latloaal Bureau of Standards?

Library, H.W. Bids

JUN 7 1963

^ecknic&l i\ot& 175

CURVES OF GROUND PROXIMITY LOSS

FOR DIPOLE ANTENNAS

L. E. VOGLER AND J. L. NOBLE

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

^ecknicai *vlot& 175

ISSUED MAY 20, 1963

CURVES OF GROUND PROXIMITY LOSS

FOR DIPOLE ANTENNAS

L. E. Vogler and J. L. Noble

Central Radio Propagation Laboratory

National Bureau of Standards

Boulder, Colorado

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. Price 30 cents
CONTENTS

Page

1. Introduction 1

2. Expressions for the Input Resistance 2

3. Discussion of Numerical Results 4

4. References 6

5. Appendix 7

6. Graphs of Ground Proximity Loss 9

li
CURVES OF GROUND PROXIMITY LOSS FOR DIPOLE ANTENNAS 1

L. E„ Vogler and J. L. Noble

Ground proximity loss, defined as the decibel ratio

of antenna input resistance to its free space resistance,

is presented in graphical form for four types of antennas:

vertical and horizontal electric and magnetic elementary

dipoles. Assuming a non-layered ground characterized

throughout by a relative dielectric Constance e and

conductivity <x, curves are given showing the ground

proximity loss for a wide range of values of ground

constants, antenna height above the ground surface,

and frequency.

1. INTRODUCTION

In the design and evaluation of radio communication systems

a knowledge of the losses in power due to the ground near antennas is

necessary. An appreciable amount of the input power to a transmitting

antenna will be absorbed by the nearby ground rather than being

radiated into space; also, the ground near a receiving antenna will

absorb power with a consequent reduction in available power to the

receiver.

The ground proximity loss of an actual antenna depends on a

number of factors: the frequency of the radio waves, the electromagnetic characteristics of the ground beneath the antenna together

with the nearby terrain features and other environmental structures,

the electromagnetic properties of the atmosphere in which the antenna

is placed, the height of the antenna above the ground surface, and the

type of antenna used. In this paper discussion will be restricted to

antennas placed in a vacuum at a variable height h above an isotropic

and homogeneous conducting half-space with relative dielectric constant

e r (referred to air as unity) and conductivity o

- ( measured in mhos

Most of the work in this report was sponsored by the Jet Propulsion

Laboratory, Pasadena, California, as part of the Lunar Point-toPoint Communication Study.

1
-2-

per meter); the magnetic permeability of the whole space is taken as

the free space value (J. . The lower half-space, corresponding to the

ground, may represent a wide variety of conditions ranging from

relatively highly conducting materials such as sea water to the very

poorly conducting grounds characterized by e 's near unity which

possibly may be encountered in lunar surface communication

[Vogler, 1963].

Four types of antennas are cot idered: the vertical and horizontal electric and magnetic elemental'/ dipoles, the current in which

i co t is assumed to vary as I e with I a constant along the antenna.

o o The elementary dipoles are assumed to be of length djt, and the

magnetic dipoles are then equivalent to circular loops of area dA = di/(3,

where (3 is the free space wave number ( = Z-n/X). For practical

short antennas having a linear distribution of current, dit should be

replaced by an effective length S. = dJt/Z,

2. EXPRESSIONS FOR THE INPUT RESISTANCE

Ground proximity loss L is defined as the decibel ratio of

t, r the antenna input resistance r to the free space radiation resistance

r

f= L = 10 1og(r/r ) , (1)

t, r i

the subscripts t or r denoting a transmitting or receiving antenna.

By assuming a sinusoidally varying current in the antenna of the form

i co t

I e , the input resistance may be obtained from the field at the

antenna through the relationships

r = E di/1 (electric dipoles) , (2a)

p, z o

r = co B dA/1 (magnetic dipoles) , (2b)

p, z o
-3-

where, referring to a cylindrical coordinate system (p, d>, z), E

p, z denotes the p or z component of the electric field at the antenna

(in volts per meter), B denotes the p or z component of the

p, z magnetic field at the antenna (in webers per square meter), and

co = 2itc/\ is the angular frequency of the wave. The horizontal

di poles are assumed to be oriented in the <|> = direction. Derivations of the electromagnetic field components E for VED , E

z p

for HED, B for VMD, and B for HMD are given in earlier

z p

literature [Sommerfeld and Renner, 1942; Wait, 1953, 1961; King,

19 56 ] and only the final expressions used in calculations will be

presented here. The above cited reference by King [1956 ] (see

Chapter VII) contains a detailed discussion of the field components

for all four antennas.

The formulas used for the calculation of the resistance ratio

r/r in ( 1) are:

VED: r/r

f = l + Re{i(3/2 Q! 3

)[l

1 (N

2

)+I

2 (N

2

)]}, r

f = 20 p

2

(di)

2

, (3a)

HED: r/r

f =l+Re{i(3/4a3

)[l

1 (l)+I

2

(N

2

)]}, r = 20 (3 2

(di)

2

cos <|> , (3b)

VMD: r/r =l+Re{i(3/2a3

)[^(l)+I (1)]}, r = 20 (3 4

(dA)

2

, (3c)

HMD: r/r =l + Re{i(3/4 a

3 )[L(N

2

)+I (1)]}, r = 20 p

4

(dA)

2

cos <|>, f 1 Z t (3d)

where

L (6) = a

Z f {

5x -M x

' A

1 e"

X

dx

,

JinA I 2 2 J (4a)

i<* L

r 2 2

6x +aJ x - A

In the remainder of this paper the letters VED, HED, VMD,

and HMD will denote, respectively, vertical electric dipole, horizontal electric dipole, vertical magnetic dipole, and horizontal

magnetic dipole.
-4-

I2(6)=r x

2 { Sx-^ x

2 .A2

|

e -x dx> (4b)

iCX R J_ 2 A 2 ^ ox +»J x - A

and

' 2

or = 2h(3 = 2h(2u/\), A = o^ N -1,

2 N = e -is, s = 60 X cr(mhos /m)

,

r

with \ being the free space wavelength and h the height of the

antenna above the ground, both measured in meters.

The variable x in the integrals of (4a) and (4b) assumes

purely imaginary values from the lower limit to zero and, from

there, takes on real values to the upper limit (see Appendix). The

integrals were numerically integrated on an electronic computer for

various values of the parameters a, e , and s. The graphs in this r report show the results of these calculations for the four different

antennas.

3. DISCUSSION OF NUMERICAL RESULTS

It is apparent from the curves that ground proximity loss can

have a considerable effect on the design of some radio communication

systems. For certain combinations of ground conductivity and frequency the loss becomes quite large as the antenna height is

decreased. On the other hand as the ratio h/\ is increased, the

effect of the ground becomes negligible and the loss approaches zero

for all conductivities and frequencies.
-5-

For a highly conducting ground and wavelength large enough

such that s—» °o, the ground proximity loss approaches the value

expected for an antenna located above an infinitely conducting plane.

Expressions for the loss in this case are well known and are given by:

VED: L = 10 log [ 1 + (3/of ) {sinor - orcosof}], (5a)

t, r

HED: L = 10 log [ 1 + (3/2 a

3

) {( 1 -a

2

) sin a - a cos a}] , (5b)

t, r

3 VMD: L = 10 log [ 1 - {3/a ) {sina - a cos a} ] , (5c)

t» r

3 2 HMD: L = 10 log [ 1 - (3/2 a ) {( 1 - a ) sina - a cos a} ] . (5d)

t, r

It should be noticed that (5a) - ( 5d) do not necessarily give a good

estimate of the ground proximity loss for highly conducting grounds

at all frequencies. The loss may be approximated by these equations

only for large values of the ratio (r(mhos/m)/f , ; i e , for s —- °o . Mc

The curves of ground proximity loss presented here may be

used in the evaluation of radio systems through the concept of system

loss [Norton, 1959 ]« System loss L is defined as the decibel ratio

of the power available at the input terminals of the transmitting antenna

to the power delivered to the receiver. In terms of the attenuation

A relative to an inverse distance field in free space between isotropic antennas separated a distance d , system loss may be written

as L = 10 log(4ird /\)

2 + A,. - (G + G ) + (L + L ), (6)

s o t t r t r

where G is the transmitting or receiving antenna gain relative to

t» r an isotropic antenna, and L is the antenna ground proximity loss

t, r defined by ( 1)

.
-6-

The authors would like to thank Mr. R. E. Wilkerson for his

assistance in some of the mathematical investigations pertaining to

this work.

4. REFERENCES

King, R. W. P. (1956). The theory of linear antennas, (Harvard

University Press, Cambridge, Mass. )

Norton, K. A. (July-Aug. 19 59). System loss in radio wave propagation, J. Research NBS 63D (Radio Prop. ), No. 1, 53-73.

Sommerfeld, A. , and F. Renner ( 1942). Strahlungsenergie und

Erdabsorption bei Dipolantennen, Ann. Phys. 41, No. 1, 1-36.

Vogler, L. E. (Jan. -Feb. 1963). Point-to-point communication on

the moon, J. Research NBS 67D (Radio Prop. ), No. 1, 5-21.

Wait, J. R. (1953). Radiation resistance of a small circular loop in

the presence of a conducting ground, J. Appl. Phys. 24, 646-649.

Wait, J. R. (1961). The electromagnetic fields of a horizontal dipole

in the presence of a conducting half-space, Can. J. Phys. 39,

1017-1028.
-7-

5. APPENDIX

The following transformation was used in the evaluation of

(4a) and (4b):

a „ . .2.2

y

6) = -i«2

f

r ay.y + a

|

e

. iydy

o L

P 2 2 J 6y +\J y + A

'U

2 2

6x - M x - A -x

2 A 2

6x +\j x - A

e dx

,

(A- 1)

a

I2

(6) = i\ y-.{ "y-V'^L l-.-^dy '1 'M 2 2

6y + 'sj y + A

I„"

2

{

2

A 2

fix - M x - A -x

2 2

6x +\| x - A

e dx, (A-2)

2 2 where Re\| x - A > . These integrals were then evaluated

numerically using 96-point Gaussian and 32-point Gauss-Laguerre

quadrature. When necessary, the second integrals on the right were

further divided into sub-intervals to insure the required accuracy.

-9-

6. GRAPHS OF GROUND PROXIMITY LOSS,

L^

r

= 10 1og(r/r

f

)

Vertical Electric Dipole (VED)

Horizontal Electric Dipole (HED)

Vertical Magnetic Dipole (VMD)

Horizontal Magnetic Dipole (HMD)

€ : relative dielectric constant of ground

r

6

o-(mhos/m): conductivity of ground

h: height in meters of antenna above ground

\: wavelength in meters
-10-

GROUND PROXIMITY LOSS FOR VED,€r = l.|

70

60

50

40

~ 30 o

20

-10.

!

f>V a

er =i.i

= 47Th/)V f n

^

03 <y/r

f

o>

....~%t X

£'

"l±£-

a>5

1

i

0.001 0.01 0.1 I 10 100 S = 60Xcr(mhos/m)= l,8x l0

4 o-(mhos/m)/f Mc

1000 10000
-11-

GROUND PROXIMITY LOSS FOR VED,€r = 2

o

70

60

50

40

30

20

-10

V 2 a=477-h/X

4

5>

4

A/

0;V

0>

...o,5.

I j2. a>5

0.01 0.1 I 10 100 1000 S=60\cr(mhos/m)= l.8x l0

4 cr(mhos/m)/f Mc
-12-

GROUND PROXIMITY LOSS FOR VED,€r = 5

70

60

50

40

~ 30

exo

20

10

-10

1

j

£ r =5

a=47rh/X

4y

jf

f

.... „<b O^

0>

!!..0.5_ '.'.. .iliUo

a>5

0.001 0.01 0,1 I 10 100 1000

S = 60\a(mhos/m)= l,8x l0

4 cr(mhos/m)/f Mc

10000
-13-

GROUND PROXIMITY LOSS FOR VED,€r =IO

(U

t T

60 e r =IO a =47rh/X

50 op> £/

40 A

a

\~ 30 o

r$3^

0>

O

20 -- rt\< Jr

10 0>

Og.

1.0 -

a>£

-in

0,01 0.1 I 10 100 1000

S = 60\cr(mhos/m)=l.8xl04 cr(Tnhos/m)/f Mc
-14-

GROUND PROXIMITY LOSS FOR VED,£r =20

70

60

50

40

~ 30 o

20

1 J

e r =20

a = 47Th/)y.

.... «<

.,0;J/

03 O/*

f

cv\.

~ 9 - " 0£,

0.5

... i n

.

a>t

10 =»

0.01 0,1 I 10 100 1000

S = 60\o-(mhos/m)= 1,8 x IOV (mhos/m)/f Mc
-15-

GROUND PROXIMITY LOSS FOR VED, € r = 50

70

60

50

40

- 30 o

20

t

€ r =50

a = 47Th/X

.0 ^

0?J

rSS^^

OyS

0>

O*.

0.5 'i.o

a>£

0.01 0,1 I 10 100 1000 S = 60Xcr(mhos/m)= l.8xl04 a(mhos/m)/fMc

10000
-16-

GROUND PROXIMITY LOSS FOR VED,€r = 80

IU

60 J

50

€r =80

a=47rh/X

40

<£/? 4P

- 30 o &

O

20 o$i/

10

0^-

... _ o . 0£.

0.5

1.0 a>5

-1

.001 0.01 0,1 1 10 100 iooo 0000

S = 60\(r(mhos/m) = 1,8 x IOV( mhos/m)/f Mc
-17-

GROUND PROXIMITY LOSS FOR H ED, C r =1.1

oO

70

60

50

40

30

20

10

€r = l.l a=47Th/X

V> r w

y ( w

cm

,' cJrff

'''"' 2>

.-'- < ^^- \ 0,^ .... 10.0 ^^-^

--..I:** 2.0 ^^.^

1 1 , ..1.

0.001 0.01 0.1 I 10 100

S =60\cr(mhos/m) = l.8 x I0 4

cr (mhos/m)/f

1000 10000

Mc
-18-

GROUND PROXIMITY LOSS FOR HED,6r = 2

70

60

50

40

~ 30

o

20

10

-10

\ a =47Th/)< ?

Sy

-- rSl y

4\

o>

n. 0^/

OS.

i JjO. a =l().0

Z. 0"

0.

i . 5

0.01 0.1 I 10 S = 60\cr(mhos/m) = l.8xl04 o-(mhos/m)/f1000 10000

Mc
-19-

GROUND PROXIMITY LOSS FOR HED,6r = 5

o

70

60

50

40

30

20

-10

a = 47Th/)<

4p,

f

f>

0>

o£.

0.5

1,0 a

--

\ 3,0 Z .0 "

MQ--

0.01 0.1 I 10 100 S = 60\cr(mhos/m) = 1. 8x l0

4 cr(mhos/m)/f

1000 10000 Mc
-20-

GROUND PROXIMITY LOSS FOR HED,€r = IO

70

60

50

40

30

20

a = 47Th/X

<y is

^ >

<• /

3?l

<JV? o^r

oV

o£.

0.5

10. ^3j 2.0

•i.o—

0.001 0.01 0.1 I 10 too

S = 60\cr(mhos/m) = l.8x l0 4cr(mhos/m)/f m c

1000 10000
-21-

GROUND PROXIMITY LOSS FOR HED,€r = 20

eno

IU

60

i

€r = 20

2=47Th/X

50

40 •/

30

aft

si

20 o«

o^Py

10

\

(.

0. 2

0.!

f1 0. ' o 2,0

10

I

c

1 I . . 1

0.01 0.1 I 10 100

S = 60\cr(mhos/m) = l.8x I0 4

cr (mhos/m)/f

1000 10000 M C
-22-

GROUND PROXIMITY LOSS FOR HED,€ r =50

TO

60

50

40

o> 30 o

20

i

( 1 =47Th/X

i

I

i i r

, cU j5 ff

( ^

3+ 2r

0.2

0.5

ic•> r """^| ,^C ^. T

.. ^•CT

| „ 'I

i i . i 100.001 0.01 0.1 I 10 100 S=60Xcx(mhos/m) = 1.8 x I0 4

cr (mhos/m)/ f

1000 10000

Mc
23-

GROUND PROXIMITY LOSS FOR HED,6r =80

70

60

50

40

o> 30 o

20

e r =80 a = 4 77-h/X

°\

(V- i>

oS

n I )5 M..< O.l 0.2

'"

0.5 KD.C) ... 2.0

....iiO

1

1

1

0.001 0.01 0.1 I 10 100 1000

S =60\cr(mhos/m) = 1.8 x l0 4cr(mhos/m)/f M
-24-

GROUND PROXIMITY LOSS FOR VMD, er = I.

o

70

60

50

40

30

20

10

-10.

€ r = 1.1 a = 47Th/ \

r\\ &

''''^e

''' &

Us

J^r

1.0

v a >!

-- -v 2 .0

0.01 0.1 I 10 100

S= 60Xcr( mhos/m ) = l.8x I0 4 a (mhos/m)/f Mc
-25-

GROUND PROXIMITY LOSS FOR VMD , e r = 2

70

60

50

40

~ 30 o

20

-10.

e r = 2 a = 47Th/ \

s^

"'^f

/' j^

;

! '"o2

Oj?-

1.0

... 4

V a >5

^-2

0.01 0.1 I 10 100 1000

S = 60 \cr ( mhos/m ) = 1.8 x I0 4 cr (mhos/m)/fMc
.26-

GROUND PROXIMITY LOSS FOR VMD , € r = 5

TO

60

50

40

^ 30 oO

20

—

r

1

€r = 5 a = 47rh/>

Mr

*'<#

,,' aw

'"' a£

J;!

10

... ill

R

' >.o

1

0.01 0.1 I 10 100 1000

S = 60 Act ( mhos/m) = 1.8 x I0 4 <x (mhos/m)/f Mc
-Z7-

GROUND PROXIMITY LOSS FOR VMD, e r = 10

70

60

50

40

TM 30 o

20

10

10

€ r = 10 a = 47Th / \

D

x

/

" ^

OjT

_0.5_

IXJ

>; v 2

0.01 0.1 I 10 100

S= 60 Xo- (mhos/m ) = 1.8 x I0 4

<r (mhos/m)/fMc
-28-

GROUND PROXIMITY LOSS FOR VMD, € r = 20

IU

60 e r = 20 a = 47rh/;V

50

40

*4- ^ 30 ... < :>\ *x* o Xt

g

20 '"'&

"'<^

--- 0. s - 10

a>5

2.C

in

0.001 0.01 01 I 10 100

S = 60 \<j ( mhos/m ) = 1.8 x IO« cr (mhos/m)/fMc
-29-

GROUND PROXIMITY LOSS FOR VMD, e r = 50

70

60

50

40

~ 30 o

20

e r = 50 a = 47Th/ \

r\o> o-V

.-*@r

- ao>*

0.2 _

0.5

... .

| a> 5 2.0

0.001 0.01 0.1 I 10 100

S = 60 \cr ( mhos/m ) = 1.8 x I04 <r (mhos/m)/fMc
-30-

GROUND PROXIMITY LOSS FOR VMD, € r = 80

o

70

60

50

40

30

20

-10

e r = 80 a = 47Th/ V

... „«0^

1 — '" _2h

t — oz

O.E

1.0—

a> 5

t 2.0

0.01 0.1 I 10 100

S = 60 Act ( mhos/m ) = 1.8 x I0 4 cr (mhos/m)/f|y/|c
-31 -

GROUND PROXIMITY LOSS FOR HMD,€r =l,l

TO

60

50

40

~ 30 o

20

10

a

€r=l.l.

= 47Th/X

fy'yf

O^

J**

'*2>

o£

0.5

1.0

a--l..0

0.01 0.1 I 10 100 S = 60Xo-(mhos/m)= l.8x l0

4 cr(mhos/m)/f

1000 10000

Mc
-32-

GROUND PROXIMITY LOSS FOR HMD, 6r =2

o

TO

60

50

40

30

20

10

-10

e r-2

a-477-h/X

""' „o ^ C^/*

oS

b,

'' 0>

o£.

0.5

1 1.0 a = 2.0 ..,

0.01 0,1 I 10 100 S = 60\cr(mhos/m)= l.8x l0

4 cr(mhos/m)/f Mc

1000 10000
-33-

GROUND PROXIMITY LOSS FOR HMD, € r = 5

70

60

50

40

~ 30 o

20

10

€r -5

a =47Th/X

*o &,

"T " ^^

o£

b.

']o>

q£

0.5

1 a = ; >.o

0.01 0.1 I 10 100 1000 S = 60\cr(mhos/m)= l.8xloV(mhos/m)/fMc

10000
-34-

GROUND PROXIMITY LOSS FOR HMD,€r = IO

O

O

70

60

50

40

30

20

]

€

f =\0

a=47rh/X

-P £

T *^s w

v- To£

o£

0.5

I'""

f"

"' 1.0 a = 2.o

0,001 0,01 0,1 I 10 100 S= 60 X a (mhos/m) = 1 .8 x l0

4 a"(mhos/m)/f|y] c

1000 10000
-35-

GROUND PROXIMITY LOSS FOR HMD,€r =20

TO

60

50

40

~ 30 o

20

~T"

a

€ r -20

= 47Th/X

-S> §>

"T" 0^/*

oj&

T 0^

^

0.5

T" 1.0 a = 2!.0

0.01 0,1 I 10 100 1000

S = 60Xcr(mhos/m)= I. 8x l0

4 cr(mhos/m)/f Mc

10000
-36-

GROUND PROXIMITY LOSS FOR HMD,€r = 50

TO

60

50

40

~ 30 o

20

-10

1

I

a

€r =50

= 47Th/>I

4-rt?SJ>

T O^/* )o^

ToA

1 ££

.I- 0,5

i" 1.0 a = 2.o

0,01 0,1 I 10 100

S = 60\a (mhos/m)= l,8x l0

4 cr(mhos/m)/f

1000 101

Mc
- 37

GROUND PROXIMITY LOSS FOR HMD, € r = 80

70

60

50

40

~ 30 o

20

t 1

Q

e

r =80

=47Th/>I

T zsst

*s£^

'T oj ^J

0.2

4-^Sh

a-2 ,0

1 I.U

...

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A U.S. GOVERNMENT PRINTING OFFICE: 1963 O - 635138

LI. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the 'following listing of the divisions and sections engaged in technical work.

In general, each section carries out specialized research, development, and engineering) in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the

front cover. WASHINGTON, D. C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering Metrology.

Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standard Refer- ence Materials. Applied Analytical Research, Crystal Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Polymers. Macromolecules: Synthesis and Structure. Polymer Chemistry. Polymer Physics. Polymer Characterization. Polymer Evaluation and Testing. Applied Polymer Standards and Research. Dental Research.

Metallurgy. Engineering Metallurgy. Microscopy and Diffraction. Metal Reactions. Metal Physics. Electrolysis and Metal Deposition.

Inorganic Solids. Engineering Ceramics. Glass. Solid State Chemistry. Crystal Growth. Physical Properties.

Crystallography.

Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Metallic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics. Operations Research. Data Accessing Systems. Components and Techniques. Computer Technology. Measurements Automation.

Engineering Applications. Systems Analysis.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Far Ultraviolet Physics. Solid State Physics. Electron Physics. Atomic Physics. Plasma Spectroscopy.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Ele- mentary Processes. Mass Spectrometry. Photochemistry and Radiation Chemistry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering Laboratory. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Cryogenic Technical Services. CENTRAL RADIO PROPAGATION LABORATORY

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Vertical Soundings Research.

Radio Propagation Engineering. Data Reduction Instrumentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Systems. Applied Electromagnetic Theory. High Frequency and Very High Frequency Research. Fre- quency Utilization. Modulation Research. Antenna Research. Radiodetermination.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. High Latitude Ionosphere

Physics. Ionosphere and Exosphere Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.

RADIO STANDARDS LABORATORY

Radio Physics. Radio Broadcast Service. Radio and Microwave Materials. Atomic Frequency and Time-Interval

Standards. Radio Plasma. Millimeter-Wave Research.

Circuit Standards. High Frequency Electrical Standards. High Frequency Calibration Services. High Frequency

Impedance Standards. Microwave Calibration Services. Microwave Circuit Standards. Low Frequency Calibration

Services.
NBS