NTIA Report TR-11-481

Improved Estimation of the Third-Order 

Harmonic Emissions of Land Mobile 

Radio Base Stations 

Eric D. Nelson

Nicholas DeMinco

NTIA Technical Report TR-11-481

Improved Estimation of the Third-Order 

Harmonic Emissions of Land Mobile 

Radio Base Stations 

Eric D. Nelson

Nicholas DeMinco

U.S. DEPARTMENT OF COMMERCE

September 2011

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 

recommendation 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.

CONTENTS

Page

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

TABLES ........................................................................................................................................ vi

ABBREVIATIONS/ACRONYMS............................................................................................... vii

EXECUTIVE SUMMARY ........................................................................................................... ix

1 INTRODUCTION ........................................................................................................................1

1.1 Background ............................................................................................................................1

1.2 Prior Electromagnetic Compatibility Analysis Methodology................................................2

1.3 Improved Electromagnetic Compatibility Analysis Methodology ........................................3

2 EMC ANALYSIS USING AN ISOTROPIC ANTENNA AND FREE SPACE 

PROPAGATION .................................................................................................................4

2.1 Determination of EIRP...........................................................................................................4

2.2 Estimation of the Received Power Level ...............................................................................4

3 EMC ANALYSIS USING DIRECTIONAL ANTENNAS AND ADVANCED 

PROPAGATION MODEL..................................................................................................5

3.1 Antenna Modeling and the Undisturbed Field Propagation Model .......................................5

3.2 Folded-dipole Antennas .........................................................................................................6

3.3 Estimation of the Received Power Level .............................................................................10

3.4 Refinement of the EMC analysis .........................................................................................16

4 CONCLUSION...........................................................................................................................18

5 REFERENCES ...........................................................................................................................19
vi

FIGURES

Figure 1. Single folded-dipole antenna on metal mast. ...................................................................6

Figure 2. Four-element collinear folded-dipole collinear array antenna on metal mast..................7

Figure 3. Geometry used for determination of vertical elevation angle at a given distance............8

Figure 4. Fundamental and third harmonic elevation pattern plot of single folded-dipole 

antenna on metal mast....................................................................................................9

Figure 5. Fundamental and third harmonic elevation pattern of four-element collinear 

folded-dipole array antenna on metal mast..................................................................10

Figure 6. Received power from a single folded-dipole transmitter antenna, 100 W EIRP, 

antenna center height of 45 m AGL, 0 dBi receive antenna, ground constants: 

σ = 0.005 S/m and εr = 15.0. ........................................................................................12

Figure 7. Received power from a four-element collinear folded-dipole array transmitter 

antenna, 100 W EIRP, antenna center height of 45 m AGL, 0 dBi receive 

antenna, ground constants: σ = 0.005 S/m and εr = 15.0. ............................................13

Figure 8. Received power from a single folded-dipole transmitter antenna, 100 W EIRP, 

antenna center height of 15 m AGL, 0 dBi receive antenna, ground constants: 

σ = 0.005 S/m and εr = 15.0. ........................................................................................15

Figure 9. Received power from a four-element collinear folded-dipole array transmitter 

antenna, 100 W EIRP, antenna center height of 15 m AGL, 0 dBi receive 

antenna, ground constants: σ = 0.005 S/m and εr = 15.0. ............................................16

Figure 10. Received power from a four-element collinear folded-dipole array transmitter 

antenna, 100 W EIRP, antenna center height of 15 m AGL, 60 dB of out of 

band rejection, 0 dBi receive antenna, ground constants: σ = 0.005 S/m and εr

= 15.0. ..........................................................................................................................17

TABLES

Page

Table 1. Received Power Plot Features as a Function of Antenna Elevation Angle .....................14
vii

ABBREVIATIONS/ACRONYMS

AGL Above Ground Level

dB decibel

dBc decibels relative to the carrier

dBm decibels relative to a milliwatt

EIRP Effective Isotropic Radiated Power

EMC Electromagnetic Compatibility

GPS Global Positioning System

ITS Institute for Telecommunication Sciences

LMR Land Mobile Radio

NEC Numerical Electromagnetics Code

NTIA National Telecommunications and Information Administration

OSM Office of Spectrum Management

UHF Ultrahigh Frequency

ix

EXECUTIVE SUMMARY

The National Telecommunications and Information Administration (NTIA) is tasked with 

protecting the radiofrequency spectrum used by the Global Positioning System (GPS) through 

appropriate spectrum measurement practices. NTIA’s Office of Spectrum Management (OSM) 

identified harmonic emissions from land mobile radio (LMR) systems as a potential source of 

interference into GPS and subsequently tasked ITS with measuring emissions from these 

sources. The task involved comparing predicted effective isotropic radiated power (EIRP) from 

an LMR base station to permitted limits under Federal Communications Commission (FCC) and 

NTIA guidelines.

This 2009 measurement effort was a sophisticated radiated emissions measurement requiring the 

use of an anechoic chamber. To restrict the number of test cases, the recommended test 

procedure prescribed the use of a “representative antenna” for the base station. The measured 

EIRP was used to perform an electromagnetic compatibility (EMC) analysis to predict 

interference. Such EMC analyses are often used to plan base station configuration and location 

based on the different separation distances and propagation losses typically encountered in 

practice. 

Using a representative antenna for these calculations complicates subsequent EMC studies for 

base stations, because a representative antenna cannot accurately embody the wide variety of 

antennas used on LMR base stations. The analysis applied to the 2009 measurement effort also 

did not consider antenna directionality, forcing the assumption that the maximum received power 

occurred at the minimum separation distance. In addition, it used a free space pathloss model that 

does not consider interactions between the radiated field and the ground. 

In this paper, we describe a study of LMR base station emissions performed using an alternative 

method for the EMC analysis that addresses all three of the limitations described above, yielding 

much more accurate EIRP estimates. This method does not require the use of the expensive 

anechoic chamber. Using parameters readily obtained from equipment datasheets, the revised 

method accurately models various base station antennas rather than using a single representative 

antenna. This reduces uncertainties in estimates of antenna gain and directivity. The method also 

integrates a proven propagation model that incorporates the interaction of ground conductivity 

and other factors to more accurately predict the received power in the proximity of an LMR base 

station. This facilitates a more detailed and accurate review of the proposed base station system’s 

emissions. 

We present detailed analyses for two common base station antennas and demonstrate the use of 

the model to examine the potential for interference from hypothetical LMR base stations into 

GPS receivers. Finally, we show how a simple modification to LMR base stations can mitigate 

the potential for interference in the GPS L2 band.

IMPROVED ESTIMATION OF THE THIRD-ORDER HARMONIC EMISSIONS OF 

LAND MOBILE RADIO BASE STATIONS 

Eric D. Nelson and Nicholas DeMinco1

NTIA/ITS2has developed an improved electromagnetic compatibility (EMC) 

analysis method that can be applied to more accurately model real scenarios for 

evaluating interference. The methodology described in this report can be used to 

conduct EMC analyses for base stations that use a variety of antennas. The model 

can be used to determine the received power in the proximity of the base station at 

both the fundamental and harmonic frequencies. It uses accurate radio-wave 

propagation models and antenna models. The antenna models can be created for 

the fundamental and third harmonic frequencies of many antennas. Fields 

adjacent to the base station antenna are heavily influenced by interactions with 

ground, and the electromagnetic fields are dominated by the side lobe structure of 

the elevation pattern of the base station antenna. The described rigorous EMC 

analysis for a base station considers all of these factors to assess interference more 

accurately than previous methods.

Key words: undisturbed field method; electromagnetic compatibility; numerical 

electromagnetics code; land mobile radio; third order harmonics; received power; 

global positioning system; folded-dipole antenna.

1 INTRODUCTION

This report explores a new method for conducting electromagnetic compatibility analyses for 

base stations that use a variety of antennas. The method systematically determines the received 

power in the proximity of a base station system at both fundamental and harmonic frequencies. It 

is based on readily obtained equipment parameters and uses accurate antenna and propagation 

models which can readily accommodate new antenna types. The model is easily extended to new 

frequency ranges.

1.1 Background

In 2004 President Bush signed National Security Presidential Directive number 39 (NSPD-39) 

which dictated measures to protect the Global Positioning System (GPS). The directive tasked

the National Telecommunications and Information Administration (NTIA) to take necessary 

measures to protect the radiofrequency spectrum used by the GPS through appropriate spectrum 

management practices. NTIA’s Office of Spectrum Management (OSM) identified harmonic 

 

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

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

2 The Institute for Telecommunication Sciences (ITS) is the research and engineering branch of the National 

Telecommunications and Information Administration (NTIA), a part of the U.S. Department of Commerce (DOC). 
2

emissions from radio systems as a potential source of interference into GPS and subsequently 

tasked ITS with measuring emissions from these sources. 

One set of measurements conducted in 2009 assessed the third-order emissions from a sample of 

UHF land mobile radio (LMR) transmitters operating at 409.2 MHz. These particular 

transmitters had the potential to generate third harmonic emissions in the GPS L2 band centered 

at 1227.6 MHz. LMR portable subscriber units and a base station transceiver were selected for 

testing. ITS performed the measurements using a customized measurement system and an 

anechoic chamber at the National Institute of Standards and Technology (NIST) in Boulder, CO. 

The measurements revealed low-level, but nonetheless observable, third-order harmonics from 

the LMRs in the GPS L2 band.

1.2 Prior Electromagnetic Compatibility Analysis Methodology

The test configuration used in 2009 for the portable LMRs included their standard whip 

antennas. The portables were manually operated by a technician within the chamber. The base 

station transceiver was operated remotely and a “representative antenna” mounted on a wooden 

tripod was used per standard practice.

3

In both cases, the emissions levels were measured using a 

reference antenna, and free space assumptions were used to compensate for propagation losses. 

This yielded power levels referenced to the output of the transmit antenna, i.e. the effective 

isotropic radiated power (EIRP). 

Referencing emissions in EIRP facilitates subsequent electromagnetic compatibility analyses. 

For portable transmitters the EIRP is all that is required to evaluate a variety of meaningful 

interference scenarios. Such analyses can accommodate the different separation distances and 

propagation losses typically encountered in practice. Since LMR portables use integrated 

antennas, the choice of antenna types is limited and fewer test cases are required to characterize

them. As a result, there is less uncertainty in the EIRP estimates and the subsequent analyses.

A much greater diversity of antenna types is used in base station applications. Actual antennas 

used in practice will vary widely from a representative antenna. For instance, a review of 

commercially available base station antennas designed for the UHF band yielded gains ranging 

anywhere from 5 to 12 dBi and designs ranging from stacked folded-dipole arrays to collinear 

omnidirectional antennas to directional yagis. 

Use of a representative antenna for such a diverse array of antenna types introduces a significant

uncertainty in the estimate of the base station’s EIRP. Moreover, the characteristics of base 

station antennas at their harmonic frequencies are not well understood, since these frequencies

are typically outside their normal operating range. Antenna product literature is silent regarding 

the antennas’ directivity or gain at the third harmonic frequency. This further complicates the 

EIRP estimate. 

Furthermore, the standard measurement procedure does not take into account the typical

transmission path between a base station and antenna. Consideration of the numerous 

components used in actual base stations can dramatically alter the findings of an EMC analysis. 

 

3

See 47 CFR 27.53 (e) and 47 CFR 90.543 (e)
3

For example, base stations typically use transmit filters. A worst-case analysis that omits filter 

effects can differ from one that includes them by more than 50 dB.

In addition, the propagation path adjacent to a real LMR base station is much more complex than 

the idealized environment of an anechoic chamber. The anechoic chamber is designed to absorb 

reflections, whereas the fields adjacent to a base station antenna are heavily influenced by 

interactions with the ground. Finally, radiated emissions measurements are performed at the 

boresight angle of the representative antenna while, in practice, radiated fields adjacent to a base 

station are dominated by the antenna’s lower sidelobes.

1.3 Improved Electromagnetic Compatibility Analysis Methodology

A rigorous EMC analysis for a base station transmitter should consider all of the factors

described above. It should incorporate an accurate model for a variety of antenna types, 

frequency ranges, and geometries encountered in practice. 

The purpose of this report is to present an improved method of EMC analysis that yields more 

accurate estimates of received power. We demonstrate the utility of this improved method by 

performing a detailed analysis of harmonic emissions of LMR base station systems in the GPS 

L2 band. The method uses analytic techniques based on first principles, is simple to implement, 

and has been validated through experimental methods. It incorporates a proven propagation 

model that is tailored to short-range propagation. 
4

2 EMC ANALYSIS USING AN ISOTROPIC ANTENNA AND FREE SPACE 

PROPAGATION

As a baseline, we consider a typical LMR base station deployment with carefully selected

characteristics representing a worst-case scenario. We then compare the results obtained using 

this simple model to our more sophisticated one and assess the possible improvements.

2.1 Determination of EIRP

Assume an LMR base station is operating at 409.2 MHz such that its third harmonic falls on the 

center of the GPS L2 band at 1227.6 MHz. Assume the base station system has a tower that 

supports an antenna with a center of radiation at 45 m above ground level (AGL). This is a 

typical base station height, since it can provide extensive coverage without triggering FAA 

height-based requirements for marking and lighting. To facilitate later intercomparisons we 

assume an EIRP of 100 W or 50 dBm at the fundamental frequency and an isotropic antenna. We 

assume the use of high performance coaxial cable at the base station. A typical 7/8" (22.2 mm) 

diameter cable has 2.5 dB/100 m attenuation at 400 MHz and 4.7 dB/100 m at 1250 MHz. Since 

the losses are low they will only differ slightly between the signal at the fundamental and third 

harmonic frequencies, so we neglect coax losses.

We can derive a rough order of magnitude estimate of third harmonic emissions by assuming 

that the transmitter generates the maximum allowable spurious emissions. LMR base station 

spurious emissions are specified to be less than -90 dBc, so the third harmonic would be at least 

90 dB down from the fundamental at the output of the transmitter. For most antennas the gain 

and directivity at the third harmonic is not typically published information. For the sake of 

simplicity, assume they are the same as those at the fundamental. As a result, we estimate the 

EIRP of the third harmonic to be -40 dBm.

2.2 Estimation of the Received Power Level

Using the estimated EIRP of the third harmonic we can complete a simple worst-case EMC

analysis. Assume a GPS receiver in the proximity of the base station at an elevation of 1.5 m. 

The closest this receiver can encroach upon the transmit antenna is 43.5 m, i.e. the difference in 

height between the two antennas. Assuming free space pathloss at 1227.6 MHz, there is 67.0 dB 

of attenuation over this distance. A GPS receiver using a 0 dBi antenna would see a received 

power level of -107.0 dBm.

Compare this receive power level to the recommended power limit for a jamming signal in the 

literature. The recommended minimum jammer to signal ratio for a carrier wave jammer is 21.9 

dB for the L2 P(Y) code ([1], pg. 236) while the nominal received power level of a GPS L2 

signal at ground level is -135.2 dBm. ([1], pg. 219). Therefore, received power in excess of -

113.3 dBm is potentially harmful to a GPS receiver. This rough order of magnitude estimate 

indicates that the received power is 6.3 dB in excess of the recommended limit. This is true for a 

single channel LMR base station that has been properly engineered.
5

3 EMC ANALYSIS USING DIRECTIONAL ANTENNAS AND ADVANCED 

PROPAGATION MODEL

The preceding analysis predicted a receive power level from the LMR harmonic emissions in 

excess of the limits. It was derived from an EIRP estimate with an assumed isotropic antenna for 

a single channel transmitter site without transmit filters. A free space pathloss model was 

employed that neglects interactions between the radiated field and the ground. Assuming the 

antenna’s directionality is not known, we found that the maximum received power occurred at 

the minimum separation distance.

It is well known that LMR base station antennas have nulls in their radiation patterns on their 

vertical axes—the point at which the separation distance is minimized—so a more complete

consideration of antenna characteristics is needed. We present an improved EMC analysis 

methodology that considers this factor. The antenna modeling aspect of our method describes the 

vertical pattern of the antenna at both the fundamental and the harmonic frequency. It 

characterizes the sidelobes. The propagation model aspect treats ground interactions. The two 

facets comprise a method that predicts multiple peaks and nulls in the received power versus 

horizontal distance from the base station, which is a well-known phenomenon. Moreover, the 

method predicts that a simple free space model based on EIRP estimates and an isotropic antenna 

actually underestimates the received power by as much as 10 dB.

3.1 Antenna Modeling and the Undisturbed Field Propagation Model

The method selected for analyzing the antennas makes extensive use of method-of-moments 

calculations and is implemented in a computer program titled the Numerical Electromagnetics 

Code (NEC) [2]. It is an accurate method for analyzing antennas in the ultrahigh frequency 

(UHF) band. It is particularly suitable for wire antennas like those used in UHF base station 

applications where the radiating elements are modeled as wire segments in a geometry that 

represents the physical structure of the antenna. The method includes the effects of the mast 

support structure of the antenna.

The ITS undisturbed field model [3] was used to perform the propagation loss computations with 

the effects of antenna patterns factored into the model. The undisturbed field model is valid for 

short and long distances and both high and low antenna heights. The development of this model 

is discussed in an NTIA/ITS report [3]. The model involves the calculation of the undisturbed 

electric field and calculation of the loss based on the amplitude of the electric field as a function 

of distance, frequency, and the ground dielectric constants. The propagation was assumed to be 

located over average ground with σ = 0.005 S/m and εr = 15.0 as defined in Table 3 of [4].

The undisturbed field is the electric field produced by a transmit antenna at different distances 

and heights above ground in the absence of field-disturbing factors in the proximity of the 

receive antenna location. The presence of a receive antenna would disturb the electric field. The 

ITS report [3] provides a detailed investigation of the differences between the undisturbed and 

disturbed (mutual coupling) methods of field computation, and shows the differences between 

the results of propagation loss computed using both methods.
6

While the disturbed-field method is more exact, it is more computationally intensive and difficult 

to calculate than the relatively simple undisturbed field based computations. The ITS report 

shows via numerous examples that, for most scenarios, the difference between the propagation 

loss computed by undisturbed field method and the disturbed-field method is minimal. This is 

especially true for the distances involved in this current analysis. 

The undisturbed electric field technique includes near-field effects, the complex two-ray model, 

antenna near-field and far-field response and the surface wave. Since this is a line-of-sight 

model, the ground is assumed to be flat over the distance of the computations with no irregular 

terrain present. For distances of less than 7.5 kilometers, the curvature of the Earth has a 

negligible effect and can be assumed to be flat for frequencies less than 1300 MHz over a 

smooth Earth [3].

3.2 Folded-dipole Antennas

Folded-dipole antennas were selected for this analysis because they are used widely in UHF base 

station applications and have simple geometries that facilitate an NEC simulation. The foldeddipole antenna has a wider bandwidth than a typical straight wire half-wavelength dipole. Both a 

single-element folded-dipole antenna and a four-element collinear vertically-stacked foldeddipole array antenna were modeled. Figure 1 shows an example of a single-element antenna 

while Figure 2 shows a phased four-element model. 

Figure 1. Single folded-dipole antenna on metal mast.

The single folded-dipole antenna consists of a single radiating element mounted with a onequarter wavelength spacing from the mast and a one-half wavelength spacing from the top of the 

antenna. The model includes the effects of the support structure which is a 5 cm diameter metal 

mast. For the sake of simplicity our analysis assumes that the antenna, i.e. the radiating element 

and the 5 cm mast, are in turn mounted on a 5 cm diameter base station tower. 

We also characterized a four-element collinear folded-dipole array antenna shown in Figure 2

modeled after a commercially available antenna. The center-to-center spacing between foldeddipoles for the model was three-fourths of a wavelength at 409.2 MHz. The elements are 

mounted at a quarter-wavelength offset from one side of the mast. Again, the antenna’s top 
7

element is centered one-half wavelength from the top of the antenna mast, and the antenna is 

itself mounted on an idealized 5 cm diameter tower. The antenna model created for these 

analyses was scaled to 409.2 MHz center frequency. 

Figure 2. Four-element collinear folded-dipole collinear array antenna on metal mast.

The close proximity of the radiating elements to the antenna mast is modeled using NEC by 

representing the physical structure of the mast with numerous wire segments. The NEC program 

calculates the antenna patterns and the input impedance of the antenna. The mutual impedance 

effects between the folded-dipole antenna elements are also taken into consideration in this 

calculation.

For both the single folded-dipole antenna and the four-element collinear folded-dipole array 

antenna models, each folded-dipole is slightly shorter than one-half wavelength to cancel the 

reactive component of the input impedance. Full cancellation of the reactive part is not 

completely achieved due to the coupling between the mast and folded-dipoles. The real part of 

the input impedance is approximately 300 ohms, which can be conveniently matched to a 300 Ω 

transmission line.

The model predicted that the antennas would have a mismatch loss of less than 1 dB at both the 

fundamental frequency of 409.2 MHz and the third harmonic of 1227.6 MHz. This is because the 

antenna exhibits an input impedance resonance at the third harmonic similar to the resonance at 

the fundamental frequency. This is a characteristic of dipole antennas. The input impedance 

would vary more at non-harmonic frequencies, and the resultant mismatch would be greater.
8

To gain an understanding of the antennas themselves, we model them separately in a free space 

environment using NEC. Later, we will incorporate them into the undisturbed field model, which

considers that the antennas’ interaction with the earth produces a reflected wave off the ground.

The elevation patterns for the single folded-dipole are shown in Figure 4 for both the 

fundamental frequency of 409.2 MHz and the third harmonic frequency of 1227.6 MHz. Figure 3

illustrates the geometry used for determination of the vertical elevation angle, which is measured 

in degrees below the horizon. The angle φ in the figure is given by: φ = arctan(h/d). 

φ h

1.5m d Figure 3. Geometry used for determination of vertical elevation angle at a given distance.
9

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Figure 4. Fundamental and third harmonic elevation pattern plot of single folded-dipole antenna 

on metal mast.

At the fundamental frequency the radiation pattern possesses a single lobe, resulting in more 

uniform coverage in elevation than what is predicted at the third harmonic frequency where there 

are multiple lobes. This is a result of the different current distributions on the antenna for each 

frequency. The peak gains are similar at both the fundamental and the third harmonic 

frequencies, but the antenna’s coverage at shorter ranges will differ due to the lower sidelobes. 

The elevation patterns for the vertically-stacked four-element collinear folded-dipole array

antenna are shown in Figure 5 for both the fundamental frequency of 409.2 MHz and the third 

harmonic frequency of 1227.6 MHz. The maximum gain at the boresight angle is similar for both 

the fundamental and the third harmonic frequencies. At the fundamental frequency the antenna

has a main lobe and multiple sidelobes with the first upper and lower sidelobes about 13 dB 

down from the main lobe. This is typical for a uniformly excited array antenna. The remaining
10

sidelobes are more than 13 dB down from the main lobe. The antenna pattern at the third 

harmonic frequency has larger sidelobes, two of which are only approximately 3 dB down from 

the main beam. There are also many more sidelobes in the antenna pattern at the third harmonic 

frequency than there are at the fundamental frequency. This is due to the different current 

distributions and relative phasing on the array antenna at the shorter wavelengths at the third 

harmonic frequency.

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Figure 5. Fundamental and third harmonic elevation pattern of four-element collinear foldeddipole array antenna on metal mast.

3.3 Estimation of the Received Power Level

The antenna patterns for the two simulated antennas were integrated into the undisturbed field

model. The undisturbed field model uses these patterns to predict the amplitudes of the direct and 

reflected waves emitted from the antenna at the various angles of incidence. Equation (1) was 
11

used to compute the received power at the fundamental frequency of 409.2 MHz using the 

propagation loss computed with the undisturbed field model.

P ( ) ( ) ( ) ( ) ( ) ( ) r t t r proploss spurious filter dB ( ) dBm P dBm G dBi G dBi L dB L dB L      

(1)

where

Pr(dBm) = the received signal power in dBm at the fundamental frequency of 409.2 MHz

Pt(dBm) = the transmitted power in dBm into the antenna terminals 

Gt(dBi) = transmitter antenna gain in decibels referenced to an isotropic antenna as a 

function of elevation angle, φ

Gr(dBi) = receiver antenna gain in decibels referenced to an isotropic antenna

Lproploss (dB) = propagation loss in dB computed by the undisturbed field model

Lspurious (dB) = spurious response rejection in dB

Lfilter (dB) = filter isolation in dB

The EIRP was normalized to 100 W peak by offsetting the transmitter power by the peak gain of 

the antenna. The undisturbed field model can be used to model the receive antenna, but for the 

sake of simplicity, a 0 dBi isotropic receive antenna was assumed. The loss terms for spurious 

response rejection and filter isolation are 0 dB at the fundamental frequency. As noted in Section 

2.1, the difference between coaxial cable losses at the fundamental and third harmonic 

frequencies is negligible, so they were not considered.

The received power level for the third harmonic frequency of 1227.6 MHz can be computed 

using (1) with the appropriate substitutions for the antenna characteristics, spurious response 

rejection, and the filter loss at this frequency. The emissions at the third harmonic are assumed to 

be a worst-case value of -90 dBc, i.e., Lspurious = 90 dB. Filter losses are considered later; 

presently they are assumed to be 0 dB.
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Recieved Third Harmonic Power at 1227.6 MHz (free space)

Received Third Harmonic Power at 1227.6 MHz

Received Fundamental Power at 409.2 MHz

Distance (m)

Received Power (dBm)

Figure 6. Received power from a single folded-dipole transmitter antenna, 100 W EIRP, antenna 

center height of 45 m AGL, 0 dBi receive antenna, ground constants: σ = 0.005 S/m and εr = 

15.0. 

Figure 6 shows the predicted received power level versus distance using the undisturbed field

method for a single folded-dipole transmitter antenna at 45 m AGL and 100 W EIRP and an 

isotropic receiver antenna at a height of 1.5 m. The transmit antenna operates at the fundamental 

frequency of 409.2 MHz and is mounted on a two-inch diameter metal mast. Also shown in this 

figure is the system’s response at 1227.6 MHz, assuming that spurious emissions were 90 dB 

below the power at the fundamental frequency. For reference, the third harmonic response is 

compared to the predicted received power assuming an isotropic transmitter antenna and free

space pathloss. The free space curve intersects the vertical axis at -107.0 dBm. This matches our 

previous estimate of received power that we obtained in Section 2.2. The undisturbed field

method predicts a spike in the power at horizontal distance of ~20 m from the base. At this 

distance, the free space and undisturbed field methods are in close agreement. However, the two 

curves diverge by more than 20 dB at 100 m, and the free space model consistently 

underestimates the received power at distances greater than 300 m. We gain a more detailed 

understanding of the environment surrounding the tower using the undisturbed field method 

because the free space model does not consider constructive interference due to ground

reflections and exaggerates the gain at the antenna’s nadir.
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Received Third Harmonic Power at 1227.6 MHz (free space)

Received Third Harmonic Power at 1227.6 MHz

Received Fundamental Power at 409.2 MHz

Distance (m)

Received Power (dBm)

Figure 7. Received power from a four-element collinear folded-dipole array transmitter antenna, 

100 W EIRP, antenna center height of 45 m AGL, 0 dBi receive antenna, ground constants: σ = 

0.005 S/m and εr = 15.0.

Similarly, Figure 7 shows the received power for the same system except with a four-element 

collinear folded-dipole array antenna. This is a more common antenna type for base station 

applications, since it provides an additional 5 dB of gain on the horizon. Again, the transmit 

power is adjusted to achieve a normalized EIRP of 100 W. This plot exhibits greater lobe 

structure than that of the single-element antenna case. 

Nulls in the received power are most easily mapped to nulls in the vertical antenna pattern by 

working backwards from maximum to minimum distances as the vertical pattern angle ranges 

from 0 to 90 degrees. Consider the fundamental frequency first. The main beam covers distances

from the horizon down to the null at approximately 120 m. The first lower lobe covers from 

120 m to 45 m. The null at 45 m corresponds to a vertical angle of approximately 45 degrees 

below the horizon, since the change in height from the transmit to receive antennas is 45 – 1.5 = 

43.5 m. The last lobe on the plot from 10 to 45 m corresponds to the second lower sidelobe. Note 

also the substantial null at the antenna’s nadir.

Consider the received power curve for the third harmonic shown in black in Figure 7. The 

various peaks illustrated in the plot occur at the following antenna elevation angles:
14

Table 1. Received Power Plot Features as a Function of Antenna Elevation Angle 

Range (m) Elevation angle, Notes

1000 2.6o main beam

250 10o 1

st lower sidelobe peak

140 18o 2

nd lower sidelobe peak

80 29o 3

rd lower sidelobe peak

55 39o 4

th lower sidelobe peak

20 66o 6

th lower sidelobe peak

Note that the maximum received power of -105 dBm occurs on the 6th lower sidelobe at 66 

degrees below the horizon. This sidelobe is only 2 dB down from the antenna’s peak gain at the 

boresight angle shown in Figure 5. This predicted received power level is 2 dB stronger than the

estimate of -107.0 dBm from Section 2.2. The undisturbed field method demonstrates that these 

stronger power levels are restricted to a very limited range of distances spanning approximately 

20 m. At all other distances, the received power is below -120 dBm. This scenario shows 

substantial divergence between the undisturbed field method and a free space method both at 

closer ranges where the free space method dramatically overestimates and at greater distances 

where it underestimates the received power by more than 10 dB.

The preceding analyses assumed a tower height of 45 m, which is a common LMR base station 

height. For the sake of completeness, an analysis was prepared for both antenna types at a lower 

antenna height. A height of 15 m served as a reasonable lower bound. Figure 8 and Figure 9

show the results of this analysis for the single-element and four-element collinear folded-dipole

antennas, respectively.
15

-180

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

0 100 200 300 400 500 600 700 800 900 1000

Received Third Harmonic Power at 1227.6 MHz (free space)

Received Third Harmonic Power at 1227.6 MHz

Received Fundamental Power at 409.2 MHz

Distance (m)

Received Power (dBm)

Figure 8. Received power from a single folded-dipole transmitter antenna, 100 W EIRP, antenna 

center height of 15 m AGL, 0 dBi receive antenna, ground constants: σ = 0.005 S/m and εr = 

15.0.

Note that the lower antenna height effectively compresses the lower vertical sidelobes into a 

narrower range adjacent to the base station. For example, compare the position of the null 

between the main beam and the first lobe as depicted in Figure 7 to that depicted in Figure 9. The 

null occurs at ~120 m for the antenna mounted at 45 m AGL and at ~45 m for the antenna 

mounted at 15 m AGL. The lower tower height also results in higher received power levels for a 

given horizontal distance. The maximum received power is ~10 dB stronger for both antenna 

types.
16

-180

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

0 100 200 300 400 500 600 700 800 900 1000

Received Third Harmonic Power at 1227.6 MHz (free space)

Received Third Harmonic Power at 1227.6 MHz

Received Fundamental Power at 409.2 MHz

Distance (m)

Received Power (dBm)

Figure 9. Received power from a four-element collinear folded-dipole array transmitter antenna, 

100 W EIRP, antenna center height of 15 m AGL, 0 dBi receive antenna, ground constants: σ = 

0.005 S/m and εr = 15.0.

3.4 Refinement of the EMC analysis

The preceding analyses predicted received power levels incumbent upon a hypothetical GPS 

receiver in close proximity to LMR base stations in excess of the maximum jammer signal level 

of -113.3 dBm. The model illustrates that the affected regions are restricted to narrow ranges 

within tens of meters from the base station. 

The model can be refined in a number of ways to yield a better estimate of received power and to 

suggest design changes that would satisfy GPS compatibility requirements. First, adjustments to 

account for different EIRPs can be readily derived from the above plots by offsetting the 

received power levels in reference to the normalized EIRP of 100 W. Another possibility is to 

model the receive antenna’s gain and directivity. In addition, measured conducted third harmonic

emission levels could be used rather than applying a worst-case assumption of -90 dBc from the 

spurious response rejection specification. In fact, according to [1], in some scenarios, modest 

decreases (on the order or 5-10 dB) in third harmonic emissions beyond our -90 dBc assumption 

would yield acceptable emission levels in the GPS L2 band.
17

Another refinement to this analysis, one that is a common best practice in LMR base station 

design and would provide the most substantial effect, is to use a transmit filter. Transmit filters

prevent emissions from adjacent collocated transmitters from feeding back into a transmitter and 

mixing to create third-order products. In this application, a filter would have the added benefit of 

suppressing harmonic emissions in the GPS L2 band. Use of a reflective lowpass filter in the 

transmission path would reduce the harmonic emissions to levels below the thermal noise floor. 

For example, our product research identified a commercially available filter for the 406–512 

MHz band with 0.3 dB of passband insertion loss, a 50 W power rating, and more than 50 dB of 

rejection at the third harmonic. Unit cost in low quantities was approximately $350. Filters with 

higher power ratings and similar performance were available for under $850. 

-220

-210

-200

-190

-180

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

0 100 200 300 400 500 600 700 800 900 1000

Received Third Harmonic Power at 1227.6 MHz - 50.0 dB

Received Third Harmonic Power at 1227.6 MHz

Received Fundamental Power at 409.2 MHz

Distance (m)

Received Power (dBm)

Figure 10. Received power from a four-element collinear folded-dipole array transmitter 

antenna, 100 W EIRP, antenna center height of 15 m AGL, 50 dB of out of band rejection, 0 dBi 

receive antenna, ground constants: σ = 0.005 S/m and εr = 15.0.

Consider the worst case of the four preceding analyses—that is, the four-element collinear 

folded-dipole array antenna mounted 15 m AGL. In Figure 10 we reproduce its received power

plot and add a curve that represents the received power with a lowpass filter installed in the 

transmit path. Observe that the predicted received power never exceeds -147 dBm—much lower 

than the -113.3 dBm interference threshold determined in Section 2.2 and even lower than the 

nominal GPS L2 signal level of -135.2 dBm. 
18

4 CONCLUSION

The use of the undisturbed field method to assess the potential for harmful emissions from LMR 

base station transmitters provided greater insight into an EMC analysis than a simple analysis 

based on an isotropic antenna and free space pathloss. The model treated ground interactions and 

accounted for the directivity of various antenna types at both fundamental and third harmonics. 

The undisturbed field method can easily be adapted to treat a variety of antenna types and 

operating frequencies. 

Adjacent to the base station, it provided finer detail and showed that the peak power is 

concentrated in a narrow range of distances. At greater distances, the undisturbed field method 

showed that the simpler isotropic antenna and free space pathloss method actually underpredicted the received power by more than 10 dB in some cases. Finally, we demonstrated that 

the use of bandpass filters would reduce UHF LMR base station emissions in the GPS L2 band 

to levels well below the nominal GPS L2 signal level. 
19

5 REFERENCES

[1] Elliot D. Kaplan, Understanding GPS: Principles and Applications, Boston, MA: Artech 

House, Inc, 1996.

[2] G.J. Burke, “Numerical Electromagnetic Code- NEC-4, Method of Moments Parts I and II,” 

Lawrence Livermore National Laboratory UCRL-MA-109338, January 1992. 

[3] N. DeMinco, “Propagation Loss Prediction Considerations for Close-In Distances and LowAntenna Height Applications,” NTIA Report TR-07-449, July 2007.

[4] G.A Hufford, A.G. Longley and W.A. Kissick, “A Guide to the Use of the ITS Irregular 

Terrain Model in the Area Prediction Mode,” NTIA Report 82-100, April 1982.

FORM NTIA-29 U.S. DEPARTMENT OF COMMERCE 

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

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION NO.

TR-11-481

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

4. TITLE AND SUBTITLE

Improved Estimation of the Third-Order Harmonic Emissions of Land Mobile Radio 

Base Stations

5. Publication Date

September 2011

6. Performing Organization Code

ITS.M

7. AUTHOR(S)

Eric D. Nelson and Nicholas DeMinco

9. Project/Task/Work Unit No.

8. PERFORMING ORGANIZATION NAME AND ADDRESS 3152011-300

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.)

NTIA/ITS has developed an improved electromagnetic compatibility (EMC) analysis method that can be applied to more 

accurately model real scenarios for evaluating interference. The methodology described in this report can be used to conduct 

EMC analyses for base stations that use a variety of antennas. The model can be used to determine the received power in the 

proximity of the base station at both the fundamental and harmonic frequencies. It uses accurate radio-wave propagation 

models and antenna models. The antenna models can be created for the fundamental and third harmonic frequencies of many 

antennas. Fields adjacent to the base station antenna are heavily influenced by interactions with ground, and the 

electromagnetic fields are dominated by the side lobe structure of the elevation pattern of the base station antenna. The 

described rigorous EMC analysis for a base station considers all of these factors to assess interference more accurately than

previous methods.

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

undisturbed field method; electromagnetic compatibility; numerical electromagnetics code; land mobile radio; third order 

harmonics; received power; global positioning system; folded-dipole antenna.

17. AVAILABILITY STATEMENT

UNLIMITED.

FOR OFFICIAL DISTRIBUTION.

18. Security Class. (This report)

Unclassified

20. Number of pages

36

19. Security Class. (This page)

Unclassified

21. Price:
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