

-30

-20

-10

0

-40 -20 0 20 40

FR-6415 Diagonal Horn

3 GHz H-Plane Response

Magnitude (dBi)

Azimuth (degrees)

Figure 2.2.2.3: E-Plane radiation pattern

for FR-6415 at 3.0 GHz.

Figure 2.2.2.4: H-Plane radiation pattern

for FR-6415 at 3.0 GHz.
sioned orthographic views in Figures

2.3.3 through 2.3.5.

Previous tests with the radar system [1]

had shown the problematic nature of

multipath signals reaching, and distorting, the straight line (through the specimen) transmission signal. Calculations

showed that an electromagnetic shield, in

the form of a roughly 2.5 m square, 3 mm

thick aluminum panel would effectively

block any multipath signals from the

data except for those due to internal

reflections within the specimen thickness.

This was accurate provided the transmitting and receiving horns were relatively

close to the test article. The distance

selected was 1 m from the backplane of

the EM shield to the aperture of each

antenna. This meant that the distance

from the receiving horn to the back side

of the specimen varied, depending on the

specimen thickness.

The EM shield contained a 914 mm

square “window” on centerline through

which the transmitted signals could pass

unobstructed, as shown in Figures 2.3.2

and 2.3.4. Multipath signals diffracting

around the edges of the shield arrived

significantly later (in the time domain)

and were thus easily eliminated using

gating windows (see section 2.6). 

In order to gain statistical data concerning the variability of the measured distance with respect to the spatial and compositional variability of the various materials, the entire specimen carrier platform

was mounted to a rail system that permitted translation of the specimen perpendicular to the line of signal transmission. In this manner, several duplicate

sets of tests could be conducted for a single specimen, but with different sections

of the specimen being located on the centerline of the transmission path.

21

-40

-30

-20

-10

0

-40 -20 0 20 40

FR-6415 Diagonal Horn

8 GHz E-Plane Response

Magnitude (dBi)

Azimuth (degrees)

-40

-30

-20

-10

0

-40 -20 0 20 40

FR-6415 Diagonal Horn

8 GHz H-Plane Response

Magnitude (dBi)

Azimuth (degrees)

Figure 2.2.2.5: E-Plane radiation pattern

for FR-6415 at 8.0 GHz.

Figure 2.2.2.6: H-Plane radiation pattern

for FR-6415 at 8.0 GHz.
22

3mm Aluminum

Sheet EM Shield

Typical 1m x 1m x 304 mm

Test Specimen

Receiving

Horn

Transmitting

Horn

Movable Platform

Rail Sub-System

Table Translation Axis

914 mm x 914 mm

Window in EM Shield

Specimen

Mounting

Platform

Figure 2.3.1: Isometric view of test stand for Phase 2 NLS tests. Mobile table is shown

with specimen in place on opposite side of EM shield from transmitting horn.

Figure 2.3.2: Isometric view of test stand for Phase 2 NLS tests showing central square

window in EM shield.
23

2.438 m

2.438 m

1.592

1.000m 1.000 m

1.592 m

914 mm

Square “Window”

1.000 m

Specimen Width

Receiver

Horn

Transmission

Horn

Specimen Thickness

(varies)

1.000 m 1.000 m

Mobile Table

Figure 2.3.3: End view of test stand for

Phase 2 NLS tests.

Figure 2.3.4: Plan view of test stand for

Phase 2 NLS tests showing central square

window in EM shield.

Figure 2.3.5: Elevation view of test stand for Phase 2 NLS tests 
2.4 Specimen Design

A total of 9 different materials were tested in this series. A summary of these is

presented in Table 2.4. More detailed statistics are given in Chapters 3 and 4. The

test articles included common construction materials such as brick, masonry

block, plain concrete, reinforced concrete,

glass, lumber, plywood, drywall, and

reinforcing bars. At least three different

thicknesses, and in some cases four, were

tested for each of the above materials. In

addition, the lumber and plywood specimens were tested in both a wet and dry

state.

Of particular note is the list of plain concrete specimens in Table 2.4. Because of

the widely varying nature of this common composite, efforts were made to

construct an experiment matrix that captured some of the most important variables. These included aggregate size,

water/cement ratio, and slump. The full

material design matrix included high and

low values for each of the above three

parameters plus three panel thicknesses

for a total of 24 plain concrete specimens.

Cylinder strengths and other data reported in Chapter 3 are for standard 28-day

water-cured cylinders.

All specimens had a 1 m by 1 m cross

section. Design thicknesses varied from

as little as 6 mm to as great as 600 mm

depending on the material and typical

usage values at commercial and residential construction sites.

The values listed in Table 2.4 are design

values. The actual values differed as a

result of batch processing errors and tolerances, material availability, and workmanship errors and tolerancing. Because

of this, detailed measurements were

taken of both the actual geometry and

material properties at the time of testing.

These more detailed data are presented

in Chapters 3 and 4. Since significant

variations existed in some situations

(notably batch processing weights for the

plain concrete) the numbers presented in

Table 2.4 should only be used as an

approximate reference.

Units in Table 2.4 are kilograms per cubic

meter for concrete density and millimeters for all thickness specifications.

2.5 Test Protocol

The data for each test consisted of a calibrated response spectrum. The theory

and hardware instrumentation which

allows for the generation of these spectra

were presented in Section 2.1and these

techniques were implemented in an automatic fashion via computer control.

The protocol for testing any specimen,

however, coinsisted of the following

steps:

Step 1: Acquire freespace response spectra. At the start and finish of each day of

testing a response spectrum was acquired

using the test setup configured as shown

in Figure 2.3.2, with no specimen loaded.

This was used to provide the denominator of Eq. 2.1.23.

Step 2: Acquire response spectrum for

the test specimen. This step follows the

previously described theoretical protocol

for discrete construction of the response

spectrum but with one important variation. Instead of a single measurement

24
being made at each frequency, the average of 128 samples of the response at

each frequency was recorded. This was

performed automatically and was done

to increase the accuracy of each individual frequency response measurement.

The same procedure was used for the

freespace measurements.

Step 3: Spatial variation tests. Ten separate tests were performed for each physical specimen. After each test the specimen platform was moved in 6 mm increments perpendicular to the signal trans25

BFRL/Construction Automation Program

NLS Phase II Test Specimen Matrix

* All specimens to be 1m x 1m square.

* Receiver Unit to be electromagnetically isolated from multipath by means

 of an aluminum plate shield (3mm thick sheet, extending 1m minimum

 about a central 914 mm x 914 mm square hole

* Transmission and receiver antennas located 1m from the specimen front face

 (2.0 m spacing between antennas)

* All tests are conducted using both frequency bandwidths available: 0.500-

 2.0 Ghz (set 1); 3-8 Ghz (set 2).

* For concrete specimens the following properties apply:

Volumetric Analysis

Properties Batch 1 Batch 2 Batch 3 Batch 4 Batch 5 Batch 6 Batch 7 Batch 8

MSA, mm 12.7 12.7 12.7 12.7 25.4 25.4 25.4 25.4

w/c 0.4 0.4 0.6 0.6 0.4 0.4 0.6 0.6

Slump low high low high low high low high

% Cement 15.8 18.2 10.5 12.1 14.1 16.0 9.4 10.7

% Water 19.9 22.9 19.9 22.9 17.8 20.2 17.8 20.2

% CA 29.9 29.9 29.9 29.9 37.9 37.9 37.9 37.9

% FA 31.9 26.5 37.2 32.6 28.6 24.3 33.3 29.7

% Paste 35.7 41.1 30.4 35.0 31.9 36.2 27.2 30.9

Theoretical Batch weights, SSD Basis, kilograms per cubic meter (kg/m^3)

Cement 497.6 572.5 331.7 381.7 445.3 504.7 296.7 336.5

Water 199.2 228.9 199.2 228.9 177.8 202.1 177.8 202.1

CA 813.3 813.3 813.3 813.3 1032.1 1032.1 1032.1 1032.1

FA 835.9 695.0 973.8 853.7 750.3 637.3 873.9 777.6

Density (kg/m^3) 2345.9 2309.6 2318.0 2277.5 2405.3 2376.2 2380.4 2348.3

Density (g/cc) 2.35 2.31 2.32 2.28 2.41 2.38 2.38 2.35

MSA = Maximum Size Aggregate (mm)

Coarse Aggregate: ASTM C33 #7 (Batch 1-4), ASTM C33 #57 (Batch 5-8)

For each bath there were 3 thickness: 102 mm, 203 mm, and 305 mm

For the remaining engineering materials the following nominal specifications apply:

Material Thickness Thickness Thickness Thickness

Reinf. Concrete # 1

1% Mesh, Grade 60 203.2 N/A N/A N/A

Reinf. Concrete #2

2% Mesh, Grade 60 203.2 N/A N/A N/A

Glass(Plain) 6.4 12.7 19.1

Drywall 6.4 9.5 12.7

Plywood 6.4 12.7 19.1 31.8

Masonry Block 203.2 406.4 609.6

Lumber 38.1 76.2 114.3 152.4

Brick 88.9 177.8 266.7

Table 2.4: Design Material Properties for Phase 2 NLS Tests
mission line between the two horns and

the test repeated until a maximum displacement of 60 mm had been achieved.

Each individual test was calibrated during the post processing cycle as described

in Section 2.1. Using these ten separate

tests, mean and standard deviation of the

frequency response spectra for a particular specimen could be determined. It

was this averaged frequency response

spectrum that was used for subsequent

time domain analyses.

2.6 Post-Processing Procedures

Several post-processing techniques were

used to improve the utility of the attenuation spectra presented in Chapters 5 and

6. First, the averaged spectrum for a

given test specimen was converted to

time domain using a chirp-Z transform

[7]. The implementation used for the

tests reported here was an embedded

function in DATAPRO (a proprietary

code developed by Flam & Russell)

which was part of the experimental

instrumentation. This transform can also

be implemented using standalone postprocessors such as Matlab [8] and other

digital signal processing packages. The

chirp-Z transform was used because it is

more flexible than an FFT. In the case of

the data presented here, there were 401

discretely sampled points which comprised the 0.5 to 2.0 GHz data and 801

points which comprised the 3.0 to 8.0

GHz data. A typical input file would be

a response spectrum like that shown in

Figure 2.6.1 for the 0.5 to 2.0 GHz test

series. In this case, the data shown are

for a 152 mm thick, double wythe brick

wall, that is, a brick wall two blocks

deep. Using a chirp-z transform, the data

in Figure 2.6.1 can be converted to the

time domain plot shown in Figure 2.6.2.

This is a particularly good data set, with

very little attenuation involved. In fact,

as can be seen for certain frequencies

around 0.75 GHz in Figure 2.6.1, the calibrated frequency response is actually

slightly greather than 1.0, implying that

constructive interference is taking place

within the wall. This will not normally

be the case, especially with thicker,

denser walls such as concrete.

The time domain plot shown in Figure

2.6.2 shows one predominant peak at a

range of slightly more than two meters.

Two observations need to be made at this

point. First, a “time domain” waveform

implies amplitude as a function of time,

usually expressed in seconds. In this

case, the scale is actually in nanoseconds,

where 1 nanosecond of travel in free

26

0

0.2

0.4

0.6

0.8

1

1.2

0.5 1 1.5 2

Calibrated Frequency Response Spectrum

for 152 mm thick Brick wall

[Sample 1 of 10]

No Post-Processing

Amplitude (calibrated decimal)

Frequency (GHz)

Figure 2.6.1: Calibrated frequency response spectrum for 152 mm thick Brick wall (no gating) for

the 0.5 to 2.0 GHz test series, Specimen #1 of 10.
space is equivalent to approximately 304

mm (1 foot). This equivalence permits a

recasting of the x-axis scale in the more

useful units of distance. The second

point is that the true distance between

the two antennas was pre-set at 2.000

meters. The peak in Figure 2.6.2 clearly

is not at 2.000 meters. The difference is

due to the slower velocity of propagation

of the signal through the material:

During its transit through the brick wall,

the signal travels (relative to our refer27

0

0.1

0.2

0.3

0.4

0.5

1 1.5 2 2.5 3 3.5 4 4.5

Calibrated Time Domain Response

for 152 mm thick Brick wall

[Sample 1 of 10]

No Post-Processing

Amplitude

Range (meters)

0

0.1

0.2

0.3

0.4

0.5

0.6

1 1.5 2 2.5 3 3.5 4 4.5

Gated Time Domain Response

for 152 mm thick Brick wall

[Sample 1 of 10]

Gated Amplitude

Range (meters)

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.5 1 1.5 2

Gated Frequency Response Spectrum

for 152 mm thick Brick wall

[Sample 1 of 10]

Amplitude (Gated, decimal)

Frequency (GHz)

Figure 2.6.2: Calibrated Time Domain Response

for 152 mm thick Brick wall (no post processing)

for the 0.5 to 2.0 GHz test series, Specimen #1 of

10.

Figure 2.6.3: Gated Time Domain Response for

152 mm thick Brick wall for the 0.5 to 2.0 GHz

test series, Specimen #1 of 10.

Figure 2.6.4: Gated response spectrum for 152

mm thick Brick wall for the 0.5 to 2.0 GHz test

series, Specimen #1 of 10.

v

c

c

r

r

where

=

=

=

=

ε

ε

v actual wave speed in matter (m/s)

 material dielectric constant 

 (dimensionless)

 vacuum speed of light (m/s)

Eq. (2.6.1)
ence frame) at a velocity less than the

speed of light in a vacuum (Eq.2.6.1). For

many engineering materials, for example

reinforced concrete, the propagation

velocity through the material can be as

much as three (3) times slower than the

speed of light in a vacuum. From Figure

2.6.3 the measured distance at the primary peak can be used to determine the

material dielectric constant by means of

Eq. 2.6.2. 

Adjacent to the predominant peak in

Figure 2.6.2 are several smaller peaks. In

general these will be much more pronounced in materials with higher water

content and where the signal to noise

ratio is lower. Even for this case there is

a substantial amount of noise in the spectrum shown in Figure 2.6.1. Noise in the

spectrum is produced primarily by internal reflections within the target. Since

the true distance was known with high

accuracy for these experiments, a range

gate [9] on the time domain can be used

to clean up the spectra.

The HP 8530A used for these experiments contains a gating feature which

allows for selective viewing of individual

portions of the time domain response.

The specific gating used was a 1 nanosecond wide Kaiser-Bessel window centered

on the peak, which effectively considered

only those data within a 6 dB amplitude

variation from the peak. The result of the

application of this gate in the time

domain is shown in Figure 2.6.3 for the

case of the brick wall previously considered. 

An inverse transform of the time domain

data yields the gated frequency response

spectra. As can be seen from Figure 2.6.4,

this is a much cleaner representation of

the attenuation characteristics of the

transmitted signal with respect to frequency. The processing of the data proceeded in a step-wise fashion as follows:

• Define the time gates to use for each

material sample using DATAPRO.

• Apply the time gating to each measurement with DATAPRO, and save

the gated frequency and time domain

data in Network Common Data Form

(netCDF).

• Read the netCDF data and perform

statistical analysis on the gated frequency and time domain data using

MatLab.

• Write out the averages and standard

deviations of the measurements for

each sample in both netCDF and

ASCII files.

In Chapters 5 and 6 the attenuation data

will be presented in the form shown in

Figure 2.6.4, but with the notable inclusion of a 1-sigma error band, based on

the replicate measurements taken for

each specimen

28

εr

x

d

t c

d

x

= + = ⋅ +

=

=

=

















2 2

1

∆ ∆ 1

∆

∆

 difference between the

 measured distance and

 the true distance (m)

t difference between the

 measured time of flight

 and the vacuum time of

 flight (s)

d material thickness (m)

Eq. (2.6.2)
29

In the following sections, the material

properties and geometry of each specimen are detailed. In general, these properties and dimensions differed from those

listed previously in Table 2.4 as the nominal design specifications for the test specimen. Deviations from the design thicknesses were most pronounced in the concrete specimens. There, imprecision in

the fabrication of the wood formwork

and deflections of the formwork under

the hydrostatic loading of the fresh concrete led to occassional differences of several millimeters in thickness across the

specimen width.

Each specimen/test combination had a

condensed alphanumeric name which

generally consisted of a one or two letter

prefix identifying the material, a specimen identification number, material

thickness identifier, frequency bandwidth

identifier, and the test number for the

current test. A total of 10 tests were performed for each specimen in which the

specimen was moved laterally (perpendicular to the signal propagation line) in

6 mm increments relative to the specimen

centerline. Thus test #10 for any given

specimen meant that the specimen was

displaced 60 mm from its original centerline relative to the centerline of the transmitted signal. An example data file name

would be:

C712L01

Where, “C” designates plain concrete,

“7” is the concrete batch number (8 were

used), “12” was the specimen thickness

identifier (in this case 305 mm = 12 inches), “L” means “low” frequency bandwidth (0.5 to 2.0 GHz), and “01” was the

first test for this specimen. 

A complete list of specimen names

(minus the within specimen test number

suffix) for tests in the Low Range series

(0.5 to 2.0 GHz) is given in Table 3.0.1. A

similar set is given for the High Range

tests (3.0 to 8.0 GHz) in Table 3.0.2. 

Individuals desiring specific digital

records of the raw, calibrated data should

refer to the nomenclature defined in

these two tables. Similar nomenclature

prefixes apply to the averaged, gated

response spectra described in detail in

Chapters 4 and 5. Requests for digital

copies of the “raw,” calibrated data

(either in the frequency or time domain)

should be addressed to the author at the

email address listed at the front of this

document. Please specify the test sets

when doing so.

3.0 Specimen Material Properties and Geometry 
30

Nominal Nominal Nominal

Parent Material Exterior Material Material Thickness Thickness Thickness Total

Specimen (Layer 1) Surface (Layer 2) (Layer 3) (Layer 1) (Layer 2) (Layer 3) Thickness

Name Condition (mm) (mm) (mm) (mm)

B1L Brick Dry 76 76

B2L Brick Dry Brick 76 76 152

B3C84L Brick Dry Concrete 76 102 178

B3C88L Brick Dry Concrete 76 203 279

B3L Brick Dry Brick Brick 76 76 76 229

B3MB8L Brick Dry Masonry Block 76 203 279

C112L Concrete Dry 305

C14L Concrete Dry 102

C18L Concrete Dry 203

C212L Concrete Dry 305

C24L Concrete Dry 102

C28L Concrete Dry 203

C312L Concrete Dry 305

C34L Concrete Dry 102

C38L Concrete Dry 203

C412L Concrete Dry 305

C44L Concrete Dry 102

C48L Concrete Dry 203

C512L Concrete Dry 305

C54L Concrete Dry 102

C58L Concrete Dry 203

C612L Concrete Dry 305

C64L Concrete Dry 102

C68L Concrete Dry 203

C712L Concrete Dry 305

C74L Concrete Dry 102

C78L Concrete Dry 203

C812L Concrete Dry 305

C84L Concrete Dry 102

C88L Concrete Dry 203

CB1L Masonry Block Dry 203 203

CB2L Masonry Block Dry Masonry Block 203 203 406

CB3L Masonry Block Dry Masonry Block Masonry Block 203 203 203 610

D25L Drywall Dry 6 6

D50L Drywall Dry 13 13

D625L Drywall Dry 16 16

G25L Glass Dry 6 6

G50L Glass Dry 1 3 1 3

G75L Glass Dry 1 9 1 9

L15DL Southern Pine Dry 38 38

L15WL Southern Pine Wet 38 38

L30DL Southern Pine Dry 76 76

L30WL Southern Pine Wet 76 76

L45DL Southern Pine Dry 114 114

L45WL Southern Pine Wet 114 114

L60DL Southern Pine Dry 152 152

L60WL Southern Pine Wet 152 152

P125DL Plywood Dry Plywood 13 19 32

P125WL Plywood Wet 13 19 32

P25DL Plywood Dry 6 6

P25WL Plywood Wet 6 6

P50DL Plywood Dry 13 13

P50WL Plywood Wet 13 13

P75DL Plywood Dry 19 19

P75WL Plywood Wet 19 19

RC881L Reinforced Concrete Dry 203 203

RC882L Reinforced Concrete Dry 203 203

RE1L Rebar Grid Dry 19 19

Table 3.1: Parent Specimen Nomenclature for Low Range Tests (0.5 to 2.0 GHz). Each

parent specimen entry has 10 individual associated tests, beginning with suffix 01 and

ending with suffix 10. The centroid of specimen 01 is aligned colinear with the direct

signal path between transmitter and receiver; specimen 10 in each set is shifted laterally 60 mm from the transmitted signal path; all other tests are uniformly spaced at 6

mm intervals between these two extremes.
31

Nominal Nominal Nominal

Parent Material Exterior Material Material Thickness Thickness Thickness Total

Specimen (Layer 1) Surface (Layer 2) (Layer 3) (Layer 1) (Layer 2) (Layer 3) Thickness

Name Condition (mm) (mm) (mm) (mm)

B1H Brick Dry 76 76

B2H Brick Dry Brick 76 76 152

B3C84H Brick Dry Concrete 76 102 178

B3C88H Brick Dry Concrete 76 203 279

B3H Brick Dry Brick Brick 76 76 76 229

B3MB8H Brick Dry Masonry Block 76 203 279

C112H Concrete Dry 305

C14H Concrete Dry 102

C18H Concrete Dry 203

C212H Concrete Dry 305

C24H Concrete Dry 102

C28H Concrete Dry 203

C312H Concrete Dry 305

C34H Concrete Dry 102

C38H Concrete Dry 203

C412H Concrete Dry 305

C44H Concrete Dry 102

C48H Concrete Dry 203

C512H Concrete Dry 305

C54H Concrete Dry 102

C58H Concrete Dry 203

C612H Concrete Dry 305

C64H Concrete Dry 102

C68H Concrete Dry 203

C712H Concrete Dry 305

C74H Concrete Dry 102

C78H Concrete Dry 203

C812H Concrete Dry 305

C84H Concrete Dry 102

C88H Concrete Dry 203

CB1H Masonry Block Dry 203 203

CB2H Masonry Block Dry Masonry Block 203 203 406

CB3H Masonry Block Dry Masonry Block Masonry Block 203 203 203 610

D25H Drywall Dry 6 6

D50H Drywall Dry 13 13

D625H Drywall Dry 16 16

G25H Glass Dry 6 6

G50H Glass Dry 1 3 1 3

G75H Glass Dry 1 9 1 9

L15DH Southern Pine Dry 38 38

L15WH Southern Pine Wet 38 38

L30DH Southern Pine Dry 76 76

L30WH Southern Pine Wet 76 76

L45DH Southern Pine Dry 114 114

L45WH Southern Pine Wet 114 114

L60DH Southern Pine Dry 152 152

L60WH Southern Pine Wet 152 152

P125DH Plywood Dry Plywood 13 19 32

P25DH Plywood Dry 6 6

P25WH Plywood Wet 6 6

P50DH Plywood Dry 13 13

P50WH Plywood Wet 13 13

P75DH Plywood Dry 19 19

P75WH Plywood Wet 19 19

RC881H Reinforced Concrete Dry 203 203

RC882H Reinforced Concrete Dry 203 203

RE1H Rebar Grid Dry 19 19

RE2H Rebar Grid Dry 19 19

Table 3.2: Parent Specimen Nomenclature for High Range Tests (3.0 to 8.0 GHz). Each

parent specimen entry has 10 individual associated tests, beginning with suffix 01 and

ending with suffix 10. The centroid of specimen 01 is aligned colinear with the direct

signal path between transmitter and receiver; specimen 10 in each set is shifted laterally 60 mm from the transmitted signal path; all other tests are uniformly spaced at 6

mm intervals between these two extremes.
3.1 Brick

The red clay brick used in this study was

a common variety used in residential and

commercial construction containing three

circular weight-reduction holes along the

longitudinal centerline (see Figure 3.1.1).

The bricks had nominal lengths of 193

mm, a width of 90 mm, and a vertical

thickness of 56 mm. The center holes differed in size with the center hole averaging 34 mm in diameter and the two end

holes averaging 37 mm diameter. The

brick is Grade MW, meeting specification

ASTM C 652. Detailed properties,

including geometry and material density

are given in Tables 3.1.1, 3.1.2, and 3.1.3.

As shown in Tables 3.1 and 3.2, there

were three “brick wall” thickness configurations tested. For convenience, three

nominally 1 x 1 meter single wythe brick

walls were fabricated, following the

dimensions listed shown in Table 3.1.1. 

32

 90.4 mm (average)

1067 mm (average)

1067 mm (average)

 181 mm (average)

1067 mm (average)

1067 mm (average)

 271 mm (average)

1067 mm (average)

1067 mm (average)

L

W

T

D1

D2

D3

Figure 3.1.1: Individual brick geometry.

Definitions of each parameter are given in Table

3.1.2 along with typical measurements and statistical parameters. Individual bricks were used to

construct typical residential and commercial

building walls of 1,2, and 3 wythe depth, as

shown in Figure 3.1.2.

Figure 3.1.2: Brick wall geometries. Top: single

wythe; Middle: double wythe; and Bottom: triple

wythe construction. An air gap of between 3 to 5

mm existed between each wall in the multiplewall tests owing to variations in placement of the

bricks. Typical mortar joint thicknesses are presented in Table 3.1.1.
In order to represent two and three

wythe thickness walls, single wythe

walls were stacked as shown in Figure

3.1.1 to achieve the necessary thickness.

On average, an air gap of 3 to 5 mm

existed between each wall. This was due

to variations in the placement of the individual bricks in each wall panel. The

walls were supported by top and bottom

steel channel sections connected by

threaded rods. Shackles, attached to the

threaded rods (not shown) allowed the

wall sections to be handled by an overhead crane.

The mortar joints averaged between 13

and 14 mm thickness, as shown in Table

3.1.1. Characteristics for the mortar are

given in Table 3.1.4 and 3.1.5 below and

include both mix proportions and density, as well as various standard measures

of the cured strength. The same mortar

specified in Tables 3.1.4 and 3.1.5 was

used in the lay up of the concrete masonry block walls described in Section 3.2,

below.

33

Bed Header

 Height Unit Unit Mortar Mortar

Sample along Wall Brick Brick Joint Joint

Number Wall Width Length Height Height Width

(mm) (mm) (mm) (mm) (mm) (mm)

1 0.0 90.3 192.4 56.5 10.3 10.8

2 63.5 90.9 190.5 56.8 12.9 11.1

3 130.2 90.3 193.4 55.6 11.4 13.3

4 200.0 91.1 192.9 55.2 15.4 10.4

5 269.9 90.1 192.1 55.7 15.2 18.5

6 336.6 89.4 192.4 54.0 15.7 14.1

7 406.4 91.1 191.7 56.2 11.8 16.4

8 476.3 91.2 192.5 55.1 16.2 12.7

9 546.1 89.4 191.1 55.4 19.2 13.3

10 619.1 91.2 191.5 55.9 13.9 11.4

11 689.0 89.8 191.4 55.5 11.1 15.0

12 755.7 88.8 192.7 54.8 15.6 14.2

13 828.7 89.8 192.9 54.4 14.3 11.8

14 898.5 91.3 192.2 55.9 12.3 17.1

15 968.4 89.1 191.6 54.8 15.8 10.5

Mean 90.3 192.1 55.4 14.1 13.4

S.D. 0.8 0.8 0.8 2.4 2.5

TABLE 3.1.1: MEASUREMENTS OF ASSEMBLED 1X1 M BRICK WALL
34

BRICK Material Data (from 10 randomly sampled units)

Grade MW Brick, meeting ASTM C 652

General Description: rectangular solid with three circular holes through the thickness

D1 D2 D3

"Left" "Center" "Right" M

 W L T Hole Hole Hole Individual

Sample Brick Brick Brick Diameter Diameter Diameter Brick

Number Width Length Thickness # 1 # 2 # 3 Weight

(mm) (mm) (mm) (mm) (mm) (mm) (g)

1a 90.8 192.5 56.0 37.2 32.9 37.0 1679.8

1b 90.3 193.1 56.3 38.4 35.3 37.3

1c 91.2 193.0 56.0 38.0 33.1 37.3

1d 90.8 192.6 56.2 38.5 34.7 37.2

1e 89.8 192.7 56.4

1f 91.0 192.2 56.6

2a 90.0 192.4 56.0 35.7 32.4 36.7 1670.7

2b 89.4 193.1 56.0 37.5 35.3 38.3

2c 89.5 192.6 56.3 35.4 31.6 36.2

2d 89.3 192.9 55.9 38.0 35.1 38.4

2e 88.5 193.4 56.4

2f 88.7 192.9 56.0

3a 90.9 193.6 56.9 37.0 32.3 37.8 1720.7

3b 90.2 193.4 57.7 37.4 35.2 38.8

3c 91.3 192.9 57.3 37.1 32.8 37.5

3d 90.8 192.5 56.5 37.4 35.2 38.6

3e 90.1 193.2 56.9

3f 90.9 192.9 56.5

4a 90.9 192.1 56.4 37.4 32.6 37.1 1702.5

4b 90.3 192.5 56.8 38.9 35.0 37.4

4c 91.1 192.3 56.4 38.2 32.6 36.6

4d 89.8 191.9 56.2 38.0 34.9 36.8

4e 88.7 191.3 56.7

4f 90.2 55.9

5a 90.9 192.8 56.0 37.0 32.8 38.0 1707.0

5b 89.9 192.5 56.5 37.2 35.4 38.3

5c 91.1 192.5 56.2 37.1 32.9 37.4

5d 91.1 192.0 55.5 37.3 35.4 37.5

5e 90.1 192.4 56.2

5f 91.1 191.9 55.4

6a 89.8 192.1 56.3 37.6 32.0 36.5 1688.9

6b 89.6 192.4 55.9 38.5 35.2 37.2

6c 90.1 192.4 55.8 38.0 32.9 37.0

6d 91.2 192.6 56.5 38.0 35.3 37.3

6e 89.9 192.5 56.3

6f 90.6 192.0 55.7

TABLE 3.1.2: STATISTICAL GEOMETRY DATA FOR BRICKS USED IN THE CONSTRUCTION OF THE WALL SPECIMENS (PART 1 OF 2)
35

7a 90.1 191.6 56.4 37.3 32.4 36.8 1675.3

7b 89.1 192.0 55.7 38.2 32.6 37.1

7c 90.2 191.9 55.1 37.9 32.4 36.0

7d 90.0 191.4 55.3 37.4 34.6 37.1

7e 89.1 191.5 55.9

7f 90.8 191.2 55.2

8a 90.0 193.4 56.4 36.9 32.2 36.3 1679.8

8b 89.6 193.6 56.5 38.5 34.5 37.3

8c 90.2 192.5 56.0 37.2 32.0 36.1

8d 90.0 193.3 56.5 37.9 34.7 37.1

8e 89.7 193.2 56.4

8f 90.0 192.9 56.0

9a 91.4 191.7 56.1 37.2 33.1 37.7 1702.5

9b 90.7 192.5 56.8 36.9 35.5 37.8

9c 91.4 192.5 56.9 37.2 32.7 37.6

9d 90.9 192.2 57.0 37.3 35.2 38.3

9e 90.5 192.5 57.0

9f 91.4 192.3 56.4

10a 91.1 191.9 57.1 37.0 33.1 37.7 1688.9

10b 91.0 192.4 57.1 37.2 34.7 38.5

10c 91.2 192.0 56.7 37.0 33.1 37.4

10d 90.8 192.2 56.1 37.0 34.9 38.3

10e 91.1 192.6 56.4

10f 91.2 192.2 56.1

WLT D1 D2 D3 M

Avg. 90.4 192.5 56.3 37.5 33.8 37.4 1691.6

S.D. 0.7 0.6 0.5 0.7 1.3 0.7 16.0

Units

Bounding Box Solid Volume [ Vs= W*L*T ] 979.0 cm3

Hole Volume [ Vh = pi *T *(D1^2 + D2^2 + D3^2)/4 ] 174.3 cm3

True Solid Volume [Vt = Vs - Vh ] 804.7 cm3

True Material Density [rho = M/Vt ] 2.1 g/cm3

Apparent (radar) Density [rhoapp = M/Vs ] 1.7 g/cm3

Where: W, L, T, D1, D2, D3, and M are defined in the above table

pi = 3.14159

TABLE 3.1.2(continued): STATISTICAL GEOMETRY DATA FOR BRICKS USED IN

THE CONSTRUCTION OF THE WALL SPECIMENS (PART 2 OF 2, INCLUDING

SUMMARY)
36

Masonry Block

Material Properties Test Axial Load Compressive Stress

# (kN) (MPa)

Ungrouted Masonry Block Sample 1 551.6 14.0

Compressive Strength 2 477.7 12.1

3 589.8 15.0

Mean 13.7

 

Mortar Cube Strength 1 59.3 23.0

(moist cured)* 51x51x51 mm 2 59.3 23.0

3 60.0 23.2

Mean 23.1

 

Mortar Cube Strength 1 43.9 17.0

(air dried)** 51x51x51 mm 2 42.6 16.5

3 40.1 15.5

Mean 16.3

* Mold break at 24 hours; subsequently cured underwater for 28 days at 22C

** Mold break at 24 hours followed by 28 days in lab air at 22C

TABLE 3.1.4: Compressive strength of the mortar used in the construction of the brick

and concrete block wall specimens B1, B2, B3, CB1, CB2, and CB3.

Component Mass for 1 Cubic Meter Mass Fraction

(kilograms) (%)

Portland Cement Type I 384.7 16.9%

Lime 61.2 2.7%

Sand 1483.0 65.3%

Water 341.9 15.1%

Density (fresh), kg/m^3 2270.8

TABLE 3.1.5: Mortar grout mix design used for the grout joints for the brick and concrete block wall specimens B1, B2, B3, CB1, CB2, and CB3.
The concrete masonry block used in this

study was also a common variety used in

residential and commercial construction

which included two large, approximately

rectangular holes set towards either end

of the block, a central thin rectangular

slot; and a cutout on one end of the type

typyically used for window frame setting. 

The blocks were manufactured by Ernest

Maier of Bladensburg, Maryland and

meets ASTM C 90. The geometry key

for the subsequent data tables is given in

Figure 3.2.1. The variable names in

Figure 3.2.1 are defined in Table 3.2.1.

The variables W, T, and L stand for the

block width, height, and length, respectively. The dimensions for the various

pockets and cutouts all have two names,

e.g. L4T and L4B. The “L4” portion

refers to the right hand cell. The “T”

and “B” suffixes indicate whether the

measurement was taken at the top or bottom of the block. These are listed in

order to account for the differences in the

the top and bottom dimensions which

result from the manufacturing process.

Tapered male mold inserts are used in

order to facilitate removal of the blocks

37

3.2 Masonry Block

W

T

L

W3T,

W3B

W4T,

W4B

L4T,L4B

L2T,

L2B

L3T, L3B

W2T,

W2B

W1T, W1B

L1T, L1B

Figure 3.2.1: Masonry block geometry. Typical exterior, average dimensions were 395 mm long, 194 mm

wide by 192 mm high. Weight reduction cells are specified in Table 3.2.1. 
from the mold after steam curing. The

difference can be significant and affects

the overall mass of the block. We list

these here for completeness, largely

because they affect the “equivalent density” of the block, as seen by the radar

pulse. To the radar pulse, the block is

seen as a series of cells, partitioned by

concrete walls. For real-time metrology

purposes, however, it will be too burdensome to include such minute details

in a time-of-flight calculation. Therefore,

we develop an equivalent density equal

to the mass of a single block divided by

the overall volume of the block, as if the

cells were not present. The equivalent

density value can be used as a measure

of the amount of time delay associated

with a pulse propagating through the

block. Those considering more detailed

analyses can make use of the data contained in Table 3.2.1.

Geometry and density summary information is given in Table 3.2.1, Part 3.

Mortar joint properties are the same as

those for the brick walls, listed in Tables

3.1.4 and 3.1.5.

38

Approx. 194 mm

Approx. 583 mm

Approx. 194 mm

Approx. 194 mm

Approx. 389 mm

Approx. 194 mm

approx. 982 mm

194 mm

approx.

approx. 982 mm

Figure 3.2.1 (opposite): Masonry block wall

geometries. Top: single row; Middle: double row;

and Bottom: triple row construction. An air gap

of between 3 to 5 mm existed between each wall

in the multiple-wall tests owing to variations in

placement of the blocks. Typical mortar joint

thicknesses are presented in Table 3.1.1, while

mortar joint properties are given in Tables 3.1.4

and 3.1.5. The mortar design was the same as

used for the brick walls.
39

L1 W1 L2T W2T L2B W2B

 W L T End End 1st Cell 1st Cell 1st Cell 1st Cell

Sample Block Block Block Notch Notch Top Top Bottom Bottom

Number Width Length Thickness Length Width Length Width Length Width

(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm)

1a 194.4 382.6 191.2 18.3 19.1 124.0 121.9 132.7 130.1

1b 194.3 381.8 192.1 18.2 18.9 123.5 121.8 132.5 129.7

1c 194.3 395.3 193.1 17.8 19.6

1d 193.9 396.9 192.4

1e 194.1 192.3

1f 194.8 191.7

2a 194.9 396.1 192.0 19.0 19.1 128.3 127.1 123.7 120.5

2b 194.5 396.1 191.9 18.9 19.2 127.5 126.2 123.6 120.6

2c 194.4 396.9 191.8 19.0 19.1 

2d 194.7 396.1 192.4 

2e 194.8 192.1 

2f 194.3 192.5 

 

3a 194.1 396.1 191.8 19.0 19.2 128.7 126.3 123.9 120.4

3b 194.6 396.1 191.9 19.3 19.3 128.1 126.9 123.8 120.4

3c 194.5 396.1 191.6 19.4 19.4 

3d 194.3 396.9 191.8 

3e 194.5 191.9 

3f 194.9 192.9 

 

4a 194.4 395.3 192.3 18.4 19.2 132.7 128.8 123.9 122.2

4b 193.5 395.3 191.6 18.1 19.4 132.7 129.1 123.5 122.6

4c 193.3 395.3 191.1 17.9 19.5 

4d 193.8 394.5 191.1 

4e 193.4 191.0 

4f 194.0 191.1 

 

5a 194.0 396.1 193.2 18.4 19.4 133.0 130.8 124.4 121.9

5b 194.0 395.3 192.2 18.7 19.4 133.0 130.4 123.7 122.1

5c 195.0 395.3 191.6 18.9 19.1 

5d 193.9 395.3 192.0 

5e 193.8 192.0 

5f 193.7 193.0 

 

6a 193.4 395.3 192.6 17.9 19.5 133.5 129.0 123.8 122.1

6b 193.8 395.3 191.5 18.3 19.3 133.2 129.6 123.6 122.5

6c 193.9 395.3 190.5 19.2 19.4 

6d 194.4 396.1 190.2 

6e 193.9 190.2 

6f 193.5 191.0 

 

7a 194.1 395.3 190.3 18.1 19.8 123.2 122.1 133.2 129.3

7b 193.9 395.3 190.7 18.3 19.1 123.7 122.7 132.9 129.5

7c 194.0 395.3 191.0 18.6 18.9 

7d 194.8 396.1 192.4 

7e 193.8 191.9 

7f 193.8 191.6 

 

8a 194.1 395.3 191.2 18.6 19.2 123.8 122.1 133.0 129.0

8b 191.4 395.3 191.4 18.2 19.2 123.8 122.3 133.2 128.7

8c 191.2 395.3 191.2 18.3 19.7 

8d 193.7 395.3 193.7 

8e 193.0 193.0 

8f 191.7 191.7 

 

9a 194.6 396.1 192.3 19.2 19.4 128.4 125.9 123.5 120.6

9b 194.5 395.3 191.5 19.0 19.2 129.5 126.9 123.6 120.9

9c 194.1 396.9 191.1 19.0 18.9 

9d 194.9 396.1 191.4 

9e 194.5 191.3 

9f 194.2 191.4 

 

10a 194.4 395.3 192.9 19.2 19.3 128.5 126.0 123.4 120.7

10b 194.4 395.3 191.9 19.1 19.2 129.8 127.1 123.5 120.9

10c 194.0 396.9 191.4 19.1 19.1 

10d 194.9 396.1 191.8 

10e 194.5 191.7 

10f 194.3 191.5 

TABLE 3.2.1 (Part 1 of 3): Masonry Block Properties
40

L3T W3T L3B W3B L4T W4T L4B W4B M

 Slot Slot Slot Slot 2nd Cell 2nd Cell 2nd Cell 2nd Cell Individual

Sample Top Top Bot. Bottom Top Top Bottom Bottom Brick

Number Len. Width Len. Width Length Width Length Width Weight

(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (g)

1a 9.0 121.2 9.4 128.7 123.1 122.4 133.3 129.1 15113.7

1b 9.1 8.8 123.9 122.0 133.1 129.0

1c

1d

1e

1f

2a 9.1 128.2 9.1 121.8 129.4 127.1 123.3 120.8 15431.5

2b 9.0 9.1 128.4 126.2 123.3 120.7

2c 

2d 

2e 

2f 

 

3a 9.0 129.4 9.0 121.7 129.4 127.0 123.6 120.8 15490.5

3b 9.1 8.8 128.3 126.3 123.5 120.7

3c 

3d 

3e 

3f 

 

4a 9.5 128.7 9.2 122.2 132.6 129.3 123.4 121.9 15113.7

4b 9.3 9.3 132.5 130.0 124.0 122.0

4c 

4d 

4e 

4f 

 

5a 9.1 128.8 9.4 121.4 133.2 129.7 123.7 122.5 15281.6

5b 9.2 9.3 133.4 129.6 124.1 122.5

5c 9.9 9.5 

5d 

5e 

5f 

 

6a 9.7 128.9 9.3 121.5 132.6 130.0 123.6 121.4 15091.0

6b 9.6 9.3 132.5 130.0 124.4 121.8

6c 9.4 

6d 

6e 

6f 

 

7a 9.3 121.7 9.6 128.9 123.3 122.0 132.4 130.0 15095.5

7b 9.0 9.4 124.1 121.9 132.7 130.5

7c 9.5 9.8 

7d 

7e 

7f 

 

8a 9.3 121.9 9.6 128.9 123.4 121.9 132.4 129.6 14941.1

8b 9.2 9.4 124.2 121.9 132.6 129.9

8c 9.3 9.5 

8d 

8e 

8f 

 

9a 9.3 129.4 9.1 121.7 127.7 127.0 123.8 120.4 15476.9

9b 9.3 9.2 128.8 126.1 123.6 120.5

9c 9.3 9.0 

9d 

9e 

9f 

 

10a 9.2 129.5 9.2 121.5 127.5 127.2 123.5 120.5 15458.7

10b 9.4 9.2 128.9 126.2 123.6 120.6

10c 9.3 

10d 

10e 

10f 

 

TABLE 3.2.1 (Part 2 of 3): Masonry Block Properties
41

L 1 W 1

W L T End End

Brick Brick Brick Notch Notch

Width Length Thickness Length Width

(mm) (mm) (mm) (mm) (mm)

Average 194.042 395.058 191.7713 18.651 19.2718267

S.D. 0.74851 3.04395 0.741718 0.4733 0.21900078

L2T W2T L2B W2B

1st Cell 1st Cell 1st Cell 1st Cell

Top Top Bottom Bottom

Length Width Length Width

(mm) (mm) (mm) (mm)

Average 128.444 126.15 126.4691 123.74

S.D. 3.74831 3.02608 4.332805 3.8632

L3T W3T L3B W3B L4T

Slot Slot Slot Slot 2nd Cell

Top Top Bot. Bottom Top

Len. Width Len. Width Length

(mm) (mm) (mm) (mm) (mm)

Average 9.28827 126.779 9.277096 123.8 128.36017

S.D. 0.21859 3.59242 0.240215 3.4449 3.6694867

W4T L4B W4B M

2nd Cell 2nd Cell 2nd Cell ndividual

Top Bottom Bottom Brick

Width Length Width Weight

(mm) (mm) (mm) (g)

Average 126.199 126.402 123.764 15249

S.D. 3.12274 4.28312 4.042952 202.35

Bounding Box Solid Volume [ Vs= (W*L*T)/1000. g/cc ]

Hole Volume [Vh = avg(L1*W1+L2*W2+L3*W3+L4*W4)*T/1000. g/cc ]

True Solid Volume [Vt = Vs - Vh ]

True Material Density [rho = M/Vt ]

Apparent (radar) Density [rhoapp = M/Vs ]

Where: W, L, T, D1, D2, D3, and M are defined in the above table

pi = 3.14159

Units

Vs 1 4 7 0 1 cc

Vh 6 3 9 8 . 9 cc

Vt 8 3 0 1 . 8 cc

rho 1.8369 g/cc

rhoapp 1.0373 g/cc

TABLE 3.2.1 (Part 3 of 3): Masonry Block Properties

Summary Table
42

Plain concrete specimens accounted for

24 of the 58 material specimens tested

during this study. This high percentage

relates to the variable nature of concrete

and the affect its constituents have on the

propagation of EM waves. In addition to

the principal geometry variable (thickness), aggregate size, water/cement ratio,

and slump were investigated. Each of

the latter variables had two levels (high

and low) while three specimen thicknesses were used for all mixes. This led to 24

total specimens. The nominal specimen

thicknesses, as shown below in Figure

3.3.1, were approximately 102 mm, 203

mm, and 305 mm. However, because of

deformations in the concrete formwork

(due to hydrostatic loading during casting), and due to the less precise method

of manufacture 

Approx. 1000 mm

Approx. 305 mm

Approx. 203 mm

Approx. 102 mm

Approx. 1000 mm

Figure 3.3.1: Plain concrete specimen geometry. Eight mixes were investigated for each of the three

geometries shown above. Specific data for each specimen are given in Tables 3.3.1 through 3.3.3.

3.3 Plain Concrete
43

Horizontal

Position SPECIMEN NAME

from Side

Edge (mm) C14 C24 C34 C44 C54 C64 C74 C84

50.8 105.7 103.4 103.7 102.7 101.9 103.9 99.9 103.8

152.4 107.1 104.0 103.9 103.0 101.7 104.0 100.0 104.8

254 108.0 104.4 104.1 103.4 101.7 99.5 100.4 105.3

355.6 108.6 104.6 104.0 103.9 101.5 103.3 101.1 105.8

457.2 109.2 105.0 104.1 103.9 101.9 103.4 101.8 105.9

558.8 109.4 104.9 104.2 103.9 102.2 102.7 102.7 105.8

660.4 109.1 104.6 104.3 103.6 102.3 102.4 103.2 105.7

762 108.7 104.1 103.8 103.6 102.0 102.3 104.0 105.4

863.6 108.2 103.3 103.5 103.3 101.9 102.3 104.4 104.2

965.2 107.5 102.1 103.3 103.1 102.1 102.4 104.6 102.3

Mean 108.1 104.0 103.9 103.4 101.9 102.6 102.2 104.9

S.D. 1.1 0.9 0.3 0.4 0.2 1.3 1.8 1.2

Vertical

Position SPECIMEN NAME

from Bottom

Edge (mm) C14 C24 C34 C44 C54 C64 C74 C84

50.8 110.9 99.8 102.2 101.7 100.1 100.0 105.3 105.0

152.4 110.5 101.4 103.4 102.7 101.6 101.4 104.6 105.8

254 110.4 102.8 104.2 103.1 102.5 102.2 103.9 106.3

355.6 110.1 103.8 104.5 103.5 102.5 103.1 103.0 106.4

457.2 109.5 104.5 104.3 103.9 102.1 103.2 102.3 106.3

558.8 109.0 104.8 104.3 103.9 101.5 103.0 101.7 105.5

660.4 108.1 105.0 103.8 103.3 101.0 102.4 101.1 104.7

762 106.9 104.4 103.4 103.0 100.1 102.2 100.4 103.7

863.6 105.6 103.7 102.9 102.6 99.3 101.9 99.3 102.8

965.2 104.3 102.8 102.3 101.8 98.7 101.7 98.2 102.1

Mean 108.5 103.3 103.5 103.0 100.9 102.1 102.0 104.9

S.D. 2.3 1.6 0.8 0.8 1.3 1.0 2.3 1.5

Averaged Vertical and Horizontal Readings (Thickness & S.D.)

Mean 108.3 103.7 103.7 103.2 101.4 102.4 102.1 104.9

S.D. 1.8 1.3 0.7 0.6 1.1 1.1 2.0 1.3

Table 3.3.1: Plain Concrete Wall Specimens, 101.6 mm Nominal Thickness. Actual specimen thicknesses along vertical and horizontal centerlines (mm) are listed below.
44

Horizontal

Position SPECIMEN NAME

from Side

Edge (mm) C18 C28 C38 C48 C58 C68 C78 C88 RC881 RC882

50.8 201.5 203.8 203.3 202.6 202.4 202.9 202.5 203.0 207.6 205.9

152.4 201.8 204.1 203.6 202.5 203.1 203.2 203.1 203.1 208.5 206.6

254 201.9 204.1 203.9 202.6 203.7 203.5 203.3 202.6 209.4 206.7

355.6 202.1 204.1 204.2 202.6 204.5 204.2 202.7 202.2 210.3 206.8

457.2 202.4 204.4 204.3 202.6 205.0 204.8 202.5 202.1 210.6 206.9

558.8 202.4 204.4 203.9 202.7 204.8 204.9 202.1 201.9 210.9 206.7

660.4 202.7 204.3 203.5 202.8 204.5 204.7 201.5 201.9 210.5 206.6

762 202.8 204.1 203.1 202.8 204.1 203.8 201.0 202.1 209.7 206.4

863.6 202.8 203.6 202.4 202.6 203.4 203.0 200.9 202.5 208.6 205.9

965.2 202.5 203.4 201.6 202.5 204.3 202.7 200.6 203.1 207.6 205.1

Mean 202.3 204.0 203.4 202.6 204.0 203.8 202.0 202.5 209.4 206.4

S.D. 0.4 0.3 0.8 0.1 0.8 0.8 1.0 0.5 1.2 0.5

Vertical

Position SPECIMEN NAME

from Bottom

Edge (mm) C18 C28 C38 C48 C58 C68 C78 C88 RC881 RC882

50.8 203.9 204.7 206.1 203.7 204.8 206.6 200.2 204.6 207.9 202.9

152.4 203.5 205.0 205.3 203.8 204.8 206.2 200.8 203.9 208.9 203.9

254 203.1 204.8 204.7 203.8 204.6 205.9 201.4 203.3 209.7 204.8

355.6 202.9 204.8 204.4 203.0 204.7 203.4 201.7 202.7 210.4 205.8

457.2 202.6 204.6 203.9 202.7 204.8 204.8 202.1 202.1 210.8 206.4

558.8 202.1 204.4 203.6 202.5 204.9 204.6 201.9 201.7 210.6 206.6

660.4 201.8 204.7 203.3 201.9 204.4 204.3 201.8 201.5 210.2 206.6

762 201.3 204.5 203.3 201.7 204.6 204.1 201.5 201.4 209.5 206.6

863.6 201.2 204.7 203.3 201.4 204.7 203.9 201.7 201.5 208.8 206.0

965.2 201.3 204.5 203.3 201.0 204.5 203.3 202.0 201.5 208.4 205.3

Mean 202.4 204.7 204.1 202.6 204.7 204.7 201.5 202.4 209.5 205.5

S.D. 1.0 0.2 1.0 1.0 0.1 1.2 0.6 1.1 1.0 1.3

Averaged Vertical and Horizontal Readings (Thickness & S.D.)

Mean 202.3 204.4 203.8 202.6 204.3 204.2 201.8 202.4 209.5 205.9

S.D. 0.7 0.4 1.0 0.7 0.7 1.1 0.8 0.9 1.1 1.0

Table 3.3.2: Plain Concrete Wall Specimens, 203.2 mm Nominal Thickness. Actual specimen thicknesses along vertical and horizontal centerlines (mm) are listed below.
45

Horizontal

Position SPECIMEN NAME

from Side

Edge (mm) C112 C212 C312 C412 C512 C612 C712 C812

50.8 307.1 312.7 306.9 307.0 306.3 308.3 304.4 308.8

152.4 307.4 310.9 307.7 308.2 305.6 308.6 305.9 309.6

254 307.5 311.4 308.4 308.8 305.0 309.0 307.2 310.5

355.6 307.6 311.6 308.5 309.4 304.8 308.9 308.1 311.1

457.2 308.0 311.8 308.6 309.8 305.0 308.8 308.4 311.7

558.8 308.0 311.8 308.8 310.0 305.0 308.8 308.4 311.9

660.4 308.0 311.5 308.7 309.9 305.0 308.5 307.8 311.3

762 307.9 311.2 308.7 309.6 305.5 308.5 307.2 310.7

863.6 307.4 310.7 308.6 309.2 305.5 307.6 306.9 309.7

965.2 307.0 309.8 308.2 308.5 305.7 306.7 306.0 308.6

Mean 307.6 311.3 308.3 309.0 305.3 308.4 307.0 310.4

S.D. 0.4 0.8 0.6 1.0 0.5 0.7 1.3 1.2

Vertical

Position SPECIMEN NAME

from Bottom

Edge (mm) C112 C212 C312 C412 C512 C612 C712 C812

50.8 306.0 308.7 304.1 306.0 306.6 305.9 307.4 307.9

152.4 306.8 310.3 306.0 307.5 306.7 307.1 308.4 310.0

254 307.6 311.5 307.3 307.3 306.5 308.0 309.1 311.4

355.6 307.9 312.1 308.0 309.4 306.1 308.6 309.2 312.0

457.2 307.9 312.1 308.4 309.8 305.3 308.8 308.8 311.9

558.8 307.9 311.6 308.8 309.9 304.5 308.4 308.3 311.4

660.4 307.7 311.1 309.0 309.8 304.1 307.2 307.9 310.5

762 307.3 310.2 308.6 309.5 303.6 305.9 307.2 309.5

863.6 306.4 309.0 308.4 308.8 303.0 304.7 306.4 308.5

965.2 305.6 310.3 308.1 308.5 302.3 303.0 305.7 307.3

Mean 307.1 310.7 307.7 308.6 304.9 306.8 307.9 310.0

S.D. 0.9 1.2 1.5 1.3 1.6 1.9 1.2 1.7

Averaged Vertical and Horizontal Readings (Thickness & S.D.)

Mean 307.4 311.0 308.0 308.8 305.1 307.6 307.4 310.2

S.D. 0.7 1.0 1.2 1.1 1.2 1.6 1.3 1.4

Table 3.3.3: Plain Concrete Wall Specimens, 304.8 mm Nominal Thickness. Actual specimen thicknesses along vertical and horizontal centerlines (mm) are listed below.
46

(as compared to, e.g. a sheet of glass or

plywood) measurable variances (on the

order of a few millimeters) in specimen

thickness across the width and height of

the concrete specimens were noted in

some cases. For completeness, Tables

3.3.1, 3.3.2, and 3.3.3 list precise thicknesses along the vertical and horizontal

centerlines of all concrete specimens.

These were measured using a digital

caliper with a spanner frame accurate to

0.01 mm (see the photo on the cover).

Table 3.3.4, above, lists the measured

properties of the as-delivered concrete

mixes. For the most part these numbers

closely match the desired numbers listed

in Table 2.4. However the reported

water/cement ratio for Batches 1 and 8

are incomplete The quantity of water 

added on site for those two batches was,

unfortunately, not reported on the delivery ticket. For comparison, the desired

w/c ratio for each mix is listed on the

final row of Table 3.3.4, which shows

general agreement with the remaining

measured values.

Properties Batch 1 Batch 2 Batch 3 Batch 4 Batch 5 Batch 6 Batch 7 Batch 8

Job # 203 204 135 136 77 78 79 80

Truck 196 198 196 164 153 153 153 153

Cement (kg) 468.2 538.6 309.1 365.9 418.2 477.3 281.8 431.8

Water (kg) 132.7 135.6 136.6 134.7 101.3 104.7 113.9 157.1

Additional Water (kg) 0* 75.8 11.4 18.9 147.6 151.4 49.3 0 * *

Total Water (kg) 132.7 211.4 148.0 153.6 248.9 256.1 163.2 157.1

Coarse Aggregate (kg) 805.6 774.1 774.1 778.6 1206.4 1251.6 1057.6 1431.1

Fine Aggregate (kg) 753.3 666.7 913.4 794.1 519.5 506.5 783.0 987.4

Nominal Volume Delivered (m^3) 0.956 0.956 0.956 0.956 0.956 0.956 0.956 1.338

Measured Density (kg/m^3) 2311 2311 2295 2300 2424 2387 2384 2392

Air Content (%) 2.0 1.3 N/A 1.3 1.5 1.0 1.4 N/A

Slump (mm) 57 165 64 222 76 171 83 165

Compressive Strength:

f'c (test 1, 28 days) [MPa] 44.1 38.5 31.9 30.1 32.1 33.0 29.7 31.2

f'c (test 2, 28 days) [MPa] 43.6 39.6 33.8 29.4 32.6 32.7 29.8 31.9

f'c (test 3, 28 days) [MPa] 44.0 40.4 30.5 29.0 33.8 35.1 29.4 31.4

28-day strength (avg) [MPa] 43.9 39.5 32.1 29.5 32.8 33.6 29.6 31.5

Mean Size Aggregate (mm) 12.7 12.7 12.7 12.7 25.4 25.4 25.4 25.4

Actual Water/Cement Ratio 0.28* 0.39 0.48 0.42 0.60 0.54 0.58 0.36**

Desired Water/ Cement Ratio 0.4 0.4 0.4 0.4 0.6 0.6 0.6 0.6

* Measurements of the amount of water added on site were missing from the delivery ticket.

** Measurements of the amount of water added on site were missing from the delivery ticket.

Table 3.3.4: Measured Concrete Mix Properties, as delivered to the Laboratory
Details of the reinforced concrete specimens are given in Figures 3.4.1 and 3.4.2. 

To allow examination of superposition

effects, duplicate rebar grids (identical to

the ones embedded in specimens RC881

and RC882) were tested in air. Geometry

for these grids are given in Figures 3.4.3

and 3.4.4. All grids were constructed

from 19 mm (#6) Grade 60 reinforcement.

47

Two reinforced concrete specimens were

fabricated for comparison with the 203

mm thick Batch #8 plain concrete specimen. Other than the presence of a reinforcing bar grid on the centerline of each

of specimens RC881 and RC882, these

were identical in all respects to specimen

C88 and were cast at the same time using

the same concrete batch. Specimen

RC881 had 1% reinforcing steel content.

This was achieved using 19 mm [#6]

Grade 60 rebar on a 140 mm square grid.

Specimen RC882 had 2% reinforcing steel

and utilized the same square grid format

as RC881 but with half the bar spacing

distance (70 mm). 

3.4 Reinforced Concrete and Rebar Grid Specimens

140 mm

19 mm ReBar

1000 mm

 203 mm

000 mm

140 mm

203 mm

000 mm

70 mm

70 mm

1000 mm

19 mm ReBar

Figure 3.4.1: Reinforced concrete specimen RC881, nominally 203 mm thick,

Batch #8 concrete mix with 1% steel.

Figure 3.4.2: Reinforced concrete specimen RC881, nominally 203 mm thick,

Batch #8 concrete mix with 2% steel.
48

140 mm

140 mm

1000 mm

1000 mm

19 mm ReBar

70 mm

70 mm

1000 mm

1000 mm

19 mm ReBar

Figure 3.4.3: Bare rebar grid (the same as

used in reinforced concrete specimen

RC881). Seven 19 mm bars each in the

horizontal and vertical directions were

used to create a square mesh with 140

mm spacing between bar centers. This

left open areas measuring 121 mm square

for an open area to solid ratio of 75.2%

Figure 3.4.4: Bare rebar grid (the same as

used in reinforced concrete specimen

RC882). Fourteen 19 mm bars each in the

horizontal and vertical directions were

used to create a square mesh with 70 mm

spacing between bar centers. This left

open areas measuring 51 mm square for

an open area to solid ratio of 53.9%
The glass used in this study was an ordinary architectural window glass produced by Libbey Owens Ford (Pilkington

Group, Toledo, Ohio). Specifically it was

soda-lime silica float glass with the

dimensions and properties shown in

Figure 3.5.1 and in Tables 3.5.1 through

3.5.3. Three thicknesses of 5.7, 12.5, and

18.6 mm were tested.

The main constituent (comprising 72% by

mass) of the glass is silicon dioxide.

Sodium oxide is added as a flux for melting temperature reduction in the form of

soda ash. Further additives, in the form

of calcium oxide (from limestone) and

magnesium oxide (from dolomite) are

typically added to improve durability.

Small amounts of iron oxide and aluminum oxide are also added to further

reduce melting temperature and improve

durability. The other components listed

in Table 3.5.1 are trace contaminants.

49

3.5 Glass 

T=5.7 mm

T = 12.5 mm

T = 18.6 mm

1000 mm

1000 mm

Figure 3.5.1: Glass panel specimens used in the Phase II NLS study. Thicknesses are

measured average values. Properties are presented in Tables 3.5.1 through 3.5.3.
50

Material Percent of Total Content

(approximate)

SiO2 72

CaO (calcium oxide, from limestone) 8.4

Fe2O3 (iron oxide, residual impurities) 0.11

Al2O3 (aluminum oxide, residual impurities) 1.1

MgO (magnesium oxide, from dolomite) 3.9

Na2O (sodium oxide, from soda ash) 13.9

K2O (potassium oxide) 0.6

SO3 (sulphur trioxide, from salt cake) 0.2

Table 3.5.1: Nominal composition of soda-lime silica float glass.

Table 3.5.2: Properties of soda-lime silica float glass (source: Libbey Owens Ford,

Toledo, Ohio).

Modulus of Rupture in Flexure for 60-second Load Duration

Mean Value 41 MPa (6000 psi) Annealed

82 MPa (12000 psi) Heat Strengthened

165 MPa (24000 psi) Tempered

Typical Design Value (probability of breakage 0.8%) 19 MPa (2800 psi) Annealed

39 MPa (5600 psi) Heat Strengthened

77 MPa (11200 psi) Tempered

Modulus of Elasticity 72000 MPa (10,400,000 psi)

Modulus of Rigidity (Shear) 30000 MPa (4,300,000 psi)

Bulk Modulus 43000 MPa (6,200,000 psi)

Poisson's Ratio 0.23

Density (nominal) 2.53 g/cc (158 lb/ft^3)

Coefficient of Thermal Stress 0.62 MPa/C (50 psi/F)

Thermal Conductivity at 24C 0.937 W-m/m^2- C (6.5 Btu-in/hr-F-ft^2)

Specific Heat at 24C 0.88 kJ/kg-C (0.21 Btu/lbm-F)

Coefficient of Linear Expansion (24C-300C) 8.3(10)^-6 mm/mm-C (4.6(10)^-6 in/in-F)

Hardness (Moh's Scale) 6

Softening Point (ASTM C338) 715 C (1219 F)

Annealing Point (ASTM C336) 548 C (1018 F)

Strain Point (ASTM C336) 511 C (952 F)

Index of Refraction

at 5(10)^14 Hz 1.523

at 3(10)^14 Hz 1.511

at 1.5(10)^14 Hz 1.499

Emissivity (Hemispherical) at 24C 0.84
51

NLS Phase II Tests: GLASS Specimens

MEASURED Specimen Thicknesses along Horizontal

and Vertical Edges (mm) 

 SPECIMEN NAME

Measurement

Number G25 G50 G75

1 5.64 12.50 18.64

2 5.69 12.50 18.62

3 5.72 12.50 18.62

4 5.72 12.47 18.62

5 5.74 12.50 18.59

6 5.64 12.52 18.59

7 5.64 12.57 18.59

8 5.64 12.57 18.59

9 5.64 12.57 18.59

10 5.69 12.57 18.59

11 5.69 12.50 18.59

12 5.69 12.47 18.59

Thickness (mm) 5.68 12.52 18.60

S.D. (mm) 0.04 0.04 0.02

WidTop (mm) 1016.8 1016.8 1016.8

WidMid(mm) 1016.8 1016.8 1017.6

WidBot(mm) 1016.8 1016.8 1016.8

Avg. Wid(mm) 1016.8 1016.8 1017.1

HeightTop(mm) 1018.4 1019.2 1017.6

HeightMid(mm) 1018.4 1019.2 1019.2

HeightBot(mm) 1018.4 1019.2 1018.4

Avg.Height(mm) 1018.4 1019.2 1018.4

Weight (g) 14618.8 31961.6 47897.0

Density (g/CC) 2.49 2.46 2.49

G25 = nominally 6.35 mm thick glass

G50 = nominally 12.70 mm thick glass

G75 = nominally 19.05 mm thick glass

Table 3.5.3: MeasuredGeometry, Mass, and Density for Glass Specimens Tested at NIST.
The U.S. Span Book for Major Lumber

Species states that “more than 90%” of

dimension lumber used in North

America comes from four commercial

species groups: Spruce-Pine-Fir; Douglas

Fir-Larch; Hemlock-Fir, and Southern

Pine. 

Typical mechanical properties for the

above four types of common construction

lumber are given in Table 3.6.1. Unless

specifically requested, one may be likely

to receive any of the above species when

asking for, as an example, a “2x12” (38 x

292 mm) residential construction plank.

Further information on material properties for these general species of lumber is

available from the Southern Forest

Products Association (New Orleans, LA);

the Southern Pine Inspection Board

(Pensacola, FL); and the Canadian Wood

Council (Ottawa, ON).

As can be seen from Table 3.6.1, the

mechanical properties of all of the above

species are similar. The specific type and

grade obtained for the NLS Phase 2 tests

was an off-the-rack “2x12x12-ft” (38 x 292

x 3658 mm) plank from the Lowe’s home

improvement center in Gaithersburg,

Maryland. The plank was manufactured

by Finlay Forest Industries (Canada) with

the specification KD-SPF #2 & Better,

which stands for: “Kiln Dried, SprucePine-Fir, Grade #2.” 

A single “2x12” plank was too narrow to

meet the nominal 1x1 m square specimen

size selected for the NLS Phase 2 test

setup. Composite specimens were thus

built up as shown in Figures 3.6.1

through 3.6.4. The nominal 37 mm thick

specimen was constructed of one layer of

planks; the 75 mm thick specimen of two

layers; the 113 mm thick specimen of

three layers; and the 151 mm thick specimen of four layers. In all cases the

planks were hammered firmly in contact

with one another prior to edge nailing

(there were no nails within the central

portion of the specimen where the measurements would be made). For specimens with more than one layer, each

layer was alternated with horizontal and

vertical layers in order to average the

affects of stud joints. 

Both dry and wet specimens were tested.

Dry specimen names have a “D” suffix;

while wet specimen names have a “W”

52

3.6 Lumber 

Species Grade Extreme Tension Horizontal Compressive Compressive Modulus of

Group Fiber Stress Parallel Shear Strength Strength Elasticity

in Bending to Grain Strength Perpendicular Parallel (psi)

MPa MPa MPa MPa MPa GPa

Spruce-Pine-Fir No. 2 6.03 2.93 0.48 2.93 7.58 9.65

Douglas Fir-Larch No. 2 5.69 3.45 0.65 4.31 9.31 11.03

Hemlock-Fir No. 2 6.89 3.79 0.52 2.55 10.00 11.03

Southern Pine No. 2 6.72 3.79 0.62 3.90 10.00 11.03

Table 3.6.1: Typical mechanical properties for the four most common species of construction lumber (source: Canadian Wood Council).
53

75 mm

1143 mm

1142 mm

37 mm

1120 mm

1143 mm

Assembly Stud

Figure 3.6.1: Specimen L15, a single layer built-up lumber specimen consisting of three

“2x12” planks mounted on a “2x4” exterior frame. Both dry and wet speciments were

tested.

Figure 3.6.2: Specimen L30, a double layer built-up lumber specimen consisting of six

“2x12” planks. Both dry and wet speciments were tested.
54

151 mm

1135 mm

1144 mm

113 mm

1145 mm

1139 mm

Figure 3.6.3: Specimen L45, a triple layer built-up lumber specimen consisting of nine

“2x12” studs. Both dry and wet speciments were tested.

Figure 3.6.4: Specimen L60, a quadruple layer built-up lumber specimen consisting of

twelve “2x12” studs. Both dry and wet speciments were tested.
of spray on both sides. The spray was

maintained for four hours after which the

specimens were allowed to “drip dry.”

They were then weighed and tested within two hours of termination of the soaking. Measured densities for both wet an

dry specimens are given in Table 3.6.2.

55

suffix. The “wet” specimens were prepared using the following procedure.

First, identical specimens to the dry specimens were set up vertically inside a

plastic “tent” area. A garden sprinkler

system was activated within this tent

such that all specimens were in the line

NLS Phase II Tests: PINE Specimens

MEASURED Specimen Thicknesses along Horizontal Centerline (mm)

 SPECIMEN NAME

Measurement

Number L15D L15W L30D L30W L45D L45W L60D L60W

Thickness 1 36.9 x 75.2 x 112.7 x 151.6 x

Thickness 2 36.5 x 75.4 x 113.5 x 151.2 x

Thickness 3 38.0 x 75.6 x 112.7 x 151.1 x

Thickness 4 36.8 x 76.2 x 113.1 x 149.8 x

Thickness 5 37.4 x 74.8 x

Thickness 6 37.4 x 75.3 x

Thickness 7 36.9 x

Thickness 8 37.6 x

Thickness 9 36.7 x

Thickness 10 36.9 x

Thickness 11 36.2 x

Thickness 12 37.1 x

Mean 37.0 75.4 113.0 150.9

S.D. 0.5 0.5 0.4 0.8

WidTop (mm) 1142.2 x 1143.8 x 1144.6 x 1135.1 x

WidMid(mm) 1141.4 x 1143.8 x 1144.6 x 1135.1 x

WidBot(mm) 1146.2 x 1143.8 x 1144.6 x 1135.1 x

Avg. Wid(mm) 1143.3 x 1143.8 x 1144.6 x 1135.1 x

HeightTop(mm) 1120.8 x 1139.8 x 1136.7 x 1143.8 x

HeightMid(mm) 1120.8 x 1142.2 x 1139.8 x 1144.6 x

HeightBot(mm) 1118.4 x 1143.0 x 1141.4 x 1144.6 x

Avg.Height(mm) 1120.0 x 1141.7 x 1139.3 x 1144.3 x

Volume (cc) 47419.1 47419.1 98489.9 98489.9 147338.0 147338.0 196023.7 196023.7

Weight (grams) 19385.8 20293.8 40179.0 41858.8 62742.8 64150.2 83399.8 84761.8

Density (g/CC) 0.409 0.428 0.408 0.425 0.426 0.435 0.425 0.432

L15D = nominally 1-1/2 inch thick lumber panel (built up), DRY

L15W = nominally 1-1/2 inch thick lumber panel (built up), WET

L30D = nominally 3 inch thick lumber panel (built up) DRY

L30W = nominally 3 inch thick lumber panel (built up) WET

L45D = nominally 4-1/2 inch thick lumber panel (built up) DRY

L45W = nominally 4-1/2 inch thick lumber panel (built up) WET

L60D = nominally 6 inch thick lumber panel (built up) DRY

L60W = nominally 6inch thick lumber panel (built up) WET

Figure 3.6.2: Pine Specimen Geometry and Properties for NLS Phase 2 Tests
Three nominal thickness plywood panel

specimens were fabricated using 6.3 mm

[1/4 in], 11.8 mm [1/2 in], and 18.8 mm

[3/4 in] plywood as shown in Figure

3.7.1. A fourth thickness was created by

doubling specimens P50 and P75 to form

the composite specimen P125 (nominally

31 mm thick). The measured specimen

thicknesses differed significantly from

the nominal warehouse label values (see

Table 3.7.1).

The plywood used in this study met the

PS-1-83 material and fabrication specification developed by the American

Plywood Association (since superceded

by PS-1-95). All were of resin joined, hotpressed construction with an A-C

Exterior-use rating. The 19 mm specimens were manufactured by Lane

Plywood Corp., while the 6 and 12 mm

panels were manufactured by Roseburg. 

Both dry and wet specimens were tested.

Dry specimen names have a “D” suffix;

while wet specimen names have a “W”

suffix. The “wet” specimens were prepared using the same procedure as for

the lumber specimens. Measured densities for both wet an dry specimens are

given in Table 3.7.1.

56

3.7 Plywood

P75

T= 18.8 mm

P50

T = 11.8 mm

P25

T = 6.3 mm

1021 mm

1017 mm

Figure 3.7.1: Nominal Geometry for Plywood Specimens Tested during the NLS Phase

2 experiments. The nominal thicknesses differed substantially from the measured ones

(see Table 3.7.1). 
Typical plywood laminate geometry is

shown in Figure 3.7.2. In all cases except

the 18.4 mm panels, an exterior veneer

was bonded to both external surfaces.

This veneer surface was usually sanded

smooth to a nominally specified material

thickness. The veneer measured approximately 2 mm thick while the central laminates averaged 4 mm thick. The 18.4

mm thick panels had exterior veneer on

only one side.

57

2.5 mm

1.9 mm

1.9 mm

P25: Nominal 6.3 mm

4 mm

4 mm

1.9 mm

1.9 mm

P50: Nominal 11.8 mm

4 mm

4 mm

4 mm

4 mm

1.9 mm

P75: Nominal 18.4 mm

Figure 3.7.2: Measured nominal cross sections layups typical for the three types of

plywood used in the NLS Phase 2 tests.

The fine-hatched layers are exterior

veneer; the coarse-hatched layers are

interior laminates. Specimen P75 had

only one exterior veneer layer. 
58

MEASURED Specimen Thicknesses along Horizontal

and Vertical Centerlines (mm)

 SPECIMEN NAME

Measurement

Number P25D P50D P75D P25W P50W P75W

1 6.5 12.5 18.5 6.4 11.8 18.6

2 6.5 12.2 18.5 6.3 11.9 18.7

3 6.2 12.0 18.5 6.2 11.5 18.6

4 6.4 11.7 18.4 6.4 11.9 18.9

5 6.2 11.6 18.4 6.3 11.6 18.9

6 6.1 12.1 18.3 6.3 11.6 18.8

7 6.4 11.5 18.5 6.3 12.2 18.7

8 6.2 11.4 18.4 6.5 12.4 18.7

9 6.2 11.5 18.5 6.5 12.2 18.7

10 6.2 11.7 18.4 6.2 11.5 18.7

11 6.2 11.5 18.4 6.1 11.5 18.7

12 6.4 11.5 18.4 6.3 12.0 18.6

Mean 6.3 11.8 18.4 6.3 11.8 18.7

S.D. 0.1 0.3 0.1 0.1 0.3 0.1

WidTop (mm) 1020.8 1017.6 1017.6 1020.8 1022.4 1020.8

WidMid(mm) 1020.8 1016.8 1017.6 1020.8 1022.4 1020.8

WidBot(mm) 1020.8 1017.6 1017.6 1020.8 1022.4 1020.8

Avg. Wid(mm) 1020.8 1017.3 1017.6 1020.8 1022.4 1020.8

HeightTop(mm) 1017.6 1016.8 1016.0 1017.6 1019.2 1017.6

HeightMid(mm) 1017.6 1016.0 1016.0 1017.6 1019.2 1019.2

HeightBot(mm) 1016.8 1016.8 1016.0 1016.8 1018.4 1019.2

Avg.Height(mm) 1017.3 1016.5 1016.0 1017.3 1018.9 1018.6

Weight (g) 3686.5 6174.4 8853.0 3686.5 6178.9 8762.2

Density (g/CC) 0.565 0.508 0.465 0.563 0.501 0.450

P25D = nominally 6.35mm thick, dry panel

P50D = nominally 12.7 mm thick, dry panel

P75D = nominally 19.05 mm thick, dry panel

P25W = nominally 6.35 mm thick, saturated (wet) panel

P50D = nominally 12.7 mm thick, saturated (wet) panel

P75D = nominally 19.05 mm thick, saturated (wet) panel

Table 3.7.1: Measured Plywood Specimen Geometry, Mass and Density Data. Both dry

and wet speciments were tested.
Drywall is typically used for interior wall

and ceiling panels in most residential and

some commercial construction. Typically,

12.7 mm panels are used for ceilings and

single layer applications; 9.5 mm panels

are used principally in the double wall

system over wood framing and in repair

and remodeling; and 6.3 mm panels are

used as a base layer for improving sound

control in double layer steel and wood

stud partitions, and for use over old wall

and ceiling surfaces. The latter is sometimes referred to as “ sound deadening

board.”

The commercial brand known as

SHEETROCK (R) manufactured by the

United States Gypsum Company

(Chicago, IL) was used in the present

study. Nominal thicknesses of 6.3 mm

(1/4 in), 9.5 mm (1/2 in), and 12.7 mm

(5/8 in) were tested. Nominal specimen

geometries are given in Figure 3.8.1.

Actual measurements of drywall panel

thickness, mass, and density are presented in Table 3.8.2.

Table 3.8.1 provides a listing of the material composition of the drywall used in

this study. 

59

3.8 Drywall

Approx. 1016 mm

Approx. 1016 mm

500

pprox. T=12.7

m

D375

Approx. T=9.5

mm

D25

Approx. T=6.3

mm

Figure 3.8.1: Nominal Geometry for

Plywood Specimens Tested during the

NLS Phase 2 experiments. 

Material % composition

Gypsum 85-95

Paper (cellulose fiber) 3 - 9

Starch 0.3-1

Glass fiber 0 - 1

Sucrose 0 - 1

Lignin Sulfonates 0 - 1

Sulfonated Naphthalene 0 - 1

Polyvinyl Alcohol 0-0.10

Calcium Stearate 0-0.01

Ammonium Salt 0-0.01

Pentasodium Salt 0-0.01

Boric Acid 0-0.01

Glycerin 0-trace

Table 3.8.1: SHEETROCK (R) material

composition [source: U.S. Gypsum].
60

NLS Phase II Tests: DRYWALL Specimens

MEASURED Specimen Thicknesses along Horizontal

and Vertical Edges (mm)

 SPECIMEN NAME

Measurement

Number D25 D375 D50

1 6.86 9.40 12.45

2 6.96 9.47 12.47

3 6.60 9.50 12.47

4 6.99 9.47 12.52

5 6.96 9.45 12.60

6 6.96 9.40 12.52

7 7.01 9.50 12.55

8 7.01 9.53 12.55

9 7.09 9.25 12.52

Mean Thickness 6.94 9.44 12.52

S.D. 0.14 0.09 0.05

WidTop (mm) 1016.0 1016.0 1014.4

WidMid(mm) 1015.2 1016.0 1015.2

WidBot(mm) 1015.2 1016.8 1016.8

Avg. Wid(mm) 1015.5 1016.3 1015.5

HeightTop(mm) 1016.0 1016.8 1016.8

HeightMid(mm) 1016.0 1016.8 1016.8

HeightBot(mm) 1016.0 1019.2 1018.4

Avg.Height(mm) 1016.0 1017.6 1017.3

Weight (g) 6197.1 6401.4 8376.3

Density (g/CC) 0.87 0.66 0.65

D25 = nominally 6.35 mm thick drywall

D375 = nominally 9.53 mm thick drywall

D50 = nominally 12.70 mm thick drywall

Table 3.8.2: Measured Drywall Specimen Geometry, Mass and Density Data. 
61

In this chapter we present a compact but

complete summary of the received signal

amplitude as a function of frequency for

various target thicknesses. These data

have been calibrated, or normalized, with

respect to a similarly recorded measurement with no target material between the

transmitter and receiver. 

The data are presented in the form of two

pairs of facing tables and graphs for

each generic material (e.g. “Brick”,

“Concrete” etc). The first pair comprise

the low band test results. For these, a

Condor Systems 48450 quad-ridged horn,

operating over a frequency range of 0.5

to 2.0 GHz, was used. The second pair of

graphs and tables present the high-band

test results. For these tests, Flam and

Russell FR-6415 range illumination horns

operating over a frequency of 3.0 to 8.0

GHz were used.

For the left page in each pair, decimal

units are used for the received, normalized amplitude; on the right page of each

pair the units are in decibels (dB). To further reinforce this difference in amplitude

scales we have used the ordinate title

“Transmission Coefficient” for decimal

data and “Received Signal Magnitude”

for decibel data. In the case of the decimal normalized data, a value of 1.0 indicates, nominally, lossless transmission

(that is, 100% of the power gets through)

while 0.0 would represent complete

absorption (or reflection) of the signal by

the target material. In the decibel units

plots, 0.0 represents no loss of signal

strength and attenutated amplitudes are

represented as negative exponents.

When we use the term “relative to free

space” to describe the normalized data, it

means that the signal penetrating the

solid structure is compared to the line-ofsight signal (in air) when the structure

was not present in the transmission path.

Conversion between the two plot pairs is

accomplished using Eq(2.1.26). The decibel scale is particularly useful for viewing the transmission characteristics of

particularly absorptive materials, such as

concrete, where signal attenuation of an

order of magnitude or more difference

can be observed between thinner and

thicker specimens. To those unfamiliar

with decibels, the decimal plots provide a

clear feeling for the ability of the NLS

approach to penetrate common engineering materials. Only in the case of thicker

concrete specimens (greater than 200

mm) was significant attenuation

observed, and that was for a transmission

power level of less than a milliwatt.

Higher transmission power can be used

to increase penetration range.

The graphs contain, usually, three sets of

curves, one group for each target thickness for the given specimen. Each set

contains a solid central line (the mean

signal amplitude) and two dotted lines

representing one standard deviation from

the mean. It was possible to construct

these statistically based curves because of

the ten independent sets of data that

were taken for each test. Since the ampli4.0 Response Spectra
tude was sampled at ten different locations for each specimen at each discrete

frequency, the standard deviation line

can be constructed on a point by point

basis for each discrete frequency of transmission. That is why the reader may

notice variations in standard deviation

with frequency.

In a few cases, usually around a particular frequency and for thin material thickness, normalized amplitudes of slightly

greater than 1.0 (decimal) or greater than

0.0 (dB) were observed. This effect can

be ascribed to instrument resolution and

to coherent superposition of many signals due to multiple internal reflections.

The latter phenomena is exploited in the

design of radomes.

In an effort to make the data more useful,

regression curves have been fitted to

most data. These are all gated spectra

(see Section 2.6).

62
63

Figure 4.1: Test setup for specimen B3L (three-wythe deep brick wall) for frequency

response determination from 0.5 to 2.0 GHz. See Figures 4.1a and 4.1b.

4.1 Brick

The following four tables (4.1a through

4.1d) present the response spectra for

brick. The ordinate values represent the

ratio of the received to transmitted signal. Figures 4.1a and 4.1b cover the band

from 0.5 to 2.0 GHz, 

while Figures 4.1c and 4.1d are for the

range 3.0 to 8.0 GHz. The decimal attenuation values are presented first, followed by the same ordinate set converted

to decibels.
64

0

0.2

0.4

0.6

0.8

1

0.5 1 1.5 2

qy g

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = full attenuation]

frequency (GHz)

B1L

B3L

B2L

Table 4.1a: Regression Coefficients (DECIMAL) for BRICK Transmission versus Frequency Curves

Plotted in Figure 4.1a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Brick Attenuation Curves (0.5-2.0GHz)

Regression Coefficients

Curve Identification Format M0 M1 M2 M3 M4 M5 M6 R

B1L Decimal 3.9639 -14.581 28.08 -29.294 17.034 -5.1913 0.64614 0.99991

B1L + sigma Decimal 4.5257 -17.17 32.792 -33.64 19.218 -5.7648 0.70796 0.99994

B1l - sigma Decimal 3.402 -11.993 23.368 -24.947 14.849 -4.6177 0.58433 0.99986

B2L Decimal 1.0632 -1.5358 2.6528 -3.1728 2.1941 -0.77778 0.10904 0.99999

B2L + sigma Decimal 1.518 -3.8092 7.087 -7.5039 4.4849 -1.4097 0.18071 0.99998

B2L - sigma Decimal 0.60845 0. 73763 -1.7813 1.1583 -0.096713 -0.14587 0.037369 0.99999

B3L Decimal 1.2692 -2.6303 4.8103 -5.7441 3.9546 -1.4052 0.1983 0.99998

B3L + sigma Decimal 1.722 -4.9095 9.2863 -10.126 6.2539 -2.0278 0.26699 0.99998

B3L - sigma Decimal 0.81643 -0.35111 0.33429 -1.362 1.6553 -0.78258 0.12961 0.99998

Figure 4.1a: Transmission Coefficients for Brick

B1L = 89 mm; B2L = 178 mm; B3L = 267 mm nominal Target Thickness.

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz. Amplitude Units: (decimal)
65

-12

-10

-8

-6

-4

-2

0

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

B1

B3

B2

Table 4.1b: Regression Coefficients (dB) for BRICK Transmission versus Frequency Curves Plotted in

Figure 4.1b. The regression equation is of the form 

Received Signal Magnitude = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the

frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Brick Attenuation Curves (0.5-2.0 GHz)

Regression Coefficients

Curve Identification Format M0 M1 M2 M3 M4 M5 M6 R

B1L dB 27.078 -131.86 253.34 -266.89 156.92 -48.302 6.0616 0.99997

B1L + sigma dB 31.421 -150.23 282.75 -289.23 165.39 -49.742 6.1277 0.99999

B1l - sigma dB 22.706 -113.45 224.06 -244.89 148.71 -46.946 6.0054 0.99993

B2L dB 1.8968 -22.766 44.568 -57.35 40.624 -14.465 2.0221 0.99999

B2L + sigma dB 7.297 -48.75 92.552 -100.87 61.756 -19.789 2.5744 0.99999

B2L - sigma dB -3.3358 2.071 -0.39509 -17.73 22.095 -10.004 1.5827 0.99999

B3L dB 5.7107 -44.841 95.34 -124.35 88.526 -31.737 4.469 0.99999

B3L + sigma dB 11.077 -70.076 140 -161.66 104.11 -34.767 4.6648 0.99999

B3L - sigma dB 0.47916 -20.635 53.628 -91.148 75.866 -29.741 4.4163 0.99998

Figure 4.1b: Received Signal Magnitude for Brick (relative to free space)

B1L = 89 mm; B2L = 178 mm; B3L = 267 mm nominal Target Thickness.

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz. Amplitude Units: (dB)
66

0

0.05

0.1

0.15

0.2

0.25

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absor

Frequency (GHz)

B1H

B3H

B2H

Table 4.1c: Regression Coefficients (dB) for BRICK Transmission versus Frequency Curves Plotted in

Figure 4.1c. The regression equation is of the form 

Received Signal Magnitude = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the

frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0-8.0 GHz GHz.

Brick Attenuation Curves (2.0-8.0 GHz)

Curve Identification

Coefficient B1H B1H + sigma B1H - sigma B2H B2H + sigma B2H - sigma B3H B3H + sigma B3H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 0.1643 0.17818 0.15042 132.71 130.74 134.67 26.089 28.255 23.922

M1 0.0072085 -0.0095906 0.024008 -191.44 -188.62 -194.26 -38.424 -41.635 -35.213

M2 -0.0004138 0.009587 -0.010415 113.49 111.65 115.33 23.418 25.391 21.445

M3 -0.0004548 -0.0033807 0.0024711 -34.4 -33.608 -35.192 -7.3919 -8.0213 -6.7625

M4 0.00010601 0.00055481 -0.0003428 4.9945 4.7294 5.2596 1.1648 1.265 1.0646

M5 -1.11E-05 -4.52E-05 2.30E-05 -0.029182 0.039 -0.097365 -0.032867 -0.035492 -0.030242

M6 4.79E-07 1.50E-06 -5.42E-07 -0.10789 -0.12011 -0.095673 -0.019848 -0.021703 -0.017993

M7 0.017073 0.018455 0.015692 0.0034948 0.0038266 0.003163

M8 -0.0011524 -0.0012397 -0.001065 -0.0002477 -0.0002719 -0.0002236

M9 3.02E-05 3.26E-05 2.79E-05 6.73E-06 7.40E-06 6.06E-06

R 1 1 1 0.99975 0.9999 0.99932 0.9995 0.99915 0.99962

Figure 4.1c: Transmission Coefficients for Brick

B1L = 89 mm; B2L = 178 mm; B3L = 267 mm nominal Target Thickness.

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0-8.0 GHz. Amplitude Units: (decimal)
67

-60

-50

-40

-30

-20

-10

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

B1H

B3H

B2H

Table 4.1d: Regression Coefficients (dB) for BRICK Transmission versus Frequency Curves Plotted in

Figure 4.1d. The regression equation is of the form 

Received Signal Magnitude = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the

frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0-8.0 GHz

Brick Attenuation Curves (2.0-8.0 GHz)

Curve Identification

Coefficient B1H B1H + sigma B1H - sigma B2H B2H + sigma B2H - sigma B3H B3H + sigma B3H - sigma

dB dB dB dB dB dB dB dB dB

M0 -15.651 -14.988 -16.294 24953 19635 34260 40922 34886 53110

M1 0.3304 -0.45205 1.0861 -36332 -28599 -49934 -61423 -52428 -79588

M2 -0.0033608 0.45549 -0.44798 21707 17029 29989 38073 32507 49346

M3 -0.02876 -0.16097 0.099196 -6665.8 -5161.9 -9354 -12282 -10463 -15999

M4 0.0065649 0.026479 -0.012619 1007.3 740.95 1490.9 2025.7 1706.4 2697.3

M5 -0.0006953 -0.0021688 0.00071188 -21.912 -0.21939 -63.032 -87.288 -64.749 -141.35

M6 2.99E-05 7.26E-05 -1.04E-05 -17.55 -17.077 -18.049 -26.917 -25.188 -28.811

M7 2.915 2.6614 3.3406 5.1505 4.6766 5.9312

M8 -0.19837 -0.17862 -0.23252 -0.37218 -0.3365 -0.43363

M9 0.0051939 0.0046684 0.0061143 0.010163 0.0091967 0.011845

R 1 1 1 0.997 0.991 0.993 0.986 0.98452 0.98

Figure 4.1d: Received Signal Magnitude for Brick (relative to free space)

B1L = 89 mm; B2L = 178 mm; B3L = 267 mm nominal Target Thickness.

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0-8.0 GHz. Amplitude Units: (dB)

69

Figure 4.2: Test setup for specimen B3C88L (single-wythe deep brick wall facing a 203

mm thick concrete wall) for frequency response determination from 3.0 to 8.0 GHz.

See Figures 4.2c and 4.2d.

4.2 Brick-Faced Concrete Wall

The following four tables (4.2a through

4.2d) present the frequency response

spectrum for a composite brick-faced

concrete wall. This is a single-wythe

brick wall followed by a 203-mm thick

plain concrete wall (Batch 8 concrete).

An air gap of approximately 3 to 5 mm

existed between the two walls, owing to

irregularities in the respective wall thicknesses.

Figures 4.2a and 4.2b cover the band

from 0.5 to 2.0 GHz, while Figures 4.2c

and 4.2d are for the range 3.0 to 8.0 GHz.

The ordinate values represent the ratio of

the received to transmittedsignal. The

decimal attenuation values are presented

first, followed by the same ordinate set

converted to decibels.
70

0

0.05

0.1

0.15

0.2

0.25

0.3

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absorption]

Frequency (GHz)

B3C84L

B3C88L

Table 4.2a: Regression Coefficients (decimal) for Composite Brick/Concrete Wall Transmission 

versus Frequency Curves Plotted in Figure 4.2a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Composite Brick/Concrete Attenuation Curves (2.0-8.0 GHz)

Curve Identification

Coefficient B3C84L B3C84L + sigma B3C84L - sigma B3C88L B3C88L + sigma B3C88L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal

M0 0.38431 0.31606 0.45255 0.16354 0.16083 0.16624

M1 -0.3322 0.18069 -0.84509 -0.32384 -0.30867 -0.33901

M2 0.50372 -0.87713 1.8846 0.67832 0.64272 0.71391

M3 -0.75838 1.0444 -2.5611 -0.87974 -0.822276 -0.93673

M4 0.58992 -0.639 1.8188 0.58042 0.532 0.62883

M5 -2.15E-01 2.05E-01 -6.36E-01 -0.1854 -0.16606 -0.20475

M6 2.99E-02 -2.71E-02 8.70E-02 0.023088 0.020194 0.025982

M7

M8

M9

R 1 1 0.99999 1 1 1

Figure 4.2a: Transmission Coefficients for Composite Brick/Concrete walls 

(relative to free space)

B3C84L = 90 mm Brick backed by 102mm of plain concrete (type 8); 

B3C88L = 90 mm Brick backed by 203mm of plain concrete (type 8).

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
71

-35

-30

-25

-20

-15

-10

0.5 1 1.5 2

qy g

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

B3C84L

B3C88L

Table 4.2b: Regression Coefficients (dB) for Composite Brick/Concrete Wall Transmission versus

Frequency Curves Plotted in Figure 4.2b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Composite Brick/Concrete Attenuation Curves (2.0-8.0 GHz)

Curve Identification

Coefficient B3C84L B3C84L + sigma B3C84L - sigma B3C88L B3C88L + sigma B3C88L - sigma

dB dB dB dB dB dB

M0 -6.6728 -10.896 -2.4035 -16.266 -18.242 -14.003

M1 -18.39 10.231 -47.343 -13.338 -1.582 -26.855

M2 37.664 -35.535 111.74 11.241 -16.478 43.241

M3 -51.957 40.694 -145.75 1.5373 35.354 -37.512

M4 35.823 -26.025 98.442 -18.011 -39.49 6.8261

M5 -1.1905E+01 8.94E+00 -3.30E+01 12.188 18.884 4.4136

M6 1.54E+00 -1.26E+00 4.37E+00 -2.3299 -3.1371 -1.3865

M7

M8

M9

R1 1 1 1 1 1

Figure 4.2b: Received Signal Magnitude (dB) for Composite Brick/Concrete Wall (relative to free space)

B3C84L = 90 mm Brick backed by 102mm of plain concrete (type 8); 

B3C88L = 90 mm Brick backed by 203mm of plain concrete (type 8).

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz
72

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

B3C84H

B3C88H

Table 4.2c: Regression Coefficients (decimal) for Composite Brick/Concrete Wall Transmission 

versus Frequency Curves Plotted in Figure 4.2c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 - 8.0 GHz.

Composite Brick/Concrete Attenuation Curves (3.0-8.0 GHz)

Curve Identification

Coefficient B3C84H B3C84H + sigma B3C84H - sigma B3C88H B3C88H + sigma B3C88H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal

M0 0.04924 0.017529 0.08095 0.013063 0.0077828 0.041694

M1 -0.037976 0.0016424 -0.077594 -0.016246 -0.00658 -0.059819

M2 0.01901 -0.0011594 0.039179 0.0098738 0.0029523 0.037251

M3 -0.0050585 0.00031375 -0.010431 -0.0032383 -0.0074505 -0.012246

M4 0.00070611 -8.09E-05 0.00014931 0.00054217 0.00010342 0.00020922

M5 -5.0523E-05 9.50E-06 -1.11E-04 -2.08E-05 -7.38E-06 -0.00010764

M6 1.49E-06 -3.67E-07 3.36E-06 -8.70E-06 2.12E-07 -2.45E-05

M7 5.07E-06

M8 -3.78E-07

M9 1.05E-08

R1 1 1 1 1 0.99999

Figure 4.2c: Transmission Coefficients for Composite Brick/Concrete walls 

(relative to free space)

B3C84L = 90 mm Brick backed by 102mm of plain concrete (type 8); 

B3C88L = 90 mm Brick backed by 203mm of plain concrete (type 8).

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 - 8.0 GHz 
73

-90

-80

-70

-60

-50

-40

-30

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

Composite Brick/Concrete Attenuation Curves (3.0-8.0 GHz)

Curve Identification

Coefficient B3C84H B3C84H + sigma B3C84H - sigma B3C88H B3C88H + sigma B3C88H - sigma

dB dB dB dB dB dB

M0 1393.3 -469.24 9746.1 2167.9 -708.51 8041.2

M1 -2210.6 648.53 -14962 -3329.8 980.76 -12115

M2 1414.7 -402.48 9492.9 2067.3 -611.45 7522.5

M3 -469.93 132.2 -3155.4 -673.47 201.82 -2459.8

M4 78.518 -2.36E+01 545.7 115.37 -36.281 428.36

M5 -2.6481000 1.7913000 -28.8580000 -6.84E+00 2.78E+00 -28.181

M6 -1.3919000 0.0912470 -6.4064000 -9.96E-01 1.54E-01 -2.95E+00

M7 0.2632800 -0.0296730 1.3543000 0.21959 -0.051084 7.23E-01

M8 -0.0198160 0.0022121 -0.1028700 -0.016009 0.0040733 -5.38E-02

M9 0.0005711 -0.0000569 0.0029316 4.29E-04 -1.16E-04 1.46E-03

R 1 1 1 0.99997 0.99999 0.99957

Figure 4.2d: Received Signal Magnitude (dB) for Composite Brick/Concrete Wall (relative to free space)

B3C84L = 90 mm Brick backed by 102mm of plain concrete (type 8); 

B3C88L = 90 mm Brick backed by 203mm of plain concrete (type 8).

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 - 8.0 GHz

Table 4.2d: Regression Coefficients (dB) for Composite Brick/Concrete Wall Transmission versus

Frequency Curves Plotted in Figure 4.2d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 3.0 - 8.0 GHz.

75

Figure 4.3: Test setup for specimen B3MB8L (single-wythe deep brick wall facing a 203

mm thick masonry block wall) for frequency response determination from 3.0 to 8.0

GHz. See Figures 4.3c and 4.3d.

4.3 Brick-Faced Masonry Block

The following four tables (4.3a through

4.3d) present the frequency response

spectrum for a composite brick-faced

masonry block wall. This is a singlewythe brick wall followed by a 203-mm

thick masonry block wall. An air gap of

approximately 3 to 5 mm existed

between the two walls, owing to irregularities in the respective wall thicknesses.

Figures 4.3a and 4.3b cover the band

from 0.5 to 2.0 GHz, while Figures 4.3c

and 4.3d are for the range 3.0 to 8.0 GHz.

The ordinate values represent the ratio of

the received to transmittedsignal. The

decimal attenuation values are presented

first, followed by the same ordinate set

converted to decibels.
76

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0.42

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absorption]

Frequency (GHz)

B3MB8L

Table 4.3a: Regression Coefficients (decimal) for Composite Brick/Masonry Block Wall Transmission 

versus Frequency Curves Plotted in Figure 4.3a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Composite Brick/Masonry Block Attenuation Curves (0.5-2.0 GHz)

Curve Identification

Coefficient B3MB8L B3MB8L + sigma B3MB8L - sigma

Decimal Decimal Decimal

M0 0.492520 0.525160 0.459890

M1 0.064577 -0.119500 0.248640

M2 -0.913710 -0.251100 -1.576300

M3 0.808720 -0.332260 1.949700

M4 -0.069060 -0.879950 -1.019300

M5 -0.132840 -0.506170 0.240800

M6 0.035009 0.090922 -0.020904

M7

M8

M9

R 0.999970 0.999830 0.999930

Figure 4.3a: Transmission Coefficients for Composite Brick/Masonry Block walls 

(relative to free space)

B3MB8L = 90 mm Brick backed by 194 mm Block Wall

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
77

-11.5

-11

-10.5

-10

-9.5

-9

-8.5

-8

-7.5

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

B3MB8L

Table 4.3b: Regression Coefficients (dB) for Composite Brick/Masonry Block Wall Transmission versus

Frequency Curves Plotted in Figure 4.3b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Composite Brick/Masonry Block Attenuation Curves (0.5-2.0 GHz)

Curve Identification

Coefficient B3MB8L B3MB8L + sigma B3MB8L - sigma

dB dB dB

M0 -10.060000 -9.308500 -10.771000

M1 22.891000 16.778000 28.728000

M2 -59.770000 -36.133000 -82.866000

M3 49.211000 8.961400 89.004000

M4 -11.871000 21.084000 -44.648000

M5 -2.299700 -15.114000 10.486000

M6 0.985250 2.892600 -0.921490

M7

M8

M9

R 0.999920 0.999650 0.999920

Figure 4.3b: Received Signal Magnitude (dB) for Composite Brick/Masonry Block Walls 

(relative to free space)

B3MB8L = 90 mm Brick backed by 194 mm Block Wall

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
78

0

0.01

0.02

0.03

0.04

0.05

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

B3MB8H

Table 4.3c: Regression Coefficients (decimal) for Composite Brick/Masonry Block Wall Transmission 

versus Frequency Curves Plotted in Figure 4.3c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Composite Brick/Masonry Block Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient B3MB8H B3MB8H + sigma B3MB8H - sigma

Decimal Decimal Decimal

M0 1.8578E+00 -5.6151E+00 9.3306E+00

M1 -2.7637E+00 8.7131E+00 -1.4240E+01

M2 1.7520E+00 -5.5957E+00 9.0997E+00

M3 -5.9409E-01 1.9059E+00 -3.0941E+00

M4 1.1269E-01 -3.5019E-01 5.7556E-01

M5 -1.0549E-02 2.5690E-02 -4.6788E-02

M6 3.9837E-05 2.2292E-03 -2.1496E-03

M7 8.9027E-05 -6.3359E-04 8.1165E-04

M8 -7.7230E-06 5.0896E-05 -6.6342E-05

M9 2.1482E-07 -1.4807E-06 1.9130E-06

R 9.9998E-01 9.9996E-01 9.9965E-01

Figure 4.3c: Transmission Coefficients for Composite Brick/Masonry Block walls 

(relative to free space)

B3MB8H = 90 mm Brick backed by 194 mm Block Wall

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
79

-60

-55

-50

-45

-40

-35

-30

-25

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

B3MB8H

Table 4.3d: Regression Coefficients (dB) for Composite Brick/Masonry Block Wall Transmission versus

Frequency Curves Plotted in Figure 4.3d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Composite Brick/Masonry Block Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient B3MB8H B3MB8H + sigma B3MB8H - sigma

dB dB dB

M0 9.3306E+00 -8.0230E+02 -1.0550E+04

M1 -1.4240E+01 1.2864E+03 1.6209E+04

M2 9.0997E+00 -8.4533E+02 -1.0406E+04

M3 -3.0941E+00 2.5916E+02 3.5390E+03

M4 5.7556E-01 -2.2454E+01 -6.4842E+02

M5 -4.6788E-02 -9.1938E+00 4.7261E+01

M6 -2.1496E-03 3.3195E+00 4.1589E+00

M7 8.1165E-04 -4.7732E-01 -1.1700E+00

M8 -6.6342E-05 3.3586E-02 9.3519E-02

M9 1.9103E-06 -9.5017E-04 -2.7076E-03

R 9.9965E-01 9.9983E-01 9.9928E-01

Figure 4.3d: Received Signal Magnitude (dB) for Composite Brick/Masonry Block Walls 

(relative to free space)

B3MB8H = 90 mm Brick backed by 194 mm Block Wall

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

81

Figure 4.4: Test setup for specimen

C112H (305 mm thick plain concrete

wall) for frequency response determination from 3.0 to 8.0 GHz. See Figures 4.4c

and 4.4d.

4.4 Plain Concrete: Batch 1 Mix

The following four tables (4.4a through

4.4d) present the frequency response

spectrum for a plain concrete wall. The

specimens in this series bear the designation C1XXL and C1XXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

The batch 1 concrete specimens had an

approximate water cement ratio of 0.4*, a

slump of 57 mm (“low”), a nominal

maximum crushed agreggate size of 12.7

mm (“small”), a cement content by

weight of 22% and an average density of

2.31 g/cc.

Figures 4.4a and 4.4b cover the band

from 0.5 to 2.0 GHz, while Figures 4.4c

and 4.4d are for the range 3.0 to 8.0 GHz.

The ordinate values represent the ratio of

the received to transmitted signal. The

decimal attenuation values are presented

first, followed by the same ordinate set

converted to decibels.

*the exact delivered value was not able to

be calculateddue to the omission of the

water added on site from the delivery

ticket.
82

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absorption]

Frequency (GHz)

C14L

C112L

C18L

Table 4.4a: Regression Coefficients (decimal) for Concrete Type 1 Transmission 

versus Frequency Curves Plotted in Figure 4.4a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 1 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C14L C14L + sigma C14L - sigma C18L C18L + sigma C18L - sigma C112L C112L + sigma C112L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 4.2829E-01 3.8905E-01 4.6752E-01 1.2864E-01 1.3301E-01 1.2426E-01 7.4321E-02 7.0682E-02 7.7960E-02

M1 -1.2022E-01 1.9569E-01 -4.3612E-01 3.2106E-02 1.4186E-03 6.2796E-02 -1.7565E-01 -1.6427E-01 -1.8703E-01

M2 -3.2189E-01 -1.1961E+00 5.5232E-01 -3.3455E-01 -2.5888E-01 -4.1022E-01 1.7475E-01 1.7119E-01 1.7830E-01

M3 4.1577E-01 1.5621E+00 -7.3058E-01 4.5016E-01 3.7132E-01 5.2901E-01 -2.8414E-02 -4.2724E-02 -1.4104E-02

M4 -1.8072E-01 -9.5228E-01 5.9083E-01 -2.8115E-01 -2.4076E-01 -3.2154E-01 -5.2759E-02 -3.6218E-02 -6.9300E-02

M5 2.2805E-02 2.8139E-01 -2.3578E-01 8.4769E-02 7.4696E-02 9.4843E-02 3.1249E-02 2.4385E-02 3.8113E-02

M6 1.8124E-03 -3.2476E-02 3.6103E-02 -9.8875E-03 -8.9169E-03 -1.0858E-02 -5.2285E-03 -4.2159E-03 -6.2412E-03

M7

M8

M9

R 0.99999 1 0.99998 1 1 1 0.99975 0.99985 0.99964

Figure 4.4a: Transmission Coefficients for Concrete Type 1 walls 

(relative to free space). Nominal thicknesses:

C14L = 102 mm; C18L = 203 mm; C112L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
83

-40

-35

-30

-25

-20

-15

-10

-5

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

C14L

C112L

C18L

Table 4.4b: Regression Coefficients (dB) for Concrete Type 1 Transmission versus Frequency Curves

Plotted in Figure 4.4b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 1 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C14L C14L + sigma C14L - sigma C18L C18L + sigma C18L - sigma C112L C112L + sigma C112L - sigma

dB dB dB dB dB dB dB dB dB

M0 -7.9286E+00 -9.7672E+00 -6.0598E+00 -1.9516E+01 -1.9965E+01 -1.9973E+01 -1.9320E+01 -1.9874E+01 -1.8879E+01

M1 5.3499E-01 1.3658E+01 -1.2776E+01 1.2151E+01 1.5324E+01 1.4838E+01 -2.7660E+01 -2.9674E+01 -2.4683E+01

M2 -1.2311E+01 -4.6550E+01 2.2368E+01 -4.3788E+01 -5.0952E+01 -4.9105E+01 -3.0002E+01 -1.3976E+01 -4.8861E+01

M3 9.3891E+00 5.2673E+01 -3.4393E+01 4.7941E+01 5.6012E+01 5.1657E+01 1.0578E+02 7.7935E+01 1.3745E+02

M4 -8.4422E-01 -2.9225E+01 2.7824E+01 -2.5801E+01 -3.0704E+01 -2.6500E+01 -9.4379E+01 -7.3213E+01 -1.1818E+02

M5 -1.4187E+00 7.9041E+00 -1.0823E+01 6.5042E+00 8.0386E+00 6.2677E+00 3.5923E+01 2.8371E+01 4.4373E+01

M6 3.9117E-01 -8.2580E-01 1.6172E+00 -5.7868E-01 -7.7288E-01 -4.9816E-01 -5.1097E+00 -4.0730E+00 -6.2674E+00

M7

M8

M9

R 0.99999 1 0.99999 1 1 1 0.9995 0.9997 0.99923

Figure 4.4b: Received Signal Magnitude (dB) for Concrete Type 1 Walls 

(relative to free space). Nominal thicknesses:

C14L = 102 mm; C18L = 203 mm; C112L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
84

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

C14H

C18H C112H

Table 4.4c: Regression Coefficients (decimal) for Concrete Type 1 Transmission 

versus Frequency Curves Plotted in Figure 4.4c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 1 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C14H C14H + sigma C14H - sigma C18H C18H + sigma C18H - sigma C112H C112H + sigma C112H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 5.1013E-01 5.2142E-01 4.9888E-01 2.7950E-02 2.8330E-02 2.7562E-02 1.8400E-03 2.1752E-03 1.4950E-03

M1 -6.8984E-01 -7.0613E-01 -6.7362E-01 -3.4066E-02 -3.4094E-02 -3.4028E-02 -2.6178E-03 -3.0958E-03 -2.1251E-03

M2 4.2180E-01 4.3185E-01 4.1180E-01 2.0177E-02 2.0062E-02 2.0288E-02 1.6111E-03 1.9038E-03 1.3094E-03

M3 -1.2626E-01 -1.2936E-01 1.2320E-01 -5.7195E-03 -5.6238E-03 -5.8140E-03 -4.6437E-04 -5.5677E-04 -3.6933E-04

M4 1.6003E-02 1.6443E-02 1.5572E-02 5.5084E-04 5.1483E-04 5.8685E-04 4.7371E-05 6.1869E-05 3.2557E-05

M5 1.0723E-03 1.0792E-03 1.0635E-03 1.2131E-04 1.2905E-04 1.1352E-04 8.3175E-06 7.9096E-06 8.6944E-06

M6 -6.7554E-04 6.8828E-04 -6.6255E-04 -4.5794E-05 -4.6798E-05 -4.4774E-05 -3.2792E-06 -3.5224E-06 -3.0203E-06

M7 9.8276E-05 1.0027E-04 9.6264E-05 6.2614E-06 6.3381E-06 6.1829E-06 4.43E-07 4.8522E-07 3.9819E-07

M8 -6.5776E-06 -6.7150E-06 -6.4393E-06 -4.1499E-07 -4.1805E-07 -4.1181E-07 -2.8770E-08 -3.1738E-08 -2.5658E-08

M9 1.7403E-07 1.7775E-07 1.7029E-07 1.1076E-08 1.1122E-08 1.1027E-08 7.5170E-10 8.3089E-10 6.6872E-10

R1 1 1 1 1 1 1 1 1

Figure 4.4c: Transmission Coefficients for Concrete Type 1 walls 

(relative to free space). Nominal thicknesses:

C14H = 102 mm; C18H = 203 mm; C112H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
85

-100

-90

-80

-70

-60

-50

-40

-30

-20

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

C14H

C112H

C18H

Table 4.4d: Regression Coefficients (dB) for Concrete Type 1 Transmission versus Frequency Curves

Plotted in Figure 4.4d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 1 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C14H C14H + sigma C14H - sigma C18H C18H + sigma C18H - sigma C112H C112H + sigma C112H - sigma

dB dB dB dB dB dB dB dB dB

M0 3.3110E+01 3.3330E+01 3.2886E+01 1.6811E+02 1.4175E+02 1.9955E+02 6.7802E+01 7.6859E+01 5.9012E+01

M1 -8.8319E+01 -8.8568E+01 -8.8062E+01 -3.2842E+02 -2.8711E+02 -3.7760E+02 -2.2797E+02 -2.3778E+02 -2.1945E+02

M2 5.3943E+01 5.4132E+01 5.3746E+01 2.0689E+02 1.8050E+02 2.3830E+02 1.4618E+02 1.5080E+02 1.4277E+02

M3 -1.6053E+01 -1.6123E+01 -1.5978E+01 -6.6763E+01 -5.7975E+01 -7.7235E+01 -4.6098E+01 -4.7412E+01 -4.5223E+01

M4 2.0035E+00 2.0173E+00 1.9879E+00 1.0358E+01 8.8556E+00 1.2155E+01 6.1910E+00 6.5559E+00 5.8463E+00

M5 1.3960E-01 1.3872E-01 1.4092E-01 -7.4879E-02 -5.8497E-03 -1.6011E-01 3.9922E-01 2.8260E-01 5.4872E-01

M6 -8.4168E-02 -8.4366E-02 -8.4032E-02 -2.5409E-01 -2.3313E-01 -2.7840E-01 -2.7700E-01 -2.4883E-01 -3.1635E-01

M7 1.2014E-02 1.2065E-02 1.1968E-02 4.3347E-02 3.9133E-02 4.8287E-02 4.27E-02 3.8631E-02 4.8422E-02

M8 -7.9082E-04 -7.9549E-04 -7.8639E-04 -3.1547E-03 -2.8359E-03 -3.5292E-03 -3.0410E-03 -2.7315E-03 -3.4760E-03

M9 2.0626E-05 2.0787E-05 2.0471E-05 8.9365E-05 8.0241E-05 1.0009E-04 8.6331E-05 7.6653E-05 9.9795E-05

R1 1 1 1 1 1 1 1 1

Figure 4.4d: Received Signal Magnitude (dB) for Concrete Type 1 Walls 

(relative to free space). Nominal thicknesses:

C14H = 102 mm; C18H = 203 mm; C112H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

87

Figure 4.5: Measuring thickness variations for a nominal 305 

mm thick concrete specimen.

4.5 Plain Concrete: Batch 2 Mix

The following four tables (4.5a through

4.5d) present the frequency response

spectrum for a plain concrete wall. The

specimens in this series bear the designation C2XXL and C2XXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

The Batch 2 concrete specimens had an

approximate water cement ratio of 0.39, a

slump of 165 mm (“high”), a nominal 

maximum crushed agreggate size of 12.7

mm (“small”), a cement content (by

weight) of 25%, and an average density

of 2.31 g/cc.

Figures 4.5a and 4.5b cover the band

from 0.5 to 2.0 GHz, while Figures 4.5c

and 4.5d are for the range 3.0 to 8.0 GHz.

The ordinate values represent the ratio of

the received to transmitted signal. The

decimal attenuation values are presented

first, followed by the same ordinate set

converted to decibels.
88

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

C24L

C212L

C28L

Table 4.5a: Regression Coefficients (decimal) for Concrete Type 2 Transmission 

versus Frequency Curves Plotted in Figure 4.5a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 2 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C24L C24L + sigma C24L - sigma C28L C28L + sigma C28L - sigma C212L C212L + sigma C212L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 1.5115E+00 1.6781E+00 1.3449E+00 1.0107E-01 1.0711E-01 9.5039E-02 3.3972E-03 3.8931E-03 2.9014E-03

M1 -5.2542E+00 -6.0063E+00 -4.5020E+00 -1.4674E-01 -1.7823E-01 -1.1524E-01 1.3835E-02 1.3173E-02 1.4496E-02

M2 9.6710E+00 1.1003E+01 8.3387E+00 1.9452E-01 2.5916E-01 1.2987E-01 -3.6608E-02 -3.4865E-02 -3.8349E-02

M3 -9.7143E+00 -1.0897E+01 -8.5322E+00 -1.9013E-01 -2.5662E-01 -1.2364E-01 4.7143E-02 4.4977E-02 4.9308E-02

M4 5.3957E+00 5.9593E+00 4.8322E+00 1.1100E-01 1.4833E-01 7.3667E-02 -3.1261E-02 -2.9872E-02 -3.2648E-02

M5 -1.5524E+00 -1.6902E+00 -1.4146E+00 -3.3090E-02 -4.4083E-02 -2.2097E-02 1.0453E-02 1.0003E-02 1.0903E-02

M6 1.7967E-01 1.9313E-01 1.6621E-01 3.8416E-03 5.1721E-03 2.5111E-03 -1.3842E-03 -1.3264E-03 -1.4421E-03

M7

M8

M9

R 0.99995 0.99996 0.99994 1.00000 1.00000 1.00000 0.99998 0.99998 0.99998

Figure 4.5a: Transmission Coefficients for Concrete Type 2 walls 

(relative to free space). Nominal thicknesses:

C24L = 102 mm; C28L = 203 mm; C212L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
89

-50

-40

-30

-20

-10

0

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

C24L

C212L

C28L

Table 4.5b: Regression Coefficients (dB) for Concrete Type 2 Transmission versus Frequency Curves

Plotted in Figure 4.5b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 2 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C24L C24L + sigma C24L - sigma C28L C28L + sigma C28L - sigma C212L C212L + sigma C212L - sigma

dB dB dB dB dB dB dB dB dB

M0 1.1993E+01 1.4623E+01 9.3794E+00 -1.8223E+01 -1.7443E+01 -1.8996E+01 -4.8331E+01 -4.7388E+01 -4.9369E+01

M1 -8.5297E+01 -9.5034E+01 -7.5738E+01 -2.3568E+01 -2.7458E+01 -1.9725E+01 2.0854E+01 1.8576E+01 2.3473E+01

M2 1.3576E+02 1.4780E+02 1.2424E+02 3.6488E+01 4.4031E+01 2.9056E+01 -5.5733E+01 -4.9608E+01 -6.2786E+01

M3 -1.1670E+02 -1.2112E+02 -1.1296E+02 -4.0541E+01 -4.7841E+01 -3.3367E+01 7.2279E+01 6.4413E+01 8.1345E+01

M4 5.0742E+01 4.9114E+01 5.2796E+01 2.4156E+01 2.8129E+01 2.0253E+01 -4.8148E+01 -4.2967E+01 -5.4120E+01

M5 -9.2480E+00 -7.6983E+00 -1.0924E+01 -6.9012E+00 -8.0748E+00 -5.7456E+00 1.6157E+01 1.4438E+01 1.8139E+01

M6 2.3748E-01 -6.4144E-02 5.5357E-01 7.3263E-01 8.7879E-01 5.8815E-01 -2.1534E+00 -1.9262E+00 -2.4154E+00

M7

M8

M9

R 0.99996 0.99997 0.99996 1 1 1 0.99998 0.99998 0.99998

Figure 4.5b: Received Signal Magnitude (dB) for Concrete Type 2 Walls 

(relative to free space). Nominal thicknesses:

C24L = 102 mm; C28L = 203 mm; C212L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
90

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

C24H

C212H C28H

Table 4.5c: Regression Coefficients (decimal) for Concrete Type 2 Transmission 

versus Frequency Curves Plotted in Figure 4.5c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 2 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C24H C24H + sigma C24H - sigma C28H C28H + sigma C28H - sigma C212H C212H + sigma C212H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 -3.3982E-02 -3.4025E-02 -3.3939E-02 5.3294E-03 3.8223E-03 6.8360E-03 -9.6950E-04 -3.5358E-04 -1.5866E-03

M1 1.0009E-01 1.0072E-01 9.9459E-02 -3.5110E-03 -1.5624E-03 -5.4590E-03 1.6303E-03 6.9823E-04 2.5642E-03

M2 -4.9740E-02 -5.0108E-02 -4.9371E-02 1.8400E-03 8.3829E-04 2.8415E-03 -1.0119E-03 -4.2150E-04 -1.6033E-03

M3 1.4413E-02 1.4541E-02 1.4285E-02 -5.0589E-04 -2.3754E-04 -7.7417E-04 3.2845E-04 1.3482E-04 5.2241E-04

M4 -2.3603E-03 -2.3827E-03 -2.3378E-03 7.2570E-05 3.3094E-05 1.1204E-04 -5.7326E-05 -2.5529E-05 -8.9183E-05

M5 1.9434E-04 1.9625E-04 1.9243E-04 -5.4904E-06 -2.4746E-06 -8.5055E-06 3.9208E-06 2.9053E-06 4.9408E-06

M6 -6.2169E-06 -6.2804E-06 -6.1534E-06 1.7894E-07 8.5542E-08 2.7231E-07 3.5814E-07 -1.9601E-07 9.1252E-07

M7 -9.37E-08 8.25E-09 -1.96E-07

M8 7.1806E-09 -3.0570E-10 1.4673E-08

M9 -2.0039E-10 9.7493E-12 -4.1069E-10

R 111111 1.00000 1.00000 1.00000

Figure 4.5c: Transmission Coefficients for Concrete Type 2 walls 

(relative to free space). Nominal thicknesses:

C24H = 102 mm; C28H = 203 mm; C212H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
91

-120

-100

-80

-60

-40

-20

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

C24H

C28H

C212H

Table 4.5d: Regression Coefficients (dB) for Concrete Type 2 Transmission versus Frequency Curves

Plotted in Figure 4.5d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 2 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C24H C24H + sigma C24H - sigma C28H C28H + sigma C28H - sigma C212H C212H + sigma C212H - sigma

dB dB dB dB dB dB dB dB dB

M0 -3.9676E+01 -3.9621E+01 -3.9723E+01 -5.4103E+02 -7.1967E+02 -3.3765E+02 -6.9460E+02 -2.1031E+02 -1.8542E+03

M1 1.5142E+01 1.5194E+01 1.5077E+01 7.2328E+02 9.9960E+02 4.0904E+02 9.3418E+02 1.9603E+02 2.7002E+03

M2 -6.6584E+00 -6.7040E+00 -6.6049E+00 -4.4701E+02 -6.2314E+02 -2.4683E+02 -5.8715E+02 -1.2102E+02 -1.7010E+03

M3 1.6625E+00 1.6817E+00 1.6408E+00 1.4860E+02 2.0657E+02 8.2690E+01 1.9317E+02 3.9744E+01 5.5968E+02

M4 -2.3213E-01 -2.3611E-01 -2.2773E-01 -2.8212E+01 -3.7647E+01 -1.7439E+01 -3.3154E+01 -7.2781E+00 -9.5167E+01

M5 1.5765E-02 1.6179E-02 1.5313E-02 2.8975E+00 3.1234E+00 2.6158E+00 1.7807E+00 6.3180E-01 4.6590E+00

M6 -3.8830E-04 -4.0531E-04 -3.6991E-04 -1.1265E-01 7.8407E-02 -3.2360E-01 3.6696E-01 8.3213E-03 1.1862E+00

M7 -0.0047492 -0.039242 0.033621 -7.76E-02 -7.02E-03 -2.41E-01

M8 4.8423E-04 3.0353E-03 -2.3566E-03 5.8257E-03 5.8149E-04 1.7946E-02

M9 -6.0888E-06 -7.8684E-05 7.4729E-05 -1.6332E-04 -1.6103E-05 -5.0273E-04

R 1 1 1 0.99999 0.99999 0.99999 1.00000 1.00000 0.99999

Figure 4.5d: Received Signal Magnitude (dB) for Concrete Type 2 Walls 

(relative to free space). Nominal thicknesses:

C24H = 102 mm; C28H = 203 mm; C212H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

93

Figure 4.6: Adjusting low frequency (0.5 to 2.0 GHz) band receiver antenna for 203 mm

concrete wall test.

4.6 Plain Concrete: Batch 3 Mix

The following four tables (4.6a through

4.6d) present the frequency response

spectrum for a plain concrete wall. The

specimens in this series bear the designation C3XXL and C3XXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

The Batch 3 concrete specimens had an

approximate water cement ratio of 0.48, a

slump of 64 mm (“low”), a nominal

maximum crushed agreggate size of 12.7

mm (“small”), a cement content (by 

weight) of 14%, and an average density

of 2.3 g/cc.

Figures 4.6a and 4.6b cover the band

from 0.5 to 2.0 GHz, while Figures 4.6c

and 4.6d are for the range 3.0 to 8.0 GHz.

The ordinate values represent the ratio of

the received to transmitted signal. The

decimal attenuation values are presented

first, followed by the same ordinate set

converted to decibels.
94

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absor

Frequency ( GHz)

C34L

C312L

C38L

Table 4.6a: Regression Coefficients (decimal) for Concrete Type 3 Transmission 

versus Frequency Curves Plotted in Figure 4.6a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 3 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C34L C34L + sigma C34L - sigma C38L C38L + sigma C38L - sigma C312L C312L + sigma C312L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 4.2776E-01 3.0514E-01 5.5038E-01 2.0234E-01 2.3758E-01 1.6710E-01 7.8438E-02 1.1841E-01 3.8467E-02

M1 8.6563E-02 9.1873E-01 -7.4561E-01 -4.5876E-01 -6.2262E-01 -2.9490E-01 -2.0568E-01 -4.1654E-01 5.1782E-03

M2 -8.0631E-01 -2.8811E+00 1.2685E+00 7.3542E-01 1.0341E+00 4.3669E-01 2.7561E-01 7.1789E-01 -1.6667E-01

M3 1.0256E+00 3.5560E+00 -1.5048E+00 -7.3591E-01 -1.0095E+00 -4.6234E-01 -1.5727E-01 -6.3031E-01 3.1577E-01

M4 -6.0124E-01 -2.2193E+00 1.0168E+00 4.1901E-01 5.5537E-01 2.8265E-01 1.6998E-02 2.9254E-01 -2.5855E-01

M5 1.6754E-01 6.9004E-01 -3.5495E-01 -1.2308E-01 -1.5863E-01 -8.7521E-02 1.5224E-02 -6.8167E-02 9.8615E-02

M6 -1.7584E-02 -8.4947E-02 4.9780E-02 1.4379E-02 1.8184E-02 1.0573E-02 -4.0641E-03 6.2091E-03 -1.4337E-02

M7

M8

M9

R 0.99999 1 0.99999 1 1 1 0.99997 0.99996 0.99994

Figure 4.6a: Transmission Coefficients for Concrete Type 3 walls 

(relative to free space). Nominal thicknesses:

C34L = 102 mm; C38L = 203 mm; C312L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
95

-45

-40

-35

-30

-25

-20

-15

-10

-5

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency ( GHz)

C34L

C312L

C38L

Table 4.6b: Regression Coefficients (dB) for Concrete Type 3 Transmission versus Frequency Curves

Plotted in Figure 4.6b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 3 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C34L C34L + sigma C34L - sigma C38L C38L + sigma C38L - sigma C312L C312L + sigma C312L - sigma

dB dB dB dB dB dB dB dB dB

M0 -8.3108E+00 -1.2347E+01 -4.2289E+00 -1.0690E+01 -8.0046E+00 -1.3357E+01 -1.9398E+01 -4.3670E+00 -3.4874E+01

M1 7.1829E+00 3.3363E+01 -1.9285E+01 -4.0618E+01 -5.1772E+01 -2.9567E+01 -3.4404E+01 -1.1452E+02 4.8087E+01

M2 -2.7770E+01 -9.1391E+01 3.6511E+01 6.3805E+01 8.1145E+01 4.6609E+01 5.4500E+00 1.7513E+02 -1.6930E+02

M3 3.0264E+01 1.0647E+02 -4.6656E+01 -6.3207E+01 -7.6055E+01 -5.0297E+01 5.5335E+01 -1.2795E+02 2.4422E+02

M4 -1.5903E+01 -6.3930E+01 3.2517E+01 3.2112E+01 3.7319E+01 2.6653E+01 -6.5451E+01 4.2428E+01 -1.7675E+02

M5 3.8767E+00 1.9206E+01 -1.1558E+01 -7.3492E+00 -8.5070E+00 -6.0346E+00 2.8585E+01 -4.3503E+00 6.2608E+01

M6 -3.2541E-01 -2.2837E+00 1.6440E+00 4.9598E-01 6.0954E-01 3.5283E-01 -4.4284E+00 -3.4795E-01 -8.6481E+00

M7

M8

M9

R 0.99999 1 0.99999 1 1 1 0.99998 0.99997 0.99996

Figure 4.6b: Received Signal Magnitude (dB) for Concrete Type 3 Walls 

(relative to free space). Nominal thicknesses:

C34L = 102 mm; C38L = 203 mm; C312L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
96

0

0.02

0.04

0.06

0.08

0.1

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absor

Frequency (GHz)

C34H

C312H

C38H

Table 4.6c: Regression Coefficients (decimal) for Concrete Type 3 Transmission 

versus Frequency Curves Plotted in Figure 4.6c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 3 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C34H C34H + sigma C34H - sigma C38H C38H + sigma C38H - sigma C312H C312H + sigma C312H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 -2.9934E-02 -3.0970E-02 -2.8898E-02 5.9671E-03 5.1018E-03 6.8326E-03 -7.1213E-04 -5.6040E-04 -8.6356E-04

M1 1.1300E-01 1.1495E-01 1.1106E-01 -3.6329E-03 -2.3919E-03 -4.8740E-03 1.2155E-03 1.0522E-03 1.3784E-03

M2 -5.6986E-02 -5.7900E-02 -5.6072E-02 1.8756E-03 1.2491E-03 2.5022E-03 -5.8874E-04 -5.0609E-04 -6.7121E-04

M3 1.6782E-02 1.7030E-02 1.6534E-02 -5.0386E-04 -3.3667E-04 -6.7107E-04 1.4238E-04 1.1990E-04 1.6482E-04

M4 -2.7576E-03 -2.7956E-03 -2.7196E-03 6.9284E-05 4.4460E-05 9.4112E-05 -1.8860E-05 -1.5502E-05 -2.2212E-05

M5 2.2586E-04 2.2892E-04 2.2280E-04 -4.9726E-06 -3.0585E-06 -6.8870E-06 1.2755E-06 1.0152E-06 1.5353E-06

M6 -7.1731E-06 -7.2733E-06 -7.0728E-06 1.5444E-07 9.5086E-08 2.1381E-07 -3.3388E-08 -2.5181E-08 -4.1582E-08

M7

M8

M9

R 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 0.99990 0.99990 0.99991

Figure 4.6c: Transmission Coefficients for Concrete Type 3 walls 

(relative to free space). Nominal thicknesses:

C34H = 102 mm; C38H = 203 mm; C312H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
97

-120

-100

-80

-60

-40

-20

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

C34H

C312H

C38H

Table 4.6d: Regression Coefficients (dB) for Concrete Type 3 Transmission versus Frequency Curves

Plotted in Figure 4.6d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 3 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C34H C34H + sigma C34H - sigma C38H C38H + sigma C38H - sigma C312H C312H + sigma C312H - sigma

dB dB dB dB dB dB dB dB dB

M0 -3.3066E+01 -3.3386E+01 -3.2716E+01 2.2593E+02 1.8339E+02 2.7831E+02 -3.2895E+04 -2.6831E+04 -4.4191E+04

M1 9.8512E+00 1.0372E+01 9.2908E+00 -3.5366E+02 -3.0015E+02 -4.1934E+02 4.9856E+04 4.0662E+04 6.6973E+04

M2 -4.1713E+00 -4.4435E+00 -3.8788E+00 1.8537E+02 1.5818E+02 2.1868E+02 -3.1374E+04 -2.5595E+04 -4.2134E+04

M3 1.0578E+00 1.1333E+00 9.7662E-01 -5.0913E+01 -4.3703E+01 -5.9724E+01 1.0327E+04 8.4242E+03 1.3877E+04

M4 -1.5147E-01 -1.6318E-01 -1.3893E-01 7.7190E+00 6.6678E+00 9.0000E+00 -1.7641E+03 -1.4369E+03 -2.3785E+03

M5 1.0370E-02 1.1332E-02 9.3415E-03 -6.1421E-01 -5.3435E-01 -7.1121E-01 9.0695E+01 7.2780E+01 1.2597E+02

M6 -2.5438E-04 -2.8671E-04 -2.1992E-04 2.0010E-02 1.7543E-02 2.2996E-02 2.0646E+01 1.7146E+01 2.6756E+01

M7 -4.2707E+00 -3.5252E+00 -5.6100E+00

M8 3.1898E-01 2.6313E-01 4.1981E-01

M9 -8.9352E-03 -7.3734E-03 -1.1758E-02

R 1 1 1 0.99998 0.99998 0.99996 0.99537 0.99640 0.99270

Figure 4.6d: Received Signal Magnitude (dB) for Concrete Type 3 Walls 

(relative to free space). Nominal thicknesses:

C34H = 102 mm; C38H = 203 mm; C312H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

99

Figure 4.7: Erik Anderson and Jose Ortiz measure thickness sections for 305 mm nominal thickness plain concrete panel.

4.7 Plain Concrete: Batch 4 Mix

The following four tables (4.7a through

4.7d) present the frequency response

spectrum for a plain concrete wall. The

specimens in this series bear the designation C4XXL and C4XXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

The Batch 4 concrete specimens had an

approximate water cement ratio of 0.42, a

slump of 222 mm (“high”), a nominal 

maximum crushed agreggate size of 12.7

mm (“small”), a cement content (by

weight) of 17%, and an average density

of 2.3 g/cc.

Figures 4.7a and 4.7b cover the band

from 0.5 to 2.0 GHz, while Figures 4.7c

and 4.7d are for the range 3.0 to 8.0 GHz.

The ordinate values represent the ratio of

the received to transmitted signal. The

decimal attenuation values are presented

first, followed by the same ordinate set

converted to decibels.
100

0

0.05

0.1

0.15

0.2

0.25

0.3

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abs

Frequency (GHz)

C44L

C412L

C48L

Table 4.7a: Regression Coefficients (decimal) for Concrete Type 4 Transmission 

versus Frequency Curves Plotted in Figure 4.7a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 4 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C44L C44L + sigma C44L - sigma C48L C48L + sigma C48L - sigma C412L C412L + sigma C412L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 3.6137E-01 3.0968E-01 4.1307E-01 1.8544E-01 1.8572E-01 1.8516E-01 2.0851E-02 2.2612E-02 1.9091E-02

M1 -2.1255E-02 3.2766E-01 -3.7017E-01 -4.3886E-01 -4.2972E-01 -4.4800E-01 -3.5753E-02 -4.7188E-02 -2.4318E-02

M2 -5.2662E-01 -1.3801E+00 3.2687E-01 7.0080E-01 6.6261E-01 7.3900E-01 5.2305E-02 8.0928E-02 2.3682E-02

M3 7.2753E-01 1.7490E+00 -2.9391E-01 -6.9923E-01 -6.4025E-01 -7.5822E-01 -3.6926E-02 -7.1389E-02 -2.4627E-03

M4 -4.3799E-01 -1.0819E+00 2.0596E-01 4.0136E-01 3.5820E-01 4.4451E-01 9.9079E-03 3.1950E-02 -1.2134E-02

M5 1.2248E-01 3.2819E-01 -8.3228E-02 -1.1955E-01 -1.0434E-01 -1.3475E-01 8.4547E-04 -6.3382E-03 8.0291E-03

M6 -1.2624E-02 -3.8909E-02 1.3660E-02 1.4208E-02 1.2124E-02 1.6292E-02 -5.9596E-04 3.4148E-04 -1.5334E-03

M7

M8

M9

R 1 1 0.99999 1 1 1 0.99993 0.99993 0.99993

Figure 4.7a: Transmission Coefficients for Concrete Type 4 walls 

(relative to free space). Nominal thicknesses:

C44L = 102 mm; C48L = 203 mm; C412L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
101

-45

-40

-35

-30

-25

-20

-15

-10

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

C44L

C412L

C48L

Table 4.7b: Regression Coefficients (dB) for Concrete Type 4 Transmission versus Frequency Curves

Plotted in Figure 4.7b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 4 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C44L C44L + sigma C44L - sigma C48L C48L + sigma C48L - sigma C412L C412L + sigma C412L - sigma

dB dB dB dB dB dB dB dB dB

M0 -9.8867E+00 -1.2183E+01 -7.5780E+00 -1.0157E+01 -1.0721E+01 -9.5919E+00 -3.2301E+01 -3.0832E+01 -3.3853E+01

M1 5.6682E+00 2.0305E+01 -9.0571E+00 -4.9691E+01 -4.5190E+01 -5.4196E+01 -2.3759E+01 -3.3321E+01 -1.3691E+01

M2 -2.6365E+01 -6.1109E+01 8.6001E+00 8.3592E+01 7.1440E+01 9.5754E+01 3.2058E+01 5.6045E+01 6.8701E+00

M3 2.8748E+01 6.9509E+01 -1.2280E+01 -8.8286E+01 -7.2830E+01 -1.0374E+02 -1.8803E+01 -4.7921E+01 1.1753E+01

M4 -1.4677E+01 -3.9980E+01 1.0792E+01 4.9417E+01 3.9394E+01 5.9425E+01 1.2067E+00 2.0074E+01 -1.8597E+01

M5 3.2913E+00 1.1272E+01 -4.7419E+00 -1.3262E+01 -1.0032E+01 -1.6482E+01 2.9157E+00 -3.3297E+00 9.4738E+00

M6 -2.1513E-01 -1.2240E+00 8.0021E-01 1.2848E+00 8.7342E-01 1.6943E+00 -7.8271E-01 4.5338E-02 -1.6525E+00

M7

M8

M9

R 1 0.99999 0.99999 1 1 1 0.99991 0.99991 0.99991

Figure 4.7b: Received Signal Magnitude (dB) for Concrete Type 4 Walls 

(relative to free space). Nominal thicknesses:

C44L = 102 mm; C48L = 203 mm; C412L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
102

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz))

C44H

C412H

C48H

Table 4.7c: Regression Coefficients (decimal) for Concrete Type 4 Transmission 

versus Frequency Curves Plotted in Figure 4.7c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 4 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C44H C44H + sigma C44H - sigma C48H C48H + sigma C48H - sigma C412H C412H + sigma C412H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 -2.5627E-02 2.0714E-02 -7.1967E-02 5.1733E-03 8.1318E-03 2.2138E-03 -4.8994E-04 1.1261E-04 -1.0896E-03

M1 9.1244E-02 3.2472E-02 1.5002E-01 -1.5825E-03 -4.9407E-03 1.7769E-03 1.1571E-03 2.7513E-04 2.0352E-03

M2 -4.5467E-02 -1.4670E-02 -7.6265E-02 7.1915E-04 2.3239E-03 -8.8623E-04 -7.4820E-04 -1.9907E-04 -1.2952E-03

M3 1.3261E-02 4.7720E-03 2.1750E-02 -1.9953E-04 -5.9600E-04 1.9710E-04 2.4319E-04 6.6759E-05 4.1915E-04

M4 -2.1831E-03 -8.8459E-04 -3.4817E-03 2.5750E-05 7.8593E-05 -2.7114E-05 -4.3159E-05 -1.6067E-05 -7.0247E-05

M5 1.7987E-04 7.5565E-05 2.8417E-04 -1.7203E-06 -5.3187E-06 1.8798E-06 3.6202E-06 3.5636E-06 3.7019E-06

M6 -5.7382E-06 -2.3110E-06 -9.1655E-06 5.6527E-08 1.5446E-07 -4.1451E-08 1.2751E-08 -6.8618E-07 7.0539E-07

M7 -2.71E-08 8.94E-08 -1.43E-07

M8 1.8784E-09 -6.4251E-09 1.0137E-08

M9 -3.9649E-11 1.8942E-10 -2.6761E-10

R 111111 1.00000 1.00000 1.00000

Figure 4.7c: Transmission Coefficients for Concrete Type 4 walls 

(relative to free space). Nominal thicknesses:

C44H = 102 mm; C48H = 203 mm; C412H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
103

-100

-90

-80

-70

-60

-50

-40

-30

-20

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz))

C44H

C412H

C48H

Table 4.7d: Regression Coefficients (dB) for Concrete Type 4 Transmission versus Frequency Curves

Plotted in Figure 4.7d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 4 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C44H C44H + sigma C44H - sigma C48H C48H + sigma C48H - sigma C412H C412H + sigma C412H - sigma

dB dB dB dB dB dB dB dB dB

M0 -3.5412E+01 -2.0154E+01 -5.0866E+01 -1.4430E+03 -8.7228E+02 -2.0460E+03 1.9642E+02 4.1401E+02 -2.2286E+02

M1 1.0029E+01 -9.3100E+00 2.9621E+01 2.1084E+03 1.2387E+03 3.0272E+03 -4.1396E+02 -7.4628E+02 2.2332E+02

M2 -4.0741E+00 5.9880E+00 -1.4270E+01 -1.3240E+03 -7.7555E+02 -1.9034E+03 2.6226E+02 4.7190E+02 -1.3794E+02

M3 9.6873E-01 -1.7747E+00 3.7494E+00 4.3794E+02 2.5777E+02 6.2831E+02 -8.5432E+01 -1.5355E+02 4.4630E+01

M4 -1.2878E-01 2.8455E-01 -5.4782E-01 -7.7080E+01 -4.6805E+01 -1.0911E+02 1.3369E+01 2.4232E+01 -7.7778E+00

M5 7.7213E-03 -2.4869E-02 4.0769E-02 5.0383E+00 3.7196E+00 6.4500E+00 -1.2659E-01 -3.4394E-01 5.3283E-01

M6 -1.3585E-04 9.1367E-04 -1.2003E-03 5.8075E-01 1.5685E-01 1.0245E+00 -3.1449E-01 -5.3878E-01 4.9230E-02

M7 -0.14127 -0.058484 -0.22823 5.27E-02 9.20E-02 -1.32E-02

M8 1.0681E-02 4.5543E-03 1.7120E-02 -3.7071E-03 -6.5376E-03 1.0548E-03

M9 -2.9446E-04 -1.2294E-04 -4.7476E-04 1.0003E-04 1.7851E-04 -3.1077E-05

R 1 1 1 0.99998 0.99999 0.99997 1.00000 1.00000 1.00000

Figure 4.7d: Received Signal Magnitude (dB) for Concrete Type 4 Walls 

(relative to free space). Nominal thicknesses:

C44H = 102 mm; C48H = 203 mm; C412H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

105

Figure 4.8: Test setup for specimen C58L (203 mm thick plain concrete wall) for frequency response determination from 0.5 to 2.0 GHz. See Figures 4.8a and 4.8b.

4.8 Plain Concrete: Batch 5 Mix

The following four tables (4.8a through

4.8d) present the frequency response

spectrum for a plain concrete wall. The

specimens in this series bear the designation C5XXL and C5XXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

The Batch 5 concrete specimens had an

approximate water cement ratio of 0.60, a

slump of 76 mm (“low”), a nominal 

maximum crushed agreggate size of 25.4

mm (“large”), a cement content (by

weight) of 17%, and an average density

of 2.42 g/cc.

Figures 4.8a and 4.8b cover the band

from 0.5 to 2.0 GHz, while Figures 4.8c

and 4.8d are for the range 3.0 to 8.0 GHz.

The ordinate values represent the ratio of

the received to transmitted signal. The

decimal attenuation values are presented

first, followed by the same ordinate set

converted to decibels.
106

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

C54L

C512L

C58L

Table 4.8a: Regression Coefficients (decimal) for Concrete Type 5 Transmission 

versus Frequency Curves Plotted in Figure 4.8a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 5 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C54L C54L + sigma C54L - sigma C58L C58L + sigma C58L - sigma C512L C512L + sigma C512L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 4.2273E-01 3.0341E-01 5.4204E-01 2.4365E-01 2.8104E-01 2.0626E-01 4.6061E-02 5.0459E-02 4.1663E-02

M1 -2.7851E-02 7.9352E-01 -8.4923E-01 -5.4943E-01 -7.4803E-01 -3.5083E-01 -5.0757E-02 -7.3741E-02 -2.7772E-02

M2 -5.9126E-01 -2.6728E+00 1.4903E+00 8.8667E-01 1.3020E+00 4.7130E-01 3.7062E-02 8.5538E-02 -1.1413E-02

M3 8.0743E-01 3.3841E+00 -1.7693E+00 -8.9354E-01 -1.3327E+00 -4.5434E-01 -8.3134E-03 -5.8203E-02 4.1576E-02

M4 -4.7886E-01 -2.1490E+00 1.1913E+00 5.1252E-01 7.6565E-01 2.5940E-01 -5.6374E-03 2.1981E-02 -3.3256E-02

M5 1.3205E-01 6.7798E-01 -4.1389E-01 -1.5168E-01 -2.2779E-01 -7.5568E-02 3.9411E-03 -4.0004E-03 1.1883E-02

M6 -1.3405E-02 -8.4572E-02 5.7763E-02 1.7882E-02 2.7236E-02 8.5275E-03 -7.1533E-04 2.1899E-04 -1.6497E-03

M7

M8

M9

R 1 1 0.99998 111111

Figure 4.8a: Transmission Coefficients for Concrete Type 5 walls 

(relative to free space). Nominal thicknesses:

C54L = 102 mm; C58L = 203 mm; C512L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
107

-40

-35

-30

-25

-20

-15

-10

-5

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

C54L

C512L

C58L

Table 4.8b: Regression Coefficients (dB) for Concrete Type 5 Transmission versus Frequency Curves

Plotted in Figure 4.8b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 5 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C54L C54L + sigma C54L - sigma C58L C58L + sigma C58L - sigma C512L C512L + sigma C512L - sigma

dB dB dB dB dB dB dB dB dB

M0 -8.4885E+00 -1.2991E+01 -3.9371E+00 -8.7038E+00 -5.9012E+00 -1.1467E+01 -2.6881E+01 -2.5534E+01 -2.8230E+01

M1 5.3858E+00 3.4842E+01 -2.4380E+01 -4.3026E+01 -5.7469E+01 -2.8820E+01 -8.2154E+00 -1.5160E+01 -1.3062E+00

M2 -2.5367E+01 -9.7866E+01 4.7841E+01 7.1051E+01 1.0023E+02 4.2400E+01 -3.1728E+00 1.1026E+01 -1.7184E+01

M3 2.7480E+01 1.1540E+02 -6.1213E+01 -7.3379E+01 -1.0335E+02 -4.3957E+01 1.1250E+01 -2.6635E+00 2.4828E+01

M4 -1.3966E+01 -7.0040E+01 4.2528E+01 3.9785E+01 5.6979E+01 2.2852E+01 -9.1801E+00 -1.8221E+00 -1.6281E+01

M5 3.1592E+00 2.1256E+01 -1.5050E+01 -1.0269E+01 -1.5525E+01 -5.0627E+00 3.3985E+00 1.3616E+00 5.3449E+00

M6 -2.1594E-01 -2.5516E+00 2.1314E+00 9.4236E-01 1.6064E+00 2.7995E-01 -4.9309E-01 -2.6006E-01 -7.1403E-01

M7

M8

M9

R 1 1 0.99998 111111

Figure 4.8b: Received Signal Magnitude (dB) for Concrete Type 5 Walls 

(relative to free space). Nominal thicknesses:

C54L = 102 mm; C58L = 203 mm; C512L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
108

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz))

C54H

C512H

C58H

Table 4.8c: Regression Coefficients (decimal) for Concrete Type 5 Transmission 

versus Frequency Curves Plotted in Figure 4.8c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 5 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C54H C54H + sigma C54H - sigma C58H C58H + sigma C58H - sigma C512H C512H + sigma C512H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 -4.4403E-02 -3.8098E-02 -5.0708E-02 2.4582E-03 1.1059E-03 3.8109E-03 -4.1218E-03 -1.3105E-02 4.8745E-03

M1 1.1728E-01 1.1081E-01 1.2376E-01 1.0306E-03 2.8488E-03 -7.8799E-04 6.9668E-03 2.0637E-02 -6.7223E-03

M2 -5.8217E-02 -5.4325E-02 -6.2108E-02 -4.4871E-04 -1.4143E-03 5.1705E-04 -4.4705E-03 -1.3087E-02 4.1568E-03

M3 1.6836E-02 1.5719E-02 1.7954E-02 1.1484E-04 3.8258E-04 -1.5296E-04 1.5075E-03 4.3593E-03 -1.3474E-03

M4 -2.7470E-03 -2.5578E-03 -2.9362E-03 -2.2079E-05 -6.2953E-05 1.8803E-05 -2.6831E-04 -7.6509E-04 2.2886E-04

M5 2.2613E-04 2.0834E-04 2.4394E-04 1.9853E-06 5.2359E-06 -1.2658E-06 1.5788E-05 4.5334E-05 -1.3736E-05

M6 -7.2667E-06 -6.5886E-06 -7.9449E-06 -5.6896E-08 -1.6192E-07 4.8142E-08 2.8865E-06 7.5716E-06 -1.8130E-06

M7 -6.53E-07 -1.71E-06 4.02E-07

M8 5.1018E-08 1.3067E-07 -2.8764E-08

M9 -1.4875E-09 -3.7223E-09 7.5060E-10

R 111111 1.00000 0.99999 1.00000

Figure 4.8c: Transmission Coefficients for Concrete Type 5 walls 

(relative to free space). Nominal thicknesses:

C54H = 102 mm; C58H = 203 mm; C512H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
109

-120

-100

-80

-60

-40

-20

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz))

C54H

C512H

C58H

Table 4.8d: Regression Coefficients (dB) for Concrete Type 5 Transmission versus Frequency Curves

Plotted in Figure 4.8d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 5 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C54H C54H + sigma C54H - sigma C58H C58H + sigma C58H - sigma C512H C512H + sigma C512H - sigma

dB dB dB dB dB dB dB dB dB

M0 -4.1911E+01 -3.5645E+01 -4.9467E+01 1.1496E+02 6.4431E+01 1.7367E+02 -6.0914E+03 -7.7427E+03 -2.0996E+03

M1 1.8910E+01 1.1238E+01 2.8272E+01 -2.1550E+02 -1.5134E+02 -2.8989E+02 9.1683E+03 1.1667E+04 3.1137E+03

M2 -8.6628E+00 -4.6207E+00 -1.3622E+01 1.1590E+02 8.2718E+01 1.5430E+02 -5.7783E+03 -7.3532E+03 -1.9552E+03

M3 2.2415E+00 1.1366E+00 3.6065E+00 -3.2698E+01 -2.3735E+01 -4.3049E+01 1.9016E+03 2.4275E+03 6.2435E+02

M4 -3.2569E-01 -1.5905E-01 -5.3311E-01 5.0993E+00 3.7660E+00 6.6358E+00 -3.2278E+02 -4.1767E+02 -9.3311E+01

M5 2.3791E-02 1.0721E-02 4.0201E-02 -4.1851E-01 -3.1495E-01 -5.3756E-01 1.5518E+01 2.2496E+01 -7.5398E-01

M6 -6.7060E-04 -2.5843E-04 -1.1936E-03 1.4090E-02 1.0812E-02 1.7849E-02 4.1007E+00 4.6249E+00 2.6407E+00

M7 -8.26E-01 -9.79E-01 -4.29E-01

M8 6.1433E-02 7.3466E-02 3.0297E-02

M9 -1.7190E-03 -2.0609E-03 -8.3300E-04

R 1 1 1 0.99999 0.99999 0.99999 0.99992 0.99976 0.99993

Figure 4.8d: Received Signal Magnitude (dB) for Concrete Type 5 Walls 

(relative to free space). Nominal thicknesses:

C54H = 102 mm; C58H = 203 mm; C512H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

111

Figure 4.9: Test setup for specimen C612H (305 mm thick plain concrete wall) for frequency response determination from 3.0 to 8.0 GHz.

4.9 Plain Concrete: Batch 6 Mix

The following four tables (4.9a through

4.9d) present the frequency response

spectrum for a plain concrete wall. The

specimens in this series bear the designation C6XXL and C6XXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

The Batch 6 concrete specimens had an

approximate water cement ratio of 0.54, a

slump of 172 mm (“high”), a nominal 

maximum crushed agreggate size of 25.4

mm (“large”), a cement content (by

weight) of 19%, and an average density

of 2.39 g/cc.

Figures 4.9a and 4.9b cover the band

from 0.5 to 2.0 GHz, while Figures 4.9c

and 4.9d are for the range 3.0 to 8.0 GHz.

The ordinate values represent the ratio of

the received to transmitted signal. The

decimal attenuation values are presented

first, followed by the same ordinate set

converted to decibels.
112

0

0.05

0.1

0.15

0.2

0.25

0.3

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

C64L

C612L

C68L

Table 4.9a: Regression Coefficients (decimal) for Concrete Type 6 Transmission 

versus Frequency Curves Plotted in Figure 4.9a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 6 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C64L C64L + sigma C64L - sigma C68L C68L + sigma C68L - sigma C612L C612L + sigma C612L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 3.9821E-01 4.3714E-01 3.5928E-01 1.8358E-01 1.9656E-01 1.7060E-01 2.7250E-02 2.6570E-02 2.6570E-02

M1 -2.9347E-01 -4.7552E-01 -1.1142E-01 -4.6695E-01 -5.3441E-01 -3.9950E-01 -4.7470E-02 -4.6196E-02 -4.6196E-02

M2 1.6115E-01 4.9084E-01 -1.6853E-01 7.6959E-01 9.0750E-01 6.3168E-01 4.8906E-02 5.4399E-02 5.4399E-02

M3 -1.7899E-01 -4.6785E-01 1.0986E-01 -7.8972E-01 -9.2990E-01 -6.4954E-01 -1.0070E-02 -2.1841E-02 -2.1841E-02

M4 1.7735E-01 3.0783E-01 4.6876E-02 4.6501E-01 5.4203E-01 3.8799E-01 -1.3669E-02 -4.4065E-03 -4.4065E-03

M5 -8.1433E-02 -1.1023E-01 -5.2640E-02 -1.4187E-01 -1.6398E-01 -1.1975E-01 8.9116E-03 5.5819E-03 5.5819E-03

M6 1.3624E-02 1.6000E-02 1.1248E-02 1.7302E-02 1.9920E-02 1.4685E-02 -1.5817E-03 -1.1241E-03 -1.1241E-03

M7

M8

M9

R 111111 0.99989 0.99987 0.99987

Figure 4.9a: Transmission Coefficients for Concrete Type 6 walls 

(relative to free space). Nominal thicknesses:

C64L = 102 mm; C68L = 203 mm; C612L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
113

-40

-35

-30

-25

-20

-15

-10

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

C64L

C612L

C68L

Table 4.9b: Regression Coefficients (dB) for Concrete Type 6 Transmission versus Frequency Curves

Plotted in Figure 4.9b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 6 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C64L C64L + sigma C64L - sigma C68L C68L + sigma C68L - sigma C612L C612L + sigma C612L - sigma

dB dB dB dB dB dB dB dB dB

M0 -7.7569E+00 -6.8515E+00 -8.6497E+00 -7.0894E+00 -6.3369E+00 -7.7260E+00 -2.9707E+01 -2.9851E+01 -2.9729E+01

M1 -8.6884E+00 -1.2284E+01 -5.1857E+00 -7.0842E+01 -7.3736E+01 -6.8661E+01 -2.3157E+01 -2.4779E+01 -2.0341E+01

M2 9.2704E+00 1.4052E+01 4.7506E+00 1.3152E+02 1.3493E+02 1.2982E+02 1.3420E+01 2.3814E+01 -1.3491E-01

M3 -1.6696E+01 -1.8498E+01 -1.5250E+01 -1.4570E+02 -1.4621E+02 -1.4721E+02 1.5231E+01 -1.2079E+00 3.5559E+01

M4 1.4858E+01 1.4043E+01 1.5921E+01 8.5023E+01 8.4038E+01 8.7252E+01 -2.2619E+01 -1.0777E+01 -3.6939E+01

M5 -6.0590E+00 -5.3103E+00 -6.8932E+00 -2.4165E+01 -2.3700E+01 -2.5008E+01 1.0211E+01 6.1139E+00 1.5106E+01

M6 9.3595E-01 7.9103E-01 1.0924E+00 2.5986E+00 2.5447E+00 2.6974E+00 -1.5993E+00 -1.0465E+00 -2.2546E+00

M7

M8

M9

R 111111 0.99981 0.99979 0.99982

Figure 4.9b: Received Signal Magnitude (dB) for Concrete Type 6 Walls 

(relative to free space). Nominal thicknesses:

C64L = 102 mm; C68L = 203 mm; C612L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
114

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz))

C64H

C612H

C68H

Table 4.9c: Regression Coefficients (decimal) for Concrete Type 6 Transmission 

versus Frequency Curves Plotted in Figure 4.9c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 6 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C64H C64H + sigma C64H - sigma C68H C68H + sigma C68H - sigma C612H C612H + sigma C612H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 -2.2557E-02 -2.3815E-02 -2.1299E-02 1.9586E+00 2.0215E+00 1.8958E+00 3.6336E-03 2.8635E-03 4.4061E-03

M1 8.2637E-02 8.5391E-02 7.9883E-02 -2.7092E+00 -2.8033E+00 -2.6151E+00 -3.1840E-03 -1.6616E-03 -4.7101E-03

M2 -4.1607E-02 -4.3128E-02 -4.0085E-02 1.5367E+00 1.5949E+00 1.4785E+00 9.5514E-04 -2.2760E-04 2.1402E-03

M3 1.2265E-02 1.2723E-02 1.1807E-02 -4.3715E-01 -4.5587E-01 -4.1843E-01 5.1962E-05 5.2865E-04 -4.2556E-04

M4 -2.0195E-03 -2.0947E-03 -1.9443E-03 5.3100E-02 5.6211E-02 4.9990E-02 -1.0931E-04 -2.1602E-04 -2.4087E-06

M5 1.6621E-04 1.7251E-04 1.5990E-04 3.4999E-03 3.3444E-03 3.6554E-03 3.1704E-05 4.4085E-05 1.9298E-05

M6 -5.3164E-06 -5.5282E-06 -5.1046E-06 -2.1168E-03 -2.1505E-03 -2.0831E-03 -4.6618E-06 -5.0312E-06 -4.2902E-06

M7 0.00030063 0.00030735 0.00029392 3.87E-07 3.12E-07 4.62E-07

M8 -1.9803E-05 -2.0283E-05 -1.9322E-05 -1.7315E-08 -8.7165E-09 -2.5909E-08

M9 5.1908E-07 5.3198E-07 5.0617E-07 3.2738E-10 4.5872E-11 6.0882E-10

R 1 1 1 0.99973 0.99974 0.99971 1.00000 1.00000 1.00000

Figure 4.9c: Transmission Coefficients for Concrete Type 6 walls 

(relative to free space). Nominal thicknesses:

C64H = 102 mm; C68H = 203 mm; C612H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
115

-120

-100

-80

-60

-40

-20

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz))

C64H

C612H

C68H

Table 4.9d: Regression Coefficients (dB) for Concrete Type 6 Transmission versus Frequency Curves

Plotted in Figure 4.9d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 6 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C64H C64H + sigma C64H - sigma C68H C68H + sigma C68H - sigma C612H C612H + sigma C612H - sigma

dB dB dB dB dB dB dB dB dB

M0 -3.8240E+01 -3.8513E+01 -3.7938E+01 3.2287E+04 3.1552E+04 3.3151E+04 -4.9613E+03 -5.1764E+03 8.6949E+03

M1 1.2897E+01 1.3478E+01 1.2273E+01 -4.8428E+04 -4.7309E+04 -4.9743E+04 7.4199E+03 7.8117E+03 -1.3554E+04

M2 -5.7874E+00 -6.1148E+00 -5.4368E+00 2.9825E+04 2.9135E+04 3.0636E+04 -4.6776E+03 -4.9546E+03 8.6321E+03

M3 1.5144E+00 1.6104E+00 1.4118E+00 -9.4197E+03 -9.2105E+03 -9.6660E+03 1.5594E+03 1.6507E+03 -2.8239E+03

M4 -2.2331E-01 -2.3875E-01 -2.0683E-01 1.4365E+03 1.4111E+03 1.4668E+03 -2.8065E+02 -2.9016E+02 4.4645E+02

M5 1.6335E-02 1.7635E-02 1.4950E-02 -1.4530E+01 -1.7287E+01 -1.1489E+01 2.0702E+01 1.7790E+01 -4.3765E+00

M6 -4.5554E-04 -5.0017E-04 -4.0803E-04 -3.2063E+01 -3.0658E+01 -3.3667E+01 1.4598E+00 2.6332E+00 -1.0919E+01

M7 5.3331 5.1294 5.5667 -4.28E-01 -6.05E-01 1.90E+00

M8 -3.7462E-01 -3.6076E-01 -3.9053E-01 3.3111E-02 4.6078E-02 -1.3981E-01

M9 1.0186E-02 9.8107E-03 1.0616E-02 -9.1484E-04 -1.2954E-03 3.9995E-03

R 1 1 1 0.99259 0.99306 0.99189 0.99977 0.99985 0.99878

Figure 4.9d: Received Signal Magnitude (dB) for Concrete Type 6 Walls 

(relative to free space). Nominal thicknesses:

C64H = 102 mm; C68H = 203 mm; C612H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

117

Figure 4.10: Concrete panel specimens lined up for low frequency (0.5 to 2.0 GHz) test

series.

4.10 Plain Concrete: Batch 7 Mix

The following four tables (4.10a through

4.10d) present the frequency response

spectrum for a plain concrete wall. The

specimens in this series bear the designation C7XXL and C7XXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

The Batch 7 concrete specimens had an

approximate water cement ratio of 0.87, a

slump of 83 mm (“low”), a nominal 

maximum crushed agreggate size of 25.4

mm (“large”), a cement content (by

weight) of 12%, and an average density

of 2.38 g/cc.

Figures 4.10a and 4.10b cover the band

from 0.5 to 2.0 GHz, while Figures 4.10c

and 4.10d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels.
118

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

C74L

C712L

C78L

Table 4.10a: Regression Coefficients (decimal) for Concrete Type 7 Transmission 

versus Frequency Curves Plotted in Figure 4.10a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 7 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C74L C74L + sigma C74L - sigma C78L C78L + sigma C78L - sigma C712L C712L + sigma C712L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 4.5326E-01 4.8295E-01 4.2358E-01 2.7709E-01 2.6557E-01 2.8862E-01 3.6287E-02 4.3184E-02 2.9391E-02

M1 -1.4898E-02 -6.4268E-02 3.4466E-02 -6.2320E-01 -5.2515E-01 -7.2125E-01 -4.6302E-02 -7.8300E-02 -1.4304E-02

M2 -5.4759E-01 -6.7594E-01 -4.1923E-01 1.0189E+00 7.5004E-01 1.2878E+00 3.9930E-02 9.9612E-02 -1.9752E-02

M3 6.3929E-01 1.0229E+00 2.5571E-01 -1.0418E+00 -6.9658E-01 -1.3871E+00 -5.7698E-03 -6.2051E-02 5.0511E-02

M4 -2.9246E-01 -6.4098E-01 5.6068E-02 6.0347E-01 3.7611E-01 8.3083E-01 -1.2483E-02 1.6532E-02 -4.1497E-02

M5 5.1100E-02 1.8731E-01 -8.5107E-02 -1.8029E-01 -1.0572E-01 -2.5487E-01 7.7221E-03 -1.0735E-04 1.5551E-02

M6 -1.0912E-03 -2.0858E-02 1.8675E-02 2.1529E-02 1.1849E-02 3.1210E-02 -1.3804E-03 -5.1387E-04 -2.2468E-03

M7

M8

M9

R 0.99999 1 0.99998 1 1 1 0.99999 0.99999 0.99999

Figure 4.10a: Transmission Coefficients for Concrete Type 7 walls 

(relative to free space). Nominal thicknesses:

C74L = 102 mm; C78L = 203 mm; C712L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
119

-40

-35

-30

-25

-20

-15

-10

-5

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

C74L

C712L

C78L

Table 4.10b: Regression Coefficients (dB) for Concrete Type 7 Transmission versus Frequency Curves

Plotted in Figure 4.10b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 7 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C74L C74L + sigma C74L - sigma C78L C78L + sigma C78L - sigma C712L C712L + sigma C712L - sigma

dB dB dB dB dB dB dB dB dB

M0 -7.4920E+00 -7.3807E+00 -7.5248E+00 -7.4629E+00 -9.3763E+00 -5.5346E+00 -2.8743E+01 -2.6123E+01 -3.1397E+01

M1 3.0412E+00 5.6047E+00 -6.6853E-03 -4.3735E+01 -3.0714E+01 -5.6858E+01 -1.0652E+01 -2.2614E+01 1.4297E+00

M2 -1.6580E+01 -2.8827E+01 -3.1769E+00 7.3574E+01 4.1529E+01 1.0585E+02 -1.9754E+00 1.9804E+01 -2.3898E+01

M3 1.4213E+01 3.4562E+01 -7.4952E+00 -7.6654E+01 -3.8504E+01 -1.1504E+02 1.7784E+01 -2.0407E+00 3.7663E+01

M4 -3.8593E+00 -1.9288E+01 1.2400E+01 4.1785E+01 1.8246E+01 6.5431E+01 -1.7212E+01 -7.3755E+00 -2.7041E+01

M5 -3.9244E-01 5.1229E+00 -6.1611E+00 -1.0986E+01 -3.7229E+00 -1.8267E+01 6.9579E+00 4.4037E+00 9.5035E+00

M6 2.4525E-01 -5.1324E-01 1.0342E+00 1.0614E+00 1.7201E-01 1.9508E+00 -1.0525E+00 -7.8032E-01 -1.3233E+00

M7

M8

M9

R 0.99999 1 0.99998 1 1 1 0.99999 0.99998 0.99999

Figure 4.10b: Received Signal Magnitude (dB) for Concrete Type 7 Walls 

(relative to free space). Nominal thicknesses:

C74L = 102 mm; C78L = 203 mm; C712L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
120

0

0.05

0.1

0.15

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz))

C74H

C712H

C78H

Table 4.10c: Regression Coefficients (decimal) for Concrete Type 7 Transmission 

versus Frequency Curves Plotted in Figure 4.10c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 7 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C74H C74H + sigma C74H - sigma C78H C78H + sigma C78H - sigma C712H C712H + sigma C712H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 9.7788E-03 2.7046E-03 1.6854E-02 7.0611E-03 6.4596E-03 7.6619E-03 -4.1998E-02 -4.5607E-02 -3.8387E-02

M1 1.4753E-01 1.5970E-01 1.3536E-01 7.0122E-03 8.3633E-03 5.6622E-03 9.4489E-02 1.0250E-01 8.6468E-02

M2 -7.1367E-02 -7.6871E-02 -6.5862E-02 -4.3674E-03 -5.0878E-03 -3.6476E-03 -7.7022E-02 -8.3429E-02 -7.0612E-02

M3 2.0328E-02 2.1769E-02 1.8888E-02 1.2982E-03 1.5007E-03 1.0959E-03 3.1878E-02 3.4449E-02 2.9307E-02

M4 -3.3935E-03 -3.6089E-03 -3.1782E-03 -2.2867E-04 -2.6107E-04 -1.9629E-04 -7.3206E-03 -7.8856E-03 -6.7554E-03

M5 2.8920E-04 3.0591E-04 2.7249E-04 2.0758E-05 2.3474E-05 1.8044E-05 8.9466E-04 9.5856E-04 8.3075E-04

M6 -9.6399E-06 -1.0163E-05 -9.1171E-06 -7.2743E-07 -8.1879E-07 -6.3611E-07 -3.8327E-05 -4.0152E-05 -3.6503E-05

M7 -3.27E-06 -3.64E-06 -2.90E-06

M8 4.4285E-07 4.8381E-07 4.0188E-07

M9 -1.4597E-08 -1.5889E-08 -1.3305E-08

R 111111 0.99965 0.99960 0.99970

Figure 4.10c: Transmission Coefficients for Concrete Type 7 walls 

(relative to free space). Nominal thicknesses:

C74H = 102 mm; C78H = 203 mm; C712H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
121

-120

-100

-80

-60

-40

-20

0

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz))

C74H

C712H

C78H

Table 4.10d: Regression Coefficients (dB) for Concrete Type 7 Transmission versus Frequency Curves

Plotted in Figure 4.10d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 7 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C74H C74H + sigma C74H - sigma C78H C78H + sigma C78H - sigma C712H C712H + sigma C712H - sigma

dB dB dB dB dB dB dB dB dB

M0 -2.9468E+01 -2.9456E+01 -2.9479E+01 -6.8692E+02 -6.5468E+02 -7.2261E+02 -3.9381E+04 -3.4233E+04 -4.9443E+04

M1 1.4362E+01 1.4582E+01 1.4136E+01 9.8928E+02 9.4123E+02 1.0425E+03 5.7992E+04 5.0488E+04 7.2723E+04

M2 -6.8886E+00 -6.9653E+00 -6.8104E+00 -6.2581E+02 -5.9582E+02 -6.5898E+02 -3.5531E+04 -3.0963E+04 -4.4548E+04

M3 1.8272E+00 1.8438E+00 1.8102E+00 2.0706E+02 1.9723E+02 2.1794E+02 1.1535E+04 1.0044E+04 1.4500E+04

M4 -2.7445E-01 -2.7663E-01 -2.7221E-01 -3.5539E+01 -3.3833E+01 -3.7432E+01 -2.0438E+03 -1.7687E+03 -2.5960E+03

M5 2.0981E-02 2.1159E-02 2.0793E-02 1.8100E+00 1.7027E+00 1.9319E+00 1.5965E+02 1.3348E+02 2.1291E+02

M6 -6.3054E-04 -6.3763E-04 -6.2287E-04 4.3131E-01 4.1803E-01 4.4519E-01 6.0144E+00 6.5202E+00 4.9270E+00

M7 -0.089354 -0.086268 -0.092659 -2.29E+00 -2.16E+00 -2.57E+00

M8 6.7230E-03 6.4956E-03 6.9668E-03 1.7580E-01 1.6354E-01 2.0171E-01

M9 -1.8969E-04 -1.8358E-04 -1.9621E-04 -4.7007E-03 -4.3733E-03 -5.4137E-03

R 111111 0.97877 0.98247 0.96779

Figure 4.10d: Received Signal Magnitude (dB) for Concrete Type 7 Walls 

(relative to free space). Nominal thicknesses:

C74H = 102 mm; C78H = 203 mm; C712H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

123

Figure 4.11: Test setup for specimen C812L (305 mm thick plain concrete wall) for frequency response determination from 3.0 to 8.0 GHz. See Figures 4.11c and 4.11d.

4.11 Plain Concrete: Batch 8 Mix

The following four tables (4.11a through

4.11d) present the frequency response

spectrum for a plain concrete wall. The

specimens in this series bear the designation C8XXL and C8XXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

The Batch 8 concrete specimens had an

approximate water cement ratio of 0.36, a

slump of 165 mm (“high”), a nominal 

maximum crushed agreggate size of 25.4

mm (“large”), a cement content (by

weight) of 14%, and an average density

of 2.38 g/cc.

Figures 4.11a and 4.11b cover the band

from 0.5 to 2.0 GHz, while Figures 4.11c

and 4.11d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels.
124

0

0.05

0.1

0.15

0.2

0.25

0.3

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

C84L

C812L

C88L

Table 4.11a: Regression Coefficients (decimal) for Concrete Type 8 Transmission 

versus Frequency Curves Plotted in Figure 4.11a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 8 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C84L C84L + sigma C84L - sigma C88L C88L + sigma C88L - sigma C812L C812L + sigma C812L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 3.9261E-01 3.2877E-01 4.5646E-01 1.9574E-01 2.1489E-01 1.7659E-01 3.7269E-02 3.8848E-02 3.5690E-02

M1 -2.5243E-01 1.7877E-01 -6.8363E-01 -4.9081E-01 -5.8680E-01 -3.9481E-01 -5.3262E-02 -6.0641E-02 -4.5883E-02

M2 4.5625E-02 -1.0246E+00 1.1158E+00 8.0792E-01 9.9712E-01 6.1872E-01 6.8098E-02 8.6298E-02 4.9900E-02

M3 -2.2586E-02 1.2787E+00 -1.3239E+00 -8.3060E-01 -1.0186E+00 -6.4256E-01 -5.4013E-02 -7.5671E-02 -3.2356E-02

M4 8.1722E-02 -7.5028E-01 9.1372E-01 4.9001E-01 5.9206E-01 3.8796E-01 2.2128E-02 3.5810E-02 8.4461E-03

M5 -5.4640E-02 2.1442E-01 -3.2370E-01 -1.4966E-01 -1.7878E-01 -1.2054E-01 -3.3519E-03 -7.7342E-03 1.0302E-03

M6 1.0761E-02 -2.3988E-02 4.5509E-02 1.8226E-02 2.1659E-02 1.4792E-02 -5.1188E-05 5.0721E-04 -6.0955E-04

M7

M8

M9

R 1 1 0.99999 1 1 1 0.99999 0.99999 0.99999

Figure 4.11a: Transmission Coefficients for Concrete Type 8 walls 

(relative to free space). Nominal thicknesses:

C84L = 102 mm; C88L = 203 mm; C812L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
125

-40

-35

-30

-25

-20

-15

-10

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

C84L

C88L

C88L

Table 4.11b: Regression Coefficients (dB) for Concrete Type 8 Transmission versus Frequency Curves

Plotted in Figure 4.11b. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Concrete Type 8 Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C84L C84L + sigma C84L - sigma C88L C88L + sigma C88L - sigma C812L C812L + sigma C812L - sigma

dB dB dB dB dB dB dB dB dB

M0 -8.1679E+00 -1.1223E+01 -5.0922E+00 -7.5025E+00 -6.1221E+00 -8.7903E+00 -2.7598E+01 -2.6900E+01 -2.8353E+01

M1 -6.0224E+00 1.3507E+01 -2.5688E+01 -6.4597E+01 -7.0406E+01 -5.9339E+01 -1.8415E+01 -2.2076E+01 -1.4415E+01

M2 2.6371E+00 -4.4385E+01 4.9984E+01 1.1751E+02 1.2639E+02 1.0988E+02 2.1544E+01 3.0913E+01 1.1338E+01

M3 -8.8756E+00 4.7127E+01 -6.5253E+01 -1.2896E+02 -1.3519E+02 -1.2414E+02 -1.5258E+01 -2.6675E+01 -2.8155E+00

M4 1.0721E+01 -2.4501E+01 4.6165E+01 7.4256E+01 7.6711E+01 7.2597E+01 3.6460E+00 1.1139E+01 -4.5284E+00

M5 -5.0736E+00 6.1611E+00 -1.6374E+01 -2.0580E+01 -2.1214E+01 -2.0164E+01 1.0297E+00 -1.4844E+00 3.7745E+00

M6 8.4753E-01 -5.8610E-01 2.2889E+00 2.0961E+00 2.1840E+00 2.0306E+00 -4.3310E-01 -9.7174E-02 -7.9992E-01

M7

M8

M9

R 1 1 0.99999 1 1 1 0.99999 0.99999 0.99999

Figure 4.11b: Received Signal Magnitude (dB) for Concrete Type 8 Walls 

(relative to free space). Nominal thicknesses:

C84L = 102 mm; C88L = 203 mm; C812L = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
126

0

0.01

0.02

0.03

0.04

0.05

0.06

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz))

C84H

C812H

C88H

Table 4.11c: Regression Coefficients (decimal) for Concrete Type 8 Transmission 

versus Frequency Curves Plotted in Figure 4.11c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 8 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C84H C84H + sigma C84H - sigma C88H C88H + sigma C88H - sigma C812H C812H + sigma C812H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 2.9799E-02 2.9505E-02 3.0093E-02 8.5008E-03 8.7618E-03 8.2397E-03 -5.0974E-04 -4.4285E-04 -5.8435E-04

M1 3.3405E-02 3.5684E-02 3.1127E-02 -5.7899E-03 -5.8974E-03 -5.6824E-03 1.3805E-03 1.3002E-03 1.4715E-03

M2 -1.7539E-02 -1.8676E-02 -1.6401E-02 2.7328E-03 2.7595E-03 2.7060E-03 -9.2188E-04 -8.7702E-04 -9.7278E-04

M3 5.3405E-03 5.6573E-03 5.0236E-03 -7.0006E-04 -7.0104E-04 -6.9909E-04 3.1953E-04 3.0631E-04 3.3446E-04

M4 -9.5007E-04 -9.9913E-04 -9.0100E-04 9.3971E-05 9.2931E-05 9.5014E-05 -6.4113E-05 -6.2093E-05 -6.6339E-05

M5 8.4011E-05 8.7818E-05 8.0204E-05 -6.4726E-06 -6.2918E-06 -6.6536E-06 7.1799E-06 7.0755E-06 7.2735E-06

M6 -2.8509E-06 -2.9672E-06 -2.7346E-06 1.8601E-07 1.7739E-07 1.9464E-07 -3.5036E-07 -3.6326E-07 -3.3041E-07

M7 -6.74E-09 -4.37E-09 -1.01E-08

M8 1.4050E-09 1.2646E-09 1.6063E-09

M9 -4.0075E-11 -3.7111E-11 -4.4564E-11

R 111111 1.00000 1.00000 1.00000

Figure 4.11c: Transmission Coefficients for Concrete Type 8 walls 

(relative to free space). Nominal thicknesses:

C84H = 102 mm; C88H = 203 mm; C812H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
127

-100

-90

-80

-70

-60

-50

-40

-30

-20

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz))

C84H

C812H

C88H

Table 4.11d: Regression Coefficients (dB) for Concrete Type 8 Transmission versus Frequency Curves

Plotted in Figure 4.11d. The regression equation is of the form 

Received Signal Magnitude (relative to free space) 

= M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Concrete Type 8 Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C84H C84H + sigma C84H - sigma C88H C88H + sigma C88H - sigma C812H C812H + sigma C812H - sigma

dB dB dB dB dB dB dB dB dB

M0 -3.0433E+01 -3.0162E+01 -3.0738E+01 2.1087E+02 2.0579E+02 2.1482E+02 -1.4288E+02 -1.5325E+02 -7.6299E+01

M1 6.5631E+00 6.5120E+00 6.6502E+00 -3.3034E+02 -3.2375E+02 -3.3550E+02 1.0867E+02 1.2633E+02 4.7141E+00

M2 -3.1947E+00 -3.1628E+00 -3.2458E+00 1.7179E+02 1.6855E+02 1.7428E+02 -6.7188E+01 -7.9231E+01 -3.0508E-01

M3 8.5973E-01 8.5119E-01 8.7357E-01 -4.6890E+01 -4.6076E+01 -4.7497E+01 2.2457E+01 2.6611E+01 1.3064E-01

M4 -1.3183E-01 -1.3059E-01 -1.3387E-01 7.0653E+00 6.9559E+00 7.1434E+00 -4.5277E+00 -5.1896E+00 -7.8233E-01

M5 9.8529E-03 9.7752E-03 9.9933E-03 -5.5888E-01 -5.5155E-01 -5.6371E-01 5.7683E-01 5.6584E-01 4.5179E-01

M6 -2.8023E-04 -2.7946E-04 -2.8291E-04 1.8103E-02 1.7918E-02 1.8205E-02 -4.9986E-02 -2.6467E-02 -1.1754E-01

M7 3.37E-03 -7.18E-04 1.62E-02

M8 -1.8481E-04 1.2875E-04 -1.1504E-03

M9 5.6351E-06 -3.7738E-06 3.3487E-05

R 1 1 1 0.99998 0.99998 0.99998 1.00000 1.00000 1.00000

Figure 4.11d: Received Signal Magnitude (dB) for Concrete Type 8 Walls 

(relative to free space). Nominal thicknesses:

C84H = 102 mm; C88H = 203 mm; C812H = 305 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

129

Figure 4.12: Test setup for specimen CB3L (3 layers deep of 203 mm masonry block,

total thickness 609 mm) for frequency response determination from 0.5 to 2.0 GHz. See

Figures 4.12a and 4.12b.

4.12 Masonry Block

The following four tables (4.12a through

4.12d) present the frequency response

spectrum for masonry block walls. The

specimens in this series bear the designation CBXXL and CBXXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

Three specimen thicknesses, 203 mm, 406

mm, and 609 mm, were tested. The average material density was 1.84 g/cc.

However, because the specimens were

hollow (see Section 3.2) the “apparent” 

density (external block volume divided

by the block mass) as seen by the radar

was approximately 1.04 g/cc. One could,

alternatively, consider the results in terms

of “apparent thickness,” that is, the total

thickness minus the internal cell width.

Figures 4.12a and 4.12b cover the band

from 0.5 to 2.0 GHz, while Figures 4.12c

and 4.12d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels. The

generally high standard deviations are

attributed to the presence of the cells.
130

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

CB1L

CB3L

CB2L

Table 4.12a: Regression Coefficients (decimal) for Masonry Block Transmission 

versus Frequency Curves Plotted in Figure 4.12a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Masonry Block Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient CB1L CB1L + sigma CB1L - sigma CB2L CB2L + sigma CB2L - sigma CB3L CB3L + sigma CB3L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 5.1710E-01 0.5979 4.3630E-01 6.1626E-01 6.3842E-01 5.9410E-01 5.3364E-02 6.0813E-02 4.5916E-02

M1 6.7249E-01 3.0885E-01 1.0361E+00 -1.3796E+00 -1.3698E+00 -1.3894E+00 1.8802E-02 1.2808E-02 2.4795E-02

M2 -3.8783E+00 -3.1181E+00 -4.6385E+00 1.5051E+00 1.4814E+00 1.5288E+00 -1.1534E-01 -1.1070E-01 -1.1997E-01

M3 5.5193E+00 4.6895E+00 6.3490E+00 -7.3537E-01 -7.5417E-01 -7.1656E-01 1.5970E-01 1.5579E-01 1.6360E-01

M4 -3.4453E+00 -2.9643E+00 -3.9262E+00 1.0979E-01 1.5817E-01 6.1411E-02 -1.0757E-01 -1.0517E-01 -1.0997E-01

M5 9.8550E-01 8.4614E-01 1.1249E+00 2.8706E-02 -2.2677E-03 5.9680E-02 3.5787E-02 3.4938E-02 3.6635E-02

M6 -1.0371E-01 -8.7903E-02 -1.1952E-01 -8.4654E-03 -1.8271E-03 -1.5104E-02 -4.6812E-03 -4.5636E-03 -4.7987E-03

M7

M8

M9

R 0.99991 9.9997E-01 0.99976 0.99999 0.99999 0.99998 1 1 1

Figure 4.12a: Transmission Coefficients for Masonry Block walls 

(relative to free space). Nominal thicknesses:

CB1L = 203 mm; CB2L = 406 mm; CB3L = 610 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
131

-35

-30

-25

-20

-15

-10

-5

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

CB1L

CB3L

CB2L

Masonry Block Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient CB1L CB1L + sigma CB1L - sigma CB2L CB2L + sigma CB2L - sigma CB3L CB3L + sigma CB3L - sigma

dB dB dB dB dB dB dB dB dB

M0 -1.7808E+01 -15.63 -2.0013E+01 -7.0249E+00 -6.5323E+00 -7.7221E+00 -2.6225E+01 -2.5053E+01 -2.7559E+01

M1 8.9222E+01 7.7737E+01 1.0084E+02 3.0414E+00 1.1823E+00 6.4468E+00 7.9288E+00 6.5269E+00 9.6252E+00

M2 -2.5509E+02 -2.2820E+02 -2.8236E+02 -7.1560E+01 -5.9690E+01 -8.8628E+01 -3.0368E+01 -2.7202E+01 -3.4191E+01

M3 3.0965E+02 2.7814E+02 3.4169E+02 1.1536E+02 9.4815E+01 1.4321E+02 3.8844E+01 3.4777E+01 4.3766E+01

M4 -1.8510E+02 -1.6588E+02 -2.0468E+02 -8.0206E+01 -6.4029E+01 -1.0135E+02 -2.5317E+01 -2.2582E+01 -2.8640E+01

M5 5.3652E+01 4.7828E+01 5.9602E+01 2.6496E+01 2.0189E+01 3.4448E+01 8.2547E+00 7.3251E+00 9.3905E+00

M6 -6.0000E+00 -5.3075E+00 -6.7093E+00 -3.4085E+00 -2.4178E+00 -4.6140E+00 -1.0622E+00 -9.3869E-01 -1.2144E+00

M7

M8

M9

R 0.9999 0.99995 0.99978 1 0.99999 0.99996 1 1 1

Figure 4.12b: Received Signal Magnitude (dB) for Masonry Block Walls 

(relative to free space). 

Nominal thicknesses: CB1L = 203 mm; CB2L = 406 mm; CB3L = 610 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 

Table 4.12b: Regression Coefficients (dB) for Masonry Block Transmission versus Frequency Curves

Plotted in Figure 4.12b. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
132

0

0.05

0.1

0.15

0.2

0.25

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz))

CB1H

CB3H

CB2H

Table 4.12c: Regression Coefficients (decimal) for Masonry Block Transmission 

versus Frequency Curves Plotted in Figure 4.12c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Masonry Block Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient CB1H CB1H + sigma CB1H - sigma CB2H CB2H + sigma CB2H - sigma CB3H CB3H + sigma CB3H - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 -3.5380E-02 -0.010959 -5.9800E-02 -5.5132E+01 -6.7389E+01 -4.2875E+01 -2.8270E+00 7.1842E+00 -1.2838E+01

M1 2.2871E-01 2.4203E-01 2.1539E-01 8.9368E+01 1.1138E+02 6.7360E+01 6.1321E+00 -8.4907E+00 2.0755E+01

M2 -1.1111E-01 -1.1792E-01 -1.0431E-01 -5.8783E+01 -7.4411E+01 -4.3155E+01 -4.8129E+00 3.9465E+00 -1.3572E+01

M3 3.0930E-02 3.2995E-02 2.8865E-02 1.9681E+01 2.5242E+01 1.4119E+01 1.7701E+00 -9.1401E-01 4.4543E+00

M4 -4.8634E-03 -5.2020E-03 -4.5247E-03 -3.2169E+00 -4.1724E+00 -2.2614E+00 -2.7302E-01 1.2444E-01 -6.7047E-01

M5 3.8809E-04 4.1636E-04 3.5982E-04 7.7397E-02 1.0086E-01 5.3934E-02 -1.4144E-02 -1.8857E-02 -9.4311E-03

M6 -1.2190E-05 -1.3123E-05 -1.1257E-05 6.3083E-02 8.3569E-02 4.2598E-02 1.2323E-02 4.3094E-03 2.0337E-02

M7 -0.011089 -0.014803 -0.0073755 -0.00197 -0.00067924 -0.0032608

M8 7.9218E-04 1.0651E-03 5.1930E-04 1.4117E-04 5.3753E-05 2.2859E-04

M9 -2.1648E-05 -2.9294E-05 -1.4003E-05 -3.9504E-06 -1.6591E-06 -6.2417E-06

R 1 1 1 0.99697 0.99777 0.99019 0.99767 0.99823 0.99641

Figure 4.12c: Transmission Coefficients for Masonry Block walls 

(relative to free space). Nominal thicknesses:

CB1H = 203 mm; CB2H = 406 mm; CB3H = 610 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
133

-60

-50

-40

-30

-20

-10

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

CB1H

CB3H

CB2H

Masonry Block Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient CB1H CB1H + sigma CB1H - sigma CB2H CB2H + sigma CB2H - sigma CB3H CB3H + sigma CB3H - sigma

dB dB dB dB dB dB dB dB dB

M0 -2.5922E+01 -23.383 -2.7998E+01 -3.3039E+04 -3.5063E+04 -2.0688E+04 -1.6712E+04 -4.4124E+03 -4.0676E+04

M1 1.1336E+01 1.0567E+01 1.0829E+01 5.0251E+04 5.3365E+04 3.1648E+04 2.5604E+04 7.3317E+03 6.1222E+04

M2 -5.2156E+00 -4.9537E+00 -4.7410E+00 -3.1459E+04 -3.3386E+04 -2.0009E+04 -1.5991E+04 -4.8237E+03 -3.7795E+04

M3 1.3617E+00 1.3182E+00 1.1910E+00 1.0179E+04 1.0764E+04 6.5944E+03 5.0189E+03 1.5009E+03 1.1918E+04

M4 -2.0058E-01 -1.9761E-01 -1.6995E-01 -1.6588E+03 -1.7298E+03 -1.1284E+03 -7.1037E+02 -1.6047E+02 -1.8037E+03

M5 1.4936E-02 1.5059E-02 1.2073E-02 6.0594E+01 5.3176E+01 6.1169E+01 -1.9803E+01 -3.4403E+01 1.4680E+01

M6 -4.3635E-04 -4.5228E-04 -3.3281E-04 2.5021E+01 2.8811E+01 1.1785E+01 2.3327E+01 1.3899E+01 4.0707E+01

M7 -4.5858 -5.1287 -2.4678 -3.6012 -1.9689 -6.6857

M8 3.2723E-01 3.6355E-01 1.8131E-01 2.4801E-01 1.3374E-01 4.6560E-01

M9 -8.8712E-03 -9.8347E-03 -4.9654E-03 -6.7025E-03 -3.6333E-03 -1.2570E-02

R 1 1 1 0.9874 0.98742 0.97947 0.98886 0.99194 0.97547

Figure 4.12d: Received Signal Magnitude (dB) for Masonry Block Walls 

(relative to free space). 

Nominal thicknesses: CB1H = 203 mm; CB2H = 406 mm; CB3H = 610 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

Table 4.12d: Regression Coefficients (dB) for Masonry Block Transmission versus Frequency Curves

Plotted in Figure 4.12d. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 3.0 to 8.0 GHz.

135

Figure 4.13: Test setup for specimen D25L (nominal 6 mm thick drywall panel) for frequency response determination from 0.5 to 2.0 GHz. See Figures 4.13a and 4.13b.

4.13 Drywall

The following four tables (4.13a through

4.13d) present the response spectrum for

drywall panels. The specimens in this

series bear the designation DXXL and

DXXH, where the “XX” defines the specimen thickness in inches, and the L and H

denote “low” (0.5 to 2.0 GHz) and

“high” (3.0 to 8.0 GHz) frequency bandwidths.

Three specimen thicknesses, 6 mm, 13

mm, and 16 mm were tested. The average material density was 0.87 g/cc. for

the 6 mm specimens and 0.66 for the 13

mm and 16 mm specimens. 

Figures 4.13a and 4.13b cover the band

from 0.5 to 2.0 GHz, while Figures 4.13c

and 4.13d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels.

Figures 4.13c and 4.13d show transmission coefficients close to or slightly

greater than 1.0 in the decimal range (0

or slightly positive in dB) for some frequencies. These may be attributed to

constructive interference within the material and to resolution limitations of the

measurement system.
136

0.9

0.92

0.94

0.96

0.98

1

0.5 1 1.5 2

D25L (fraction)

D25L+sigma (fraction)

D25L-sigma (fraction)

D50L (fraction)

D50L+sigma (fraction)

D50L-sigma (fraction)

D625L (fraction)

D625L+sigma (fraction)

D625L-sigma (fraction)

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absorption]

Frequency (GHz)

D25L

D625L

D50L

Table 4.13a: Regression Coefficients (decimal) for Drywall Transmission 

versus Frequency Curves Plotted in Figure 4.13a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Drywall Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient D25L D25L + sigma D25L - sigma D25L D25L + sigma D25L - sigma D25L D25L + sigma D25L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 1.0120E+00 1.0217 1.0024E+00 1.0132E+00 1.0145E+00 1.0119E+00 1.0138E+00 1.0146E+00 1.0129E+00

M1 -4.5483E-02 -4.8958E-02 -4.2010E-02 -4.5454E-02 -3.5784E-02 -5.5134E-02 -4.7934E-02 -3.8792E-02 -5.7076E-02

M2 -3.4007E-02 -1.2588E-02 -5.5421E-02 -3.6504E-02 -2.5642E-02 -4.7347E-02 -3.1643E-02 -2.1601E-02 -4.1683E-02

M3 6.3383E-02 4.0933E-02 8.5828E-02 6.7589E-02 4.9882E-02 8.5277E-02 6.1056E-02 4.4591E-02 7.7520E-02

M4 -4.9455E-02 -3.6062E-02 -6.2845E-02 -5.2301E-02 -3.9673E-02 -6.4917E-02 -4.8109E-02 -3.6322E-02 -5.9895E-02

M5 1.9210E-02 1.4778E-02 2.3640E-02 2.0169E-02 1.5548E-02 2.4787E-02 1.8817E-02 1.4497E-02 2.3137E-02

M6 -2.8969E-03 -2.3007E-03 -3.4930E-03 -3.0254E-03 -2.3664E-03 -3.6840E-03 -2.8515E-03 -2.2354E-03 -3.4676E-03

M7

M8

M9

R 111111111

Figure 4.13a: Transmission Coefficients for Drywall Panels 

(relative to free space). Nominal thicknesses:

D25L = 6 mm; D50L = 13 mm; D625L = 16 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
137

-1

-0.8

-0.6

-0.4

-0.2

0

0.5 1 1.5 2

D25L (dB)

D25L+sigma (dB)

D25L-sigma (dB)

D50L (dB)

D50L+sigma (dB)

D50L-sigma (dB)

D625L (dB)

D625L+sigma (dB)

D625L-sigma (dB)

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

D25L

D625L

D50L

Drywall Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient D25L D25L + sigma D25L - sigma D25L D25L + sigma D25L - sigma D25L D25L + sigma D25L - sigma

dB dB dB dB dB dB dB dB dB

M0 1.0177E-01 0.18498 1.7610E-02 1.1164E-01 1.2358E-01 9.9376E-02 1.1682E-01 1.2507E-01 1.0830E-01

M1 -3.7653E-01 -4.0794E-01 -3.4359E-01 -3.7506E-01 -2.9825E-01 -4.4994E-01 -3.9706E-01 -3.2439E-01 -4.6797E-01

M2 -3.4312E-01 -1.4362E-01 -5.4856E-01 -3.6647E-01 -2.5031E-01 -4.8986E-01 -3.2299E-01 -2.1556E-01 -4.3673E-01

M3 5.9856E-01 3.8808E-01 8.1527E-01 6.3649E-01 4.6043E-01 8.2014E-01 5.7808E-01 4.1465E-01 7.4814E-01

M4 -4.6255E-01 -3.3449E-01 -5.9483E-01 -4.8783E-01 -3.6305E-01 -6.1772E-01 -4.5065E-01 -3.3436E-01 -5.7141E-01

M5 1.7912E-01 1.3599E-01 2.2380E-01 1.8759E-01 1.4186E-01 2.3520E-01 1.7566E-01 1.3297E-01 2.1999E-01

M6 -2.6954E-02 -2.1080E-02 -3.3050E-02 -2.8084E-02 -2.1552E-02 -3.4886E-02 -2.6556E-02 -2.0457E-02 -3.2890E-02

M7

M8

M9

R 111111111

Figure 4.13b: Received Signal Magnitude (dB) for Drywall Panels 

(relative to free space). 

D25L = 6 mm; D50L = 13 mm; D625L = 16 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 

Table 4.13b: Regression Coefficients (dB) for Drywall Transmission versus Frequency Curves Plotted in

Figure 4.13b. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
138

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

D50H

D625H

D25H

Table 4.13c: Regression Coefficients (decimal) for Drywall Transmission 

versus Frequency Curves Plotted in Figure 4.13c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Drywall Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient D25H D25H + sigma D25H - sigma D50H D50H + sigma D50H - sigma D625H D625H + sigma D625H - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 6.0134E-01 0.6047 5.9799E-01 8.6272E-01 8.6619E-01 8.5924E-01 9.8255E-01 9.8641E-01 9.7872E-01

M1 2.6860E-01 2.6803E-01 2.6914E-01 5.1441E-02 5.1697E-02 5.1196E-02 -3.2132E-02 -3.1460E-02 -3.2842E-02

M2 -9.2323E-02 -9.1855E-02 -9.2782E-02 1.0819E-02 1.0781E-02 1.0852E-02 4.8537E-02 4.8387E-02 4.8706E-02

M3 2.0894E-02 2.0748E-02 2.1038E-02 -6.2370E-03 -6.2465E-03 -6.2261E-03 -1.5920E-02 -1.5911E-02 -1.5935E-02

M4 -2.8179E-03 -2.7969E-03 -2.8385E-03 9.8820E-04 9.9094E-04 9.8523E-04 2.0619E-03 2.0650E-03 2.0595E-03

M5 1.8957E-04 1.8807E-04 1.9105E-04 -7.8599E-05 -7.8834E-05 -7.8347E-05 -1.2109E-04 -1.2181E-04 -1.2041E-04

M6 -4.8090E-06 -4.7647E-06 -4.8524E-06 2.7051E-06 2.7115E-06 2.6983E-06 2.8106E-06 2.8488E-06 2.7737E-06

M7

M8

M9

R 0.99999 0.99999 0.99999 111111

Figure 4.13c: Transmission Coefficients for Drywall Panels 

(relative to free space). Nominal thicknesses:

D25H = 6 mm; D50H = 13 mm; D625H = 16 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
139

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

D50H

D625H

D25H

Drywall Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient D25H D25H + sigma D25H - sigma D50H D50H + sigma D50H - sigma D625H D625H + sigma D625H - sigma

dB dB dB dB dB dB dB dB dB

M0 -3.6610E+00 -3.6213 -3.7009E+00 -1.3024E+00 -1.2673E+00 -1.3376E+00 -4.6243E-01 -4.2225E-01 -5.0279E-01

M1 2.4242E+00 2.4133E+00 2.4352E+00 5.6703E-01 5.6717E-01 5.6687E-01 1.6090E-01 1.5967E-01 1.6215E-01

M2 -7.9028E-01 -7.8451E-01 -7.9606E-01 4.7116E-02 4.6465E-02 4.7784E-02 1.7497E-01 1.7647E-01 1.7346E-01

M3 1.6723E-01 1.6559E-01 1.6887E-01 -4.6679E-02 -4.6521E-02 -4.6841E-02 -6.9699E-02 -7.0386E-02 -6.9001E-02

M4 -2.1237E-02 -2.1002E-02 -2.1474E-02 8.2634E-03 8.2438E-03 8.2837E-03 7.9927E-03 8.1647E-03 7.8183E-03

M5 1.3407E-03 1.3236E-03 1.3579E-03 -7.1352E-04 -7.1179E-04 -7.1530E-04 -3.4621E-04 -3.6632E-04 -3.2581E-04

M6 -3.1210E-05 -3.0705E-05 -3.1716E-05 2.5864E-05 2.5785E-05 2.5944E-05 4.9902E-06 5.8154E-06 4.1533E-06

M7

M8

M9

R 0.99999 1 0.99999 111111

Figure 4.13d: Received Signal Magnitude (dB) for Drywall Panels 

(relative to free space). 

D25H = 6 mm; D50H = 13 mm; D625H = 16 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

Table 4.13d: Regression Coefficients (dB) for Drywall Transmission versus Frequency Curves Plotted in

Figure 4.13d. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 3.0 to 8.0 GHz.

141

Figure 4.14: Test setup for specimen G75H (19 mm thick silica float glass panel) for frequency response determination from 3.0 to 8.0 GHz. See Figures 4.14c and 4.14d.

4.14 Glass

The following four tables (4.14a through

4.14d) present the frequency response

spectrum for silica float glass panels (typical architectural window glass). The

specimens in this series bear the designation GXXL and GXXH, where the “XX”

defines the specimen thickness in inches,

and the L and H denote “low” (0.5 to 2.0

GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

Three specimen thicknesses, 6 mm, 13

mm, and 19 mm were tested. The average material density was 2.49 g/cc.

Figures 4.14a and 4.14b cover the band

from 0.5 to 2.0 GHz, while Figures 4.14c

and 4.14d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels.
142

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abs

Frequency (GHz)

G25L

G75L

G50L

Table 4.14a: Regression Coefficients (decimal) for Glass Transmission 

versus Frequency Curves Plotted in Figure 4.14a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Drywall Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient G25L G25L + sigma G25L - sigma G50L G50L + sigma G50L - sigma G755L G75L + sigma G75L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 1.1348E+00 1.1684 1.1011E+00 1.0531E+00 1.0393E+00 1.0669E+00 9.3305E-01 9.3003E-01 9.3608E-01

M1 -5.0150E-01 -7.2417E-01 -2.7884E-01 -6.5103E-01 -5.9802E-01 -7.0403E-01 -5.5790E-01 -5.5488E-01 -5.6091E-01

M2 5.7774E-01 1.1067E+00 4.8839E-02 8.2106E-01 7.4504E-01 8.9708E-01 7.2419E-01 7.4382E-01 7.0456E-01

M3 -4.8200E-01 -1.0649E+00 1.0088E-01 -7.3820E-01 -6.5504E-01 -8.2134E-01 -6.7911E-01 -6.9777E-01 -6.6044E-01

M4 2.3613E-01 5.8282E-01 -1.1057E-01 3.7675E-01 3.2360E-01 4.2989E-01 3.7057E-01 3.7817E-01 3.6298E-01

M5 -5.6425E-02 -1.6422E-01 5.1369E-02 -9.4567E-02 -7.7528E-02 -1.1160E-01 -1.0184E-01 -1.0365E-01 -1.0002E-01

M6 4.4928E-03 1.8198E-02 -9.2124E-03 8.5765E-03 6.4328E-03 1.0720E-02 1.0703E-02 1.0928E-02 1.0478E-02

M7

M8

M9

R 1 0.99999 1111111

Figure 4.14a: Transmission Coefficients for Glass Panels 

(relative to free space). Nominal thicknesses:

G25L = 6 mm; G50L = 13 mm; G75L = 19 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
143

-5

-4

-3

-2

-1

0

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

G25L

G75L

G50L

Drywall Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient G25L G25L + sigma G25L - sigma G50L G50L + sigma G50L - sigma G755L G75L + sigma G75L - sigma

dB dB dB dB dB dB dB dB dB

M0 1.1444E+00 1.4489 8.4091E-01 5.5734E-01 4.1902E-01 6.9685E-01 -4.8576E-01 -5.2131E-01 -4.4929E-01

M1 -4.1804E+00 -6.1723E+00 -2.1976E+00 -6.1539E+00 -5.6180E+00 -6.6977E+00 -6.0418E+00 -5.9921E+00 -6.0979E+00

M2 4.6468E+00 9.3273E+00 -3.0783E-03 7.5398E+00 6.7300E+00 8.3727E+00 7.8315E+00 7.9813E+00 7.7003E+00

M3 -3.8722E+00 -8.9783E+00 1.1898E+00 -6.7859E+00 -5.8482E+00 -7.7565E+00 -7.5311E+00 -7.6129E+00 -7.4755E+00

M4 1.8625E+00 4.8889E+00 -1.1357E+00 3.3498E+00 2.7485E+00 3.9725E+00 4.1246E+00 4.1251E+00 4.1408E+00

M5 -4.1623E-01 -1.3588E+00 5.1816E-01 -7.6848E-01 -5.8022E-01 -9.6312E-01 -1.1108E+00 -1.1074E+00 -1.1190E+00

M6 2.6245E-02 1.4666E-01 -9.3270E-02 5.5140E-02 3.2328E-02 7.8674E-02 1.1126E-01 1.1148E-01 1.1156E-01

M7

M8

M9

R 1 0.99999 1111111

Figure 4.13b: Received Signal Magnitude (dB) for Glass Panels 

(relative to free space). 

G25L = 6 mm; G50L = 13 mm; G75L = 19 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 

Table 4.14b: Regression Coefficients (dB) for Glass Transmission versus Frequency Curves Plotted in

Figure 4.14b. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
144

0.75

0.8

0.85

0.9

0.95

1

1.05

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

G50H

G25H

G75H

Table 4.14c: Regression Coefficients (decimal) for Glass Transmission 

versus Frequency Curves Plotted in Figure 4.14c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Drywall Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient G25L G25L + sigma G25L - sigma G50L G50L + sigma G50L - sigma G755L G75L + sigma G75L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 -2.8863E-01 -0.29862 -2.7864E-01 -2.2856E-01 -2.1475E-01 -2.4237E-01 -6.1924E-01 -6.1640E-01 -6.2206E-01

M1 1.0385E+00 1.0523E+00 1.0247E+00 1.2246E+00 1.2160E+00 1.2332E+00 1.4234E+00 1.4239E+00 1.4229E+00

M2 -4.5350E-01 -4.5982E-01 -4.4718E-01 -5.9079E-01 -5.8724E-01 -5.9435E-01 -6.2104E-01 -6.2104E-01 -6.2103E-01

M3 1.1776E-01 1.1936E-01 1.1615E-01 1.6438E-01 1.6359E-01 1.6517E-01 1.5583E-01 1.5588E-01 1.5579E-01

M4 -1.7566E-02 -1.7793E-02 -1.7339E-02 -2.5655E-02 -2.5558E-02 -2.5751E-02 -2.2182E-02 -2.2205E-02 -2.2160E-02

M5 1.3553E-03 1.3719E-03 1.3386E-03 2.0271E-03 2.0210E-03 2.0332E-03 1.6405E-03 1.6436E-03 1.6374E-03

M6 -4.1583E-05 -4.2080E-05 -4.1086E-05 -6.2768E-05 -6.2618E-05 -6.2919E-05 -4.8891E-05 -4.9022E-05 -4.8760E-05

M7

M8

M9

R 0.99999 0.99999 0.99999 1 1 1 0.99999 0.99999 0.99999

Figure 4.14c: Transmission Coefficients for Glass Panels 

(relative to free space). Nominal thicknesses:

G25H = 6 mm; G50H = 13 mm; G75H = 19 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
145

-2

-1.5

-1

-0.5

0

0.5

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

G50H

G25H

G75H

Drywall Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient G25L G25L + sigma G25L - sigma G50L G50L + sigma G50L - sigma G755L G75L + sigma G75L - sigma

dB dB dB dB dB dB dB dB dB

M0 -1.4824E+01 -14.878 -1.4768E+01 -1.2190E+01 -1.1992E+01 -1.2390E+01 -1.7088E+01 -1.7006E+01 -1.7171E+01

M1 1.2201E+01 1.2295E+01 1.2107E+01 1.1883E+01 1.1734E+01 1.2034E+01 1.4896E+01 1.4856E+01 1.4937E+01

M2 -5.1640E+00 -5.2059E+00 -5.1217E+00 -5.4546E+00 -5.3915E+00 -5.5186E+00 -6.2841E+00 -6.2665E+00 -6.3019E+00

M3 1.2814E+00 1.2915E+00 1.2712E+00 1.4330E+00 1.4183E+00 1.4479E+00 1.5197E+00 1.5157E+00 1.5237E+00

M4 -1.8346E-01 -1.8482E-01 -1.8209E-01 -2.1186E-01 -2.0995E-01 -2.1379E-01 -2.0985E-01 -2.0941E-01 -2.1030E-01

M5 1.3703E-02 1.3798E-02 1.3608E-02 1.5879E-02 1.5751E-02 1.6007E-02 1.5169E-02 1.5147E-02 1.5192E-02

M6 -4.0969E-04 -4.1242E-04 -4.0695E-04 -4.6484E-04 -4.6153E-04 -4.6819E-04 -4.4443E-04 -4.4402E-04 -4.4486E-04

M7

M8

M9

R 0.99999 0.99999 0.99999 1 1 1 0.99999 0.99999 0.99999

Figure 4.13d: Received Signal Magnitude (dB) for Glass Panels 

(relative to free space). 

G25H = 6 mm; G50H = 13 mm; G75H = 19 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

Table 4.14d: Regression Coefficients (dB) for Glass Transmission versus Frequency Curves Plotted in

Figure 4.14d. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 3.0 to 8.0 GHz.

147

Figure 4.15: Test setup for specimen L45DH (114 mm thick spruce-pine-fir panel) for

frequency response determination from 3.0 to 8.0 GHz. See Figures 4.15c and 4.15d.

4.15 Lumber (Dry)

The following four tables (4.15a through

4.15d) present the response spectrum for

lumber panels (fabricated from sprucepine-fir grade material). The specimens

in this series bear the designation LXXDL

and LXXDH, where the “XX” defines the

specimen thickness in inches, “D” is for

dry, and the L and H denote “low” (0.5 to

2.0 GHz) and “high” (3.0 to 8.0 GHz) frequency bandwidths.

Four nominal specimen thicknesses, 38

mm, 76 mm, 114 mm, and 152 mm were

tested. 

The average material density (dry) varied

from 0.409 (38 mm thickness) to 0.425

g/cc (152 mm thickness).

Figures 4.15a and 4.15b cover the band

from 0.5 to 2.0 GHz, while Figures 4.15c

and 4.15d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels.
148

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absorption]

Frequency (GHz)

L15DL

L60DL

L45DL

L30DL

Table 4.15a: Regression Coefficients (decimal) for Lumber (Spruce-Pine-Fir) (Dry) Transmission 

versus Frequency Curves Plotted in Figure 4.15a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Southern Pine (Dry) Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient L15DL L15DL + sigma L15DL - sigma L30DL L30DL + sigma L30DL - sigma L45DL L45DL + sigma L45DL - sigma L60DL L60DL + sigma L60DL - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 9.5901E-01 0.8799 1.0381E+00 1.0967E+00 6.6067E-01 1.5328E+00 1.0438E+00 1.0630E+00 1.0246E+00 0.70229 0.6112 0.79339

M1 -6.7361E-01 -1.5271E-01 -1.1945E+00 -1.1459E+00 1.5488E+00 -3.8407E+00 -1.0973E+00 -1.1666E+00 -1.0280E+00 -0.1929 0.50888 -0.89468

M2 1.2281E+00 9.8449E-02 2.3577E+00 2.3858E+00 -3.8969E+00 8.6684E+00 2.2033E+00 2.5822E+00 1.8244E+00 0.0104 -1.8942 1.915

M3 -1.5147E+00 -3.5713E-01 -2.6722E+00 -2.9633E+00 4.2928E+00 -1.0219E+01 -2.8437E+00 -3.6361E+00 -2.0513E+00 -0.13737 2.3401 -2.6148

M4 9.9192E-01 3.8382E-01 1.6000E+00 1.8198E+00 -2.6144E+00 6.2540E+00 1.8338E+00 2.5558E+00 1.1119E+00 0.18676 -1.4812 1.8547

M5 -3.1470E-01 -1.5803E-01 -4.7137E-01 -5.2911E-01 8.4657E-01 -1.9048E+00 -5.6575E-01 -8.6565E-01 -2.6585E-01 -0.086031 0.47541 -0.64747

M6 3.8690E-02 2.3302E-02 5.4078E-02 5.8620E-02 -1.1231E-01 2.2955E-01 6.7384E-02 1.1412E-01 2.0647E-02 0.013748 -0.061096 0.088591

M7

M8

M9

R 1 0.99999 0.99999 1 0.99999 0.99999 1 1 1 1 1 0.99999

Figure 4.15a: Transmission Coefficients for Lumber (Spruce-Pine-Fir) (Dry) Panels 

(relative to free space). Nominal thicknesses:

L15DL = 38 mm; L30DL = 76 mm; L45DL = 114 mm; L60DL = 152 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
149

-9

-8

-7

-6

-5

-4

-3

-2

-1

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

L15DL

L60DL

L45DL

L30DL

Southern Pine (Dry) Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient L15DL L15DL + sigma L15DL - sigma L30DL L30DL + sigma L30DL - sigma L45DL L45DL + sigma L45DL - sigma L60DL L60DL + sigma L60DL - sigma

dB dB dB dB dB dB dB dB dB dB dB dB

M0 -3.7815E-02 -0.99962 9.3376E-01 1.3400E+00 -3.7974E+00 6.5128E+00 1.0902E+00 1.7270E+00 4.6826E-01 -2.934 -4.8032 -1.0456

M1 -8.4443E+00 -2.3448E+00 -1.4619E+01 -1.2841E+01 1.8338E+01 -4.4237E+01 -1.4021E+01 -1.7810E+01 -1.0341E+01 -3.3868 10.035 -16.942

M2 1.6274E+01 3.3533E+00 2.9377E+01 2.6101E+01 -4.5579E+01 9.8259E+01 2.8164E+01 4.0526E+01 1.6023E+01 2.7721 -32.384 38.268

M3 -2.0175E+01 -7.2370E+00 -3.3321E+01 -3.0397E+01 5.1258E+01 -1.1254E+02 -3.4100E+01 -5.3670E+01 -1.4723E+01 -6.2594 38.441 -51.38

M4 1.3042E+01 6.4411E+00 1.9765E+01 1.6748E+01 -3.2410E+01 6.6148E+01 1.9815E+01 3.5306E+01 4.3990E+00 5.5957 -23.991 35.451

M5 -4.0665E+00 -2.4365E+00 -5.7324E+00 -4.1246E+00 1.0884E+01 -1.9188E+01 -5.3377E+00 -1.1280E+01 5.9489E-01 -2.1818 7.6408 -12.09

M6 4.9020E-01 3.4087E-01 6.4375E-01 3.4943E-01 -1.4847E+00 2.1876E+00 5.3373E-01 1.4148E+00 -3.4778E-01 0.31941 -0.97486 1.6245

M7

M8

M9

R 1 0.99999 0.99998 1 0.99999 0.99999 11111 0.99999

Figure 4.15b: Received Signal Magnitude (dB) for Lumber (Spruce-Pine-Fir) (Dry) Panels 

(relative to free space). 

L15DL = 38 mm; L30DL = 76 mm; L45DL = 114 mm; L60DL = 152 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 

Table 4.15b: Regression Coefficients (dB) for Lumber (Spruce-Pine-Fir) (Dry) Transmission versus

Frequency Curves Plotted in Figure 4.15b. The regression equation is of the form Received Signal

Magnitude = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
150

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

L15DH

L45DH

L30DH

L60DH

Table 4.15c: Regression Coefficients (decimal) for Lumber (Spruce-Pine-Fir) (Dry) Transmission 

versus Frequency Curves Plotted in Figure 4.15c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Southern Pine (Dry) Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient L15DH L15DH + sigma L15DH - sigma L30DH L30DH + sigma L30DH - sigma L45DH L45DH + sigma L45DH - sigma L60DH L60DH + sigma L60DH - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 -1.6053E-01 -0.1402 -1.8087E-01 -1.1390E-01 -1.3643E-01 -9.1373E-02 2.6982E-03 1.6294E-02 -1.0895E-02 0.027905 -0.55338 0.60919

M1 7.7684E-01 7.5711E-01 7.9657E-01 5.0837E-01 5.5793E-01 4.5882E-01 2.2310E-01 2.2229E-01 2.2392E-01 0.10128 0.84398 -0.64141

M2 -3.5007E-01 -3.3793E-01 -3.6222E-01 -2.3602E-01 -2.6942E-01 -2.0261E-01 -1.0581E-01 -1.0439E-01 -1.0723E-01 -0.051557 -0.4363 0.33319

M3 9.4176E-02 9.0607E-02 9.7746E-02 6.3589E-02 7.4898E-02 5.2280E-02 2.9468E-02 2.9094E-02 2.9841E-02 0.015359 0.11931 -0.088593

M4 -1.4603E-02 -1.4048E-02 -1.5159E-02 -9.6970E-03 -1.1746E-02 -7.6483E-03 -4.7322E-03 -4.6898E-03 -4.7746E-03 -0.002721 -0.01815 0.012708

M5 1.1667E-03 1.1238E-03 1.2096E-03 7.5784E-04 9.4529E-04 5.7040E-04 3.8913E-04 3.8709E-04 3.9117E-04 0.00024545 0.0014365 -0.00094556

M6 -3.6915E-05 -3.5611E-05 -3.8219E-05 -2.3524E-05 -3.0289E-05 -1.6759E-05 -1.2625E-05 -1.2584E-05 -1.2665E-05 -8.57E-06 -4.59E-05 2.88E-05

M7

M8

M9

R 0.99999 0.99999 0.99999 0.99999 0.99999 1 1 1 11 0.99999 0.99998

Figure 4.15c: Transmission Coefficients for Lumber (Spruce-Pine-Fir) (Dry) Panels 

(relative to free space). Nominal thicknesses:

L15DH = 38 mm; L30DH = 76 mm; L45DH = 114 mm; L60DH = 152 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
151

-30

-25

-20

-15

-10

-5

0

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

L15DH

L45DH

L30DH

L60DH

Southern Pine (Dry) Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient L15DH L15DH + sigma L15DH - sigma L30DH L30DH + sigma L30DH - sigma L45DH L45DH + sigma L45DH - sigma L60DH L60DH + sigma L60DH - sigma

dB dB dB dB dB dB dB dB dB dB dB dB

M0 -1.6547E+01 -16.087 -1.7010E+01 -2.0122E+01 -2.1139E+01 -1.9108E+01 -2.4170E+01 -2.2925E+01 -2.5546E+01 -39.722 -122.06 44.041

M1 1.2399E+01 1.1961E+01 1.2837E+01 1.1806E+01 1.3596E+01 1.0015E+01 1.1601E+01 1.0823E+01 1.2481E+01 25.664 129.83 -80.242

M2 -5.4636E+00 -5.2319E+00 -5.6952E+00 -5.2732E+00 -6.3741E+00 -4.1711E+00 -5.4335E+00 -5.0375E+00 -5.8805E+00 -13.004 -66.517 41.368

M3 1.4022E+00 1.3393E+00 1.4649E+00 1.3594E+00 1.7045E+00 1.0137E+00 1.4424E+00 1.3394E+00 1.5582E+00 3.5173 17.838 -11.022

M4 -2.0711E-01 -1.9790E-01 -2.1623E-01 -1.9937E-01 -2.5806E-01 -1.4055E-01 -2.1806E-01 -2.0345E-01 -2.3446E-01 -0.53078 -2.6343 1.6025

M5 1.5876E-02 1.5207E-02 1.6532E-02 1.5069E-02 2.0182E-02 9.9424E-03 1.6930E-02 1.5891E-02 1.8095E-02 0.040883 0.20152 -0.12182

M6 -4.8509E-04 -4.6620E-04 -5.0340E-04 -4.5414E-04 -6.3196E-04 -2.7576E-04 -5.2171E-04 -4.9207E-04 -5.5528E-04 -1.24E-03 -6.22E-03 3.80E-03

M7

M8

M9

R 0.99999 0.99999 0.99999 0.99999 0.99999 11111 0.99998 0.99997

Figure 4.15d: Received Signal Magnitude (dB) for Lumber (Spruce-Pine-Fir) (Dry) Panels 

(relative to free space). 

L15DH = 38 mm; L30DH = 76 mm; L45DH = 114 mm; L60DH = 152 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

Table 4.15d: Regression Coefficients (dB) for Lumber (Spruce-Pine-Fir) (Dry) Transmission versus

Frequency Curves Plotted in Figure 4.15d. The regression equation is of the form Received Signal

Magnitude = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 3.0 to 8.0 GHz.

153

Figure 4.16: Adjusting the test

setup for specimen L30WH (76

mm thick spruce-pine-fir panel,

soaked) for frequency response

determination from 3.0 to 8.0

GHz. See Figures 4.16c and 4.16d.

4.16 Lumber (Wet)

The following four tables (4.16a through

4.16d) present the frequency response

spectrum for lumber panels (fabricated

from spruce-pine-fir grade material). The

specimens in this series bear the designation LXXWL and LXXWH, where the

“XX” defines the specimen thickness in

inches, the “W” is for wetted, and the L

and H denote “low” (0.5 to 2.0 GHz) and

“high” (3.0 to 8.0 GHz) frequency bandwidths.

Four nominal specimen thicknesses, 38

mm, 76 mm, 114 mm, and 152 mm were

tested. 

The average material density (dry) varied

from 0.428 (38 mm thickness) to 0.432

g/cc (152 mm thickness). All specimens

were soaked (see Section3.6) and allowed

to drip dry prior to testing.

Figures 4.16a and 4.16b cover the band

from 0.5 to 2.0 GHz, while Figures 4.16c

and 4.16d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels.
154

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absorption]

Frequency (GHz)

L15WL

L60WL

L30WL

L45WL

Table 4.16a: Regression Coefficients (decimal) for Lumber (Spruce-Pine-Fir) (Wet) Transmission 

versus Frequency Curves Plotted in Figure 4.16a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Southern Pine (Wet) Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient L15WL L15WL + sigma L15WL - sigma L30WL L30WL + sigma L30WL - sigma L45WL L45WL + sigma L45WL - sigma L60WL L60WL + sigma L60WL - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 0.82917 0.8378 8.2054E-01 1.5830E+00 1.5221E+00 1.6440E+00 1.1196E+00 1.0745E+00 1.1648E+00 0.5885 0.4282 0.7488

M1 1.1303E-01 1.0732E-01 1.1873E-01 -3.1336E+00 -2.6777E+00 -3.5895E+00 -1.5041E+00 -1.1608E+00 -1.8474E+00 -0.02743 0.97531 -1.0302

M2 -3.7344E-01 -3.4554E-01 -4.0130E-01 5.8085E+00 4.6394E+00 6.9775E+00 3.1182E+00 2.3416E+00 3.8949E+00 -0.49513 -2.8042 1.814

M3 4.4380E-01 4.0972E-01 4.7782E-01 -6.1830E+00 -4.7250E+00 -7.6409E+00 -4.3139E+00 -3.4808E+00 -5.1470E+00 0.59934 3.2148 -2.0162

M4 -2.7125E-01 -2.5054E-01 -2.9194E-01 3.4540E+00 2.4928E+00 4.4151E+00 3.0586E+00 2.5872E+00 3.5300E+00 -0.3189 -1.8841 1.2463

M5 8.3517E-02 7.7323E-02 8.9701E-02 -9.4668E-01 -6.2403E-01 -1.2693E+00 -1.0456E+00 -9.0865E-01 -1.1825E+00 0.076928 0.55233 -0.39848

M6 -1.0280E-02 -9.5533E-03 -1.1005E-02 1.0027E-01 5.6856E-02 1.4369E-01 1.3817E-01 1.2201E-01 1.5433E-01 -0.006383 -0.064204 0.051439

M7

M8

M9

R 0.99999 0.99999 0.99999 1111111 0.99999 1

Figure 4.16a: Transmission Coefficients for Lumber (Spruce-Pine-Fir) (Wet) Panels 

(relative to free space). Nominal thicknesses:

L15WL = 38 mm; L30WL = 76 mm; L45WL = 114 mm; L60WL = 152 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
155

-12

-10

-8

-6

-4

-2

0

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

L15WL

L60WL

L45WL

L30WL

Southern Pine (Wet) Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient L15WL L15WL + sigma L15WL - sigma L30WL L30WL + sigma L30WL - sigma L45WL L45WL + sigma L45WL - sigma L60WL L60WL + sigma L60WL - sigma

dB dB dB dB dB dB dB dB dB dB dB dB

M0 -1.6379E+00 -1.5452 -1.7318E+00 5.2482E+00 4.3055E+00 6.1990E+00 3.7409E+00 3.0867E+00 4.4101E+00 -4.8427 -8.1666 -1.4954

M1 1.2351E+00 1.1492E+00 1.3250E+00 -2.6780E+01 -2.0308E+01 -3.3310E+01 -3.0069E+01 -2.5626E+01 -3.4615E+01 0.92997 21.109 -19.411

M2 -4.0036E+00 -3.6454E+00 -4.3737E+00 4.5340E+01 2.9237E+01 6.1598E+01 6.7570E+01 5.8019E+01 7.7366E+01 -9.9686 -55.544 35.994

M3 4.7313E+00 4.3030E+00 5.1727E+00 -4.2576E+01 -2.2729E+01 -6.2622E+01 -8.7389E+01 -7.7467E+01 -9.7589E+01 9.9268 60.716 -41.306

M4 -2.8839E+00 -2.6255E+00 -3.1500E+00 1.8234E+01 5.1944E+00 3.1410E+01 5.7273E+01 5.1787E+01 6.2927E+01 -4.3506 -34.261 25.823

M5 8.8617E-01 8.0903E-01 9.6549E-01 -2.7354E+00 1.6494E+00 -7.1680E+00 -1.8263E+01 -1.6692E+01 -1.9887E+01 0.70746 9.644 -8.3072

M6 -1.0890E-01 -9.9835E-02 -1.1821E-01 -4.9102E-02 -6.4178E-01 5.5022E-01 2.2689E+00 2.0844E+00 2.4601E+00 -0.001346 -1.07 1.0765

M7

M8

M9

R 0.99999 0.99999 0.99999 1111111 0.99999 1

Figure 4.16b: Received Signal Magnitude (dB) for Lumber (Spruce-Pine-Fir) (Wet) Panels 

(relative to free space). 

L15WL = 38 mm; L30WL = 76 mm; L45WL = 114 mm; L60WL = 152 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 

Table 4.16b: Regression Coefficients (dB) for Lumber (Spruce-Pine-Fir) (Wet) Transmission versus

Frequency Curves Plotted in Figure 4.16b. The regression equation is of the form Received Signal

Magnitude = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
156

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

L15WH

L45WH

L30WH

L60WH

Table 4.16c: Regression Coefficients (decimal) for Lumber (Spruce-Pine-Fir) (Wet) Transmission 

versus Frequency Curves Plotted in Figure 4.16c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Southern Pine (Wet) Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient L15WH L15WH + sigma L15WH - sigma L30WH L30WH + sigma L30WH - sigma L45WH L45WH + sigma L45WH - sigma L60WH L60WH + sigma L60WH - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 -5.1516E-01 -0.5695 -4.6082E-01 -1.0443E-01 -4.4426E-01 2.3541E-01 -2.2519E-02 -2.7090E-02 -1.7948E-02 -0.0024898 -0.034619 0.029639

M1 1.0381E+00 1.0963E+00 9.7992E-01 2.9343E-01 7.0730E-01 -1.2044E-01 1.2780E-01 1.3997E-01 1.1564E-01 0.053956 0.096654 0.011259

M2 -5.0131E-01 -5.2291E-01 -4.7972E-01 -1.4270E-01 -3.4337E-01 5.7961E-02 -6.5971E-02 -7.1493E-02 -6.0450E-02 -0.027229 -0.049981 -0.0044763

M3 1.4337E-01 1.4687E-01 1.3987E-01 4.1823E-02 9.1866E-02 -8.2199E-03 1.9824E-02 2.1421E-02 1.8228E-02 0.0081103 0.014416 0.0018047

M4 -2.2760E-02 -2.2794E-02 -2.2726E-02 -6.9503E-03 -1.3652E-02 -2.4865E-04 -3.3180E-03 -3.5615E-03 -3.0746E-03 -0.0013754 -0.0023315 -0.000 41928

M5 1.8207E-03 1.7813E-03 1.8602E-03 5.8470E-04 1.0369E-03 1.3252E-04 2.7643E-04 2.9458E-04 2.5828E-04 0.00011554 0.0001905 4.06E-05

M6 -5.7089E-05 -5.4657E-05 -5.9521E-05 -1.9244E-05 -3.1108E-05 -7.3796E-06 -8.9116E-06 -9.4551E-06 -8.3682E-06 -3.71E-06 -6.07E-06 -1.34E-06

M7

M8

M9

R 0.99999 0.99999 0.99998 0.99999 0.99995 0.99985 111111

Figure 4.16c: Transmission Coefficients for Lumber (Spruce-Pine-Fir) (Wet) Panels 

(relative to free space). Nominal thicknesses:

L15WH = 38 mm; L30WH = 76 mm; L45WH = 114 mm; L60WH = 152 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
157

-35

-30

-25

-20

-15

-10

-5

0

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

L25WH

L45WH

L30WH

L60WH

Southern Pine (Wet) Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient L15WH L15WH + sigma L15WH - sigma L30WH L30WH + sigma L30WH - sigma L45WH L45WH + sigma L45WH - sigma L60WH L60WH + sigma L60WH - sigma

dB dB dB dB dB dB dB dB dB dB dB dB

M0 -2.4127E+01 -23.007 -2.5726E+01 -3.3675E+01 -4.7522E+01 -1.9352E+01 -3.3121E+01 -3.1267E+01 -3.5990E+01 -29.032 -42.859 -15.978

M1 1.7162E+01 1.5642E+01 1.9324E+01 1.9658E+01 3.6289E+01 2.4386E+00 1.3001E+01 1.1461E+01 1.5680E+01 0.013127 17.649 -16.597

M2 -7.4272E+00 -6.5329E+00 -8.6725E+00 -9.1433E+00 -1.7010E+01 -9.8940E-01 -6.0203E+00 -5.2200E+00 -7.3560E+00 1.1032 -7.9784 9.6254

M3 1.9329E+00 1.6662E+00 2.3000E+00 2.4510E+00 4.3448E+00 4.8597E-01 1.5954E+00 1.4003E+00 1.9127E+00 -0.48865 1.9399 -2.7567

M4 -2.8797E-01 -2.4385E-01 -3.4788E-01 -3.7372E-01 -6.1530E-01 -1.2287E-01 -2.3610E-01 -2.1145E-01 -2.7472E-01 0.10049 -0.25444 0.42987

M5 2.2031E-02 1.8285E-02 2.7059E-02 2.9349E-02 4.4547E-02 1.3561E-02 1.7226E-02 1.5847E-02 1.9247E-02 -0.011401 0.015403 -0.036062

M6 -6.6578E-04 -5.4104E-04 -8.3228E-04 -9.1427E-04 -1.2710E-03 -5.4369E-04 -4.7452E-04 -4.5573E-04 -4.9550E-04 5.21E-04 -2.93E-04 1.26E-03

M7

M8

M9

R 0.99999 0.99999 0.99999 0.99999 0.99992 0.99984 111111

Figure 4.16d: Received Signal Magnitude (dB) for Lumber (Spruce-Pine-Fir) (Wet) Panels 

(relative to free space). 

L15WH = 38 mm; L30WH = 76 mm; L45WH = 114 mm; L60WH = 152 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

Table 4.16d: Regression Coefficients (dB) for Lumber (Spruce-Pine-Fir) (Wet) Transmission versus

Frequency Curves Plotted in Figure 4.16d. The regression equation is of the form Received Signal

Magnitude = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 3.0 to 8.0 GHz.

159

Figure 4.17: Test setup for specimen P50H (13 mm dry plywood panel) for frequency

response determination from 3.0 to 8.0 GHz. See Figures 4.17c and 4.17d.

4.17 Plywood (Dry)

The following four tables (4.17a through

4.17d) present the frequency response

spectrum for plywood panels. The specimens in this series bear the designation

PXXDL and PXXDH, where the “XX”

defines the specimen thickness in inches,

“D” for dry, and the L and H denote

“low” (0.5 to 2.0 GHz) and “high” (3.0 to

8.0 GHz) frequency bandwidths.

Four nominal specimen thicknesses, 6

mm, 13 mm, 19 mm, and 32 mm were

tested. 

The average material density (dry) varied

from 0.565 (6 mm thickness) to 0.465 g/cc

(19 mm thickness). 

Figures 4.17a and 4.17b cover the band

from 0.5 to 2.0 GHz, while Figures 4.17c

and 4.17d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels.
160

0.75

0.8

0.85

0.9

0.95

1

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

P25DL

P125DL

P75DL

P50DL

Table 4.17a: Regression Coefficients (decimal) for Plywood (Dry) Transmission 

versus Frequency Curves Plotted in Figure 4.17a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Southern Pine (Dry) Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient P25DL P25DL + sigma P25DL - sigma P50DL P50DL + sigma P50DL - sigma P75DL P75DL + sigma P75DL - sigma P125DL P125DL + sigmaP125DL - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 1.0640E+00 1.0586 1.0693E+00 1.0607E+00 1.0392E+00 1.0822E+00 1.0293E+00 1.0115E+00 1.0471E+00 1.0427 1.0366 1.0488

M1 -1.9480E-01 -2.0136E-01 -1.8824E-01 -1.9577E-01 -1.1324E-01 -2.7831E-01 -1.7839E-01 -1.0433E-01 -2.5245E-01 -0.39032 -0.36903 -0.41163

M2 1.4377E-01 2.0014E-01 8.7404E-02 1.4143E-01 1.1263E-02 2.7161E-01 1.0333E-01 -1.4440E-02 2.2109E-01 0.452 0.42903 0.47499

M3 -1.0416E-01 -1.5899E-01 -4.9341E-02 -9.8323E-02 5.2038E-02 -2.4869E-01 -4.3341E-02 9.1697E-02 -1.7837E-01 -0.43949 -0.41076 -0.46825

M4 4.1431E-02 6.8583E-02 1.4281E-02 3.4895E-02 -6.1276E-02 1.3107E-01 -4.1308E-03 -9.0292E-02 8.2026E-02 0.25116 0.23078 0.27155

M5 -3.2702E-03 -1.1323E-02 4.7825E-03 -3.6758E-04 2.9967E-02 -3.0704E-02 1.2587E-02 3.9836E-02 -1.4660E-02 -0.070414 -0.063708 -0.077125

M6 -1.1922E-03 -1.0925E-04 -2.2752E-03 -1.6501E-03 -5.4140E-03 2.1141E-03 -3.3267E-03 -6.7284E-03 7.4775E-05 0.0074462 0.006607 0.0082861

M7

M8

M9

R 111111111111

Figure 4.17a: Transmission Coefficients for Plywood (Dry) Panels 

(relative to free space). Nominal thicknesses:

P25DL = 6 mm; P50DL = 13 mm; P75DL = 19 mm; P125DL = 32 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
161

-2.5

-2

-1.5

-1

-0.5

0

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

P25DL

P125DL

P75DL

P50DL

Southern Pine (Dry) Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient P25DL P25DL + sigma P25DL - sigma P50DL P50DL + sigma P50DL - sigma P75DL P75DL + sigma P75DL - sigma P125DL P125DL + sigmaP125DL - sigma

dB dB dB dB dB dB dB dB dB dB dB dB

M0 5.4784E-01 0.50124 5.9586E-01 5.2046E-01 3.3170E-01 7.1115E-01 2.5407E-01 9.3873E-02 4.1607E-01 0.4172 0.35737 0.47769

M1 -1.6494E+00 -1.7001E+00 -1.6098E+00 -1.6565E+00 -9.2550E-01 -2.4008E+00 -1.5237E+00 -8.5406E-01 -2.2048E+00 -3.6322 -3.4135 -3.8551

M2 1.1830E+00 1.6349E+00 7.6405E-01 1.1466E+00 -3.4798E-02 2.3662E+00 7.7456E-01 -3.0824E-01 1.8885E+00 4.2968 4.0184 4.5867

M3 -8.7390E-01 -1.2808E+00 -5.1196E-01 -7.9810E-01 5.9151E-01 -2.2398E+00 -2.4793E-01 1.0152E+00 -1.5537E+00 -4.3415 -3.9734 -4.7253

M4 3.3208E-01 5.2435E-01 1.6743E-01 2.5451E-01 -6.3178E-01 1.1728E+00 -1.3730E-01 -9.4202E-01 6.9417E-01 2.5 2.2461 2.7635

M5 -9.7020E-03 -6.8722E-02 4.1569E-02 2.3782E-02 2.9992E-01 -2.6134E-01 1.5509E-01 4.0690E-01 -1.0442E-01 -0.6916 -0.61123 -0.77465

M6 -1.4473E-02 -5.9404E-03 -2.2189E-02 -1.9714E-02 -5.3422E-02 1.4941E-02 -3.7016E-02 -6.8001E-02 -5.1910E-03 0.070952 0.061315 0.080875

M7

M8

M9

R 111111111111

Figure 4.17b: Received Signal Magnitude (dB) for Plywood (Dry) Panels 

(relative to free space). 

P25DL = 6 mm; P50DL = 13 mm; P75DL = 19 mm; P125DL = 32 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 

Table 4.17b: Regression Coefficients (dB) for Plywood (Dry) Transmission versus Frequency Curves

Plotted in Figure 4.17b. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
162

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

P25DH

P75DH

P50DH

P125DH

Table 4.17c: Regression Coefficients (decimal) for Plywood (Dry) Transmission 

versus Frequency Curves Plotted in Figure 4.17c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Southern Pine (Dry) Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient P25DH P25DH + sigma P25DH - sigma P50DH P50DH + sigma P50DH - sigma P75DH P75DH + sigma P75DH - sigma P125DH P125DH + sigmaP125DH - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 -2.5942E-01 -0.25971 -2.5913E-01 -2.9631E-01 -3.0708E-01 -2.8556E-01 -3.4218E-01 -3.4493E-01 -3.3943E-01 -0.77519 -0.76401 -0.78638

M1 1.1761E+00 1.1810E+00 1.1712E+00 1.2065E+00 1.2249E+00 1.1881E+00 1.2313E+00 1.2446E+00 1.2181E+00 1.4203 1.4006 1.44

M2 -5.2085E-01 -5.2329E-01 -5.1842E-01 -5.3419E-01 -5.4267E-01 -5.2571E-01 -5.5401E-01 -5.6025E-01 -5.4776E-01 -0.64104 -0.62729 -0.65479

M3 1.3813E-01 1.3873E-01 1.3754E-01 1.4034E-01 1.4243E-01 1.3825E-01 1.4561E-01 1.4724E-01 1.4398E-01 0.175 0.17035 0.17964

M4 -2.1341E-02 -2.1416E-02 -2.1265E-02 -2.1311E-02 -2.1597E-02 -2.1025E-02 -2.1813E-02 -2.2052E-02 -2.1573E-02 -0.027135 -0.026321 -0.02794 9

M5 1.7078E-03 1.7123E-03 1.7033E-03 1.6745E-03 1.6946E-03 1.6543E-03 1.6823E-03 1.7004E-03 1.6643E-03 0.0021554 0.0020844 0.0022265

M6 -5.4157E-05 -5.4258E-05 -5.4057E-05 -5.2242E-05 -5.2812E-05 -5.1672E-05 -5.1546E-05 -5.2085E-05 -5.1007E-05 -6.77E-05 -6.53E-05 -7.02E-05

M7

M8

M9

R 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999

Figure 4.17c: Transmission Coefficients for Plywood (Dry) Panels 

(relative to free space). Nominal thicknesses:

P25DH = 6 mm; P50DH = 13 mm; P75DH = 19 mm; P125DH = 32 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
163

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

P25DH

P75DH

P50DH

P125DH

Southern Pine (Dry) Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient P25DH P25DH + sigma P25DH - sigma P50DH P50DH + sigma P50DH - sigma P75DH P75DH + sigma P75DH - sigma P125DH P125DH + sigmaP125DH - sigma

dB dB dB dB dB dB dB dB dB dB dB dB

M0 -1.3704E+01 -13.624 -1.3783E+01 -1.3497E+01 -1.3504E+01 -1.3489E+01 -1.3703E+01 -1.3598E+01 -1.3809E+01 -23.512 -23.382 -23.644

M1 1.3197E+01 1.3153E+01 1.3242E+01 1.2736E+01 1.2811E+01 1.2661E+01 1.2495E+01 1.2493E+01 1.2497E+01 19.042 18.84 19.247

M2 -5.8051E+00 -5.7850E+00 -5.8254E+00 -5.5360E+00 -5.5706E+00 -5.5008E+00 -5.4318E+00 -5.4346E+00 -5.4291E+00 -7.9679 -7.8332 -8.1035

M3 1.4778E+00 1.4722E+00 1.4834E+00 1.3948E+00 1.4026E+00 1.3867E+00 1.3660E+00 1.3668E+00 1.3651E+00 1.9912 1.9465 2.0361

M4 -2.1707E-01 -2.1614E-01 -2.1800E-01 -2.0241E-01 -2.0334E-01 -2.0147E-01 -1.9646E-01 -1.9657E-01 -1.9635E-01 -0.28871 -0.28094 -0.29652

M5 1.6594E-02 1.6512E-02 1.6676E-02 1.5281E-02 1.5332E-02 1.5228E-02 1.4632E-02 1.4636E-02 1.4628E-02 0.021917 0.021241 0.022595

M6 -5.0589E-04 -5.0306E-04 -5.0876E-04 -4.6046E-04 -4.6149E-04 -4.5940E-04 -4.3452E-04 -4.3446E-04 -4.3458E-04 -0.00066748 -0.00064438 -0.0 0069069

M7

M8

M9

R 1 1 1 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999

Figure 4.17d: Received Signal Magnitude (dB) for Plywood (Dry) Panels 

(relative to free space). 

P25DH = 6 mm; P50DH = 13 mm; P75DH = 19 mm; P125DH = 32 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

Table 4.17d: Regression Coefficients (dB) for Plywood (Dry) Transmission versus Frequency Curves

Plotted in Figure 4.17d. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.

165

Figure 4.18: Test setup for specimen P50WH (13 mm wetted plywood panel) for frequency response determination from 3.0 to 8.0 GHz. See Figures 4.18c and 4.18d.

4.18 Plywood (Wet)

The following four tables (4.18a through

4.18d) present the frequency response

spectrum for plywood panels. The specimens in this series bear the designation

PXXWL and PXXWH, where the “XX”

defines the specimen thickness in inches,

“W” for wetted, and the L and H denote

“low” (0.5 to 2.0 GHz) and “high” (3.0 to

8.0 GHz) frequency bandwidths.

Four nominal specimen thicknesses, 6

mm, 13 mm, 19 mm, and 32 mm were

tested. The average material density

(dry) varied from 0.563 (6 mm thickness)

to 0.450 g/cc (19 mm thickness). All

specimens were 

soaked (see Section3.6) and allowed to

drip dry prior to testing.

Figures 4.18a and 4.18b cover the band

from 0.5 to 2.0 GHz, while Figures 4.18c

and 4.18d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels. 
166

0.65

0.7

0.75

0.8

0.85

0.9

0.95

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

P25WL

P125WL

P75WL

P50WL

Table 4.18a: Regression Coefficients (decimal) for Plywood (Wet) Transmission 

versus Frequency Curves Plotted in Figure 4.18a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Southern Pine (Wet) Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient P25WL P25WL + sigma P25WL - sigma P50WL P50WL + sigma P50WL - sigma P75WL P75WL + sigma P75WL - sigma P125WL P125WL + sigma P125WL - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 1.0715E+00 1.0596 1.0835E+00 1.0104E+00 9.9931E-01 1.0215E+00 1.0216E+00 1.0396E+00 1.0035E+00 0.88958 0.88273 0.89642

M1 -5.1379E-01 -4.6696E-01 -5.6063E-01 -4.0697E-01 -3.4299E-01 -4.7093E-01 -4.7879E-01 -5.9385E-01 -3.6373E-01 -0.35921 -0.32298 -0.39542

M2 6.5154E-01 5.8763E-01 7.1546E-01 4.8159E-01 3.7487E-01 5.8828E-01 6.1525E-01 8.8380E-01 3.4669E-01 0.45257 0.4002 0.50492

M3 -6.8482E-01 -6.0528E-01 -7.6437E-01 -4.8797E-01 -3.6648E-01 -6.0941E-01 -6.4398E-01 -9.2288E-01 -3.6506E-01 -0.47169 -0.40785 -0.53552

M4 3.9133E-01 3.3679E-01 4.4588E-01 2.7305E-01 1.9309E-01 3.5299E-01 3.8164E-01 5.3967E-01 2.2361E-01 0.28825 0.24475 0.33174

M5 -1.0695E-01 -8.9282E-02 -1.2462E-01 -7.2673E-02 -4.6325E-02 -9.9013E-02 -1.1075E-01 -1.5848E-01 -6.3019E-02 -0.087469 -0.073059 -0.10187

M6 1.1073E-02 8.8668E-03 1.3280E-02 7.1755E-03 3.7536E-03 1.0596E-02 1.2431E-02 1.8393E-02 6.4684E-03 1.04E-02 8.50E-03 1.22E-02

M7

M8

M9

R 1111111111 1 1

Figure 4.18a: Transmission Coefficients for Plywood (Wet) Panels 

(relative to free space). Nominal thicknesses:

P25WL = 6 mm; P50WL = 13 mm; P75WL = 19 mm; P125WL = 32 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 
167

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation]

Frequency (GHz)

P25WL

P125WL

P75WL

P50WL

Southern Pine (Wet) Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient P25DL P25DL + sigma P25DL - sigma P50DL P50DL + sigma P50DL - sigma P75DL P75DL + sigma P75DL - sigma P125DL P125DL + sigma P125DL - sigma

dB dB dB dB dB dB dB dB dB dB dB dB

M0 7.0553E-01 0.58131 8.3281E-01 1.5955E-01 3.8468E-02 2.8353E-01 2.8839E-01 4.5981E-01 1.1864E-01 -0.94451 -1.0293 -0.85734

M1 -4.8813E+00 -4.3672E+00 -5.4141E+00 -3.9717E+00 -3.2770E+00 -4.6835E+00 -4.7902E+00 -5.8705E+00 -3.7218E+00 -4.0194 -3.566 -4.4868

M2 6.3624E+00 5.5619E+00 7.2098E+00 4.8050E+00 3.5842E+00 6.0674E+00 6.4163E+00 8.8947E+00 3.9708E+00 5.2694 4.5475 6.0259

M3 -6.8000E+00 -5.7896E+00 -7.8685E+00 -4.9824E+00 -3.5458E+00 -6.4754E+00 -6.9476E+00 -9.4600E+00 -4.4767E+00 -5.7184 -4.8052 -6.6774

M4 3.7592E+00 3.1060E+00 4.4449E+00 2.7254E+00 1.7845E+00 3.7048E+00 4.1048E+00 5.5241E+00 2.7081E+00 3.5288 2.9131 4.1734

M5 -9.5921E-01 -7.6311E-01 -1. 1632E+00 -6.8494E-01 -3.8123E-01 -1. 0011E+00 -1.1648E+00 -1.6003E+00 -7.3461E-01 -1.0652 -0.86587 -1.273

M6 8.8941E-02 6.6363E-02 1.1217E-01 6.0964E-02 2.2489E-02 1.0098E-01 1.2631E-01 1.8197E-01 7.1064E-02 1.25E-01 9.96E-02 1.51E-01

M7

M8

M9

R 1111111111 1 1

Figure 4.18b: Received Signal Magnitude (dB) for Plywood (Wet) Panels 

(relative to free space). 

P25WL = 6 mm; P50WL = 13 mm; P75WL = 19 mm; P125WL = 32 mm 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Low Range Data: 0.5 to 2.0 GHz 

Table 4.18b: Regression Coefficients (dB) for Plywood (Wet) Transmission versus Frequency Curves

Plotted in Figure 4.18b. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
168

0.5

0.6

0.7

0.8

0.9

1

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

P25WH

P75WH

P50WH

Table 4.18c: Regression Coefficients (decimal) for Plywood (Wet) Transmission 

versus Frequency Curves Plotted in Figure 4.18c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Southern Pine (Wet) Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient P25DH P25DH + sigma P25DH - sigma P50DH P50DH + sigma P50DH - sigma P75DH P75DH + sigma P75DH - sigma

decimal decimal decimal decimal decimal decimal decimal decimal decimal

M0 -5.3832E-01 -0.55892 -5.1773E-01 -6.1972E-01 -6.7122E-01 -5.6822E-01 -1.5508E-01 -2.0561E-01 -1.0454E-01

M1 1.0774E+00 1.1034E+00 1.0513E+00 1.1971E+00 1.2663E+00 1.1279E+00 5.5829E-01 6.3090E-01 4.8567E-01

M2 -4.9546E-01 -5.0702E-01 -4.8391E-01 -5.5889E-01 -5.9176E-01 -5.2601E-01 -2.3524E-01 -2.7270E-01 -1.9778E-01

M3 1.3596E-01 1.3865E-01 1.3326E-01 1.5623E-01 1.6459E-01 1.4786E-01 7.1457E-02 8.1998E-02 6.0916E-02

M4 -2.0459E-02 -2.0797E-02 -2.0122E-02 -2.4482E-02 -2.5612E-02 -2.3352E-02 -1.3020E-02 -1.4663E-02 -1.1376E-02

M5 1.5497E-03 1.5713E-03 1.5281E-03 1.9475E-03 2.0219E-03 1.8732E-03 1.1992E-03 1.3306E-03 1.0679E-03

M6 -4.6217E-05 -4.6780E-05 -4.5656E-05 -6.1050E-05 -6.2882E-05 -5.9218E-05 -4.2450E-05 -4.6630E-05 -3.8270E-05

M7

M8

M9

R 1 1 1 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999

Figure 4.18c: Transmission Coefficients for Plywood (Wet) Panels 

(relative to free space). Nominal thicknesses:

P25WH = 6 mm; P50WH = 13 mm; P75WH = 19 mm.

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 
169

-6

-5

-4

-3

-2

-1

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

P25WH

P75WH

P50WH

Southern Pine (Wet) Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient P25DH P25DH + sigma P25DH - sigma P50DH P50DH + sigma P50DH - sigma P75DH P75DH + sigma P75DH - sigma

dB dB dB dB dB dB dB dB dB

M0 -1.9642E+01 -19.793 -1.9490E+01 -2.3351E+01 -2.3431E+01 -2.3241E+01 -2.3092E+01 -2.3829E+01 -2.2334E+01

M1 1.2480E+01 1.2718E+01 1.2240E+01 1.7474E+01 1.7708E+01 1.7203E+01 1.6171E+01 1.7327E+01 1.4982E+01

M2 -4.8766E+00 -4.9855E+00 -4.7668E+00 -7.3831E+00 -7.4714E+00 -7.2766E+00 -6.8619E+00 -7.4655E+00 -6.2402E+00

M3 1.2182E+00 1.2434E+00 1.1929E+00 1.8786E+00 1.8931E+00 1.8596E+00 1.8090E+00 1.9734E+00 1.6394E+00

M4 -1.7620E-01 -1.7931E-01 -1.7307E-01 -2.7588E-01 -2.7627E-01 -2.7490E-01 -2.8506E-01 -3.0952E-01 -2.5979E-01

M5 1.3127E-02 1.3325E-02 1.2927E-02 2.1008E-02 2.0869E-02 2.1109E-02 2.3759E-02 2.5625E-02 2.1828E-02

M6 -3.8798E-04 -3.9321E-04 -3.8274E-04 -6.3750E-04 -6.2726E-04 -6.4678E-04 -7.9178E-04 -8.4878E-04 -7.3275E-04

M7

M8

M9

R 1 1 1 0.99999 0.99999 0.99999 0.99999 0.99999 0.99999

Figure 4.18d: Received Signal Magnitude (dB) for Plywood (Wet) Panels 

(relative to free space). 

P25WH = 6 mm; P50WH = 13 mm; P75WH = 19 mm.

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

High Range Data: 3.0 to 8.0 GHz 

Table 4.18d: Regression Coefficients (dB) for Plywood (Wet) Transmission versus Frequency Curves

Plotted in Figure 4.18d. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.

171

Figure 4.19: Specimens RC881 (left) and RC882 (right). Concrete batch was the same as

for specimens C88. The results of these specimens are compared in this section with

the reinforced samples.

4.19 Reinforced Concrete

The following four tables (4.19a through

4.19d) present the frequency response

spectrum for reinforced concrete walls.

The specimens in this series bear the designation RC88XL and RC88XH, where

the “X” defines the percent reinforcement, and the L and H denote “low” (0.5

to 2.0 GHz) and “high” (3.0 to 8.0 GHz)

frequency bandwidths.

All specimens were fabricated from Batch

8 concrete and were nominally 203 mm

thick. The reinforcement grids are as

shown in Figure 4.19 (below) and were

identical to those in the rebar grid tests

described in Section 4.20.

Figures 4.19a and 4.19b cover the band

from 0.5 to 2.0 GHz, while Figures 4.19c

and 4.19d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels. 

140 mm

19 mm ReBar

1000 mm

 203 mm

000 mm

140 mm

203 mm

000 mm

70 mm

70 mm

1000 mm

19 mm ReBar
172

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

RC881L

RC882L

C88L

Table 4.19a: Regression Coefficients (decimal) for Reinforced Concrete Transmission 

versus Frequency Curves Plotted in Figure 4.19a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Reinforced Concrete Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C88L C88L + sigma C88L - sigma RC881L RC881L + sigma RC881L - sigma RC882L RC882L + sigma RC882L - sigma

Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal Decimal

M0 1.9574E-01 2.1489E-01 1.7659E-01 0.11632 0.12819 0.10445 8.8034E-02 9.2206E-02 8.3863E-02

M1 -4.9081E-01 -5.8680E-01 -3.9481E-01 -0.038559 -0.097943 0.020824 -1.2997E-01 -1.5205E-01 -1.0789E-01

M2 8.0792E-01 9.9712E-01 6.1872E-01 -0.14826 -0.033705 -0.26282 1.5164E-01 2.0077E-01 1.0251E-01

M3 -8.3060E-01 -1.0186E+00 -6.4256E-01 0.14603 0.038506 0.25355 -1.4795E-01 -2.0002E-01 -9.5885E-02

M4 4.9001E-01 5.9206E-01 3.8796E-01 -0.014967 0.039006 -0.068939 1.0358E-01 1.3238E-01 7.4778E-02

M5 -1.4966E-01 -1.7878E-01 -1.2054E-01 -0.023988 -0.038072 -0.0099049 -4.0443E-02 -4.8468E-02 -3.2418E-02

M6 1.8226E-02 2.1659E-02 1.4792E-02 0.0065792 0.0080924 0.0050661 6.2570E-03 7.1446E-03 5.3694E-03

M7

M8

M9

R 1 1 1 0.99999 0.99999 0.99999 1 1 1

Figure 4.19a: Transmission Coefficients for Reinforced Concrete Walls 

(relative to free space). Nominal thicknesses:

All Specimens are 203 mm Thick. Low Range Data: 0.5 to 2.0 GHz 

C88L = Unreinforced Reference; RC881L = 1% Steel; RC882L = 2% Steel 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).
173

-38

-36

-34

-32

-30

-28

-26

-24

-22

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation ]

Frequency (GHz)

RC881L

C88L

RC882L

Reinforced Concrete Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient C88L C88L + sigma C88L - sigma RC881L RC881L + sigma RC881L - sigma RC882L RC882L + sigma RC882L - sigma

dB dB dB dB dB dB dB dB dB

M0 -7.5025E+00 -6.1221E+00 -8.7903E+00 -18.774 -18.305 -19.105 -1.9363E+01 -1.8639E+01 -2.0090E+01

M1 -6.4597E+01 -7.0406E+01 -5.9339E+01 -7.8074 -8.4393 -8.0524 -2.5150E+01 -2.8706E+01 -2.1612E+01

M2 1.1751E+02 1.2639E+02 1.0988E+02 18.292 14.693 24.066 4.1211E+01 4.8086E+01 3.4491E+01

M3 -1.2896E+02 -1.3519E+02 -1.2414E+02 -59.486 -49.468 -72.189 -5.6320E+01 -6.1846E+01 -5.1128E+01

M4 7.4256E+01 7.6711E+01 7.2597E+01 64.724 55.575 75.611 4.4126E+01 4.6001E+01 4.2547E+01

M5 -2.0580E+01 -2.1214E+01 -2.0164E+01 -28.832 -25.23 -32.996 -1.7168E+01 -1.7299E+01 -1.7155E+01

M6 2.0961E+00 2.1840E+00 2.0306E+00 4.5809 4.0568 5.1773 2.5310E+00 2.4960E+00 2.5836E+00

M7

M8

M9

R 1 1 1 0.99999 0.99998 0.99999 1 1 1

Figure 4.19b: Received Signal Magnitude (dB) for Reinforced Concrete Walls 

(relative to free space). 

All Specimens are 203 mm Thick. Low Range Data: 0.5 to 2.0 GHz 

C88L = Unreinforced Reference; RC881L = 1% Steel; RC882L = 2% Steel 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves). 

Table 4.19b: Regression Coefficients (dB) for Reinforced Concrete Transmission versus Frequency Curves

Plotted in Figure 4.19b. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
174

0

0.001

0.002

0.003

0.004

0.005

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

RC881H

RC882H

C88H

Table 4.19c: Regression Coefficients (decimal) for Reinforced Concrete Transmission 

versus Frequency Curves Plotted in Figure 4.19c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Reinforced Concrete Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C88H C88H + sigma C88H - sigma RC881H RC881H + sigma RC881H - sigma RC882H RC882H + sigma RC882H - sigma

Decimal Decimal Decimal decimal decimal decimal decimal decimal decimal

M0 8.5008E-03 8.7618E-03 8.2397E-03 0.0072087 0.0070249 0.0073922 2.8272E-03 4.6088E-03 1.0470E-03

M1 -5.7899E-03 -5.8974E-03 -5.6824E-03 -0.0039265 -0.0035561 -0.0042964 3.0774E-04 -1.7448E-03 2.3586E-03

M2 2.7328E-03 2.7595E-03 2.7060E-03 0.0017313 0.0015383 0.0019241 -3.6695E-04 6.4895E-04 -1.3821E-03

M3 -7.0006E-04 -7.0104E-04 -6.9909E-04 -0.00041259 -0.00035941 -0.00046571 1.3022E-04 -1.4153E-04 4.0176E-04

M4 9.3971E-05 9.2931E-05 9.5014E-05 4.91E-05 4.08E-05 5.74E-05 -2.7350E-05 1.3654E-05 -6.8327E-05

M5 -6.4726E-06 -6.2918E-06 -6.6536E-06 -2.89E-06 -2.20E-06 -3.57E-06 2.7480E-06 -5.1612E-07 6.0100E-06

M6 1.8601E-07 1.7739E-07 1.9464E-07 7.07E-08 4.80E-08 9.33E-08 -9.9968E-08 5.9965E-09 -2.0587E-07

M7

M8

M9

R1 1 1 1 11111

Figure 4.19c: Transmission Coefficients for Reinforced Concrete Walls 

(relative to free space). Nominal thicknesses:

All Specimens are 203 mm Thick. High Range Data: 3.0 to 8.0 GHz 

C88L = Unreinforced Reference; RC881L = 1% Steel; RC882L = 2% Steel 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).
175

-75

-70

-65

-60

-55

-50

-45

-40

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

RC881H

RC882H

C88H

Reinforced Concrete Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient C88H C88H + sigma C88H - sigma RC881H RC881H + sigma RC881H - sigma RC882H RC882H + sigma RC882H - sigma

dB dB dB dB dB dB dB dB dB

M0 2.1087E+02 2.0579E+02 2.1482E+02 51.337 41.974 61.136 5.5418E+00 5.2986E+01 -5.1414E+01

M1 -3.3034E+02 -3.2375E+02 -3.3550E+02 -126.92 -115.03 -139.33 -7.7524E+01 -1.3466E+02 -9.0516E+00

M2 1.7179E+02 1.6855E+02 1.7428E+02 65.976 59.989 72.206 4.3696E+01 7.1752E+01 1.0178E+01

M3 -4.6890E+01 -4.6076E+01 -4.7497E+01 -18.072 -16.501 -19.7 -1.3085E+01 -2.0244E+01 -4.5693E+00

M4 7.0653E+00 6.9559E+00 7.1434E+00 2.7352 2.5093 2.9684 2.1692E+00 3.1667E+00 9.8904E-01

M5 -5.5888E-01 -5.5155E-01 -5.6371E-01 -0.21832 -0.20148 -0.23561 -1.9028E-01 -2.6190E-01 -1.0607E-01

M6 1.8103E-02 1.7918E-02 1.8205E-02 0.0071561 0.0066503 0.0076719 6.8546E-03 8.9184E-03 4.4448E-03

M7

M8

M9

R 0.99998 0.99998 0.99998 1 1 0.99999 0.99999 1 0.99997

Figure 4.19d: Received Signal Magnitude (dB) for Reinforced Concrete Walls 

(relative to free space). 

All Specimens are 203 mm Thick. High Range Data: 3.0 to 8.0 GHz.

C88L = Unreinforced Reference; RC881L = 1% Steel; RC882L = 2% Steel 

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves). 

Table 4.19d: Regression Coefficients (dB) for Reinforced Concrete Transmission versus Frequency Curves

Plotted in Figure 4.19d. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.

177

Figure 4.20a: Specimen

RE1H (19 mm diameter

reinforcing bars on 140

mm centers). Frequency

test range: 3.0 to 8.0 GHz.

See Figure 5.20c and

5.20d.

Figure 4.20b: Specimen

RE2L (19 mm diameter

reinforcing bars on 70 mm

centers). Frequency test

range: 0.5 to 2.0 GHz. See

Figure 5.20a and 5.20b.

4.20 Rebar Grid

The following four tables (4.20a through

4.20d) present the frequency response

spectrum for steel reinforcing rod (rebar)

grids. The specimens in this series bear

the designation REXL and REXH, where

the “X” defines the volumetric percentage of reinforcement relative to specimens C88L and C88L. The L and H

denote “low” (0.5 to 2.0 GHz) and

“high” (3.0 to 8.0 GHz) frequency bandwidths.

All specimens were fabricated from 19

mm diameter Grade 60 (yield stress 414

MPa) steel deformed reinforcement.

The reinforcement grids are as shown

in Figure 4.20 (below) and were identical to the grids used in the reinforced

concrete specimens (Section 4.19).

Figures 4.20a and 4.20b cover the band

from 0.5 to 2.0 GHz, while Figures 4.20c

and 4.20d are for the range 3.0 to 8.0

GHz. The ordinate values represent the

ratio of the received to transmitted signal. The decimal attenuation values are

presented first, followed by the same

ordinate set converted to decibels. 
178

0

0.2

0.4

0.6

0.8

1

0.5 1 1.5 2

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete absor

Frequency (GHz)

RE1RL

RE2RL

Table 4.20a: Regression Coefficients (decimal) for Reinforcing Bar Grid Transmission 

versus Frequency Curves Plotted in Figure 4.20a. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 0.5 to 2.0 GHz.

Rebar Grid Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient RE1L RE1L + sigma RE1L - sigma RE2L RE2L + sigma RE2L - sigma

decimal decimal decimal decimal decimal decimal

M0 6.5645E-01 8.2826E-01 4.8464E-01 0.10422 0.14179 0.066658

M1 -2.2744E-02 -7.7363E-01 7.2813E-01 0.41864 0.23067 0.60661

M2 1.6691E-01 1.3736E+00 -1.0398E+00 -1.1158 -0.74372 -1.4878

M3 -2.9442E-01 -1.1575E+00 5.6858E-01 1.399 1.0271 1.771

M4 3.8773E-01 6.5343E-01 1.2206E-01 -0.78225 -0.57795 -0.98654

M5 -1.9888E-01 -2.1713E-01 -1.8064E-01 0.19803 0.13932 0.25673

M6 3.4080E-02 3.0091E-02 3.8070E-02 -0.01821 -0.011311 -0.02511

R1 1 1 1 1 1

Figure 4.20a: Transmission Coefficients for Rebar Grids (relative to free space). 

RE1RL = 19 mm bars on 140 mm square grid

RE2RL = 19 mm bars on 70 mm square grid

Low Range Data: 0.5 to 2.0 GHz

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).
179

-16

-14

-12

-10

-8

-6

-4

-2

0

0.5 1 1.5 2

Received Signal Magnitude (dB)

[ 0.0 dB = no attenuation ]

Frequency (GHz)

RE1RL

RE2RL

Rebar Grid Attenuation Curves (0.5 to 2.0 GHz)

Curve Identification

Coefficient RE1L RE1L + sigma RE1L - sigma RE2L RE2L + sigma RE2L - sigma

dB dB dB dB dB dB

M0 -3.9873E+00 -1.4936E+00 -6.4737E+00 -17.993 -15.847 -20.151

M1 1.9272E+00 -9.4768E+00 1.3243E+01 18.812 7.8252 29.851

M2 -3.8192E+00 1.5906E+01 -2.3237E+01 -57.469 -35.195 -79.823

M3 4.4558E+00 -1.1665E+01 2.0102E+01 82.429 59.686 105.22

M4 -1.0471E+00 5.4843E+00 -7.2203E+00 -54.714 -42.114 -67.325

M5 -4.2203E-01 -1.6182E+00 6.4328E-01 17.214 13.59 20.836

M6 1.4873E-01 2.1424E-01 1.0173E-01 -2.0991 -1.6744 -2.5231

R1 1 1 1 1 1

Figure 4.20b: Received Signal Magnitude (dB) for Rebar Grids 

(relative to free space). 

RE1RL = 19 mm bars on 140 mm square grid

RE2RL = 19 mm bars on 70 mm square grid

Low Range Data: 0.5 to 2.0 GHz

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

ble 4.20b: Regression Coefficients (dB) for Rebar Grid Transmission versus Frequency Curves Plotted

in Figure 4.20b. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

he correlation coefficient, R, is defined in the text. Data are for the Frequency Range 0.5 to 2.0 GHz.
180

0.5

0.6

0.7

0.8

0.9

1

345678

Transmission Coefficient (decimal)

[1.0 = complete transmission; 0.0 = complete abso

Frequency (GHz)

RE1H

RE2H

Table 4.20c: Regression Coefficients (decimal) for Rebar Grid Transmission 

versus Frequency Curves Plotted in Figure 4.20c. The regression equation is of the form 

Transmission Coefficient = M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6 etc.

where F is the frequency in GHz. The correlation coefficient, R, is defined in the text.

Data are for the Frequency Range 3.0 to 8.0 GHz.

Rebar Grid Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient RE1H RE1H + sigma RE1H - sigma RE2H RE2H + sigma RE2H - sigma

decimal decimal decimal decimal decimal decimal

M0 -7.9473E-01 -8.0232E-01 -7.8714E-01 -0.27782 -0.34225 -0.21339

M1 1.4472E+00 1.4722E+00 1.4222E+00 0.79174 0.89753 0.68593

M2 -6.6937E-01 -6.8407E-01 -6.5467E-01 -0.39285 -0.45472 -0.33097

M3 1.8363E-01 1.8772E-01 1.7953E-01 0.11412 0.13276 0.09548

M4 -2.7857E-02 -2.8395E-02 -2.7318E-02 -0.017376 -0.02043 -0.014322

M5 2.1365E-03 2.1666E-03 2.1065E-03 0.0012969 0.0015537 0.0010402

M6 -6.4617E-05 -6.5075E-05 -6.4159E-05 -3.76E-05 -4.63E-05 -2.90E-05

R1 1 1 1 1 1

Figure 4.20c: Transmission Coefficients for Rebar Grids (relative to free space). 

RE1RL = 19 mm bars on 140 mm square grid

RE2RL = 19 mm bars on 70 mm square grid

High Range Data: 3.0 to 8.0 GHz

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).
181

-6

-5

-4

-3

-2

-1

0

345678

Received Signal Magnitude (dB)

[0.0 dB = no attenuation ]

Frequency (GHz)

RE1H

RE2H

Rebar Grid Attenuation Curves (3.0 to 8.0 GHz)

Curve Identification

Coefficient RE1H RE1H + sigma RE1H - sigma RE2H RE2H + sigma RE2H - sigma

dB dB dB dB dB dB

M0 -2.1005E+01 -2.0424E+01 -21.586 -1.3237E+01 -13.573 -12.921

M1 1.5522E+01 1.5067E+01 15.974 4.5845E+00 5.4441 3.7409

M2 -6.2548E+00 -6.0698E+00 -6.4368 -1.5544E+00 -2.1036 -1.0108

M3 1.5567E+00 1.5137E+00 1.5988 4.8611E-01 0.65674 0.31651

M4 -2.2387E-01 -2.1759E-01 -0.23002 -8.3460E-02 -0.11186 -0.055158

M5 1.6654E-02 1.6118E-02 0.017182 6.7194E-03 0.009133 0.004309

M6 -4.9322E-04 -4.7366E-04 -0.00051259 -2.0257E-04 -0.00028454 -0.0001206

R 1 1 11 1 1

Figure 4.20d: Received Signal Magnitude (dB) for Rebar Grids 

(relative to free space). 

RE1RL = 19 mm bars on 140 mm square grid

RE2RL = 19 mm bars on 70 mm square grid

High Range Data: 3.0 to 8.0 GHz

Dotted Curves represent +/- 1 standard deviation from mean (Solid Curves).

Table 4.20d: Regression Coefficients (dB) for Rebar Grid Transmission versus Frequency Curves Plotted

in Figure 4.20d. The regression equation is of the form Received Signal Magnitude =

M0+M1*F+M2*F^2+M3*F^3+M4*F^4+M5*F^5+M6*F^6, where F is the frequency in GHz.

The correlation coefficient, R, is defined in the text. Data are for the Frequency Range 3.0 to 8.0 GHz.
The above data represent a fairly comprehensive set of information concerning the

most common construction materials and

their susceptibility to penetration by electromagnetic (EM) radiation in the 0.5 to

8.0 GHz (60 cm to 4 cm wavelength)

range.

Perhaps the most striking aspect of these

data is the relative “transparency” of the

majority of these materials to EM waves

within the frequency range tested, which

constituted relatively long wavelength

radiation as compared with, for example,

visible light. As an example, the average

power of the received signal for a broadband pulse in the 0.5 to 2.0 GHz regime

incident upon a 3-wythe thick (267 mm)

brick wall was on the order of 40% that

of the transmitted signal power. And this

was for a transmission power level of

only 1 mW. Similar characteristics apply

to masonry block walls, a staple of commercial construction practice. A one mW

signal penetrating three layers of masonry block (610 mm thick) was received at a

power level of approximately 0.05 mW,

still well above the noise threshold of the

receiving instrumentation.

Other materials more common to residential construction -- plywood, lumber

studs, glass, and drywall -- were penetrated even more easily. A 13 mm thick

plywood panel dissipated only 10% of

the power of the transmitted signal; two

layers of solid fir planks (76 mm thick)

dissipated 30% of the transmitted signal

strength; a 19 mm thick glass panel dissipated 30%; and a 13 mm thick drywall

panel dissipated only 6% of the transmitted power. In a few special cases for

thinner specimens subjected to signals in

the 3.0 to 8.0 GHz regime (specifically the

drywall and glass specimens), the

received signal, at certain discrete frequencies, approached or slightly exceeded the transmitted power level. This is a

well known phenomenon of resonance

that is exploited in radome design. 

The strongest signal absorption ocurred

for concrete specimens. However, measurable signals were acquired for slabs of

up to 305 mm thick. Previous tests

[Stone, 1996] indicated a limiting thickness penetration of between 0.5 to 0.75 m

for a 1 mW signal). 

Several observations concerning reinforced concrete are worth discussing.

The most important appears to be a relative EM penetration insensitivity to significant changes in the concrete constituents. A 100% increase in aggregate

size has no observable effect on received

signal power. Nor, apparently, does the

water-cement ratio. The most measurable effect appears to be related to the

slump (a measure of the flow-ability of

the mixture per ASTM standard procedures). Even this, however, is not a dramatic effect: an 8% reduction in received

signal power for a 4-fold increase in

slump (see Figure 5.1).

Another useful means of comparing the

transparency of engineering materials is

to calculate the signal loss per unit thickness (expressed in dB/mm). This quanti182

5.0 Summary
ty, for a limited number of tests involving

various materials, is plotted in Figure 5.2

as a function of the measured material

density (in g/cc). For this plot, the density for the brick and masonry block specimens was the true density of the solid

material (not counting the cores).

Likewise, the loss per unit thickness for

the brick and masonry block specimens

was calculated on the assumption that

the EM signal penetrated the thinnest

sidewall distance, propagated across the

air gap in the cells, and then continued

through the opposite wall, with the

power dissipation occurring only during

the penetration of the front and rear

walls. Despite the scatter in the data,

Figure 5.2 strongly supports the notion

that, at least in non-conducting materials,

the signal loss per unit thickness is proportional to the material density. 

In general, the signal attenuation

(dB/mm) increases with increasing frequency. A one milliwatt signal penetrating a 305 mm thick concrete wall will

undergo a loss of approximatey 90 dB at

8 GHz. While this can be recovered from

the background noise in a laboratory setting, that is not guaranteed in an industrial situation such as a constructiion site

or busy inner city complex.

The data presented herein were taken

largely to prepare for the development of

NLS metrology systems, since accurate

distance measurement will require compensation of the range errors which

result from propagation delays as the signal travels through the solid material. In

their present form, the data should be of

general use as a material reference handbook to mobile and portable communica183

0

0.05

0.1

0.15

0.2

0.25

0.3

50 100 150 200 250

Transmission through Concrete

at 1.0 GHz

y = 0.28943 + -0.00042377x R= 0.76263

Transmission Coefficient

Slump (mm)

0

0.05

0.1

0.15

0.2

0.25

0.3

50 100 150 200 250

y = 0.27064 + -0.00056787x R= 0.7763

Transmission Coefficient

Slump (mm)

Transmission through Concrete

at 1.5 GHz

Figure 5.1: Signal attenuation versus slump relationship considering all eight concrete

mixtures at two representative discrete frequencies (1.0 and 1.5 GHz) for 102 mm thick

plain concrete specimens.
tions equipment researchers and designers, whose tasks involve the calculation

and simulation of signal attenuation

throughout office structures and the like.

From a practical standpoint, the data presented herein strongly support the future

development of NLS surveying and

tracking systems -- surveying through

“solid walls.” Within the RF spectrum

investigated herein, measurable signals,

which can subsequently be used to reconstruct time-of-flight distances, can be

received through substantial thicknesses

of most common construction materials. 

A forthcoming report will investigate the

frequency dependency of the material

dielectric and conductivity constants and

will develop simplified regression equations for the prediction of propagation

delay times. These latter quantities will

be more specifically developed for

embedded position error compensation

systems for NLS metrology. 

184

0

0.05

0.1

0.15

0.2

0.25

0 0.5 1 1.5 2 2.5

Atten (db/mm) 1GHz

Atten (db/mm) 1.5 GHz

y = 0.015451 + 0.046999x R= 0.75951

y = 0.022399 + 0.056185x R= 0.82902

Normalized Attenuation (db/mm)

Density (g/cc)

Pine/Fir

(dry)

Plywood

(dry)

Drywall

Masonry

Block

Concrete

Batch 1

Glass

Brick

Figure 5.2: Signal loss per unit material thickness (expressed in dB/mm) as a function

of the material density (g/cc). The above data represent a very small sampling of the

available database at only two discrete frequencies. Attenuation increases, generally,

with increasing signal frequency.
[1] Stone, W.C., Non-Line-of-Sight (NLS)

Metrology, NIST Construction

Automation Program Report No. 1, NISTIR 5825, National Institute of Standards

and Technology, Gaithersburg, MD, Feb.

1996

[2] Stone, W.C., Ed., Proceedings of the

NIST Construction Automation

Workshop, March 30-31, 1995, NIST

Construction Automation Program

Report No. 2, NISTIR 5856, National

Institute of Standards and Technology,

Gaithersburg, MD, May 1996, pp 13-22;

29-42.

[3] Stone, W.C., “Surveying Through Solid

Walls,” Proceedings, ISARC-14, June 8-11,

1997, Pittsburgh, PA. pp. 22-40.

[4] Ulaby, F.T., Whitt, M., and Sarabandi,

K., AVNA - Based Polarimetric

Scatterometers, IEEE Antennas and

Propagation Magazine, October 1990, pp.

6-17.

[5] Blejer, D.J., Frost, C.E., and

Scarborough, S.M., Theory and

Measurements of Buried and Partially

Buried Trihedrals for Ground Penetration

Radar, Project Report GPR-3, MIT Lincoln

Lab, 22 February 1995.

[6]Churchill, R., Complex Variables and

Applications, McGraw-Hill, 1984.

[7] Rabiner, L.R., and Gold, B., Theory and

Application of Digital Signal Processing,

Prentice-Hall, 1975, pp. 356-399.

[8]Krauss, T.P., Shure, L., and Little, J.N.,

Signal Processing Toolbox, The Math

Works, Inc., Natick, MA, September 1995.

pp. 1.56-1.57.

[9] HP 8530A Microwave Receiver

Operating Manual, HP Part No. 08350-

90010, February 1993, Edition 2, pp. 13.12

- 13.14.

[10] Scarborough, S, Frost, C, and Blejer,

D., Range Accuracy Experiment, Internal

Report from MIT Lincoln Lab to NIST,

November 1, 1996.

[11] Blejer, D., Frost, C., and Scarborough,

S., “SAR Imaging of mine-like targets over

ultra-wide bandwidths,” SPIE Vol. 2496,

April 1995, pp 54-69.

* Any mention of commercial products is

for information only; it does not imply

recommendation or endorsement by the

National Institute of Standards and

Technology nor does it imply that the

products mentioned are necessarily the

best available for the purpose.

185

6.0 References
A.1

Appendix A: MatLab Scripts

The following pages contain MatLab scripts for post-processing the test data in order

to create the tables and plots presented in Chapter 4. The radar data acquisition and

storage program was a proprietary code (DataPro) developed by Flam & Russell.

Following the acquisition of the initial frequency power spectra for each test, DataPro

was used to perform three subsequent digital signal processing steps: 1) Conversion of

the frequency domain data to time domain (using a chirp-Z algorithm); 2) Time

domain gating (using a band-pass filter) to eliminate unwanted multipath signals; and

3) production of a gated frequency spectra (using an inverse FFT algorithm). Any of

these steps could have also been accomplished using standard commercial packages

such as MatLab, IDL etc. Unprocessed frequency domain data (ten complete frequency

response spectras for each material specimen) from these tests are available through

NIST (and amount to approximately 600 Mbytes of disk space). Also available, as indicated earlier, are digital copies of the gated time and frequency data.

Time domain gating of the above data was centered on the average peak time for the

ten sample files taken for each specimen. A 1 nanosecond gate, was used for the low

frequency data (0.5 to 2.0 GHz) and a 0.5 nanosecond gate was used for the high frequency data (3.0 to 8.0 GHz). For convenience, and machine portability, the data

processed using DataPro were stored in Network Common Data Form (netCDF) at the

conclusion of each test. NetCDF is a computing platform independent data format

developed by the University Corporation for Atmospheric Research (UCAR, Boulder,

CO) for the National Science Foundation. The data can be accessed and manipulated

with a set of FORTRAN and C-callable subroutines contained in a self-extracting

archive file named ‘NETCDF.EXE’ which is available from UCAR, NSF, and USGS. 

In order to provide more easily usable data the netCDF data files were subsequently

post-processed using a series of MatLab routines which read the data, performed statistical functions (average and standard deviation calculations), peak detection, data

decimation, etc. and wrote the subsequent processed data to ASCII format output files.

These files were then subsequently used for plotting of the data on a PowerMac 8100

using Excel and KaleidaGraph. The MatLab program flow, with a brief functional

description of each routine, is as follows:

NISTGATE - Tabulates and plots statistics of specified netCDF files.

+---GATEAVG - Computes Statistics for specified netCDF files.

| +---DOSFILES - Generates a list of files from a wildcard specification.

| +---CDFLAMIN - Extracts data from a netCDF format FR959 radar data file.

| +---MEXCDF - Provides netCDF interface.

+---GFRETBL - Tabulates gated frequency domain response statistics.

+---FDBPLOT - Plots gated frequency domain response statistics.
A.2

+---GTIMTBL - Tabulates gated time domain response statistics.

+---RDBPLOT - Plots gated time domain response statistics.

MADBCOLS - Adds dB columns to multiple tabulated statistic files.

+---DOSFILES - Generates a list of files from a wildcard specification.

+---ADDBCOLS - Adds columns for average and standard deviation in dB

to a file containing tabulabulated statistics.

All of the above routines were written by Carl Frost at MIT Lincoln Lab.

NISTGATE:

function nistgate(tag)

%NISTGATE tabulates and plots statistics for specified Gated NIST NLS 

% files in netCDF format, given a data set identifier or 'tag'. 

% example:

% nistgate('B1L')

% Created Sept 3, 1996 by C. E. Frost

orient tall %Set plot mode 

c=.2998; %Speed of light in Gigameters/sec

[favg,fdev,f]=gateavg([tag,'*.GDF']); %Get frequency stats for 'tag'.

if favg > 0 

gfretbl(f,favg,fdev,[tag,'.GFR']); %Write the table file.

subplot(2,1,1); %Plot frequency on top half.

fdbplot(f,favg,fdev,['"',tag,'" GATED FREQUENCY RESPONSE']); %Plot.

end

[tavg,tdev,t,r0]=gateavg([tag,'*.GDT']); %Get time stats for 'tag'.

if tavg > 0

r=c*t+r0; %Compute absolute range

gtimtbl(r,tavg,tdev,[tag,'.GTI']); %Write the table file.

subplot(2,1,2); %Plot range(time) on bottom half.

rdbplot(r,tavg,tdev,['"',tag,'" GATED TIME DOMAIN RESPONSE']); %Plot.

end

eval(['print -dps ',tag,'.PS']); %Generate postscript plot file.

GATEAVG:

function [avg,stdev,x,r0]=gateavg(filespec)

%GATEAVG procuces a matrix of averages and standard deviations for the 

% netCDF files matching the input file specification.

% example:

% [avg,stdev,x,r0]=gateavg(filespec)

% where:

% filespec is a wild card netCDF file specification

% avg is the average of the file contents
A.3

% stdev is the standard deviation of the file contents

% x is the frequency or time scale

% r0 is the calibration range in meters

% The length of the data arrays in the files must match.

% Created Sept 3, 1996 by C. E. Frost

[filelist,nfiles] = dosfiles(filespec);

if nfiles > 0

[y,x,r0]=cdflamin(filelist(1,:));

for n=2:nfiles,

y=[y,cdflamin(filelist(n,:))];

end

y=abs(y');

avg=mean(y)';

stdev=std(y)';

else

disp(['ERROR ',filespec,' NOT FOUND']);

y=-1;avg=-1;stdev=-1;

end

DOSFILES:

function [list, count]=dosfiles(filespec)

%DOSFILES returns a list of files matching the input file specification.

% and an optional file count.

% Returns -1 on error

% example:

% [list, count]=dosfiles(filespec)

%

% For use only with the MS Windows version of Matlab.

%

% Created Sept 3, 1996 by C. E. Frost

tempfile=tempname; %Get a temp file name from Matlab.

unix(['dir ',filespec,' /b > ',tempfile]); %Direct the bare directory command

%results to the temp file.

fid=fopen(tempfile,'r'); %Open the temp file, readonly.

count=0; %Initialize the count.

list = fgetl(fid); %Get the first entry.

if list >= 0, %Check for empty list.

count=1; %Set the file count to 1.

name = fgetl(fid); %Get the next entry.

while name >= 0, %Loop until EOF.

list=str2mat(list,name); %Build the file name list.

count=count+1; %Increment the file count. 

name = fgetl(fid); %Get the next entry.
A.4

end

end

fclose(fid); %Close the temp file.

delete(tempfile) %Delete the temp file.

CDFLAMIN:

function [y,x,r0]=cdflamin(path)

%CDFLAMIN extracts data from a netCDF format Flam & Russel 959 file.

% example:

% [y,x,r0]=cdflamin(path)

% where:

% y is the frequency or time domain data.

% x is the frequency(GHz) or time(ns) scale.

% r0 is the calibration range in meters.

% Created Sept 3, 1996 by C. E. Frost. This version is capable

% of extracting data only from netCDF FR959 files containing

% one polarization, and one antenna position.

old_ncopts=mexcdf('SETOPTS',0); %Set mode to NOVERBOSE

cdfid=mexcdf('OPEN', path, 'NOWRITE'); %Open the file readonly

% Get the file content properties:

[ndims, nvars, natts, recdim, status] = mexcdf('INQUIRE', cdfid);

dimlen=zeros(1,ndims); %Initialize the dimension length matrix

for dimid=0:ndims-1, %Populate the dimension length matrix

[dimname,dimlen(1,dimid+1)]=mexcdf('DIMINQ',cdfid,dimid);

end

for varid=0:nvars-1, %Parse through the variables for what we want

[varname,dtype,ndims,dim,natts,status] = mexcdf('VARINQ',cdfid,varid);

if strcmp(upper(varname),'FREQUENCY'), %Get the frequency or time variable

[freqdim,nfreq,status]=mexcdf('DIMINQ',cdfid,dim);

x =mexcdf('VARGET',cdfid,varid,zeros(1,ndims),dimlen(dim+1));

end

if strcmp(upper(varname),'FREQUENCY_DOMAIN'), %Get the Time/Freq Domain

data

count=[dimlen(dim(1:ndims-1)+1),1]; %Form the count matrix

rcorner=zeros(1,ndims); %Form the real corner matrix

icorner=[zeros(1,ndims-1),1]; %Form the imaginary corner matrix

%Extract and combine the real and imaginary components.

y=mexcdf('VARGET',cdfid,varid,rcorner,count)...

+i*mexcdf('VARGET',cdfid,varid,icorner,count);

end

end

%Get the calibration range.

r0=mexcdf('ATTGET',cdfid,mexcdf('PARAMETER','NC_GLOBAL'),'calibration_range_
A.5

Meters');

mexcdf('CLOSE',cdfid);

MEXCDF:

% MEXCDF provides an interface between netCDF and MATLAB. 

% This Mex-file invokes the complete C-Language NetCDF interface,

% as described in the NetCDF Users Guide. All of the specified

% NetCDF input arguments are required. All output arguments are

% optional.

%

% Matlab Syntax:

%

% [out1, out2, ...] = mexcdf('operation', in1, in2, ...)

%

% Extensions:

%

% 1. Dimensions and variables accessible by id or name.

% 2. Attributes accessible by name or number.

% 3. Parameters accessible by number or name.

% 4. Prepended "nc" not necessary for operation names.

% 5. Prepended "NC_" not necessary for specifying parameters.

% 6. Parameter names not case-sensitive.

% 7. Required lengths default to actual lengths via -1.

% 8. Scaling via "scale_factor" and "add_offset" attributes.

% 9. SETOPTS to set NetCDF options. NC_FATAL is disabled.

% 10. ERR to get the error-code of the most recent operation.

% 11. PARAMETER to access parameters by name.

% 12. USAGE to list NCMEX syntax.

%

%

% NetCDF OPERATIONS

% cdfid = mexcdf('CREATE', 'path', cmode); 

% cdfid = mexcdf('OPEN', 'path', mode);

% status = mexcdf('ENDEF', cdfid);

% status = mexcdf('CLOSE', cdfid);

% [ndims, nvars, natts, recdim, status] = mexcdf('INQUIRE', cdfid);

% status = mexcdf('REDEF', cdfid);

% status = mexcdf('SYNC', cdfid);

% status = mexcdf('ABORT', cdfid);

% len = mexcdf('TYPELEN', datatype);

% old_fillmode = mexcdf('SETFILL', cdfid, fillmode);

% old_ncopts = mexcdf('SETOPTS', ncopts);

% ncerr = mexcdf('ERR');
A.6

% code = mexcdf('PARAMETER', 'NC_...');

%

% DIMENSIONS

% status = mexcdf('DIMDEF', cdfid, 'name', length);

% dimid = mexcdf('DIMID', cdfid, 'name');

% ['name',length,status] = mexcdf('DIMINQ', cdfid, dimid); 

% status = mexcdf('DIMRENAME', cdfid, 'name');

% 

% VARIABLES

% status = mexcdf('VARDEF', cdfid, 'name', datatype, ndims, [dim]);

% status = mexcdf('VARID', cdfid, 'name');

% ['name',datatype,ndims,[dim],natts, status] = mexcdf('VARINQ', cdfid, varid);

% status = mexcdf('VARPUT1', cdfid, varid, [coords], value);

% ['name',dtype,ndims,[dim],natts, status] = mexcdf('VARINQ', cdfid, varid);

% [value,status] = mexcdf('VARGET1', cdfid, varid, [coords]);

% status = mexcdf('VARPUT', cdfid, varid, [start], [count], [value]);

% [value,status] = mexcdf('VARGET', cdfid, varid, [start], [count]);

% status = mexcdf('VARRENAME', cdfid, varid, 'name');

% 

% ATTRIBUTES

% status = mexcdf('ATTPUT', cdfid, varid, 'name', datatype, len, [value]);

% [datatype, len, status] = mexcdf('ATTINQ', cdfid, varid, 'name');

% [value], len, status] = mexcdf('ATTGET', cdfid, varid, 'name');

% status = mexcdf('ATTCOPY', incdf, invar, 'name', outcdf, outvar);

% ['name', status] = mexcdf('ATTNAME', cdfid, varid, attnum);

% status = mexcdf('ATTRENAME', cdfid, varid, 'name', 'newname');

% status = mexcdf('ATTDEL', cdfid, varid, 'name');

GFRETABL:

function gfretbl(f,favg,fdev,outfile)

%GFRETBL tabulates frequency domain statistical data.

% Created Sept 3, 1996 by C. E. Frost

fid=fopen(outfile,'w');

fprintf(fid,' %15.15s %15.15s %15.15s\n','frequency (GHz)','average','std. deviation');

fprintf(fid,' %15.7g %15.7g %15.7g\n',[f,favg,fdev]');

fclose(fid);

FDBPLOT:

function fdbplot(f,favg,fdev,tag)

%FDBPLOT plots average frequency domain data with one standard devation

% upper and lower bounds in dB.

% Created Sept 3, 1996 by C. E. Frost
A.7

plot(f,20*log10(favg),f,20*log10(favg-fdev),'g',f,20*log10(favg+fdev),'g');

xlabel('FREQUENCY (GHz)');

ylabel('AVERAGE MAGNITUDE (dB)');

title(tag);

GTIMTBL:

function gtimtbl(r,tavg,tdev,outfile)

%GTIMTBL tabulates time domain statistical data.

% Created Sept 3, 1996 by C. E. Frost

fid=fopen(outfile,'w');

fprintf(fid,' %15.15s %15.15s %15.15s\n','range (m)','average','std. deviation');

fprintf(fid,' %15.7g %15.7g %15.7g\n',[r,tavg,tdev]');

fclose(fid);

RDBPLOT:

function rdbplot(r,tavg,tdev,tag)

%RDBPLOT plots average time domain data with one standard devation

% upper and lower bounds in dB.

% Created Sept 3, 1996 by C. E. Frost

plot(r,20*log10(tavg),r,20*log10(tavg-tdev),'g',r,20*log10(tavg+tdev),'g');

xlabel('RANGE (m)');

ylabel('AVERAGE MAGNITUDE (dB)');

title(tag);

MADBCOLS:

function madbcols(filespec)

%MADBCOLS adds columns for the average and standard deviation in dB 

% for the gated spectrum and time domain tables produced by

% GFRETBL and GTIMTBL matching the input file specification.

%

% example: 

% madbcols('B*.GTI')

%

% For use only with the MS Windows version of Matlab.

% 

% Created Sept 19, 1996 by C. E. Frost

[files,nfiles]=dosfiles(filespec); % Get file list matching filespec

if nfiles > 0

for n=1:nfiles

disp(files(n,:)); % Display the file name

addbcols(files(n,:)); % Add the dB columns to the table
A.8

end

end

DOSFILES: (Previously defined above)

ADDBCOLS:

function addbcols(infile)

%ADDBCOLS reads in an existing time or frequency domain file containing

% tabulated statistical data, and adds two columns for the

% average and standard deviations in dB.

% Created Sept 19, 1996 by C. E. Frost

fid=fopen(infile,'r'); %Open the input file to read.

hdr=fgetl(fid); %Read in the header line without \n

[dat,ndat]=fscanf(fid,'%g',[3,inf]); %Read the data into a 3 row matrix.

fclose(fid); %Close the input file.

%Append the new column headers to the old:

hdr=[hdr,sprintf(' %15.15s %15.15s\n','average(db)','std. dev(db)')];

dbavg=20*log10(dat(2,:)); %Convert the average to dB.

dbdev=20*log10(dat(3,:)); %Convert the standard deviation to dB.

dat=[dat',dbavg',dbdev']'; %Transpose, concatenate, and transpose

fid=fopen(infile,'w'); %Open the file to write

fprintf(fid,'%s',hdr); %Write the header.

%Write out the data in five columns:

fprintf(fid,' %15.7g %15.7g %15.7g %15.7g %15.7g\n',dat);

fclose(fid); %Close the fil;e

end;