U.S. DEPARTMENT OF COMMERCE • National Telecommunications and Information Administration

report series

NTIA Report TR-12-484

Free-Field Measurements of the 

Electrical Properties of Soil Using the 

Surface Wave Propagation Between 

Two Monopole Antennas

January 2012

NTIA Report TR-12-484

Free-Field Measurements of the 

Electrical Properties of Soil Using the 

Surface Wave Propagation Between 

Two Monopole Antennas

Nicholas DeMinco

Robert T. Johnk

Paul McKenna

Chriss A. Hammerschmidt

J. Wayde Allen

U.S. DEPARTMENT OF COMMERCE

December 2011

iii

DISCLAIMER

Certain commercial equipment and materials are identified in this report to specify adequately 

the technical aspects of the reported results. In no case does such identification imply 

recommendations or endorsement by the National Telecommunications and Information 

Administration, nor does it imply that the material or equipment identified is the best available 

for this purpose.

v

CONTENTS

Page

FIGURES....................................................................................................................................... vi

TABLES ........................................................................................................................................ ix

1 Introduction...................................................................................................................................1

2 Monopole Transmission Measurement System............................................................................3

3 Ground-Wave Propagation Computation Method and The Development of the 

Undisturbed-Field Model...........................................................................................................6

4 Electric Field Penetration Depth of the Soil and its Effect on Ground-Wave 

Propagation ..............................................................................................................................12

4.1 Computed Sensitivity of Propagation Loss to Values of Epsilon (εr) and 

Sigma (σ) .................................................................................................................................15

5 Soil Dielectric Properties Obtained at Table Mountain Using Monopole 

Transmission Measurements....................................................................................................16

6 Conclusion ..................................................................................................................................19

7 References...................................................................................................................................20

APPENDIX A Figures showing results of Computations and Measurements for 

Dielectric Constant and Conductivity Determination with All Antenna Heights 

Equal to Zero............................................................................................................................21
vi

FIGURES

Page

Figure 1. Schematic diagram of the monopole measurement system............................................. 3

Figure 2. Flowchart of the sequence used to post process the monopole transmission 

measurements. ............................................................................................................. 5

Figure 3. (a) Ungated and time-gated (0–36 ns) amplitude spectra for 700 MHz 

resonant monopoles separated at d = 8 m. (b) Corresponding gated and 

ungated time-domain waveforms. ............................................................................... 5

Figure 4. Skin depth for 1/e E-field attenuation versus frequency for various media 

types........................................................................................................................... 14

Figure 5. Skin depth for 1/e E-field attenuation versus frequency for various media 

types for lower frequencies........................................................................................ 14

Figure A-1. Propagation loss versus frequency for three types of ground for a 

distance of 10 meters. ................................................................................................ 21

Figure A-2. Propagation loss versus epsilon for sigma = 0.001 and distance = 10.0 

meters with frequency as a parameter. ...................................................................... 22

Figure A-3. Propagation loss versus epsilon for sigma 0.020 and distance = 10.0 

meters with frequency as a parameter. ...................................................................... 22

Figure A-4. Propagation loss versus sigma for epsilon = 4.0 and distance = 10.0 

meters with frequency as a parameter. ...................................................................... 23

Figure A-5. Propagation loss versus sigma for epsilon = 25.0 and distance = 10.0 

meters with frequency as a parameter. ...................................................................... 23

Figure A-6. Propagation loss versus frequency for epsilon = 4.0 with sigma as a 

parameter for a distance of 10 meters with all curves merging together................... 24

Figure A-7. Comparisons of propagation loss predictions with monopole 

measurements (August 2009) at 150.5 MHz. ............................................................ 24

Figure A-8. Comparisons of propagation loss predictions with monopole 

measurements (August 2009) taken at 250 MHz. ..................................................... 25

Figure A-9. Comparisons of propagation loss predictions with monopole 

measurements (August 2009) taken at 430 MHz. ..................................................... 25

Figure A-10. Comparisons of propagation loss predictions with monopole 

measurements (August 2009) at 700 MHz. ............................................................... 26
vii

Figure A-11. Comparisons of propagation loss predictions with monopole 

measurements (August 2009) at 915 MHz. ............................................................... 26

Figure A-12. Corrected measured propagation loss data (August 2009) versus 

distance compared to predicted loss for 30 MHz with εr = 6.0 and σ as a 

parameter. .................................................................................................................. 27

Figure A-13. Corrected measured propagation loss data (August 2009) versus 

distance compared to predicted loss for 60 MHz with εr = 6.0 and σ as a 

parameter. .................................................................................................................. 27

Figure A-14. Corrected measured propagation loss data (August 2009) versus 

distance compared to predicted loss for 30 MHz with εr = 7.0 and σ as a 

parameter. .................................................................................................................. 28

Figure A-15. Corrected measured propagation loss data (August 2009) versus 

distance compared to predicted loss for 60 MHz with εr = 7.0 and σ as a 

parameter. .................................................................................................................. 28

Figure A-16.Corrected measured propagation loss data (August 2009) versus 

distance compared to predicted loss for 30 MHz with εr = 6.5 and σ as a 

parameter. .................................................................................................................. 29

Figure A-17. Corrected measured propagation loss data (August 2009) versus 

distance compared to predicted loss for 60 MHz with εr = 6.5 and σ as a 

parameter. .................................................................................................................. 29

Figure A-18. Corrected measured propagation loss data versus distance compared to 

predicted loss for 30 MHz with εr = 6.7 and σ as a parameter. ................................. 30

Figure A-19. Corrected measured propagation loss data (August 2009) versus 

distance compared to predicted loss for 60 MHz with εr = 6.7 and σ as a 

parameter. .................................................................................................................. 30

Figure A-20. Comparisons of propagation loss predictions with monopole 

measurements (May 2010) at 150 MHz with σ = 0.005............................................ 31

Figure A-21. Comparisons of propagation loss predictions with monopole 

measurements (May 2010) at 250 MHz with σ = 0.005............................................ 31

Figure A-22. Comparisons of propagation loss predictions with monopole 

measurements (May 2010) at 430 MHz with σ = 0.005............................................ 32

Figure A-23. Comparisons of propagation loss predictions with monopole 

measurements (May 2010) at 700 MHz with σ = 0.005............................................ 32

Figure A-24. Comparisons of propagation loss predictions with monopole 

measurements (May 2010) at 915 MHz with σ = 0.005............................................ 33
viii

Figure A-25. Comparisons of propagation loss with monopole measurements (May 

2010) at 60 MHz with varying σ and εr = 7.0............................................................ 33

Figure A-26. Comparisons of propagation loss with monopole measurements (May 

2010) at 90 MHz with varying σ and εr = 7.0............................................................ 34

Figure A-27. Comparisons of propagation loss with monopole measurements (May 

2010) at 60 MHz with varying σ and εr = 7.5............................................................ 34

Figure A-28. Comparisons of propagation loss with monopole measurements (May 

2010) at 60 MHz with varying σ and εr = 8.0............................................................ 35

Figure A-29. Comparisons of propagation loss with monopole measurements (May 

2010) at 120 MHz with varying σ and εr = 9.0.......................................................... 35
ix

TABLES

Page

Table 1. Values of permittivity (ε) for the distance range of 8 to 10 meters at 

frequencies at and above 150.0 MHz (August 2009 data)......................................... 16

Table 2. Values of εr for the various distances, frequencies, and permittivity for the 

distance range of 8 to 10 meters for frequencies below 150 MHz (August 

2009 Data). ................................................................................................................ 17

Table 3. Values of εr at different frequencies at a distance of 8.3 meters (May 2010 

data). .......................................................................................................................... 18

Table 4. Values of conductivity and permittivity, for various frequencies for the 

single distance of 8.3 meters (May 2010 data). ......................................................... 18

FREE-FIELD MEASUREMENTS OF THE ELECTRICAL PROPERTIES OF SOIL 

USING THE SURFACE WAVE PROPAGATION BETWEEN TWO MONOPOLE 

ANTENNAS 

Nicholas DeMinco, Robert T. Johnk, Paul McKenna, 

Chriss A. Hammerschmidt, J. Wayde Allen1

This report describes one of three free-field radio frequency (RF) measurement 

systems that are currently being developed by engineers at the Institute for 

Telecommunication Sciences (NTIA/ITS). The objective is to provide estimates 

of the electrical properties of the ground (permittivity and conductivity) over 

which the measurement systems are deployed. This measurement system uses 

transmission loss measurements between two monopoles placed close to the 

ground at specific separation distances. Soil properties are extracted by comparing 

measured data with known analytical models and optimizing the results. 

Key words: antenna; radio-wave propagation; deconvolution; Fourier transform; frequency 

domain; gating; monopole antenna; reflectivity, signal processing, S-parameters, 

time domain; transmission loss; propagation measurement

1 INTRODUCTION

A near-earth propagation measurements program was initiated at the Institute for 

Telecommunication Sciences (NTIA/ITS) Table Mountain Field Site (TMFS) in August 2009 

under the sponsorship of the Naval Research Laboratory (NRL). A second set of measurements 

sponsored by the Table Mountain Research Project were performed in May 2010. The purpose of 

these efforts was to develop improved propagation prediction tools and models for close-in 

distances (2–250 m) and low antenna heights (0–3 m). While comparing measured and modeled 

results, questions arose about the assumed dielectric permittivity and conductivity of the soil at 

the TMFS. These ground constants can have a significant influence on RF propagation 

predictions near the ground and need to be accurately characterized. 

The system described in Section 2 of this report performs two-port transmission measurements 

between two resonant ground-plane mounted monopoles placed at various separation distances 

ranging from 2 to 250 meters. The measurements were conducted along a main access road at 

various road positions using stepped-frequency transmission measurements over the Earth 

between the monopoles. For the set of measurements taken in August 2009, the separation 

distances were varied within the full range; for the second set of measurements taken in May

2010, the separation distance was fixed at 8.3 meters. It is desirable to locate the antennas as 

close to ground as possible, so that the predominant mode of propagation is by means of the 

surface wave. The monopoles were placed 8.9 centimeters above ground to simplify feeding the 

 

1 The authors are with the Institute for Telecommunication Sciences, National Telecommunications and Information 

Administration, U.S. Department of Commerce, Boulder, CO 80305.
2

antenna from below the ground plane while maintaining the antenna height as close to zero with 

respect to a wavelength as possible. 

For the frequencies under consideration (30 to 915 MHz), this is essentially equivalent to a zero 

height antenna, because the wavelengths are between 0.328 and 10.0 meters. The propagation 

between the antennas is predominantly via the Norton surface wave [1]–[3], because the 

antennas are very close to the Earth. At this height, the direct and reflected waves cancel each 

other, resulting in only the surface wave component of the ground wave as the mechanism for 

radio-wave propagation. The skin depth of the propagating wave into the soil is significant, so 

the use of the surface wave effectively probes the ground, resulting in an aggregate measure of 

the ground constants of the soil. Actual skin depths for different values of sigma (σ) and epsilon 

(εr) will be presented in Section 4.
3

2 MONOPOLE TRANSMISSION MEASUREMENT SYSTEM

The system, a schematic of which is shown in Figure 1, uses a vector network analyzer (VNA) to 

perform stepped-frequency transmission (S-parameter) measurements over a wide frequency 

range between two resonant monopoles separated at a distance d. The monopoles are mounted at 

the center of circular aluminum ground planes, and are coaxially fed on the bottom side of the

ground planes. Each antenna is soldered to a coaxial feedthrough that provides a type-N 

connection from the bottom. Dielectric spacers on the plates provide enough clearance for a 

coaxial cable to feed the monopoles. 

The nominal height of the ground planes is h1=h2=8.9 cm. The VNA is configured to perform 

stepped-frequency measurements of the S-parameter S21. Measurement data were acquired over a 

frequency range from 300 kHz to 6 GHz. Data for the analysis was extracted from this 

measurement set over a frequency range subset of 30 MHz to 915 MHz, because of the limited 

dynamic range outside the operating frequency range of the resonant monopole antennas.

The system is calibrated by connecting the transmitting and receiving cables together and 

performing a through calibration. The cables are then connected to the antennas and the 

transmission loss is measured.

VNA

S21

(ground)

Tx

Monopole

Rx

Monopole

d

h1 h2

Tx

Port 2

Tx

Port 1

RF Cable RF Cable

VNA

S21

(ground)

Tx

Monopole

Rx

Monopole

d

h1 h2

Tx

Port 2

Tx

Port 1

RF Cable RF Cable

Figure 1. Schematic diagram of the monopole measurement system.

Both magnitude and phase information are acquired, which permits transformations to and from 

the time and frequency domain. This capability provides more insight into the propagation over 

the ground and permits processing to enhance accuracy and signal fidelity by windowing the 

stepped frequency data and time gating the time domain waveform. 

A flow chart showing the signal processing sequence is shown in Figure 2. These steppedfrequency data are windowed to suppress undesired out-of-band effects, then inverse Fourier 

transformed to obtain a time-domain waveform. Time gating is then applied to isolate the desired 

propagation events and to improve signal-to-noise performance. Finally, the gated waveform is
4

Fourier transformed to yield the gated S21g. Figure 3 depicts the results of this process and shows 

the influence on the amplitude spectra when the effects of a nearby reflector are removed using 

time gating. The corresponding ungated and gated time domain waveforms are shown in Figure 

3(b). The presence of a nearby scatterer manifests itself in the secondary wavelet that follows the 

main propagation event. After this packet is gated out and Fourier transformed, the resulting S21

is smoothed out and systematic scalloping is removed. A combination of signal processing and 

time gating were used to remove the effects of nearby reflectors and scatters to isolate the 

coupling between the antennas. This produces a significant improvement in signal fidelity and 

signal-to-noise ratio.

The surface wave loss measurements at the TMFS were performed by measuring the propagation 

loss between two matched monopole antennas each mounted on a separate circular ground 

planes using techniques described in the previous paragraphs. The ground constants are 

determined by using the measured loss of the surface wave between two antennas at known 

distances. The antennas were a set of quarter-wave monopoles resonant at 150, 250, 430, 700, 

and 915 MHz. The ground planes were approximately one-quarter wavelength in radius. The 

antennas were spaced at known separation distances and placed on the ground at a height of 

approximately zero meters (8.9 cm) above ground. Practical limitations of feeding the antennas 

prevented heights less than 8.9 cm, but analysis has verified that there is a negligible difference 

in results between the 8.9 cm and zero antenna heights.

The approach was to compute the propagation losses between the two antennas at the fixed 

distances for a variety of ground constants and frequencies and match the measured losses to the 

appropriate curves to obtain the various ground constants. The distances between the antennas at 

which measurements were taken in 2009 included: 2, 3, 4, 5, 8, 10, 15, 20, 25, 30, 35, 40, 50, 80, 

100, 150, 180, 200, and 250 meters. Data for this scenario reflects a road section with a flat 

terrain measurement environment. The portion of the path used for performing the measurements 

was line-of-sight. The frequency was stepped from 300 kHz to 6000 MHz while the antennas 

remained stationary at each of the distances listed above. In 2010, a second set of measurement 

data was taken at the same location, but only at a fixed distance of 8.3 meters.
5

Stepped-Frequency

S21(f)

Window (BP Filter)

fhigh

f

low

Inverse Fourier Transform

Time-Domain Waveform

Time Gate

Fourier Transform

S21g(f)

Stepped-Frequency

S21(f)

Stepped-Frequency

S21(f)

Window (BP Filter)

fhigh

f

low

Inverse Fourier Transform

Time-Domain Waveform

Time Gate

Fourier Transform

S21g(f)

Figure 2. Flowchart of the sequence used to post process the monopole transmission

measurements.

(a)

0 400 800 1200 1600 Frequency (MHz)

-140

-120

-100

-80

-60

|S21| (dB)

250 MHz Monopole S21

S21 time gated

0 20 40 60 80 100 Time (ns)

-0.00012

-8E-005

-4E-005

0

4E-005

8E-005

0.00012

s21(t)

desired propagation

packet

spurious reflection

(b)

0 400 800 1200 1600 Frequency (MHz)

-140

-120

-100

-80

-60

|S21| (dB)

250 MHz Monopole S21

S21 time gated

0 20 40 60 80 100 Time (ns)

-0.00012

-8E-005

-4E-005

0

4E-005

8E-005

0.00012

s21(t)

desired propagation

packet

spurious reflection

Figure 3. (a) Ungated and time-gated (0–36 ns) amplitude spectra for 700 MHz resonant 

monopoles separated at d = 8 m. (b) Corresponding gated and ungated time-domain waveforms.
6

3 GROUND-WAVE PROPAGATION COMPUTATION METHOD AND THE 

DEVELOPMENT OF THE UNDISTURBED-FIELD MODEL 

The ground wave includes the direct line-of-sight space wave, the ground-reflected wave, and 

the Norton surface wave that propagates along the Earth. The Norton surface wave will hereafter 

be referred to as a surface wave in this report. Propagation of the ground wave depends on the 

relative geometry of the transmitter and receiver locations and antenna heights. The radio wave 

propagates primarily as a surface wave when both the transmitter and receiver antennas are close 

to the Earth (approximately 0.25 wavelength or less), because the direct and ground-reflected 

waves in the space wave components of the ground wave cancel each other out. As a result, the 

surface wave is the only wave component that continues to propagate. 

This cancellation occurs because the elevation angle is zero, the two waves (direct and reflected) 

are equal amplitude and opposite in phase, and they travel the same distance. The surface wave is 

predominantly vertically polarized, since the ground conductivity effectively attenuates most of 

the horizontal electric field component at a rate many times that for the vertical component of the 

electric field. When one or both antennas are elevated above the ground to a significant height 

with respect to a wavelength (greater than 0.25 wavelength), the space wave predominates. 

When the antennas are close to the ground with respect to a wavelength, the surface wave 

propagates along and is guided by the Earth’s surface. This is similar to the way that an 

electromagnetic wave is guided along a transmission line. The attenuation of this wave is directly 

affected by the ground constants of the Earth along which it travels [1]. Charges induced in the 

Earth by the surface wave travel with the surface wave and create a current in the Earth. The 

Earth carrying this current can be modeled as a leaky capacitor ( a capacitive reactance shunted 

by a resistance). The characteristics of the Earth as a conductor are therefore represented by this 

equivalent parallel resistor-capacitor circuit. The Earth’s conductivity acts as a resistor and the 

Earth’s dielectric constant acts as a capacitor. As the surface wave passes over the surface of the 

Earth, it is attenuated due to the current flowing through the Earth’s resistance. Energy is taken 

from the surface wave to supply the losses in the ground. 

Since the equivalent circuit of the Earth is a resistor of resistance R (ohms) and capacitor of 

capacitance C (Farads) in parallel, more current flows through the resistance at lower 

frequencies, R<<1/ωC (ω = 2πf where f is the frequency in Hertz); and the attenuation factor is 

then primarily dependent on the conductivity of the Earth and the frequency. At lower HF 

frequencies, AM broadcast (medium frequencies), and lower frequencies in the LF band (below 

300 kHz), the Earth can be regarded as being purely resistive in nature. For frequencies above 

about 150 MHz, the impedance represented by the Earth is primarily capacitive, so the 

attenuation factor for the surface wave at a given physical distance is determined by the 

dielectric constant of the Earth and the frequency [1]. The impedance of the capacitor decreases 

with increasing frequency.

The ITS Undisturbed-Field Model was originally developed for very short-range propagation for 

distances of 2 to 30 meters. Subsequently, the model was shown to be accurate for flat terrain up 

to 2 kilometers [2]. The minimum distance is based on staying at distances greater than the 

distance within which the reactive field of the antenna is present. This is a distance of one 

wavelength. Extensive testing with exact models at close-in distances has verified the 
7

computation accuracy for distances as close as 2 meters over the 150 MHz to 6000 MHz 

frequency band [2].

This method involves the calculation of the undisturbed electric field as a function of antenna 

heights, distance, frequency, and the ground constants from which the path loss is derived. The 

undisturbed field is that electric field produced by a transmitting antenna at different distances 

and heights above ground without any field-disturbing factors such as other receiver antennas in 

the proximity of the receiver antenna location. The undisturbed electric field technique includes 

near-field effects of the transmit antenna, the complex two-ray model, antenna near-field and farfield response, and the surface wave. Since this is a line-of-sight model, the ground is assumed to 

be flat over the distance of 2 kilometers or less with no irregular terrain present. For distances of 

less than 5 kilometers, the curvature of the Earth has a negligible effect and can be assumed to be 

flat for frequencies less than 6 GHz over a smooth Earth [3]. The model was originally 

developed for antenna heights of 1 to 3 meters, but further improvements in the model have 

demonstrated that the model can be used for antenna height ranges from 0 to 1 meter. It is valid 

for frequencies from 150 MHz to 6000 MHz [2].

The space wave component (direct and reflected waves) and surface wave component of the ITS 

Undisturbed-Field Model are based on the Sommerfeld integral arising from the solution for the 

field due to an elemental dipole above a uniform, finitely-conducting, dielectric half space [4]–

[6]. The half space is bounded by the Earth-air interface. Norton [4], [5], in his effort to simplify 

the expressions developed by Sommerfeld [7], derived equations that clearly show the surface 

wave and space wave components. Jordan [8] simplified Norton’s equations by deleting the 

higher order terms for the vertical and radial directed components of the electric field in 

cylindrical coordinates. These higher order terms represent the induction and near field of the 

antenna and diminish rapidly with distance. Jordan [8] further reduced the equation complexity 

by combining the vector equations for the vertical and radial directed field components, and then 

separating the resulting equation into a total space (direct and reflected waves) and surface wave 

components. At distances within the line of sight, the field strength of the space and the surface 

wave for vertical polarization is given by [4], [5] and [8]:

30 cos

1 2

1 2

















 

 

r

e

R

r

e

E i IkL

ikr

v

ikr

space

(1)

 

2

2

2

2 2 2

2

sin 30 1 1 2 cos 1

2

ikr

surface v

e

E i IkL R A u u

r







 

        

, (2)

where:

k = 2π/λ,

A is the flat-Earth attenuation function,

I is the peak dipole current amplitude in amperes,

L is the length of the dipole in meters,

u

2

= (εr-iσ/ωε0)

-1

,

ω is the angular frequency and is equal to 2πf,
8

f is the radio frequency in Hertz,

μ is the magnetic permeability of the Earth, μ = μr ·4π·10-7henries per meter,

μr is the relative permeability of the Earth,

ε =εr·ε0= εr·8.85·10-12= the permittivity of the Earth in Farads per meter,

εr is the relative permittivity of the Earth,

ε0 is the permittivity of free space in Farads per meter,

σ is the conductivity of the Earth in Siemens per meter,



is the angle representing the direction of the incident wave measured with respect to 

the Earth’s surface,

h1 is the height of the transmitter antenna in meters,

h2 is the height of the receiver antenna in meters,

d is the horizontal distance along the Earth.

The distance 

   

2

1

2

1 2

2

r1  d  h  h

is the distance between the dipole and the observation point 

in meters.

The distance 

   

1

2

2 2

2 1 2 r d h h   

is the distance between the dipole image and the observation 

point in meters. 

Rv is the complex reflection coefficient for vertical polarization and is given by:







 













 







2

0 0

2

0 0

sin cos

sin cos

















  

































  



















i i

i i

R

r r

r r

v

(3)

Equations (1) through (3) are different for horizontal polarization and can be found in [8]. 

The attenuation function, A, is the ratio of the electric field from a short vertical dipole over the 

lossy Earth’s surface to that field from the same short vertical dipole located on a flat perfectly 

conducting surface, and takes into account the ground losses. There are two forms of the 

attenuation function presented in this report. The ITS Undisturbed Field Model was developed in 

several versions, with each version improving on the previous versions. In response to a request 

from the NTIA Office of Spectrum Management, model development was initiated to 

specifically address the application of propagation loss predictions for very low antenna heights 

and close-in distances [2]. 

The original concept for development of a propagation model [2] used the Numerical 

Electromagnetic Code (NEC) software [12], which uses a method of moments technique in 

electromagnetics to compute the electric field versus frequency, ground constants, antenna 

heights, and distances. This electric field is then converted to a basic transmission loss as 

described in [2]. This original method was cumbersome and required running the NEC software 
9

many times to get results over a variety of input parameters and scenarios to create lookup tables 

to cover the various parameter ranges. This was Version 0 of the ITS Undisturbed-Field Model. 

Version 0 needed to be streamlined into a more efficient and flexible computation method in the 

form of a computer model that would rapidly compute propagation loss to be used in system 

performance computations and other analysis applications. In response to a Naval Research 

Laboratory request to further develop the initial concept into a fast efficient computation model, 

Version 1 was developed. The approximate attenuation function described by (4) and (5) is used 

in Version 1 of the Undisturbed-Field Model which is described in this section. It uses simple 

algebraic equations to perform the calculations. Version 2 uses the more exact representation of 

the attenuation function and is valid for a wider variety of parameters than Version 1. It uses a 

more complex mathematical algorithm to perform its computations when compared to the simple 

equations of Version 1. Version 2 contains the more precise form of the attenuation function that

is used in the ITS Undisturbed-Field Model to perform the propagation loss computation in this 

analysis.

Version 1 of the ITS Undisturbed Field Model uses the original Norton approximation to the 

attenuation function. Norton simplified the exact and more complex equations for the surface 

wave attenuation function into two forms that are more amenable to calculation. Version 1 with

the Norton approximations to the flat-Earth attenuation [4], [5] function of the surface wave can 

be easily implemented on a programmable calculator and is reasonably accurate for line-of-sight 

propagation [6]. 

The Version 1 attenuation function, A, is given by:

for p0 < 4.5 and all b: 

 

2 0

0 0

5

0.43 0.01 0 8

sin

2

p

p p p

A e b e



 

   

          

(4a)

for p0 > 4.5 and all b:

 

0

5

0 8

0

1

sin

2 3.7 2

p p

A b e

p

    

           

, (4b)

where for vertical polarization:

   

 

   

2

0 2

2

1

3

cos

54 10

1

tan

18 10

r

R km f MHz b

p

x

f MHz

b

x











   







(5a)
10

and for horizontal polarization:

 

   

4

0

1

3

6 10

cos

1

tan

18 10

r

R km x

p

b

f MHz

b

x

 













, (5b)

where:

 

3

2 R km r 10

 

is the distance between the observation point and the dipole image in 

km,

σ is the conductivity of the Earth in Siemens per meter,

εr is the relative permittivity of the Earth,

f(MHz) is the frequency in MHz. 

These results are approximations. More exact results were sought for implementation in the ITS 

Undisturbed-Field Model.

Version 2 uses Norton’s more exact mathematical algorithm to compute the attenuation function 

for the more precise approximations ((6) and (7)) to the flat-Earth attenuation function. It is 

accurate for a wider range of parameters, but is more difficult to implement. This was derived by 

Norton from the original Sommerfeld formulation [7] for the flat-Earth attenuation function of 

the vertically polarized surface wave [5] and is given by:

 

1

1 1 1

p A i p e erfc i p 

   , (6)

where

2 2 2 2

1 0 2

i b k r p i p e

  

  

     

(7a)

  N r

N

1 cos

1

  

(7b)

1

2

1

2 0

r

k

N i

k







 

      

(7c)

1 0

2 0 0

r

k i

k



  



  

 

     



(7d)

   

2

1

2

1 2

2

r2  d  h  h

(7e)
11 1 2

2

cos .

r

h h

r







(7f)

The horizontal component of the surface wave attenuates at a rate several orders of magnitude 

greater than the vertical component and has a magnitude that is negligible in comparison to the 

vertically polarized component of the surface wave [8].

Equations (6) and (7) are implemented in Version 2 of the ITS Undisturbed-Field Model used for 

computation of the propagation losses. The complementary error function, designated by erfc in 

(6), is described in [9]. The parameters p0 and b are as defined above (see (5a) and (5b)), and

i  1 .

The field strength at small distances is directly proportional to the square root of the power 

radiated by the transmitter and the directivity of the antenna in the horizontal and vertical planes. 

If the antenna is non-directional in the horizontal plane and has a vertical directional pattern that 

is proportional to the cosine of the elevation angle (this corresponds to a short vertical antenna), 

then the electric field at one kilometer for an effective radiated power of one kilowatt is 300 

mV/m [1]. The flat-Earth attenuation function, A, depends on frequency, distance, and the 

ground constants of the Earth along which the wave is traveling. A numerical distance, p0, and 

phase angle, b, can be computed and are functions of frequency, ground constants, and distance 

in wavelengths. 

If the numerical distance, p0, is less than one, then the attenuation function is very close to one, 

and, as a result, for distances close to the transmitting antenna the losses in the Earth have very 

little effect on the electric-field strength of the surface wave. In this region, the electric field 

strength is inversely proportional to distance. For situations where the numerical distance 

becomes greater than unity, the attenuation function rapidly decreases in magnitude. When the 

numerical distance becomes greater than 10, the attenuation factor is also inversely proportional 

to distance. In this circumstance, the combination of the attenuation factor and the un-attenuated 

electric field being inversely proportional to distance results in the electric field strength of the 

surface wave being inversely proportional to the square of the distance.
12

4 ELECTRIC FIELD PENETRATION DEPTH OF THE SOIL AND ITS EFFECT ON 

GROUND-WAVE PROPAGATION

The depth to which the ground currents and electric field penetrate below the Earth’s surface and 

still maintain an appreciable magnitude is determined by the average values of the Earth 

conductivity (σ) and relative permittivity (εr), and the frequency. Penetration depth is similar to a 

skin depth phenomenon in a good conductor, but the Earth is a poor conductor. The skin depth 

ranges from a fraction of a meter at the highest frequencies for VHF communications to tens of 

meters at AM broadcast and lower frequencies. For this reason, ground-wave propagation at the 

lower frequencies is not particularly dependent on properties at the actual ground surface. 

Therefore, a recent rainfall which would result in a dramatic change of permittivity at the ground 

surface would not significantly affect propagation at MF and LF frequencies. However, at VHF 

frequencies a recent rainfall could affect the propagation of radio waves due to the additional 

moisture content of the ground near the ground surface.

The electric field strength at a distance z below the surface of the Earth is given by [10]: 

0

,

z E E e



(8)

where:

E0 is the electric field intensity at the surface of the Earth,

z is the depth in meters below the surface of the Earth,

α is the attenuation per meter of the electric field intensity

The attenuation per meter α is given by:

2

1 1 1 ,

2 2



  



 

      

(9)

where:

ω is the angular frequency and is equal to 2πf,

f is radio frequency in Hertz,

μ is the magnetic permeability of the Earth μ = μr · 4π x 10-7 Henries per meter,

μr is the relative permeability,

ε = the permittivity of the Earth = εr · (8.85 x 10-12 ) Farads per meter,

εr is the relative permittivity of the Earth,

σ is the conductivity of the Earth in Siemens per meter.
13

The distance the wave must travel in a lossy medium to reduce its amplitude to e

-1

=0.368 of its 

value at the surface is δ = 1/α meters and is called the skin depth of the lossy medium. For other 

values of attenuation of the electric field, r=e

-αz, one can use α to determine the distance z below 

the surface where the electric field is attenuated to that ratio r. The ratio r is always less than or 

equal to 1. The distance z is given by:

ln r

z - ,





(10)

where lnr is the natural logarithm of r. 

An example is where f=300 kHz, μr = 1 for a nonmagnetic Earth, εr = 15 for average ground, σ = 

.005 for average ground. The attenuation α is calculated as .0751 per meter and δ is calculated as 

1/α = 13.32 meters.

The skin depth is the distance at which the electric field is e-1or .368 (36.8 percent) of its value 

at the surface of the Earth [10]. The electric field at this large percentage does not represent a 

significant attenuation of the electric field. Some applications may require a lower electric field 

percentage such as 10 percent. If the distance, z, at which the electric field is .1 (10 percent) of its 

value at the surface is desired, then ln r is ln (.1) = -2.3026, and α = .0751, so 

z . / .      2 3026 30 66  

meters. Figure 4 shows the skin depth of several types of media as a 

function of frequency. The skin depth does not vary by significant amounts for each media type 

at these frequencies. Figure 4 demonstrates how significant the different ground constants are in 

affecting the magnitude of the skin depth. It shows that the skin depth is quite large for poor and 

average ground. Figure 5 is an expansion of Figure 4 along the frequency axis to show the skin 

depth in the 100 kHz to 10 MHz range, and demonstrates how large the skin depths are below 

2 MHz.
14

0

2.5

5.0

7.5

10.0

12.5

0

1x10

3 2x103 3x103 4x103 5x103 6x103

Sigma = 5.0, Epsilon = 81.0 Sea Water

Sigma = 0.010, Epsilon = 81.0 Fresh Water

Sigma = 0.020, Epsilon = 25.0 Good Ground

Sigma = 0.005, Epsilon = 15.0, Average Ground

Sigma = 0.005, Epsilon = 6.0 Less Than Average Ground

Sigma = 0.001, Epsilon = 4.0 Poor Ground

Frequency (MHz)

Skin Depth (m)

Skin Depth for 1/e E-Field Attenuation Versus Frequency With Media Type as Parameter

Figure 4. Skin depth for 1/e E-field attenuation versus frequency for various media types.

0

10

20

30

40

0 2 4 6 8 10

 = 5.0, 

r

= 81.0 Sea Water

 = 0.010, 

r

= 81.0 Fresh Water

 = 0.020, 

r

= 25.0 Good Ground

 = 0.005, 

r

= 6.0 Less Than Average Ground

 = 0.005, 

r

= 15.0 Average Ground

 = 0.001, 

r

= 4.0 Poor Ground

Frequency (MHz)

Skin Depth (meters)

Figure 5. Skin depth for 1/e E-field attenuation versus frequency for various media types for 

lower frequencies.
15

4.1 Computed Sensitivity of Propagation Loss to Values of Epsilon (εr) and Sigma (σ)

The Undisturbed-Field Model [2] developed at ITS was used to perform all propagation loss 

prediction computations as a function of antenna heights, relative dielectric constant (εr) , 

conductivity (σ), frequency, and distance. The results of these computations are shown in the 

figures in Appendix A. The model has been verified with comparisons to more exact models [2]

and measured data.

Figure A-1 shows the propagation loss for three types of ground for a distance of 10 meters for 

antenna heights at zero meters. There is a significant difference in the predicted propagation loss 

between poor (εr = 4.0, σ = 0.001) and good ground (εr = 25.0, σ = 0.020). As part of this 

analysis effort, a study was performed to determine the sensitivity of the propagation loss to 

variations in conductivity (σ) and relative permittivity (εr). Figures A-2 through A-5 show the 

sensitivity of propagation loss to σ and εr for a separation distance of 10 meters. The heights of 

the transmitter and receiver antennas for all figures in the Appendix are equal to zero. The 

computations and measurements are based on heights of 8.9 centimeters which is equivalent to a 

zero height at these frequencies. Computations at heights of 8.9 centimeters and 0.0 centimeters 

verify this assumption. Figure A-2 shows that for a low conductivity, the loss is very dependent 

on the value of εr, but Figure A-3 shows that for a higher σ the loss has less dependence on εr, 

particularly for frequencies at and below 150 MHz. Figures A-4 and A-5 show that the loss is 

dependent on σ only for frequencies at and below 150 MHz. The sensitivity to variation in σ is 

greater for lower values of εr. Figure A-4 has a value of εr = 4 and a higher sensitivity to changes 

in σ, whereas Figure A-5 has a value of ε r = 25 and a much lower sensitivity to variations in σ. 

Figure A-6 is a plot of loss versus σ with an expanded scale and shows how insensitive the loss 

is to variations in σ for frequencies above 150 MHz. Figure A-6 shows that there is some 

capability to determine σ from lower frequency data at and below 150 MHz.
16

5 SOIL DIELECTRIC PROPERTIES OBTAINED AT TABLE MOUNTAIN USING 

MONOPOLE TRANSMISSION MEASUREMENTS

Figures A-7 through A-11 show the results of comparing predictions to measurements for data

taken in late August of 2009. The distance and vertical scales were expanded for better vertical 

scale resolution. Measured data was originally recorded over separation distances ranging from 2

to 250 meters using monopole antenna pairs resonant at the five frequencies (150.5, 250, 430, 

700 and 915 MHz). The data show that the dielectric constants vary over the distance of the 

measurement path. Most data analysis took place over shorter distances. This study concentrated 

on distances in the 5 to 15 meter range. The ground at Table Mountain is not homogeneous, 

which accounts for the erratic variation of loss versus distance shown in Figures A-7 through A11.

These data were available to determine the ground parameters of σ and εr for the measured data 

collected in August 2009. Since the values of σ could not be determined at the frequencies above 

150 MHz as discussed in Section 3.1, only εr was obtained from these plots. This is due to the 

lack of sensitivity of the propagation loss at or above 150 MHz to values of σ. At lower 

frequencies below 150 MHz, the loss is insensitive to variations in εr, but sensitive to variations 

in σ. The permittivity varies as a function of distance and frequency. Table 1 shows the results of 

extracting the values of permittivity from Figures A-7 through A-11 (August 2009 data) for a 

conductivity of σ = 0.005 Siemens per meter. Table 2 shows the values of σ from Figures A-12 

through A-19 (August 2009 data). The average value of εr in Table 1 is approximately 6.0 for the 

first three values of Table 1 and 7.0 for the entire table, so the values of εr of 6.0 to 7.0 were used 

to determine σ, because εr is known to be relatively constant in the 30 to 150 MHz region [11].

Referring to Figures A-2 and A-3 the loss versus εr curves are relatively flat between εr = 6.0 and 

7.0 for frequencies less than 150 MHz. 

Table 1. Values of permittivity (ε) for the distance range of 8 to 10 meters at frequencies at and 

above 150.0 MHz (August 2009 data).

Frequency (MHz) Permittivity, εr Conductivity, σ (S/m)

150.5 7.0 to 8.0 0.005

250.0 6.0 to 7.0 0.005

430.0 4.0 to 5.0 0.005

700.0 7.0 to 9.0 0.005

915.0 8.0 to 9.0 0.005

The analysis using the lower frequencies below 150 MHz was performed to determine σ by 

compensating the measured data to take into account the reduced efficiency of the antennas when 

operating below 150 MHz and then comparing these measured data to the predictions at these 

lower frequencies. The distance range was reduced to 7 to 9 meters to allow expansion of the 

vertical scales for better resolution.
17

Using data at lower frequencies below 150 MHz, this compensation technique was used to 

extract σ, from the measured data shown in Figures A-12 to A-19. The monopole antennas are 

narrowband and resonant at their design frequencies. The raw measured data shows the maximal 

response of these antennas at their resonant frequencies. The compensation technique included a 

correction by applying an impedance mismatch loss in addition to an adjustment of average gain 

at the lower frequencies.

This mismatch and gain compensation information was obtained by modeling the 150 MHz 

monopole antennas at frequencies below 150 MHz using the method of moments technique of 

the NEC software [12]. The NEC software can compute an antenna’s radiation pattern, gain, and 

input impedance characteristics. The physical and electrical structure of the 150 MHz resonant 

monopole on a circular ground plane was used as input to the NEC software. When this antenna 

is analyzed at frequencies other than 150 MHz with the NEC software, the gain, input 

impedance, and radiation pattern are computed at the other frequencies computed. 

The mismatch loss was computed from the computed input impedance using conventional 

techniques as found in [8]. The total degradation in gain and efficiency at frequencies below 150 

MHz was obtained by adding the gain degradation and the impedance mismatch loss. Using the 

150 MHz monopole provided useful data down to 30 MHz. The results from Figures A-12 

through A-19 are summarized in Table 2 for the frequencies listed.

Table 2. Values of εr for the various distances, frequencies, and permittivity for the distance 

range of 8 to 10 meters for frequencies below 150 MHz (August 2009 Data).

Frequency (MHz) Permittivity, εr Conductivity, σ (S/m)

30.0 6.0 0.005

60.0 6.0 0.009

30.0 6.5 0.005

60.0 6.5 0.007

30.0 6.7 0.004

60.0 7.0 0.007

30.0 7.0 0.004

60.0 7.0 0.006

A second set of measured data was recorded in May 2010 using the same stepped frequency 

technique using sets of monopole antennas resonant at 150.5, 250, 430, 700, and 915 MHz, but 

only at a single distance of 8.3 meters. A limited amount of data was available from these 

measurements. It was determined that the relative permittivity (εr) and conductivity (σ) were 

higher for this set of measurements. The results of these May 2010 measurements are shown in 

Figures A-20 through A-24, which are expanded plots for better resolution. These figures were 

used to determine εr of the ground at and above 150 MHz. Table 3 summarizes the values of εr

extracted from Figures A-20 through A-24 for σ = 0.005 Siemens/meter.
18

Table 3. Values of εr at different frequencies at a distance of 8.3 meters (May 2010 data).

Frequency (MHz) Permittivity, εr Conductivity, σ (S/m)

150.5 9.0 to 10.0 0.005

250.0 10.0 0.005

430.0 7.5 0.005

700.0 9.0 0.005

915.0 9.0 0.005

These values of εr from Figures A-20 through A-24 were used to determine the conductivity in

Figures A-25 through A-29 at frequencies below 150 MHz. 

The higher values for εr of the May 2010 data when compared to measurements of the previous 

year (August 2009) were thought to be a result of increased moisture content due to the heavier 

rainfall that occurred prior to the May 2010 measurements. Soil conditions were drier when the 

previous measurements were taken, in August 2009. For both sets of measurements the ground 

was not homogeneous, but this surface wave technique of determining the ground constants 

results in an aggregate measure of the non-homogeneous ground at Table Mountain. 

Figures A-25 through A-29 present the results of comparing the May 2010 measured data to the 

predictions, with plots expanded for better resolution. These figures were used to determine σ of 

the ground for the second set of measurements using the lower frequency compensation 

technique described previously at frequencies below 150 MHz, since σ could not be resolved 

from the measurements above 150 MHz. The plots in these Figures are expanded with better 

vertical scale resolution to facilitate the extraction of data. Table 4 summarizes the results of

extracting the values of σ from Figures A-25 through A-29. Referring to Figures A-2 and A-3 the 

loss versus εr curves are relatively insensitive to changes in εr between εr = 7.0 to 9.0, which were 

the εr values used in Table 4 for determining σ.

Table 4. Values of conductivity and permittivity, for various frequencies for the single distance 

of 8.3 meters (May 2010 data).

Frequency (MHz) Permittivity, εr Conductivity, σ (S/m)

30.0 7.0 0.008

30.0 7.5 0.006

30.0 8.0 0.005

90.0 7.0 0.005

120.0 9.0 0.007
19

6 CONCLUSION

It was determined that the propagation loss of the surface wave is relatively insensitive to σ (the 

conductivity), but does show significant variation with respect to εr (the relative dielectric 

constant) for frequencies including and above about 150 MHz. Lower frequencies below 150 

MHz do show some variation with σ, and small variations at these lower frequencies can be used 

to determine σ. At higher frequencies, the variation of propagation loss could not be used to 

determine σ. This method can be used as a comparison to a vertical incidence (reflection 

coefficient) measurement/analysis effort that is currently underway, and could provide possible 

verification of values of εr obtained with the vertical incidence method. 

Future work would include examining these data above and below 150 MHz using a computer 

program with an optimization algorithm to determine the values of εr and σ. Another area of 

future work would include developing a method that would use the phase angle of the transfer 

function S21 from the measured data with a propagation loss prediction algorithm that contains 

phase angle as an alternative method of obtaining the σ from data at frequencies above and 

below 150 MHz. Separation of the transfer function into real and imaginary components could 

provide better resolution for determination of the σ for comparison to the mathematical 

expressions for propagation loss of the surface wave.
20

7 REFERENCES

[1] F.E Terman, Electronic and Radio Engineering, New York: McGraw-Hill Book Co., 1955, 

pp.803–808.

[2] N. DeMinco, “Propagation loss prediction considerations for close-in distances and lowantenna height applications,” NTIA Report TR-07-449, July 2007.

[3] A. Picquenard, Radio-Wave Propagation, New York: John Wiley& Sons, 1974, p.80.

[4] K.A. Norton, “The calculation of ground-wave field intensity over a finitely conducting 

spherical Earth,” Proceedings of the Institute of Radio Engineers, Vol. 29, No. 12, 

December 1941, pp 623–639.

[5] K.A. Norton, “The propagation of radio waves over the surface of the Earth and in the 

upper atmosphere,” Part I, Proc. IRE, Vol. 24, Oct. 1936, pp 1367–1387; Part II, Proc. 

IRE, Vol. 25, Sept. 1937, pp. 1203–1236.

[6] R. Li. “The accuracy of Norton’s empirical approximations for ground-wave attenuation,” 

IEEE Trans. Ant. Prop., AP-31, No. 4, pp. 624-628, July 1983.

[7] A. Sommerfeld, “Propagation of waves in wireless telegraphy,” Ann. D. Phys. 28, pp.665-

736, March 1909.

[8] E.C. Jordan, Electromagnetic Waves and Radiating Systems, New Jersey: Prentice Hall, 

1968, pp.628–650.

[9] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, National Bureau 

of Standards AMS 55, U.S. Government Printing Office: Washington, D.C., June 1964, pp. 

297–329.

[10] C.A. Balanis, Advanced Engineering Electromagnetics, New York: John Wiley and Sons, 

1989, pp.145–154.

[11] International Telecommunications Union (ITU-R), “Electrical characteristics of the surface 

of the Earth,” ITU-R Recommendation P.527-3, 1992.

[12] G.J. Burke, “Numerical Electromagnetics Code- NEC-4, method of moments Parts I and 

II,” University of California Lawrence Livermore Laboratory Report UCRL-MA-109338, 

Livermore, California, 1983.
21

APPENDIX A FIGURES SHOWING RESULTS OF COMPUTATIONS AND 

MEASUREMENTS FOR DIELECTRIC CONSTANT AND CONDUCTIVITY 

DETERMINATION WITH ALL ANTENNA HEIGHTS EQUAL TO ZERO 

0

25

50

75

100

125

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

Good Ground: Sigma = 0.020, Epsilon = 25.0

Average Ground: Sigma = 0.005, Epsilon = 15.0

Poor Ground: Sigma = 0.001, Epsilon = 4.0

Frequency (MHz)

Loss (dB)

Loss Versus Frequency for Three Types of Ground

Figure A-1. Propagation loss versus frequency for three types of ground for a distance of 10

meters.
22

20

30

40

50

60

70

80

90

100

110

120

0 5 10 15 20 25

Frequency = 5750 MHz

Frequency = 2260 MHz

Frequency = 915 MHz

Frequency = 430 MHz

Frequency = 150 MHz

Frequency = 90 MHz

Frequency = 60 MHz

Frequency = 30 MHz

Epsilon

Loss (dB)

Figure A-2. Propagation loss versus epsilon for sigma = 0.001 and distance = 10.0 meters with 

frequency as a parameter.

20

30

40

50

60

70

80

90

100

110

120

0 5 10 15 20 25

Frequency = 5750 MHz

Frequency = 2260 MHz

Frequency = 915 MHz

Frequency = 430 MHz

Frequency = 150 MHz

Frequency = 90 MHz

Frequency = 60 MHz

Frequency = 30 MHz

Epsilon

Loss (dB)

Figure A-3. Propagation loss versus epsilon for sigma 0.020 and distance = 10.0 meters with 

frequency as a parameter.
23

20

30

40

50

60

70

80

90

100

110

120

0 0.005 0.010 0.015 0.020

Frequency = 5750 MHz

Frequency = 2260 MHz

Frequency = 915 MHz

Frequency = 430 MHz

Frequency = 150 MHz

Frequency = 90 MHz

Frequency = 60 MHz

Frequency = 30 MHz

Sigma (Siemens per meter)

Loss (dB)

Figure A-4. Propagation loss versus sigma for epsilon = 4.0 and distance = 10.0 meters with 

frequency as a parameter.

20

30

40

50

60

70

80

90

100

110

120

0 0.005 0.010 0.015 0.020

Frequency = 5750 MHz

Frequency = 2260 MHz

Frequency = 915 MHz

Frequency = 430 MHz

Frequency = 150 MHz

Ferquency = 90 MHz

Frequency = 60 MHz

Frequency = 30 MHz

Sigma (Siemens per meter)

Loss (dB)

Figure A-5. Propagation loss versus sigma for epsilon = 25.0 and distance = 10.0 meters with 

frequency as a parameter.
24

20

30

40

50

60

70

0 50 100 150 200 250 300 350 400 450 500

Sigma = 0.020 Siemens per meter

Sigma = 0.010 Siemens per meter

Sigma = 0.003 Siemens per meter

Sigma = 0.001 Siemens per meter

Frequency (MHz)

Loss (dB)

Loss Versus Frequency for Epsilon = 4.0 With Sigma as Parameter for d = 10.0m

h

1

= 0.0 m h

2

=0.0 m Sigma varies from 0.001 to 0.020 with all curves merging together

Figure A-6. Propagation loss versus frequency for epsilon = 4.0 with sigma as a parameter for a 

distance of 10 meters with all curves merging together.

30

32

34

36

38

40

42

44

46

48

50

5 6 7 8 9 10 11 12 13 14 15

Prediction, .005, 8.0

Prediction, .005, 7.0

Predictions, .005, 6.0

Gated Measurements

Distance (m)

Loss (dB)

Figure A-7. Comparisons of propagation loss predictions with monopole measurements (August 

2009) at 150.5 MHz.
25

30

32

34

36

38

40

42

44

46

48

50

52

54

56

58

60

5 6 7 8 9 10 11 12 13 14 15

Prediction, .005, 7.0

Prediction, .005, 5.0

Predictions, .005 , 6.0

Gated Measurements

Distance (m)

Loss (dB)

Figure A-8. Comparisons of propagation loss predictions with monopole measurements (August 

2009) taken at 250 MHz.

40

42

44

46

48

50

52

54

56

58

60

62

64

66

68

70

5 6 7 8 9 10 11 12 13 14 15

Prediction, .005, 4.0

Prediction, .005, 5.0

Predictions, .005, 6.0

Gated Measurements

Distance (m)

Loss (dB)

Figure A-9. Comparisons of propagation loss predictions with monopole measurements (August 

2009) taken at 430 MHz.
26

50

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

5 6 7 8 9 10 11 12 13 14 15

Prediction, .005, 10.0

Prediction, .005, 8.0

Prediction, .005, 7.0

Gated Measurements

Distance (m)

Loss (dB)

Figure A-10. Comparisons of propagation loss predictions with monopole measurements 

(August 2009) at 700 MHz.

60

62

64

66

68

70

72

74

76

78

80

5 6 7 8 9 10 11 12 13 14 15

Prediction, .005, 10.0

Prediction, .005, 8.0

Prediction, .005, 7.0

Gated Measurements

Distance (m)

Loss (dB)

Figure A-11. Comparisons of propagation loss predictions with monopole measurements 

(August 2009) at 915 MHz.
27

15

16

17

18

19

20

21

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Sigma = 0.005

Sigma = 0.004

Sigma = 0.003

Corrected Measured Data

Distance (meters)

Loss (dB)

Figure A-12. Corrected measured propagation loss data (August 2009) versus distance compared 

to predicted loss for 30 MHz with εr = 6.0 and σ as a parameter.

25

26

27

28

29

30

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Sigma = 0.010

Sigma = 0.009

Sigma = 0.008

Sigma = 0.007

Corrected Measured Data

Distance (meters)

Loss (dB)

Figure A-13. Corrected measured propagation loss data (August 2009) versus distance compared 

to predicted loss for 60 MHz with εr = 6.0 and σ as a parameter.
28

15

16

17

18

19

20

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Corrected Measured Data

Sigma = 0.005

Sigma = 0.004

Sigma = 0.003

Distance (meters)

Loss (dB)

Figure A-14. Corrected measured propagation loss data (August 2009) versus distance compared 

to predicted loss for 30 MHz with εr = 7.0 and σ as a parameter.

25

26

27

28

29

30

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Corrected Measured Data

Sigma = 0.007

Sigma = 0.006

Sigma = 0.005

Sigma = 0.004

Distance (meters)

Loss (dB)

Figure A-15. Corrected measured propagation loss data (August 2009) versus distance compared 

to predicted loss for 60 MHz with εr = 7.0 and σ as a parameter.
29

15

16

17

18

19

20

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Sigma = 0.005

Sigma = 0.004

Sigma = 0.003

Corrected Measured Data

Distance (meters)

Loss (dB)

Figure A-16.Corrected measured propagation loss data (August 2009) versus distance compared 

to predicted loss for 30 MHz with εr = 6.5 and σ as a parameter.

25

26

27

28

29

30

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Sigma = 0.009

Sigma = 0.008

Sigma = 0.007

Sigma = 0.006

Corrected Measured Data

Distance (meters)

Loss (dB)

Figure A-17. Corrected measured propagation loss data (August 2009) versus distance compared 

to predicted loss for 60 MHz with εr = 6.5 and σ as a parameter.
30

15

16

17

18

19

20

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Sigma = 0.005

Sigma = 0.004

Sigma = 0.003

Corrected Measured Data

Distance (meters)

Loss (dB)

Figure A-18. Corrected measured propagation loss data versus distance compared to predicted 

loss for 30 MHz with εr = 6.7 and σ as a parameter.

25

26

27

28

29

30

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Sigma = 0.007

Sigma = 0.006

Sigma = 0.005

Corrected Measured Data

Distance (meters)

Loss (dB)

Figure A-19. Corrected measured propagation loss data (August 2009) versus distance compared 

to predicted loss for 60 MHz with εr = 6.7 and σ as a parameter.
31

30

35

40

45

50

5 6 7 8 9 10 11 12 13 14 15

Epsilon = 9.0

Epsilon = 10.0

Epsilon = 11.0

Measured Data noted at vertex

Distance (m)

Loss (dB)

Figure A-20. Comparisons of propagation loss predictions with monopole measurements (May 

2010) at 150 MHz with σ = 0.005.

30

35

40

45

50

55

60

5 6 7 8 9 10 11 12 13 14 15

Epsilon = 9.0

Epsilon = 10.0

Epsilon = 11.0

Measured Data noted at Vertex

Distance (m)

Loss (dB)

Figure A-21. Comparisons of propagation loss predictions with monopole measurements (May 

2010) at 250 MHz with σ = 0.005.
32

40

45

50

55

60

65

70

5 6 7 8 9 10 11 12 13 14 15

Epsilon = 7.0

Epsilon = 8.0

Epsilon = 9.0

Measured Data Noted at Vertex

Distance (m)

Loss (dB)

Figure A-22. Comparisons of propagation loss predictions with monopole measurements (May 

2010) at 430 MHz with σ = 0.005.

50

55

60

65

70

75

80

5 6 7 8 9 10 11 12 13 14 15

Epsilon = 8.0

Epsilon = 9.0

Epsilon = 10.0

Measured Data Noted at Vertex

Distance (m)

Loss (dB)

Figure A-23. Comparisons of propagation loss predictions with monopole measurements (May 

2010) at 700 MHz with σ = 0.005.
33

50

55

60

65

70

75

80

5 6 7 8 9 10 11 12 13 14 15

Epsilon = 8.0

Epsilon = 9.0

Epsilon = 10.0

Measured Data Noted at Vertex

Distance (m)

Loss (dB)

Figure A-24. Comparisons of propagation loss predictions with monopole measurements (May 

2010) at 915 MHz with σ = 0.005.

25

26

27

28

29

30

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Measured Data at Vertex

Sigma = 0.009

Sigma = 0.008

Sigma = 0.007

Distance (meters)

Loss (dB)

Figure A-25. Comparisons of propagation loss with monopole measurements (May 2010) at 60 

MHz with varying σ and εr = 7.0.
34

30

31

32

33

34

35

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Measured Data at Vertex

Sigma = 0.006

Sigma = 0.005

Sigma = 0.004

Distance (meters)

Loss (dB)

Figure A-26. Comparisons of propagation loss with monopole measurements (May 2010) at 90 

MHz with varying σ and εr = 7.0.

25

26

27

28

29

30

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Measured Data at Vertex

Sigma = 0.007

Sigma = 0.006

Sigma = 0.005

Distance (meters)

Loss (dB)

Figure A-27. Comparisons of propagation loss with monopole measurements (May 2010) at 60 

MHz with varying σ and εr = 7.5.
35

25

26

27

28

29

30

7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0

Measured Data Noted at Vertex

Sigma = 0.004

Sigma = 0.006

Sigma = 0.005

Distance (meters)

Loss (dB)

Figure A-28. Comparisons of propagation loss with monopole measurements (May 2010) at 60

MHz with varying σ and εr = 8.0.

35

36

37

38

7.1 7.3 7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9

Measured Data Noted at Vertex

Sigma = 0.0065

Sigma = 0.006

Sigma = 0.005

Distance (meters)

Loss (dB)

Figure A-29. Comparisons of propagation loss with monopole measurements (May 2010) at 120 

MHz with varying σ and εr = 9.0.

FORM NTIA-29 U.S. DEPARTMENT OF COMMERCE 

(4-80) NAT’L. TELECOMMUNICATIONS AND INFORMATION ADMINISTRATION

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION NO.

TR-12-484

2. Government Accession No. 3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

Free-Field Measurements of the Electrical Properties of Soil Using the Surface Wave 

Propagation Between Two Monopole Antennas

5. Publication Date

January 2012

6. Performing Organization Code

NTIA/ITS.E

7. AUTHOR(S)

Nicholas DeMinco, Robert T. Johnk, Paul McKenna, Chriss A. Hammerschmidt, J. 

Wayde Allen

9. Project/Task/Work Unit No.

3141000-300

8. PERFORMING ORGANIZATION NAME AND ADDRESS

Institute for Telecommunication Sciences

National Telecommunications & Information Administration

U.S. Department of Commerce

325 Broadway

Boulder, CO 80305

10. Contract/Grant Number.

11. Sponsoring Organization Name and Address

National Telecommunications & Information Administration

Herbert C. Hoover Building

14th & Constitution Ave., NW

Washington, DC 20230

12. Type of Report and Period Covered

14. SUPPLEMENTARY NOTES

15. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or 

literature survey, mention it here.)

This report describes one of three free-field, radio-frequency (RF) measurement systems that are currently being developed 

by engineers at the Institute for Telecommunication Sciences (NTIA/ITS).The objective is to provide estimates of the 

electrical properties of the ground (permittivity and conductivity) over which they are deployed. This measurement system 

uses transmission loss measurements between two monopoles placed close to the ground at specific separation distances. Soil 

properties are extracted by comparing measured data with known analytical models and optimizing the results.

16. Key Words (Alphabetical order, separated by semicolons)

17. AVAILABILITY STATEMENT

UNLIMITED.

FOR OFFICIAL DISTRIBUTION.

18. Security Class. (This report)

Unclassified

20. Number of pages

51

19. Security Class. (This page)

Unclassified

21. Price:

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