1The author is with the Institute for Telecommunication Sciences, National

Telecommunications and Information Administration, U.S. Department of Commerce, Boulder,

CO 80305.

A-1

Figure A.1. Amplitude probability distribution.

APPENDIX A. TUTORIAL ON USING AMPLITUDE PROBABILITY DISTRIBUTIONS

TO CHARACTERIZE THE INTERFERENCE

OF ULTRAWIDEBAND TRANSMITTERS TO NARROWBAND RECEIVERS

Robert J. Achatz1

A.1 Introduction

The amplitude probability distribution function (APD) is used in radio engineering to describe

signal amplitude statistics. The APD and its corresponding graph, shown in Figure A.1,

succinctly express the probability that a signal amplitude exceeds a threshold. For example, the

APD in Figure A.1 shows that the signal amplitude rarely exceeds high voltages. Statistics such

as percentiles, deciles, and the median can be read directly from the APD. Other statistics such as

average power can be computed with the APD.

The “signal” the APD characterizes is often noise or interference. For example, APDs are

commonly used to characterize the amplitude statistics of non-Gaussian noise produced by
A-2

lightning or unintentional emissions from man-made electrical or electronic devices. Numerous

studies have shown that average noise power alone cannot predict the performance of receivers

operating in non-Gaussian noise. APD statistics are needed for accurate predictions.

Today, many radio engineers are unfamiliar with the APD and its applications. This is because

most modern receivers are designed to operate in bands with (zero-mean) Gaussian noise which

is completely characterized by the average noise power statistic alone. Consequently, APD

statistics are not needed for more accurate predictions.

Recently, federal spectrum regulators have been asked to allow emissions from ultrawideband

(UWB) transmitters to overlay bands licensed to services that use narrowband receivers. Critics

have charged that UWB transmitters may cause interference to ‘victim’ narrowband receivers. 

The amplitude statistics of this potential interference are dependent upon the specifications of the

UWB signal and the band limiting filter in the narrowband receiver. The APD can be used to

characterize this interference and correlate UWB signal and band limiting filter specifications to

narrowband receiver performance.

The purpose of this tutorial is to introduce basic APD concepts to radio engineers and spectrum

regulators who have not previously used the APD. It is hoped that these concepts will provide a

firm basis for discussions on regulation of UWB transmitters. Emphasis is placed on

understanding features likely to be found in band limited UWB signal APDs. These features are

demonstrated with “tutorial” APDs of Gaussian noise, sinusoid (continuous wave) signals, and 

periodically pulsed sinusoid signals. Although the audience is intended to be broad, a limited

number of mathematic expressions are used to avoid the ambiguity found in everyday language. 

A.2 Signal Amplitude Characterization

A.2.1 APD Fundamentals

A bandpass signal is a signal whose bandwidth is much less than the center frequency. Bandpass

signals are expressed mathematically as 

s(t) = A(t)cos(2Bf

c+2(t)) ,

where A(t) is the baseband amplitude, 2(t) is the baseband phase, and fc is the center frequency. 

The amplitude and phase define the complex baseband signal, A(t)ej2(t), whose spectrum is

centered about 0 Hz.

The amplitude is always positive and is considered to be a random variable, A, when

characterized by an APD. Formally, a new random variable, An

, is present at each sampling

instant. The set {A1,A2, ... AN} is called the random sample of the random variable A if each 
A-3

random variable is independent and identically distributed. Realizations or values of the random

sample are denoted by the set {a1,a2, ... aN}. 

Associated with every random variable is a probability density function (PDF). The discrete PDF

expresses the probability that a random variable “A” will have a realization equal to “ai”:

p(ai) = P(A=ai) ,

where P() is the probability of its argument. PDF values are positive and the area under a PDF is

equal to 1.0.

The cumulative distribution function CDF expresses the probability that a random variable “A”

will have a realization less than or equal to “a”:

c(a) = P(A#a) .

The discrete CDF is obtained by integrating the discrete PDF

c a p ai ,

i

( ) = ∑ ( )

for all ai less than or equal to a. CDF values range from 0.0 to 1.0. 

Radio engineers are generally more concerned about how often a noise or interference amplitude

exceeds a threshold. Thus they often prefer to use the complement of the CDF (CCDF) or APD. 

The APD function expresses the probability that a random variable “A” will have a realization

greater than “a”:

cc(a) = P(A>a) .

The discrete APD is obtained by subtracting the discrete CDF from 1.0.

cc(a) = 1.0-c(a) .

For clarification, Figure A.2 shows graphs of the discrete PDF, CDF, and APD for the random

sample realizations:

{a1,a2,...a10} = {1,2,3,3,1,4,4,3,4,3} volts.

The discrete PDF is estimated from the histogram. By convention, the axes of the APD are

oriented differently from the axes of the CDF and PDF.
A-4

Figure A.2. Example histogram (a), probability

density function (b), cumulative

distribution function (c), and amplitude

probability distribution function (d).
A-5

Figure A.3. Language of statistics.

A.2.2 Statistic fundamentals

Statistics are functions that operate on the random sample. The statistic value is the result of a

statistic operating on random sample values. Figure A.3 illustrates these relationships. Common

statistical functions are percentile, mean or average, and root mean square (RMS). First-order

statistics, addressed in this tutorial, assume the random variables are independent and identically

distributed. Second-order statistics, not addressed in this tutorial, measure the correlation

between these random variables. Stationary statistics are independent of time whereas nonstationary statistics are functions of time. Noise and interference amplitude statistics are nonstationary in many cases. Thus radio engineers sometimes measure the statistics of the amplitude

statistics such as the median average noise power.

Percentile amplitude statistics can be read directly from the APD. Peak and median amplitude

statistics are the most widely used percentile statistics. The peak statistic is sometimes arbitrarily

defined by the amplitude that is exceeded 0.0001% of the time:

Vp = cc-1(0.000001) ,

where a = cc-1(P(A>a)). The median statistic is defined by the amplitude that is exceeded 50% of

the time:

Vmedian = cc-1(0.5) .
A-6

The mean and RMS statistics are determined directly from the random sample values. The mean

statistic is defined by:

V ,

N

a mean n

n

= ∑

1

where N is the number of samples. The mean-logarithm statistic is defined by:

V ,

N

a mean n

n

−log = ∑ log ( )

1

10

and the RMS statistic is defined by: 

V .

N

RMS an

n

= ∑

1 2

The discrete APD and its corresponding discrete PDF can be used to calculate the mean and RMS

statistics if the random sample values are no longer available. The choice of histogram bin size

may affect the accuracy of these statistics. In this case the mean statistic is defined by: 

V a p a , mean i

i

i = ∑ ( )

where ai represents a discrete PDF value. The mean logarithm statistic is defined by: 

V a p a , mean i i

i

−log = ∑ log ( ) ( )10

and the RMS statistic is defined by:

V a p a .

RMS i i

i

= ∑

2

( )

As a reference, statistical values for the tutorial PDF presented in section 2.1 are 4.0, 3.0, 2.8,

0.4, and 3.0 for the peak, median, mean, mean logarithm, and RMS statistics.

A.2.3 Graphing the APD

The APD of Gaussian noise is of particular interest to radio engineers because it is encountered in

many practical applications. The amplitude of Gaussian noise is Rayleigh distributed. A Rayleigh

distributed random variable is represented by a straight, negatively-sloped line on a Rayleigh

graph. Figure A.4 shows the APDs of Gaussian and non-Gaussian noise on a Rayleigh graph.

The Rayleigh graph displays probability on the x-axis and amplitude on the y-axis. The

probability is scaled by the function 

x = 0.5log10(-ln(P(A>a))) ,
A-7

Figure A.4. Gaussian noise and non-Gaussian noise APDs plotted

on a Rayleigh graph.

and converted to percent to represent the “percent (of samples or time) exceeding ordinate.” The

amplitude in volts is converted to units of power such as dBW, i.e. scaled by the function

y = 20log10(A) ,

or alternatively it is displayed in dB relative to a standard noise power density or noise power.

Figure A.4 shows the statistics of Gaussian noise on a Rayleigh graph. Gaussian noise average

power or RMS voltage corresponds to the power or voltage that is exceeded 37% of the time. 

Gaussian noise peak voltage is approximately 10 dB above RMS voltage. Gaussian noise average

voltage, median voltage, and average-logarithm voltage are approximately 1dB, 2 dB, and 2.5 dB

below RMS voltage respectively.
A-8

Figure A.5. Random noise (a), amplitude (b), and

power spectral density (c).

A.3 Tutorial APDs

A.3.1 Random Noise

Band limited random noise, i.e. the random noise present after a band limiting filter, is a randomamplitude and random-phase bandpass “signal” defined by

n(t) = A(t)cos(2Bf

c+2(t)) .

Band limited random noise is represented in the frequency domain by a power spectral density

(PSD) in units of watts/Hz. The random noise “signal,” amplitude, and PSD are shown in

Figure A.5. 

Band limited noise average power is computed from the noise PSD 

P N f df ,

f BW

f BW

c

c

=

−

+

∫

( )

/

/

2

2
A-9

Figure A.6. Bandlimited Gaussian noise APDs with two

different bandwidths. BW1 is greater than

BW2.

where N(f) is the noise PSD in units of watts/Hz. Band limited white noise power density is

constant over the band limiting filter bandwidth. As a result, the average noise power is directly

proportional to the filter bandwidth and the RMS amplitude is directly proportional to the square

root of bandwidth. This is sometimes referred to as the “10log10 bandwidth” rule. The amplitude

of band limited Gaussian noise is Rayleigh distributed. Figure A.6 shows the APD of band limited

white-Gaussian noise (WGN) for two different bandwidths on a Rayleigh graph.

A.3.2 Sinusoid Signal

The sinusoid (continuous wave) signal is a narrowband, constant amplitude and constant phase

signal. It is defined by

s(t) = Acos(2Bf

c+2) .

The signal, signal amplitude, and amplitude spectrum are shown in Figure A.7. The APD of the

sinusoid signal is a flat line from the lowest to the highest percentile on a Rayleigh graph. 

Changing the receiver center frequency can change the amplitude of the sinusoid signal.
A-10

Figure A.8. Sinusoid signal APD without (a)

and with (b) random noise. 

Sinusoid signal with random

noise has Rician amplitude

statistics. The Gaussian noise

APD (c) is included for

reference.

Figure A.7. Sinusoid signal (a), signal

amplitude (b), and amplitude of

the signal spectrum (c).

Widening the bandwidth of a receiver filter in the presence of noise causes the statistics to be

Rician. Rician statistics are dependent on the ratio of the sinusoid power to the noise power. 

The Rician APD corresponds to the sinusoid signal APD when noise is absent and the Rayleigh

APD when the signal is absent. Sinusoid, Rician, and Rayleigh APDs are depicted in Figure A.8.

A.3.3 Periodically Pulsed Sinusoid

The periodically pulsed sinusoid is a deterministic, time-varying amplitude and constant phase

signal defined by

s(t) = A(t)cos(2Bf

c+2) .

The amplitude varies between ‘on’ and ‘off’ pulse states. The ‘on’ duration is the pulse width

(PW) and the repetition rate of pulses is the pulse repetition rate (PRR) or the pulse repetition

frequency (PRF). Amplitude spectrum lines are spaced at the PRR. Amplitude spectrum nulls

are spaced by the reciprocal of the PW. The signal, signal amplitude, and amplitude of the signal

spectrum are shown in Figure A.9.
A-11

Figure A.9. Periodically pulsed sinusoid signal (a), signal amplitude

(b), and amplitude of signal spectrum (c).

The APD of a periodically pulsed sinusoid is dependent on the receiver center frequency, band

limiting filter parameters, and pulse parameters. Pulse overlap distortion is significant until the

band limited pulse bandwidth (BW) exceeds the PRR. The band limited pulse is the pulse present

at the output of the receiver filter. Analytically the band limited pulse is obtained by convolving

the pulse shape with the receiver filter impulse response. Band limited pulses with minimal

overlap are considered independent or resolved. The transmitted pulse shape is fairly well

preserved when the filter BW is greater than 2/PW. The two graphs in Figure A.10 show a

succession of APDs with the different receiver center frequency and BW combinations listed in

Table A.1. The first graph has filter BWs less than the PRR while the second graph has filter

BWs greater than the PRR.
A-12

Figure A.10. Periodically pulsed sinusoid APD with pulse

repetition frequencies less than (a) and greater

than (b) the receiver filter bandwidth. See Table

A.1 for receiver center frequency and filter

bandwidth conditions for curves a-f.
A-13

Table A.1. Figure A.10 APD Conditions

Figure, Curve Receiver Center Frequency Bandwidth

A.10a, a Tuned to spectral line Filter BW<< PRR

A.10a, b Tuned to spectral line Filter BW< PRR

A.10a, c Tuned off spectral line Filter BW< PRR

A.10b, d Tuned to pulse center frequency Band limited pulse BW>PRR

A.10b, e Tuned to pulse center frequency Band limited pulse BW>>PRR

A.10b, f Tuned to pulse center frequency Band limited pulse BW > 2/PW

The APD takes on three characteristics when the filter bandwidth is less than the PRR, as shown

in Figure A.10a. If the center frequency is tuned to a spectral line frequency and the filter

bandwidth is able to resolve the line, it has a sinusoid APD (a). If the center frequency is tuned to

a spectral line frequency, but the filter bandwidth is wider than necessary to resolve the line, it can

have a Rician APD (b). If the center frequency is tuned to avoid a spectral line frequency, it has a

Rayleigh APD (c).

Pulse overlap distortion decreases as the band limited pulse BW increases beyond the PRR as

shown in Figure A.10b. The APDs are clearly non-Gaussian. The APD is somewhat curved at

the lower probabilities for narrow filter bandwidths where there is pulse overlap (d). The APD

flattens at low probabilities for wider filter bandwidths where the pulse overlap is minimal (f).

The low probability amplitudes correspond to the band limited pulse amplitudes. The high

probability amplitudes correspond to the receiver noise amplitudes. The amplitudes at low

probabilities are proportional to filter BW corresponding to a ‘20log10 bandwidth rule’. The

amplitudes at high probabilities are proportional to the square root of filter BW corresponding to

the ‘10log10 bandwidth rule’. The transition probability between these two domains is related to

the band limited pulse duty cycle.
A-14

A.3.4 Summary Table 

Table A.2. summarizes the APD dependencies for the three tutorial signals.

Table A.2. Tutorial Signal APD Dependencies

Signal Receiver Center

Frequency

Receiver Filter Other Parameters

WGN No BW

Sinusoid with WGN Yes BW

Periodically-pulsed

sinusoid with WGN

Yes BW PW, PRR

A.4 Band Limited UWB APDs

A.4.1 UWB Signals

The UWB signal is a train of pulses whose widths (in time) are “ultrashort” and bandwidths (in

frequency) are “ultrawide”. Like the periodically pulsed sinusoid, the pulses are defined by a PW

and PRR. Unlike the periodically pulsed sinusoid, the impulses do not modulate a carrier

frequency prior to being transmitted. 

For some applications the pulse train may be pulse position modulated by a time-dither sequence. 

Time-dithering attenuates the discrete spectral line PSD component caused by periodic pulse

transmission and introduces a continuous, random noise PSD component. The effectiveness of

dithering is dependent on time-dither characteristics such as the distribution of dithering times, the

reference time of the time-dithered pulse (absolute or relative to the last pulse), and the length of

the time-dither sequence.

UWB signals are used in radar and communication devices. These devices reduce power

requirements and alleviate spectral congestion by “gating” the pulse train off when continuous

transmissions are not needed. They also use uncorrelated dither sequences to minimize

interference to other UWB devices operating in the same room or building.

Figure A.11 shows a UWB undithered pulse train, a dithered pulse train, and a gated and dithered

pulse train. Figure A.11 also shows an example UWB signal PSD with continuous and discrete

components.
A-15

Figure A.11. Undithered (a), dithered (b), and dithered and

gated (c) ultawideband signal. Dithered

ultrawideband signal power spectral density

(d) showing discrete and continuous

components. The discrete components are

represented as a curve because the lines

cannot be resolved graphically.

A.4.2 Band Limited UWB Signals

The bandwidth of the interfering UWB signal is typically several orders of magnitude wider than

that of the band limiting filters in the victim narrowband receiver. Thus the pulse shape and BW

of the band limited pulse corresponds to the impulse response and BW of the receiver filter. 

Pulses are independent or resolved when the filter BW is greater than the PRR. Pulses that were

independent or resolved before dithering may not be when dithering is introduced. To remain

resolved, the pulse repetition period must be greater than the sum of the pulse duration and the

maximum dither time.
A-16

Figure A.12. Locations of band limiting filters in narrowband receivers.

Band limiting can occur in several of the narrowband receiver functions including demodulation,

detection, and signal parameter estimation. Signal parameter estimation is necessary to provide

frequency, phase, amplitude, and timing information to the demodulation and detection functions. 

The bandwidths associated with each of these functions may differ by several orders of

magnitude. The relationships among these functions are shown in Figure A.12. 

A.4.3 Band Limited UWB Signal APDs

The undithered UWB signal APD will behave similarly to the periodically pulsed sinusoid APD as

the filter bandwidth is varied from less than the PRR towards filter bandwidths much greater than

the PRR. The dithered UWB signal APD will also behave similarly to the periodically pulsed

sinusoid APD as long as the dithered pulses remain resolved. Figure A.13 shows an example of

the changes that might happen to an unresolved dithered UWB signal APD when dithering is

varied and BW is constant. These effects of dithering are only one possibility among many which

are dependent on frequency, dithering distribution, dither reference time, length of dither

sequence, gating, modulation, and filtering. In filter bandwidths less than the PRR increased

dithering caused this APD to progress from the sinusoid APD to the Rician APD and finally to the

Rayleigh APD. The receiver center frequency in this case was tuned to a spectral line. This

progression is illustrated in Figure A.13a. In filter bandwidths comparable to the PRR, increased

dithering caused this APD to progress from the non-Gaussian noise APD towards the Gaussian

noise APD with Rayleigh distributed amplitudes. This progression is illustrated in Figure A.13b.
A-17

Figure A.13. Effects of increased dithering when

band limiting filter bandwidth is less

than (a) and comparable to (b) the

pulse repetition frequency.
A-18

Figure A.14. Spectrum analyzer block diagram.

A.5 APD Special Topics

A.5.1 APD Measurement

Spectrum analyzer measurements can be used to estimate the APD or an amplitude statistic such

as peak voltage. A block diagram of a spectrum analyzer is shown in Figure A.14. The received

signal is converted to an intermediate frequency, band limited by the variable resolution bandwidth

filter, and compressed by the log amplifier. Compression by the log amplifier extends the dynamic

range of the measurement. The envelope detector extracts the amplitude from the band limited

and compressed signal. The video bandwidth filter is used to (video) average the amplitude. The

peak detector holds the highest amplitude since it was last reset.

The statistics of the APD are derived from independent amplitude measurements. The amplitude

measurements are considered independent if the sample time is 5 to 10 times the resolution

bandwidth. The peak detector is bypassed and video averaging is disabled during an APD

measurement. A histogram of the amplitude measurements is used to estimate the APD as shown

in Section 2.1.

The peak voltage statistic is measured with the peak detector. Video averaging is disabled during

peak detection. Average voltage statistics are measured with the video bandwidth filter. The log

amplifier is bypassed and the peak detector is disabled for this measurement. The integration-time

of the video bandwidth filter is long enough to suppress variation but surely more than the

reciprocal of the resolution bandwidth. Average logarithm voltage statistics are measured in the

same manner as the average voltage; however, the signal is log amplified.
A-19

A.5.2 APD of the Sum of Band Limited UWB Signals

APDs of band limited UWB signals are often collected individually in a laboratory setting. These

APDs are useful for studying the interference of one UWB signal. However, in everyday life,

more than one UWB device may be transmitting at a time. The statistics of the aggregate signal

are conditional on the distributions of the individual band limited UWB signals and the number of

signals that are to be added. Assuming the phases of the band limited UWB signals are uniformly

distributed, four cases of interest emerge as shown in Table A.3.

Table A.3. Distributions of Four Aggregate APD Cases

Distributions of band limited UWB signals

Number of UWB signals Rayleigh Any Distribution

Few (1) Rayleigh (3) Non-Rayleigh

Many (2) Rayleigh (4) Rayleigh

In case 1 and 2 all the band limited UWB signals have Rayleigh distributions and the aggregate is

also Rayleigh distributed. Case 4 is Rayleigh distributed by virtue of the central limit theorem of

statistics. In cases 1,2, and 4 the aggregate power is simply the sum of the individual UWB signal

powers. Measurement system average noise power can be removed from individual APDs before

summing. In addition the average power of the individual APD may have to be reduced by

attenuation due to the propagation channel to compensate for differences in location.

Case number 3 is more difficult for two reasons. First measurement system noise statistics cannot

be removed from the measured statistics. Second, the computation of the aggregate APD

requires using the joint statistics of a band limited UWB signal amplitude and phase distributions. 

For these reasons it is best to measure these statistics as an aggregate.

A.5.3 Performance Prediction

Characterizing the band limited UWB signal with an APD is not enough. Ultimately the effect

that the amplitude statistics have on victim receiver performance has to be determined. The band

limited UWB interference takes three guises: sinusoidal interference, Gaussian noise with

Rayleigh distributed amplitudes, and non-Gaussian noise. The APD is particularly useful for

predicting the performance of non-Gaussian noise.

For example, Figure A.15 shows how the non-Gaussian noise APD can be used to predict bit

error rate (BER) for non-coherent binary frequency-shift keying. The straight, sloped APD is the

result of band limited Gaussian noise produced in the receiver. The stepped APD is the result of

band limited non-Gaussian interference. The average receiver noise power is represented by a
A-20

Figure A.15. Estimation of bit error rate from a nonGaussian noise APD.

horizontal line on the graph. The signal-to-noise ratio (SNR) is represented as another horizontal

line SNR dB above the noise power line. The BER is approximately one-half the probability

where the SNR line intersects the APD curve.

Many modern digital receivers use elaborate error correction and time-interleaving techniques to

correct errors in the received bit sequence. In such receivers, the corrected BER delivered to the

user will be substantially different from the received BER. Computation of BERs in these

receivers will require much more detailed interference information than is contained in the APDs. 

For example, second-order statistics of noise amplitudes describing the time of arrival of noise

amplitudes may be needed.
A-21

A.6 Concluding Remarks

This tutorial has shown that the APD is a useful tool for describing the UWB signal and analyzing

UWB signal interference to victim narrowband receivers. It is useful because it 1) is measurable,

2) provides a variety of statistical values, and 3) can be used to aid in receiver performance

prediction.

The APD gives insight to the potential interference from UWB signals in a wide variety of

receiver bandwidths and UWB characteristics, especially when the combination of interferer and

victim produces non-Gaussian interference in the victim receiver. If the interference is Gaussian,

victim receiver performance degradation is correlated to the interfering signal average power

alone and there is no need for further analysis using the APD. If the interference is non-Gaussian

or sinusoidal, information in the APD may be critical to quantifying its effect on victim receiver

performance degradation. Band limited UWB interference becomes increasingly non-Gaussian as

the victim narrowband receiver bandwidth increases beyond the UWB signal PRR. Band limited

UWB interference becomes increasingly sinusoidal as the victim narrowband receiver bandwidth

decreases below the UWB signal PRR and a spectral line is present within the receiver bandwidth.

Spectrum regulators frequently use amplitude statistics such as peak, RMS, or average logarithm

voltage to regulate transmitters. Further work is needed to determine if these statistics are

strongly correlated to narrowband receiver performance. If these statistics are not correlated to

receiver performance, it may be necessary to set regulatory limits in terms of the APD itself.

A.7 Bibliography

[1] A.D. Spaulding and R.T. Disney, “Man-made radio noise, part 1:Estimates for business,

residential, and rural areas,” OT Report 74-38, Jun. 1974.

[2] A.D. Spaulding, “Digital system performance software utilizing noise measurement data,”

NTIA Report 82-95, Feb. 1982.

[3] A.D. Spaulding,”The natural and man-made noise environment in personal communication

services bands,” NTIA Report 96-330, May 1996.

[4] R.J. Achatz, Y. Lo, P.B. Papazian, R.A. Dalke, and G.A. Hufford, “Man-made noise in the

136-138-MHz VHF meteorological satellite band,” NTIA Report 98-355, Sep. 1998.

[5] R.A. Dalke, “Radio Noise,” in the Wiley Encyclopedia of Electrical and Electronics

Engineering, Vol. 18., J.G. Webster, Ed.,John Wiley & Sons, Inc., New York: N.Y., 1998, pp.

128-140.
A-22

[6] R.J. Matheson, “Instrumentation problems encountered making man-made electromagnetic

noise measurements for predicting communication system performance,” IEEE Transactions on

Electromagnetic Compatibility, Volume EMC-12, Number 4, Nov. 1970.

[7] J.S. Bendat and A.G. Piersol, Measurement and Analysis of Random Data, New York, NY:

John Wiley & Sons, Inc, 1966.

[8] P.L. Meyer, Introductory Probability and Statistical Applications, Second Edition, Reading,

Mass: Addison-Wesley Publishing Company, 1970.
1

The author is with the Institute for Telecommunication Sciences, National

Telecommunications and Information Administration, U.S. Department of Commerce, Boulder,

CO 80305.

B-1

st wt t d k T [ ] ( ) k

k

Np

() () () = ∗ − −−

=

∑δ 1 1

1

w(t) ( t f ) e a [ ] c t f ) = − 12 1 − c 2 2

π (π ( )

APPENDIX B. SIMULATIONS OF TIME AND SPECTRAL

CHARACTERISTICS OF ULTRAWIDEBAND SIGNALS AND THEIR

EFFECTS ON RECEIVERS

Edmund A. Quincy1

B.1 Introduction

In this appendix a class of time-dithered, time-hopped UWB systems is modeled and simulated

from an analytic description of the system. These simulated time waveforms and Fourier

spectrum results are analyzed to show the effect of a receiver’s intermediate frequency (IF)

bandwidth (BW) on peak and average power. These peak and average power curves provide the

basis for establishing a normalized bandwidth correction factor (BWCF) curve and equation. The

BWCF is used to estimate peak power over a range of bandwidths from average power

measurements made in a 1 MHz BW as prescribed by the FCC for Part 15 devices. Simulation of

the UWB devices complements measurements and other analytic model results for these devices.

B.2 UWB Model

The simulated time-dithered ultrawideband system block diagram is shown in Figure B.1. The

system transmits a quasi-periodic, very low duty cycle, dithered pulse train s(t) where delta

functions (narrow pulses in hardware) are pulse position modulated (PPM) and shaped with a

Gaussian 2nd derivative filter w(t). The analytic expression for s(t) and w(t) are provided in (1)

and (1a) where dk is the total dither in time units and Np is the number of pulses in the pulse train.

In the simulation results the number of pulses was set at 100 (10,000 ns). This was estimated to

be similar to the observation window of a spectrum analyzer measurement. The model employed

here is similar to that used by Win and Scholtz [1] except that their pulse trains were infinite in

length, which led to smoothed spectral lines corresponding to this infinite observation window.
B-2

Uniform

Random Dither

PPM

Pulse

Generator

w(t), W(f)

Xtrans

Pulse Train

s(t), S(f)

Binary

Data Dither

+

Clock

Figure B.1. Time-dithered ultrawideband system model.

(2) 

(2a)

The shaping filter for a specific hardware configuration depends on the transmit and receive

antennas and may deviate some from this model. The specific pulse shape is probably not as

important a factor in determining a receiver’s narrow IF BW response as the pulse width and

corresponding BW. The receiver IF filtering will remove pulse shape details if the pulse is

sufficiently narrow and the corresponding BW sufficiently wide, compared to the receiver IF

bandwidth. Shape details are filtered out in these simulations, as will be seen in the IF output

pulses. In this system the dither consists of two components: a pseudo-random time-hopping

dither and a data dither. Usually the time-hopping dither is large compared to the data dither. In

our case the time-hopping dither was uniformly distributed between 0 and 0.5T (50% dither);

whereas the data dither represented binary 0s and 1s with 0 or 0.045T (4.5% dither). The timehopping dither values are commonly generated from a pseudo-noise sequence. An undithered

pulse repetition rate (PRR ) of 10 MHz was used, which made the nominal pulse train period 

T= 100 ns. Simulation results were also obtained for the 0 or the non-dithered case where the

waveforms are periodic with a period T=100 ns resulting in a line spectra with a fundamental

frequency equal to the PRR .

B.3 UWB Simulation

The simulation and power calculation processes are shown in the flow diagram of Figure B.2. 

A periodic impulse train is dithered by the combined amount of dither and then Fourier

transformed using the FFT (Fast Fourier Transform). Then the spectrum is shaped using the

Gaussian 2nd derivative filter transfer function W(f) described by the analytic expression in (2a).

Alternatively, the complex Fourier spectrum, S(f), can be calculated using the analytic expression 

in (2).
B-3

Figure B.2. Simulation and power calculation process.

The transmitted 50% dithered pulse train is shown in the top Figure B.3 plot and an individual

pulse is shown in the bottom plot. The transmitted pulse width was approximately 1 ns and the

corresponding wideband spectrum peaked at 2 GHz with 40 dB down from the peak occurring at

frequencies of 0.25 GHz and 5 GHz. The transmitter spectra are shown in Figure B.4 with

dithered pulse train spectrum (before shaping) shown in the top and the shaped transmitter output

spectrum shown in the bottom. Note that the spectrum before shaping appears quite noise-like

with 50% dither. This random appearance can change significantly with less dither, particularly

below 25% dither. With dithers greater than 50% the random appearance does not change

significantly. With BWs of 100 MHz or less centered about the peak at 2 GHz, the spectrum still

appears quite flat even after shaping.

The transmitter output in Figure B.2 is fed through an ideal channel to a receiver (victim or

spectrum analyzer) where the signal is mixed down to a center frequency of 300 MHz. This

frequency fc now is also the peak frequency of the spectrum. That is, the original peak frequency

fp=2 GHz was mixed down to 300 MHz. Next the mixer output is filtered by a Gaussian-shaped

filter with an adjustable bandwidth. A Gaussian shape was chosen for three reasons: (1) the

spectrum analyzer response, used to make measurements at an IF frequency, resembles a nonsymmetric Gaussian; (2) as more stages of IF filtering are employed, their composite response

usually tends towards a Gaussian; and (3) simplicity. Bandwidths were employed from 100 MHz

down to 0.3 MHz. The IF filter was followed by an envelope detector implemented by computing

the waveform magnitude and lowpass filtering it with a 6-pole Butterworth filter using a BW of

200 MHz. Higher bandwidths allowed some ripple through at the IF frequency.
B-4

0 100 200 300 400 500 600 700 800 900 1000

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Time in nSec

Amplitude

15.5 16 16.5 17

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Time in nSec

Amplitude

Figure B.3. Normalized 2nd derivative Gaussian dithered pulse train (50%

dither); Top: full record, Bottom: exploded view.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

−30

−20

−10

0

10

Frequency in GHz

In Power Spec. in dB (Watts/Hz)

Gaus 2nd Deriv Filter I/O Spectra (Code & Data Dither) [fp=2 GHz,]−−18−Apr−2000

In: PkInPwrSpec(dB/Hz)=13.9794, AvInputPower(dB)=−33.0103

Data Dith = 0 or 0.2ns, Code Dith = 0−50ns 

No. Shift Pos.=4003, Max Shift=50.2ns 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 −100

−80

−60

−40

−20

Frequency in GHz

Out Power in dB (Watts/Hz)

Gaus 2nd Deriv Filt Out: PkXtrSpecPwr(dB/Hz)=11.9234, AvTransPower(dB)=−43.5397

Figure B.4. Transmitter spectra (50% dither); Top: before Gaussian filter,

Bottom: after Gaussian filter.
B-5

220 240 260 280 300 320 340 360 380

−100

−50

0

Frequency in MHz

Magnitude in dB

Victim Receiver Gaussian IF Response to UWB Device (fIF=300 MHz, BW3db=30 MHz, PRF=10 MHz)

IF Filtered Spectrum 

AvRecSpecPwr (Watts) = 7.9201e−007

100 150 200 250 300 350 400 450 500 550 600

−2

0

2

x 10−3

Time in nSec

Amplitude

Pulse Train Out of IF 

 PeakInstRecPwr (Max Pk Sq) = 1.0116e−005

100 150 200 250 300 350 400 450 500 550 600

0.5

1

1.5

2

x 10−3

Time in nSec

Env Amplitude 

Env Det Wav with Butterworth LPF (ButBW=200 MHz)

Figure B.5. Receiver 30 MHz IF bandwidth (50% dither); Top: output spectrum,

Middle: pulsetrain, and Bottom: envelope detected pulse train.

An example output is shown in Figure B.5 employing an IF BW of 30 MHz. The top plot shows

the filtered received spectrum centered at 300 MHz, the center plot contains the pulse train out of

the IF showing the pulsed RF oscillating at approximately the 300 MHz IF frequency. The

bottom plot displays the envelope waveform out of the IF filter. Note the variable spacing of the

pulses corresponding to the 50% dither. At a BW of 30 MHz the pulses out of the IF just touch

each other. For wider BWs they are completely separated and for narrower BWs they are

overlapped, causing peaking in the envelope as observed in Figures B.6 and B.7 for 10 MHz and

3 MHz IF bandwidths respectively. Figures B.8 compare this peaking effect of the detected

envelope for these same 3 BWs over a record length of 100 pulses (10,000 ns). It is particularly

interesting to compare the 50% and 0 dither cases. With the periodic (no dither) pulse train, the

IF filter gets pinged by pulses at a regular interval and just provides periodic pulses out of the

detector without peaking. At a BW of 3 MHz the 50% randomly dithered pulse train creates

significant peaks and valleys (1 down to 0), whereas the periodic pulse train has a constant

envelope coming out of the IF filter.
B-6

270 280 290 300 310 320 330

−100

−50

0

Frequency in MHz

Magnitude in dB

Victim Receiver Gaussian IF Response to UWB Device (fIF=300 MHz, BW3db=10 MHz, PRF=10 MHz)

IF Filtered Spectrum 

AvRecSpecPwr (Watts) = 2.6449e−007

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

−1

−0.5

0

0.5

1

x 10−3

Time in nSec

Amplitude

Pulse Train Out of IF 

 PeakInstRecPwr (Max Pk Sq) = 1.2889e−006

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0.2

0.4

0.6

0.8

1

Time in nSec

Env Amplitude 

Env Det Wav with Butterworth LPF (ButBW=200 MHz)

Figure B.6. Receiver 10 MHz IF bandwidth (50% dither); Top: output

spectrum, Middle: pulse train, and Bottom: envelope

detected pulse train.

280 285 290 295 300 305 310 315 320 −100

−50

0

Frequency in MHz

Magnitude in dB

Victim Receiver Gaussian IF Response to UWB Device (fIF=300 MHz, BW3db=3 MHz, PRF=10 MHz)

IF Filtered Spectrum 

AvRecSpecPwr (Watts) = 6.314e−008

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

−5

0

5

x 10−4

Time in nSec

Amplitude

Pulse Train Out of IF 

 PeakInstRecPwr (Max Pk Sq) = 4.8328e−007

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0

0.5

1

Time in nSec

Env Amplitude 

Env Det Wav with Butterworth LPF (ButBW=200 MHz)

Figure B.7. Receiver 3 MHz IF bandwidth (50% dither); Top: output

spectrum, Middle: pulse train, and Bottom: envelope

detected pulse train.
B-7

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(BWIF=30 MHz)−−29−Aug−2000

Time in nSec

Normalized LPF Received Waveform Magnitude

Figure B.8.A. Receiver IF envelope for 30 MHz bandwidth with 50% dither.

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

BW3dbIF=30 MHz−−31−Aug−2000

Time in nSec

Normalized LPF Received Waveform Magnitude

Figure B.8.B. Receiver IF envelope for 30 MHz bandwidth with 0% dither.
B-8

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(BWIF=10 MHz)−−29−Aug−2000

Time in nSec

Normalized LPF Received Waveform Magnitude

Figure B.8.C. Receiver IF envelope for 10 MHz bandwidth with 50% dither. 

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

BW3db=10 MHz−−31−Aug−2000

Time in nSec

Normalized LPF Received Waveform Magnitude

Figure B.8.D. Receiver IF envelope for 10 MHz bandwidth with 0% dither. 
B-9

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(BWIF=3 MHz)−−28−Aug−2000

Time in nSec

Normalized LPF Received Waveform Magnitude

Figure B.8.E. Receiver IF envelope for 3 MHz bandwidth with 50% dither. 

100 150 200 250 300 350 400 450 500 550 600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Rec UWB Env Det (Using LP Butterworth) Waveform (BW3db=3 MHz, Xtrans PW=1 nsec, PRF=10 MHz )−−31−Aug−2000

Time in nSec

Normalized LPF Received Waveform Magnitude

Figure B.8.F. Receiver IF envelope for 3 MHz bandwidth with 0% dither.
B-10

B.4 Power Calculations in Receiver IF Bandwidths

Figures B.9 show the received instantaneous peak and average power computed from the

simulated time waveforms for receiver IF bandwidths ranging from 0.3 MHz to 100 MHz. These

powers were normalized to the average power in a BW of 1 MHz (a 1-MHz BW is specified by

the FCC for Part 15 average measurements). Consequently, the average power curves all go

through 0 dB at 1 MHz. These curves provide the basis to develop bandwidth correction factors

(BWCF). The BWCFs are used to estimate the amount of peak power at a given BW, starting

with measuring the average power in this 1-MHz BW.

In addition to peak and average power curves, another guideline is provided. This straight line on

a log-log plot is the 10 log10(BW) average power trend line. It follows the average power quite

well for 50% dither (both pre-detection and post-detection); however, for the non-dithered case it

follows the average power only for BWs greater than or equal to 10 MHz where the pulses are

separated. As pulses overlap for narrower BWs of this non-dithered case, the envelope is

constant and the peak and average power are constant as expected. Consequently the power does

not change as a function of BW. Another way to look at this is in the frequency domain. An

undithered PRR of 10 MHz results in a spectral line at 10 MHz and its harmonics. There is

therefore a line at 2 GHz which is down converted to 300 MHz, the center frequency of the IF

filter. As the BW increases above 10 MHz, more lines are included in the passband and the

power increases linearly with BW. At 10 MHz and below there is a single line in the passband so

that the power remains constant. This is in contrast to the 50% dithered case for narrow BWs

where the peak and average powers change according to a 10 log10BW rule.

For both the 50% dithered and non-dithered cases, the peak power for BWs greater than or equal

to 10 MHz (also the PRR ) increases as 20 log10(BW). This is the BW where pulses become

distinct in the pulsetrain at the output of the IF, as can be seen in the envelopes shown in Figure

B.8.C through Figure B.8.F.

B.5 Reference

[1] M.Z. Win and R.B. Scholtz, “Impulse radio: How it works,” IEEE Communications

Letters, pp. 10-12, Jan. 1998.
B-11

10-1 100 101 102 -20

-15

-10

-5

0

5

10

15

20

25

30

UWB Predetection Characteristics (fc=2 GHz, PW=1 ns, PRF=10 MHz, No Dither)

IF Bandwidth (MHz)

10Log(BW)-10 Av Power Trend

Peak UWB Power 

Average UWB Power 

Figure B.9.B. Receiver peak and average power dependence on IF

bandwidth (predetection, no dither).

10-1 100 101 102 -20

-15

-10

-5

0

5

10

15

20

25

UWB Post Detection Characteristics (fc=2 GHz, PW=1 ns, PRF=10 MHz, No Dither)

IF Bandwidth (MHz)

10Log(BW)-10 Av Power Trend

Peak UWB Power 

Average UWB Power 

Figure B.9.A. Receiver peak and average power dependence on IF

bandwidth (post detection, no dither).
B-12

10-1 100 101 102 -10

-5

0

5

10

15

20

25

30

35

40

UWB Post Detection Characteristics (fc=2 GHz, PW=1 ns, PRF=10 MHz, 50% Dither)

IF Bandwidth (MHz)

10Log(BW) Av Power Trend

Peak UWB Power 

Average UWB Power 

Figure B.9.C. Receiver peak and average power dependence on IF

bandwidth (post-detection, 50% dither).

10-1 100 101 102 -10

-5

0

5

10

15

20

25

30

35

40

UWB Predetection Characteristics (fc=2 GHz, PW=1 ns, PRF=10 MHz, 50% Dither)

IF Bandwidth (MHz)

10Log(BW) Av Power Trend

Peak UWB Power 

Average UWB Power 

Figure B.9.D. Receiver peak and average power dependence on IF

bandwidth (pre-detection, 50% dither).
1The author is with the Institute for Telecommunication Sciences, National

Telecommunications and Information Administration, U.S. Department of Commerce, Boulder,

Colorado 80305.

2

 In this appendix, quantities in linear units (e.g., milliwatts) are written in lower case;

decibel quantities [10 log (linear power ratio)] are written in upper case.

C-1

APPENDIX C. CONVERSION OF POWER MEASURED IN A CIRCUIT TO INCIDENT

FIELD STRENGTH AND INCIDENT POWER DENSITY, AND CORRECTIONS TO

MEASURED EMISSION SPECTRA FOR NON-CONSTANT EFFECTIVE APERTURE

MEASUREMENT ANTENNAS

Frank Sanders1

This appendix derives conversions between power measured in a circuit and incident field strength

and effective radiated power from a transmitter.2 Necessary corrections to measured emission

spectra for non-constant effective aperture measurement antennas are also derived and explained.

C.1 Directivity, Gain, Effective Antenna Aperture, and Antenna Correction Factor

The starting point is directivity and gain, which are both measures of how well energy is

concentrated in a given direction. Directivity, d, is the ratio of power density, pden in that

direction, to the power density that would be produced if the power were radiated isotropically,

pden-iso:

(C.1)

The reference can be linearly or circularly polarized. By geometry, directivity is:

d (C.2)

p

E d

den

E

=

∫ ∫

4

2

p

m Ω

where E is the field strength [1]. Directivity makes reference only to power in space around the

antenna; it is unrelated to power at the antenna terminals. There is loss between the terminals and

free space. Gain, g, includes these antenna losses; gain is the field intensity produced in the given

direction by a fixed input power, pin, to the antenna. Gain and directivity are related by 

efficiency, ,:
C-2

(C.3)

or,

(C.4)

Through reciprocity, directivity is independent of transmission or reception, as is gain. Effective

antenna aperture, ae is unrelated to the physical aperture of an antenna. ae is defined as:

(C.5)

where 8 is the free-space wavelength. Note that ae has the units of area. For an antenna matched

to a load, the power in the load, pload, is related to the free-space power density by ae:

(C.6)

If pload is in a 50-ohm circuit and pden is in a free-space impedance of 377 ohms, then the following

relations apply:

(C.7a)

and

(C.7b)

Rewriting Eq. C.6 gives:

(C.8)

Note that the voltage in the circuit, V

2

load, is in units of volts, but that the free-space field strength,

V

2

space is in units of volts/m. The effective aperture, in units of m2

, converts the free-space power

density on the right to the power in a circuit on the left.
C-3

At this point, we introduce the antenna correction factor, acf, which is defined as follows:

(C.9)

Note that acf has the units of m-2. Rewriting Eq. C.8 with this substitution for acf gives:

(C.10)

Because ae is dependent upon both gain and frequency, so is acf. Substituting Eq. C.5 into

Eq. C.6 gives:

(C.11)

If the frequency, f, is in megahertz, then the substitution [8= c/(fA106) = 3A108/(fA106)] gives:

(C.12)

which, calculating the constant term values, gives:

(C.13)

Taking 10log(acf) gives ACF in dB:

(C.14)

C.2 Free Space Field Strength Conversion

Signals are commonly measured in circuits as either voltages or log-detected voltages

proportional to power. In either case, the signal measurement within a circuit is usually converted

to equivalent power in the circuit impedance. This conversion is usually accomplished

automatically within the measurement device (e.g., a spectrum analyzer). This measured power

within a circuit, pload, is converted to incident field strength using either the antenna correction 
C-4

factor or antenna gain relative to isotropic, as follows. Writing Eq. C.6 with a substitution for ae

from Eq. C.5 gives:

(C.15)

and substituting for (8= c/f), f = 106Af(MHz), and c = 3A108 m/s gives:

(C.16)

For power in milliwatts and field strength in microvolts/meter, the conversions (power, mW) =

1000A(power, W) and (field strength, v/m) = 10-6A(field strength, μV/m) are used:

(C.17)

which, upon computing the constant terms, becomes:

(C.18)

Taking 10log of both sides gives:

(C.19)

Rearrangement of terms yields:

. (C.20)

Note that Pload is related to the power measured within a circuit (e.g., a spectrum analyzer) by the

correction for path gain between the antenna and the analyzer: Pload = Pmeas - (path gain to

antenna). This changes Eq. C.20 to:

(C.21)

Eq. C.21 is key for the conversion of measured power in a circuit into incident field strength in

dBμV/m. For example, suppose that an antenna has gain G = 17 dB, at a frequency of 2300
C-5

MHz, with 28 dB path gain between the antenna and the spectrum analyzer. The measured power

is -12 dBm on the spectrum analyzer display. Then field strength is +87 dBμV/m.

If an equation is required to relate field strength in dBμV/m to the ACF, then Eq. C.8 is used to

relate acf to voltage in a circuit and free-space field strength:

(C.22)

Converting power in watts into power in milliwatts, and converting voltage in volts/meter into

microvolts/meter, gives

(C.23)

which, upon computing the group of constant terms, gives:

(C.24)

and which, taking 10log of both sides, means that

(C.25)

Rearranging terms and substituting [Pmeas - (path gain)] for Pload:

(C.26)

For example, suppose a measurement of -12 dBm is taken on a spectrum analyzer, with 28 dB net

gain in the path between the antenna and the analyzer, and measurement antenna acf of 111

(corresponding to G = 17 dBi at 2300 MHz, as in the example above). Then ACF = 20.5 dB, and

the corresponding free-space field strength is computed using Eq. C.26 to be +87 dBμV/m.

C.3 Effective Isotropic Radiated Power Conversion

It may be necessary to know the effective isotropic radiated power (EIRP) that a device transmits. 

The conversion from measured power in a circuit to EIRP is described in this section.
C-6

Free space loss must be determined: For transmit power (watts) pt; transmit antenna gain relative

to isotropic gt; receive antenna gain relative to isotropic gr; receive power (watts) pr; and receive

antenna effective aperture ae; the effective isotropic radiated power is

(C.27)

and

(C.28)

with r being the distance between the transmit and receive antennas.

The effective aperture of the antenna is the effective aperture of an isotropic antenna multiplied by

the antenna's gain over isotropic, or

(C.29)

A change to decibel units makes Eq. C.28:

(C.30)

Substituting c/f for 8,

(C.31)

If frequency is in megahertz and distance is in meters, then Eq. C.31 becomes

(C.32)

which yields

(C.33)

or

(C.34)
C-7

Similarly, for r in kilometers, Eq. C.31 becomes

(C.35)

and Eq. C.31 for r in miles is

(C.36)

For measurements of Part 15, Part 18, and ultrawideband transmitters, Eq. C.34 is convenient. If

the gain of the receive antenna is known and the received power has been measured at a known

distance from the emitter, then Eq. C.34 can be rearranged to yield EIRP:

(C.37)

If the received power is measured in dBm rather than dBW, Eq. C.37 becomes 

(C.38)

If EIRP in decibels relative to a picowatt (dBpW) is required, then Eq. C.38 becomes:

 . (C.39)

For example, if a value of -10 dBm is measured at a frequency of 2450 MHz, with an antenna gain

+16.9 dBi, at a distance of 3 meters, then the EIRP value is +113 dBpW.

Effective radiated power relative to a dipole (ERPdipole) is sometimes required. EIRP is 2.1 dB

higher than ERPdipole.

Finally, the conversion to incident power density is considered. The incident power density, Pden,

in W/m2, is equal to the incident field strength squared (units of (V/m)

2

), divided by the ohmic

impedance of free space:

(C.40)

Using more common units for field strength of (dBμV/m), and more common units for incident

power of (μW/cm2):

(C.41)
C-8

gives

(C.42)

The incident power density is thus 

 (C.43)

or

 (C.44)

C.4 Correction of Measured Emission Spectra for Non-Constant Effective Aperture

Measurement Antennas

With reference to Eq. C.5, the effective aperture of an isotropic antenna as a function of

frequency, f, is:

(C.45)

or

(C.46)

If gain relative to isotropic, g, is arbitrarily normalized to 4B, then the functional dependence of

effective aperture on frequency is clear:

(C.47)

The effective aperture of a constant-gain isotropic antenna decreases as the square (i.e., 20 log) of

the frequency. If an isotropic antenna were realized physically, and were then used to measure an

emission spectrum, it would be necessary to correct the measured spectrum for this drop in

aperture with increasing frequency.

For an isotropic antenna, the measured spectrum amplitudes would have to be increased as

(20log(frequency)) to represent the energy that would be coupled into a constant effective

aperture. Parabolic reflector antennas in principle have constant apertures; their gain nominally
C-9

5

6

7

8

9

10

11

12

13

14

15

16

17

18

1000 4000 7000 10000 13000 16000

figc-1.ep

Frequency (MHz)

Double-Ridged Horn Gain (dBi)

Figure C.1. Broadband double-ridged waveguide antenna gain as a function of

frequency. The effective aperture would be constant if the gain curve

varied as 20log frequency).

increases at the rate of (20 log(frequency)). Consequently emission spectra measured with highperformance parabolic antennas do not require antenna aperture corrections.

Wideband horn antennas represent an intermediate case between the (-20 log) decrease in

effective aperture of theoretical isotropic antennas and the constant-aperture condition of nominal

parabolic reflector antennas. For example, the gain curve of a widely used double-ridged

waveguide horn (Figure C.1) increases with frequency, but at the rate of approximately

(6.7 log(frequency)). Since this is [(20-6.7)log] = 13.3 log below a constant-aperture condition,

the spectra measured with such an antenna must be corrected at the rate of (13.3 log(frequency)).

Operationally, this correction is performed by ITS engineers as follows: The spectrum is measured

across a given frequency range and the uncorrected curve is stored. During the data analysis

phase, the original spectrum is corrected relative to an arbitrarily chosen frequency, according to

the following equation:

(C.48)
C-10

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

1000 2000 3000 4000 5000

20

30

40

50

60

70

80

90

100

110

figc-2.ep

Correction function:

y=y+(13.3*(log(x/1000)))

Spectrum corrected to

constant-aperture

measurement antenna gain

Uncorrected

spectrum

Frequency (MHz)

Peak Power (dBm)

Peak Field Strength at 1 m (dBuV/m)

Figure C.2. Demonstration of emission spectrum measurement corrected

to a constant effective aperture measurement antenna. With

this correction it becomes possible to add a second axis for

incident field strength.

For example, if a spectrum is measured between 1 GHz and 5 GHz, a convenient reference

frequency might be 1 GHz, since the corrected spectrum will then have a zero correction at the

left-hand side of the graph. The correction will increase from zero at 1 GHz to a maximum of

9.3 dB at 5 GHz on the right-hand side of the graph, as in Figure C.2.

The graph’s power-axis label needs to reflect the fact that the spectrum has been rendered as

measured with a constant-effective-aperture antenna. This can be done in two ways. The first is to

reference the antenna’s gain relative to isotropic at the reference frequency. If the antenna in

question had 5.9 dBi gain at the reference frequency of 1 GHz, then the axis label could read:

“Power measured with constant-aperture antenna, 5.9 dBi gain at 1 GHz (dBm).”

The label above might as easily refer to the antenna correction factor (acf) of the antenna at the

reference frequency. The second method is to compute the effective aperture of the antenna and

quote that in the label. In this example, the gain of 5.9 dBi at 1 GHz yields an effective aperture in

Eq. C.45 of 3.1A10-7 m2. The corresponding axis label could read: 

“Power measured with antenna of constant effective aperture 3.1A10-7 m2 (dBm)”

While accurate, this expression’s reference to an effective aperture is unconventional.

An advantage of correcting a measured emission spectrum to constant measurement antenna

effective aperture is that a second axis can be added to the right-hand side of the graph showing
C-11

field strength. With the effective aperture correction having been made, the field strength becomes

an additive factor to the power measured in a circuit. In this example (5.9 dBi gain at 1 GHz,

constant aperture correction made to the rest of the spectrum), Eq. C.21 is used to arrive at the

following conversion to field strength:

(C.49)

or

(C.50)

Figure C.2 shows an example of a corrected spectrum with the field strength axis added in

accordance with Eq. C.48 and Eq. C.50.

C.5 References

[1] E. C. Jordan, Ed., Reference Data for Engineers: Radio, Electronics, Computer, and

Communications, Seventh ed., Macmillan, 1989, pg. 32-33.
This Page Intentionally Left Blank

This Page Intentionally Left Blank
1The authors are with the Institute for Telecommunication Sciences, National

Telecommunications and Information Administration, U.S. Department of Commerce, Boulder,

CO 80305.

2The authors are with the Radio-Frequency Technology Division, National Institute for

Standards and Technology, U. S. Department of Commerce, Boulder, CO 80305.

D-A-1

APPENDIX D. EMISSION DATA FOR ULTRAWIDEBAND TRANSMITTERS

Frank Sanders,1 Brent Bedford,1 Robert T. Johnk,2 and Robert Matheson1, David R. Novotny2

This appendix contains measured emission spectra and time waveforms for five ultrawideband

transmitters, and also for a Part 15 device (specifically, an electric drill). Measurement techniques

are described in Sections 5 and 6. Analysis and commentary are provided in 

Section 8.
D-A-2

-4

-2

0

2

4

0 5 10 15 20 25

Time (nanoseconds)

V

olts

Figure D.A.1. Device A, conducted time-domain waveform.

-80

-60

-40

-20

0

4000 5000 6000 7000

Frequency (MHz)

dB

m

Figure D.A.2. Device A, conducted power spectrum, )f = 16.67 MHz.
D-A-3

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

4700 4900 5100 5300 5500 5700 5900 6100 6300

10

20

30

40

50

60

70

80

90

100

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

f2r1-7.ep

Frequency (MHz)

Peak Power Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength at 1 m (dBuV/m)

Figure D.A.3. Device A, spectra as a function of measurement bandwidth.

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

100 Hz

300 Hz

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

f2r8.ep

Signal Relative to 3 MHz as a Function of Bandwidth (dB)

Figure D.A.4. Device A, peak signal level as a function of bandwidth.
D-A-4

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.1 0.2 0.3 0.4 0.5

f2r57.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.5. Device A, emission in 10-kHz video bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.1 0.2 0.3 0.4 0.5

f2r58.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.6. Device A, emission in 3-kHz video bandwidth.
D-A-5

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.1 0.2 0.3 0.4 0.5

f2r59.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.7. Device A, emission in 1-kHz video bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.1 0.2 0.3 0.4 0.5

Part 15 measurement converges on

measurement system noise floor

for this device.

Device A turned off

Device A turned on

Spectrum analyzer would

not provide less than

300 Hz video bandwidth

for this Part 15 measurement.

f2r60.ep, plus f2r61.dat

Time (seconds)

Received Signal Level (dBm)

Figure D.A.8. Device A, emission in 300-Hz video bandwidth: converges 

 on measurement system noise floor.
D-A-6

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

5700 MHz

f2r62.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.9. Device A, peak emission in 3-MHz IF bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

f2r63.ep 5700 MHz

Time (seconds)

Received Signal Level (dBm)

Figure D.A.10 Device A, peak emission in 1-MHz IF bandwidth.
D-A-7

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

f2r64.ep 5700 MHz

Time (seconds)

Received Signal Level (dBm)

Figure D.A.11. Device A, peak emission in 300-kHz IF bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

5700 MHz

f2r65.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.12. Device A, peak emission in 100-kHz IF bandwidth.
D-A-8

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

0 0.005 0.010 0.015 0.020

5700 MHz f2r66.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.13. Device A, peak emission in 30-kHz IF bandwidth.

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

0 0.005 0.010 0.015 0.020

5700 MHz

f2r67.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.14. Device A, peak emission in 10-kHz IF bandwidth.
D-A-9

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

0 0.005 0.010 0.015 0.020

5700 MHz

f2r68.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.15. Device A, peak emission in 3-kHz IF bandwidth.

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

0 0.005 0.010 0.015 0.020

f2r70.ep 5700 MHz

Time (seconds)

Received Signal Level (dBm)

Figure D.A.16. Device A, peak emission in 1-kHz IF bandwidth.
D-A-10

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

0 0.005 0.010 0.015 0.020

5700 MHz

f2r71.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.17. Device A, peak emission in 300-Hz IF bandwidth.

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

0 0.005 0.010 0.015 0.020

5700 MHz

f2r72.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.18. Device A, peak emission in 100-Hz IF bandwidth.
D-A-11

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

0 0.005 0.010 0.015 0.020

f2r73.ep 5700 MHz

Time (seconds)

Received Signal Level (dBm)

Figure D.A.19. Device A, peak emission in 30-Hz IF bandwidth.

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

-70

0 0.005 0.010 0.015 0.020

5700 MHz

f2r74.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.A.20. Device A, peak emission in 10-Hz IF bandwidth.
D-A-12

Figure D.A.21. Device A, spectrum fine structure.
D-A-13

-150

-130

-110

-90

-70

-50

.001 .1 1 5 10 20 35 50 70 80 90 95 99

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

Percent exceeding ordinate

d

B

m

Figure D.A.22. Device A, APDs.
D-A-14

Figure D.A.23. Device A, detector summary.
D-B-1

-10

-5

0

5

10

5 10 15 20

Time (nanoseconds)

V

olts

Figure D.B.1. Device B, conducted time-domain waveform.

-50

-30

-10

10

0 1000 2000 3000 4000

Frequency (MHz)

dB

Figure D.B.2. Device B, conducted power spectrum, )f = 20 MHz.
D-B-2

50

70

90

110

130

1000 2000 3000 4000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.B.4. Device B, radiated peak field strength at 1 m, )f = 20 MHz.

-0.2

-0.1

0

0.1

0.2

0 10 20 30 40

Time (nanoseconds)

Volts

Figure D.B.3. Device B, radiated time-domain waveform.
D-B-3

70

80

90

100

110

120

1250 1500 1750

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.B.5. Device B, radiated peak field strength at 1 m, )f = 20 MHz.

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

1150 1250 1350 1450 1550 1650 1750 1850

20

30

40

50

60

70

80

90

100

110

f3r1-6.ep

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

Frequency (M Hz)

Peak Power Through Constant Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength at 1 m (dBuV/m)

Figure D.B.6. Device B, spectra as a function of bandwidth, 16-kB/s voice

mode.
D-B-4

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

1150 1250 1350 1450 1550 1650 1750 1850

20

30

40

50

60

70

80

90

100

110

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

f2r1-6.ep

Frequency (M Hz)

Peak Power Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength at 1 meter (dBuV/m)

Figure D.B.8. Device B, spectra as a function of bandwidth, 128-kB/sec

voice mode.

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 20 40 60

f3r25.ep

100 Hz

300 Hz

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

Dimensionless units

A

mplitude as a Function of Bandwidth Relative to 3 MHz

Figure D.B.7. Device B, in 16-kB/sec voice mode, bandwidth progression

stairstep.
D-B-5

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 20 40 60

f2r7.ep

100 Hz

300 Hz

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

A

mplitude as a Function of Bandwidth Relative to 3 MHz

Figure D.B.9. Device B, in 128-kB/sec voice mode, bandwidth progression

stairstep.

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 0.1 0.2 0.3 0.4 0.5

f13r7.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.10. Device B, 0.5 seconds, 128-kBit/sec mode.
D-B-6

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 0.02 0.04 0.06 0.08 0.10

f13r8.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.11. Device B, 128-kBit/sec mode, 0.1 seconds.

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 0.005 0.010 0.015 0.020

f13r9.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.12. Device B, 128-kBit/second mode, 0.02 seconds.
D-B-7

-0.005

0

0.005

0.010

0.015

0 0.001 0.002 0.003 0.004 0.005

f13r11.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.14. Device B, 128-kBit/second mode, 0.005 seconds, external 

detector.

-0.005

0

0.005

0.010

0.015

0 0.005 0.010 0.015 0.020

f13r10.ep

Time (seconds)

Log Volts

Figure D.B.13. Device B, 128-kBit/second mode, 0.02 seconds, external

log detector.
D-B-8

-0.005

0

0.005

0.010

0.015

0 0.0002 0.0004 0.0006 0.0008 0.0010

f13r12.ep

Time (seconds)

Log Volts

Figure D.B.15. Device B, 128-kBit/second mode, 0.001 seconds, external

log detector.

-0.005

0

0.005

0.010

0.015

0

0.2x10

-4

0.4x10

-4

0.6x10

-4

0.8x10

-4

1.0x10

-4

f13r13.ep

Time (seconds)

Log Volts

Figure D.B.16. Device B, 128-kBit/second mode, 0.1 msec, external log

detector.
D-B-9

-0.005

0

0.005

0.010

0.015

0

0.2x10

-5

0.4x10

-5

0.6x10

-5

0.8x10

-5

1.0x10

-5

f13r14.ep

Time (seconds)

Log Volts

Figure D.B.17. Device B, 128-kBit/second mode, 10 us, external log

detector.

-0.005

0

0.005

0.010

0.015

0

0.2x10

-5

0.4x10

-5

0.6x10

-5

0.8x10

-5

1.0x10

-5

Missing pulse

at this location

is part of data

encoding scheme

for this device

f13r15.ep

Time (seconds)

Log Volts

Figure D.B.18. Device B, 128-kBit/second mode, 10 us, external log

detector.
D-B-10

-0.005

0

0.005

0.010

0.015

0

0.2x10

-5

0.4x10

-5

0.6x10

-5

0.8x10

-5

1.0x10

-5

Missing pulse is

part of data

encoding scheme

for this device

f13r16.ep

Time (seconds)

Log Volts

Figure D.B.19. Device B, 128-kBit/second mode, 10 us, external log

detector.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r20.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.20. Device B, 128-kBit/second mode, 3-MHz IF bandwidth.
D-B-11

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r21.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.21. Device B, 128-kBit/second mode, 1-MHz IF bandwidth.

-80

-40

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r22.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.22. Device B, 128-kBit/second mode, 300-kHz IF bandwidth.
D-B-12

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r23.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.23. Device B, 128-kBit/second mode, 100-kHz IF bandwidth.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r24.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.24. Device B, 128-kBit/second mode, 30-kHz IF bandwidth.
D-B-13

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r25.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.25. Device B, 128-kBit/second mode, 10-kHz IF bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r26.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.26. Device B, 128-kBit/second mode, 3-kHz IF bandwidth.
D-B-14

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r27.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.27. Device B, 128-kBit/second mode, 1-kHz IF bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r28.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.28. Device B, 128-kBit/second mode, 300-Hz IF bandwidth.
D-B-15

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r29.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.29. Device B, 128-kBit/second mode, 100-Hz IF bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

peak detected

1325 MHz

f13r30.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.30. Device B, 128-kBit/second mode, 30-Hz IF bandwidth.
D-B-16

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

1660 MHz

sample detected

f13r36.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.31. Device B, 128-kBit/second mode, 3-MHz video bandwidth.

-90

-75

-60

-45

-30

0 0.005 0.010 0.015 0.020

f13r37.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.32. Device B, 128-kBit/second mode, 1-MHz video bandwidth.
D-B-17

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

1660 MHz

sample detector

f13r39.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.34. Device B, 128-kBit/second mode, 100-kHz video

bandwidth.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

1660 MHz

sample detector

f13r38.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.33. Device B, 128-kBit/second mode, 300-kHz video

bandwidth.
D-B-18

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

1660 MHz

sample detector

f13r40.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.35. Device B, 128-kBit/second mode, 30-kHz video bandwidth.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

1660 MHz

sample detector

f13r41.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.36. Device B, 128-kBit/second mode, 10-kHz video bandwidth.
D-B-19

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

sample detector

1660 MHz

f13r42.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.37. Device B, 128-kBit/second mode, 3-kHz video bandwidth.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

sample detector

1660 MHz

f13r43.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.38. Device B, 128-kBit/sec mode, 1-kHz video bandwidth.
D-B-20

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

sample detector

1660 MHz

f13r44.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.39. Device B, 128-kBit/second mode, 300-Hz video bandwidth.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

sample detector

1660 MHz

f13r45.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.40. Device B, 128-kBit/second mode, 100-Hz video bandwidth.
D-B-21

-80

-40

0 0.005 0.010 0.015 0.020

sample detector

1660 MHz

F13r46.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.41. Device B, 128-kBit/second mode, 30-Hz video bandwidth.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0 0.005 0.010 0.015 0.020

sample detector

f13r47.ep 1660 MHz

Time (seconds)

Received Signal Level (dBm)

Figure D.B.42. Device B, 128-kBit/second mode, 10-Hz video bandwidth.
D-B-22

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 0.1 0.2 0.3 0.4 0.5

1325 MHz

f3r13.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.43. Device B, 16-kBit/second mode, 3-MHz IF bandwidth,

positive peak detector.

0.2

0.4

0.6

0.8

1.0

0

0.2x10

-4

0.4x10

-4

0.6x10

-4

0.8x10

-4

1.0x10

-4

1325 MHz

f3r16.ep

Time (seconds)

Log Volts

Figure D.B.44. Device B, 16-kBit/second mode, external log detector.
D-B-23

0

0.01

0.02

0

1x10

-5

2x10

-5

3x10

-5

4x10

-5

5x10

-5

1325 MHz

f3r21.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.B.45. Device B, 16-kBit/second mode, external detector.
D-B-24

-130

-110

-90

-70

-50

-30

.001 .1 1 5 10 20 35 50 70 80 90 95 99

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

Percent exceeding ordinate

d

B

m

Figure D.B.46. Device B, 16 kb/s APDs.
D-B-25

-130

-110

-90

-70

-50

-30

.001 .1 1 5 10 20 35 50 70 80 90 95 99

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

Percent exceeding ordinate

d

B

m

Figure D.B.47. Device B, 128 kb/s APDs.
D-B-26

Figure D.B.48. Device B, detector summary.
D-B-27

Figure D.B.49. Device B, detector summary
This Page Intentionally Left Blank

This Page Intentionally Left Blank
D-C-1

-0.02

-0.01

0

0.01

0.02

5 10 15

Time (nanoseconds)

V

olts

Figure D.C.1. Device C, radiated time-domain waveform.

40

50

60

70

80

90

1000 2000 3000 4000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.C.2. Device C, radiated peak field strength at 1 m, )f = 20 MHz.
D-C-2

40

50

60

70

80

90

1000 2000 3000 4000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.C.3. Device C, radiated peak field strength at 1 m, )f = 20 MHz.

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

1000 2000 3000 4000 5000

20

30

40

50

60

70

80

90

100

110

intrson2.ep

Nominal 500 ns (2 MHz) pulse rate,

with 6 ns pulse-to-pulse dither.

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz 3 M Hz

10 M Hz

20 MHz

Frequency, MHz

Peak Power Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength at 1 m (dBuV/m)

Figure D.C.4. Device C, 1.25% pulse-to-pulse dithered.
D-C-3

0

0.0025

0.0050

0.0075

0.0100

0

0.2x10

-5

0.4x10

-5

0.6x10

-5

0.8x10

-5

1.0x10

-5

f21r6.ep

Time (seconds)

Received Signal Level (log volts)

Figure D.C.6. Device C, time waveform for 10 microseconds, 18-Ghz

envelope detector.

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

f2r7.ep

100 Hz

300 Hz

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

1 MHz 300 kHz

3 MHz

Received Power, Relative to 3 MHz Bandwidth (dB)

Figure D.C.5. Device C, bandwidth progression stairstep.
D-C-4

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0

0.5x10

-7

1.0x10

-7

1.5x10

-7

2.0x10

-7

f21r8.ep

Time (seconds)

Received Signal Level (log volts)

Figure D.C.8. Device C, time waveform, 200 nsec, bandwidth-limited by

oscilloscope.

0

0.0025

0.0050

0.0075

0.0100

0

0.2x10

-6

0.4x10

-6

0.6x10

-6

0.8x10

-6

1.0x10

-6

f21r7.ep

Time (seconds)

Received Signal Level (log volts)

Figure D.C.7. Device C, time waveform, 1 microsecond, 18-GHz envelope

detector.
D-C-5

-100

-80

-60

-40

-20

0

0 0.005 0.010

f7r6.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.C.10. Device C, Part 15 measurement in 3-kHz video bandwidth.

-100

-80

-60

-40

-20

0

0 0.005 0.010

f7r5.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.C.9. Device C, Part 15 measurement in 10-kHz video bandwidth.
D-C-6

-100

-80

-60

-40

-20

0

0 0.005 0.010

f7r8.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.C.12. Device C, Part 15 measurement in 300-Hz video

bandwidth.

-100

-80

-60

-40

-20

0

0 0.005 0.010

f7r7.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.C.11. Device C, Part 15 measurement in 1-kHz video bandwidth.
D-C-7

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

2107 2109 2111 2113 2115

f3r2.ep

Frequency (MHz)

Recevied Signal Level (dBm)

Figure D.C.14. Device C, sample-detected to show how lines are not

normally visible.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

2107 2109 2111 2113 2115

f3r1.ep

Frequency (MHz)

Recevied Signal Level (dBm)

Figure D.C.13. Device C, peak-detected to show lines in noise.
D-C-8

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 0.004 0.008 0.012

f21r5.ep 3 MHz

Time (seconds)

Peak Detected Power at 1 m on 8 dBi Gain Horn (dBm)

Figure D.C.16. Device C, output in 12 milliseconds.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

2107 2109 2111 2113 2115

f3r3.ep

Frequency (MHz)

Recevied Signal Level (dBm)

Figure D.C.15. Device C, video-averaged with peak detector to force lines

to show.
D-C-9

-120

-110

-100

-90

-80

-70

-60

-50

0

0.5x10

-6

1.0x10

-6

1.5x10

-6

2.0x10

-6

f21r10.ep

Time (seconds)

Measured Power at 1 m on 8 dBi Gain Horn (dBm)

Figure D.C.18. Device C, time waveform in 10-MHz bandwidth.

-120

-110

-100

-90

-80

-70

-60

-50

-40

0

0.5x10

-6

1.0x10

-6

1.5x10

-6

2.0x10

-6

f21r11.ep

Time (seconds)

Measured Power at 1 m on 8 dBi Gain Horn (dBm)

Figure D.C.17. Device C, time waveform in 20-MHz bandwidth.
D-C-10

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

0 0.2 0.4 0.6 0.8 1.0

f21r4.ep

Time (seconds)

Power at 1 m on 8 dBi Gain Horn (dBm)

Figure D.C.20. Device C, output in one second.

-120

-100

-80

-60

-40

-20

0 0.01 0.02 0.03 0.04 0.05

f4r1.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.19. Device C, time waveform in 55 ms, 3-MHz IF bandwidth.
D-C-11

-120

-100

-80

-60

-40

-20

0 0.01 0.02 0.03 0.04 0.05

f4r3.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.22. Device C, time waveform, 55 ms, 300-kHz IF bandwidth.

-120

-100

-80

-60

-40

-20

0 0.01 0.02 0.03 0.04 0.05

f4r2.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.21. Device C, time waveform, 55 ms, 1-MHz IF bandwidth.
D-C-12

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.01 0.02 0.03 0.04 0.05

f4r5.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.24. Device C, time waveform, 55 ms, 30-kHz IF bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.01 0.02 0.03 0.04 0.05

f4r4.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.23. Device C, time waveform, 55 ms, 100-kHz IF bandwidth.
D-C-13

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

0 0.01 0.02 0.03 0.04 0.05

f4r8.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.26. Device C, time waveform, 55 ms, 1-kHz IF bandwidth.

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.01 0.02 0.03 0.04 0.05

f4r7.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.25. Device C, time waveform, 55 ms, 3-kHz IF bandwidth.
D-C-14

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

0 0.01 0.02 0.03 0.04 0.05

f4r12.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.28. Device C, time waveform, 55 ms, 10-Hz IF bandwidth.

-140

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

0 0.01 0.02 0.03 0.04 0.05

f4r11.ep

Sample detection

Time (seconds)

Received Signal Level (dBm)

Figure D.C.27. Device C, time waveform, 55 ms, 30-Hz IF bandwidth.
D-C-15

-140

-120

-100

-80

-60

-40

.001 .1 1 5 10 20 35 50 70 80 90 95 99

20 MHz

10 MHz

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

10 MHz

20 MHz

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure D.C.29. Device C, APDs, between lines.
D-C-16

-150

-130

-110

-90

-70

-50

.001 .1 1 5 10 20 35 50 70 80 90 95 99

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure D.C.30. Device C, APDs, on lines.
D-C-17

Figure D.C.31. Device C, detector summary (between spectral lines).
D-C-18

Figure D.C.32. Device C, detector summary (on spectral lines).
D-D-1

-2

-1

0

1

2

5 10

Time (nanoseconds)

V

olts

Figure D.D.1. Device D, conducted time-domain waveform.

-60

-40

-20

0

0 2000 4000 6000

Frequency (MHz)

dB

m

Figure D.D.2. Device D, conducted power spectrum, )f = 49.95 MHz.
D-D-2

-0.030

-0.015

0

0.015

0.030

10 20 30

Time (nanoseconds)

V

olts

Figure D.D.3. Device D, radiated time-domain waveform.

40

50

60

70

80

90

1000 2000 3000 4000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.D.4. Device D, radiated peak field strength at 1 m, 

)f = 19.98 MHz.
D-D-3

40

50

60

70

80

90

1000 2000 3000 4000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.D.5. Device D, radiated peak field strength at 1 m, 

)f = 19.98 MHz.

-120

-110

-100

-90

-80

-70

-60

-50

-40

1000 2000 3000 4000 5000

20

30

40

50

60

70

80

90

ut1spec.ep

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

Cellular

signals

Frequency (M Hz)

Peak Power, Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength, dBuV/m, at 1 m

Figure D.D.6. Device D, absolute dither, 1-MHz nominal PRR, no gating.
D-D-4

-120

-110

-100

-90

-80

-70

-60

-50

-40

1000 2000 3000 4000 5000

20

30

40

50

60

70

80

90

ut13spec.ep

y=y+(13.3*(log(x/1000)))

20 MHz

10 MHz

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

Cellular

signals

Frequency (M Hz)

Peak Power, Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength, dBuV/m, at 1 m

Figure D.D.8. Device D, absolute dither, 10-MHz nominal PRR, 

no gating.

-120

-110

-100

-90

-80

-70

-60

-50

-40

1000 2000 3000 4000 5000

20

30

40

50

60

70

80

90

ut5spec.ep

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

Cellular

signals

Frequency (M Hz)

Peak Power, Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength, dBuV/m, at 1 m

Figure D.D.7. Device D, absolute dither, 1-MHz nominal PRR, 

25% gating.
D-D-5

-120

-110

-100

-90

-80

-70

-60

-50

-40

1000 2000 3000 4000 5000

20

30

40

50

60

70

80

90

ut17spec.ep

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

Cellular

signals

Frequency (M Hz)

Peak Power, Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength, dBuV/m, at 1

Figure D.D.9. Device D, absolute dither, 10-MHz nominal PRR, 

25% gating.

-80

-70

-60

-50

-40

-30

-20

-10

0

ut1prog.ep

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

300 Hz

100 Hz

1 MHz

3 Mhz

Level Relative to 3 MHz Bandwidth (dB)

Figure D.D.10. Device D, 1-MHz nominal PRR, no gating, 25% dither

(absolute time base).
D-D-6

-80

-70

-60

-50

-40

-30

-20

-10

0

ut13prog.ep

100 Hz

300 Hz

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 Mhz

Level Relative to 3 MHz Bandwidth (dB)

Figure D.D.12. Device D, 10-MHz nominal PRR, no gating, 25% dither

(absolute time base) stairstep.

-80

-70

-60

-50

-40

-30

-20

-10

0

ut5prog.ep

100 Hz

300 Hz

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

Level Relative to 3 MHz Bandwith (dB)

Figure D.D.11. Device D, 1-MHz nominal PRR, 25% gating, 25% dither

(absolute time base) stairstep.
D-D-7

0.4

0.6

0.8

1.0

0

0.2x10

-6

0.4x10

-6

0.6x10

-6

0.8x10

-6

1.0x10

-6

20mhz.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.D.14. Device D, 10-MHz nominal PRR, no gating, 25% dither,

20-MHz measurement bandwidth.

-80

-70

-60

-50

-40

-30

-20

-10

0

ut17prog.ep

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

1 Hz

300 Hz

100 Hz

Level Relative to 3 MHz Bandwidth (dB)

Figure D.D.13. Device D, 10-MHz nominal PRR, 25% gating, 25% dither

(absolute time base) stairstep.
D-D-8

0.6

0.7

0.8

0.9

0

0.2x10

-6

0.4x10

-6

0.6x10

-6

0.8x10

-6

1.0x10

-6

10mhz.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.D.15. Device D, 10-MHz nominal PRR, no gating, 25% dither,

10-MHz measurement bandwidth.

-38.5

-38.0

-37.5

-37.0

-36.5

-36.0

0 0.005 0.010 0.015 0.020

3mpktime.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.D.16. Device D, 10-MHz nominal PRR, no gating, 25% dither, 3-

MHz measurement bandwidth.
D-D-9

-38.0

-37.5

-37.0

-36.5

1557 1559 1561 1563

3mhzline.ep

Frequency (MHz)

Received Signal Level (dBm)

Figure D.D.18. Device D, 10-MHz nominal PRR, no gating, 25% dither, 3-

MHz bandwidth.

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

3msample.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.D.17. Device D, 10-MHz nominal PRR, no gating, 25% dither, 3-

MHz bandwidth, sample detector.
D-D-10

-55

-50

-45

-40

1557 1559 1561 1563

300kline.ep

Frequency (MHz)

Received Signal Level (dBm)

Figure D.D.20. Device D, 10-MHz nominal PRR, no gating, 25% dither, 

300-kHz measurement bandwidth.

-45

-42

-39

1557 1559 1561 1563

1mhzline.ep

Frequency (MHz)

Received Signal Level (dBm)

Figure D.D.19. Device D, 10-MHz nominal PRR, no gating, 25% dither, 

1-MHz measurement bandwidth..
D-D-11

-60

-55

-50

-45

1557 1559 1561 1563

100kline.ep

Frequency (MHz)

Received Signal Level (dBm)

Figure D.D.21. Device D, 10-MHz nominal PRR, no gating, 25% dither,

100-kHz measurement bandwidth.

-80

-70

-60

-50

1559.0 1559.5 1560.0 1560.5 1561.0

30kline.ep

Frequency (MHz)

Received Signal Level (dBm)

Figure D.D.22. Device D, 10-MHz nominal PRR, no gating, 25% dither,

30-kHz measurement bandwidth.
D-D-12

-100

-90

-80

-70

-60

1559.9 1560.1

3kline.ep

Frequency (MHz)

Received Signal Level (dBm)

Figure D.D.24. Device D, 10-MHz nominal PRR, no gating, 25% dither, 3-

kHz measurement bandwidth.

-80

-70

-60

1559.5 1559.7 1559.9 1560.1 1560.3 1560.5

10kline.ep

Frequency (MHz)

Received Signal Level (dBm)

Figure D.D.23. Device D, 10-MHz nominal PRR, no gating, 25% dither,

10-kHz measurement bandwidth.
D-D-13

-70

-60

-50

-40

0 0.005 0.010 0.015 0.020

peakgate.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.D.26. Device D, 10-MHz nominal PRR, 25% gating, 25% dither, 

3-MHz peak-detected bandwidth.

-90

-70

1559.9 1560.1

1kline.ep

Frequency (MHz)

Received Signal Level (dBm)

Figure D.D.25. Device D, 10-MHz nominal PRR, no gating, 25% dither, 1-

kHz measurement bandwidth.
D-D-14

-100

-80

-60

-40

0 0.005 0.010 0.015 0.020

sampgate.ep

Time (seconds)

Received Signal Level (dBm)

Figure D.D.27. Device D, 10-MHz nominal PRR, 25% gating, 25% dither, 

3-MHz sample-detected bandwidth.

-120

-100

-80

-60

-40

-20

1559.90 1559.95 1560.00 1560.05 1560.10

ut1-line.ep

Code length

gives 1 kHz

line spacing

Frequency (MHz)

Measured Power, in 50 ohms (dBm)

Figure D.D.28. Device D, 1-kHz emission lines with 1-MHz nominal PRR,

no gating, 25% dither.
D-D-15

-120

-100

-80

-60

-40

-20

1559.980 1559.995 1560.010 1560.025

ut5-line.ep

Code length

gives 1 kHz

line spacing

Frequency (MHz)

Measured Power, in 50 ohms (dBm)

Figure D.D.29. Device D, 1-kHz emission lines with 1-MHz nominal PRR,

25% gating, 25% dither.

-120

-100

-80

-60

-40

-20

1559.90 1559.95 1560.00 1560.05 1560.10

ut13line.ep

Code length

gives 10 kHz

line spacing

Frequency (MHz)

Measured Power, in 50 ohms (dBm)

Figure D.D.30. Device D, 10-kHz emission lines with 10-MHz nominal

PRR, no gating, 25% dither.
D-D-16

-120

-100

-80

-60

-40

-20

1559.95 1560.00 1560.05 1560.10

ut17line.ep

Frequency (MHz)

Measured Power in 50 ohms (dBm)

Figure D.D.31. Device D, 10-kHz emission line with 10-MHz nominal

PRR, 25% gating, 25% dither.

-80

-40

0 0.02 0.04 0.06 0.08 0.10

ut1pt15.ep

Time (seconds)

Part 15 Level, in 50 ohms (dBm)

Figure D.D.32. Device D, Part 15, 1-MHz nominal PRR, no gating, 25%

dither, 10-Hz video bandwidth.
D-D-17

-80

-40

0 0.02 0.04 0.06 0.08 0.10

ut5pt15.ep

Time (seconds)

Part 15 Level, in 50 ohms (dBm)

Figure D.D.33. Device D, Part 15, 1-MHz nominal PRR, 25% gating, 25%

dither, 10-Hz video bandwidth.

-80

-40

0 0.02 0.04 0.06 0.08 0.10

ut13pt15.ep

Time (seconds)

Part 15 Level, in 50 ohms (dBm)

Figure D.D.34. Part 15, 10-MHz nominal PRR, no gating, 25% dither, 

10-Hz video bandwidth.
D-D-18

-80

-40

0 0.02 0.04 0.06 0.08 0.10

ut17pt15.ep

Time (seconds)

Part 15 Level, in 50 ohms (dBm)

Figure D.D.35. Device D, Part 15, 10-MHz nominal PRR, 25% gating, 25%

dither, 10-Hz video bandwidth.
D-D-19

-150

-130

-110

-90

-70

-50

.001 .1 1 5 10 20 35 50 70 80 90 95 99

20 MHz

10 MHz

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

1 MHz

300 kHz

3 MHz

10 MHz

20 MHz

r_d1_b3.ep

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure D.D.36. Device D, 10-MHz PRR, 100% gating, APDs.
D-D-20

-150

-130

-110

-90

-70

-50

.001 .1 1 5 10 20 35 50 70 80 90 95 99

20 MHz

10 MHz

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

10 MHz

20 MHz

r_d2_b3.ep

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure D.D.37. Device D, 10-MHz PRR, 25% gating, APDs.
D-D-21

-150

-130

-110

-90

-70

-50

.001 .1 1 5 10 20 35 50 70 80 90 95 99

20 MHz

10 MHz

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

10 MHz

20 MHz

r_d3_b3.ep

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure D.D.38. Device D, 1-MHz PRR, 100% gating, APDs.
D-D-22

-150

-130

-110

-90

-70

-50

.001 .1 1 5 10 20 35 50 70 80 90 95 99

20 MHz

10 MHz

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

10 MHz 20 MHz

r_d4_d3.ep

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure D.D.39. Device D, 1-MHz PRR, 25% gating, APDs.
D-D-23

Figure D.D.40. Device D, 1-MHz PRR, 25% gating, detector summary.
D-D-24

Figure D.D.41. Device D, 1-MHz PRR, 100% gating, detector summary.
D-D-25

Figure D.D.42. Device D, 10-MHz PRR, 25% gating, detector summary.
D-D-26

Figure D.D.43. Device D, 10-MHz PRR, 100% gating, detector summary.
D-E-1

70

90

110

130

150

500 1000 1500 2000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.E.2. Device E, (300 MHz) radiated peak field strength at 1 m, 

)f = 49.99 MHz.

-0.5

0

0.5

1.0

0 5 10 15 20

Time (nanoseconds)

Volts

Figure D.E.1. Device E, (300 MHz) radiated time-domain waveform.
D-E-2

-0.15

-0.05

0.05

0.15

4 8 12

Time (nanoseconds)

Volts

Figure D.E.3. Device E, (900 MHz) radiated time-domain waveform.

85

95

105

115

1000 2000 3000 4000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.E.4. Device E, (900 MHz) radiated peak field strength at 1 m, 

)f = 49.99 MHz.
D-E-3

-0.10

-0.05

0

0.05

5 10

Time (nanoseconds)

Volts

Figure D.E.5. Device E, (1500 MHz) radiated time-domain waveform.

75

85

95

105

1000 2000 3000 4000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.E.6. Device E, (1500 MHz) radiated peak field strength at 1 m, )f

= 49.99 MHz.
D-E-4

-120

-110

-100

-90

-80

-70

-60

1000 1400 1800 2200

20

30

40

50

60

70

e_spec.ep

Measurement system

noise floor

Frequency (M Hz)

Peak Power Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength at 1 m (dBuV/m)

Figure D.E.8. Device E, (1500 MHz head) spectra as a function of

measurement bandwidth.

95

97

99

101

103

105

1000 1500 2000

Frequency (MHz)

Field Strength (dBuv/m)

Figure D.E.7. Device E, (1500 MHz) radiated peak field strength at 1 m, )f

= 49.99 MHz.
D-E-5

-80

-70

-60

-50

-40

0 0.05 0.10 0.15 0.20 0.25

e-gating.ep

Time (seconds)

Power in 3 MHz Bandwidth (dBm)

Figure D.E.10. Device E, gating behavior.

-60

-50

-40

-30

-20

-10

0

0 10 20 30 40 50 60

e-band.ep

100 Hz

300 Hz

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 M Hz

3 MHz

Dimensionless Units

Power Relative to 3 MHz IF Bandwidth (dB)

Figure D.E.9. Device E, power as a function of measurement bandwidth

stairstep.
D-E-6

-0.0005

0

0.0005

0.0010

0

1x10

-5

2x10

-5

3x10

-5

4x10

-5

5x10

-5

e-train.ep

Time (seconds)

Log Volts (dB)

Figure D.E.11. Device E, pulse train.

-0.0010

-0.0005

0

0.0005

0.0010

0

1x10

-7

2x10

-7

3x10

-7

4x10

-7

5x10

-7

e-pulse.ep

Time (seconds)

Log Volts (dB)

Figure D.E.12. Device E, individual pulse (bandwidth-limited at 50 MHz).
D-E-7

-130

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

0 0.005 0.010 0.015 0.020

e-part15.ep

Part 15 measurement

runs into measurement

system noise floor

Time (seconds)

Power in 1 MHz IF Bandwidth and 10 Hz Video Bandwidth

Figure D.E.13. Device E, Part 15 measurement.

-120

-110

-100

-90

-80

-70

-60

0 0.005 0.010 0.015 0.020

e-20msec.ep

Time (seconds)

Power in 3 MHz Bandwidth

Figure D.E.14. Device E, 20-msec time waveform.
D-E-8

-150

-130

-110

-90

-70

-50

.001 .1 1 5 10 20 35 50 70 80 90 95 99

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

Percent exceeding ordinate

d

B

m

Figure D.E.15. Device E, APDs.
D-E-9

Figure D.E.16. Device E, detector summary.
This Page Intentionally Left Blank

This Page Intentionally Left Blank
D-F-1

-120

-110

-100

-90

-80

-70

-60

-50

-40

1000 2000 3000 4000 5000

20

30

40

50

60

70

80

90

drilspec.ep

cellular

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

Frequency (M Hz)

Peak Power, Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Peak Field Strength, dBuV/m, at 1 m

Figure D.F.1. Electric drill, emission spectrum as a function of bandwidth.

-120

-110

-100

-90

-80

-70

-60

-50

-40

1000 1500 2000 2500 3000

20

30

40

50

60

70

80

90

drilspc2.ep

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

Frequency (M Hz)

Peak Power, Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Field Strength, dBuV/m, at 1 m

Figure D.F.2. Electric drill, emission spectrum from 1-3 GHz as a function

of bandwidth.
D-F-2

-140

-130

-120

-110

-100

-90

-80

-70

-60

1000 2000 3000 4000 5000

0

10

20

30

40

50

60

70

drilm3_1.ep

minimum

mean

maximum

Frequency (M Hz)

Power Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Field Strength, dBuV/m, at 1 m

Figure D.F.3. Electric drill, sample-detected electric drill spectrum, 3 MHz

bandwidth, max, mean, and min curves.

-140

-130

-120

-110

-100

-90

-80

-70

-60

1000 1500 2000 2500 3000

0

10

20

30

40

50

60

70

drilm3_2.ep

minimum

mean

maximum

Frequency (M Hz)

Power Through Constant-Aperture Antenna (5.9 dBi at 1 GHz) @ 1 m (dBm)

Field Strength, dBuV/m, at 1 m

Figure D.F.4. Electric drill, sample-detected electric drill spectrum, 3 MHz

bandwidth, max, mean, and min curves.
D-F-3

-108

-106

-104

-102

-100

0 0.005 0.010 0.015 0.020

Noise burst every 16 ms;

Burst length 6 ms

f10r13.ep

1575 MHz

Time (seconds)

Power at 1 m on 9 dBi Horn (dBm)

Figure D.F.6. Electric drill, Part 15 measurement, 1-MHz IF bandwidth, 

1-kHz video bandwidth.

-90

-80

-70

-60

-50

0 0.005 0.010 0.015 0.020

noise burst every 16 msec;

burst length approx. 6 msec

driltime.ep

Time (seconds)

Power at 1 m on 9 dBi Gain Horn (dBm)

Figure D.F.5. Electric drill, time waveform in 3 MHz bandwidth, sample

detected, for 20 msec.
D-F-4

-108

-106

-104

-102

-100

0 0.005 0.010 0.015 0.020

f10r14.ep

Noise burst every 16 ms;

Burst length 6 ms

1575 MHz

Time (seconds)

Power at 1 m on 9 dBi Horn (dBm)

Figure D.F.7. Electric drill, Part 15 measurement, 1-MHz IF bandwidth,

300-Hz video bandwidth.

-108

-106

-104

-102

-100

0 0.005 0.010 0.015 0.020

f10r15.ep

Noise burst every 16 ms;

Burst length 6 ms

1575 MHz

Time (seconds)

Power in 50 ohms at 1 m on 9 dBi Horn (dBm)

Figure D.F.8. Electric drill, Part 15 measurement, 1-MHz IF bandwidth,

100-Hz video bandwidth.
D-F-5

-108

-106

-104

-102

-100

0 0.005 0.010 0.015 0.020

f10r16.ep

Noise burst every 16 ms;

Burst length 6 ms

1575 MHz

Time (seconds)

Power at 1 m on 9 dBi Horn (dBm)

Figure D.F.9. Electric drill, Part 15 measurement, 1-MHz IF bandwidth, 30-

Hz video bandwidth.

-108

-106

-104

-102

-100

0 0.005 0.010 0.015 0.020

f10r17.ep

Noise burst every 16 ms;

Burst length 6 ms

1575 MHz

Time (seconds)

Power in 50 ohms at 1 m on 9 dBi Horn (dBm)

Figure D.F.10. Electric drill, Part 15 measurement, 1-MHz IF bandwidth,

10-Hz video bandwidth.
D-F-6

-108

-106

-104

-102

-100

0 0.005 0.010 0.015 0.020

f10r19.ep

1575 MHz

Time (seconds)

Spectrum

Analyzer Noise Level (dBm)

Figure D.F.11. Electric drill, terminated spectrum analyzer input with 

1-MHz IF bandwidth, 10-Hz video bandwidth.
D-F-7

-150

-130

-110

-90

-70

-50

.001 .1 1 5 10 20 35 50 70 80 90 95 99

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

r_f1_2.ezp

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure D.F.12. Electric Drill, APDs.
D-F-8

Figure D.F.13. Electric Drill, detector summary.
1The author is with the Institute for Telecommunication Sciences, National

Telecommunications and Information Administration, U.S. Department of Commerce, Boulder,

CO 80305.

E-1

Arbitrary Waveform Generator Atten

GPIB GPIB

Arbitrary Waveform Generator Narrow Pulse

Generator

Narrow Pulse

Generator

Atten

Computer/Controller Spectrum Analyzer

Figure E.1. Aggregate measurements block diagram.

APPENDIX E. SUMMARY OF AGGREGATE MEASUREMENTS

Frank Sanders1

Device description. A pair of UWB pulsers were procured by ITS and operated for the purpose

of assessing the emission levels in various IF bandwidths as a function of nominal pulse

repetition rate (PRR), dither, and the number of pulsers in an aggregate. These pulsers produce

UWB impulses at times precisely controlled by signals from an arbitrary waveform generator. 

Therefore, these pulsers can be controlled to provide a wide range of PRR, dither, and gating

combinations, depending on the programming of the arbitrary waveform generators. An

independent (and non-synchronized) generator was used to control each pulser. 

Figure E.1 shows the measurement system used for the aggregate measurements.

Arbitrary waveform generators were programmed to give average PRRs of 100 kHz and 10 MHz,

50% dithered or non-dithered. This dithering is based on delay relative to a fixed time base.

When both pulsers were in use, their respective wideband peak amplitudes were matched to

within 0.2 dB.
E-2

Measurement comments. The general technique for investigating aggregate UWB signals was

to independently measure APDs from each of two UWB sources, then combine the UWB

sources and measure an APD from the combined sources. This technique was followed for all of

the aggregate measurements, with the only variable being the modulation parameters of two

UWB signals.

Figures E.2 and E.3 show the wide range peak emission spectra of single pulsers using a 100-kHz

PRR and 50% dithering, and a 10-MHz PRR and 50% dithering, respectively. Figure E.4 shows

the peak bandwidth progression for a pulser with 10 MHz PRR and 50% dithering.

Figure E.5 shows video-averaged measurements for a single dithered pulser (10 MHz PRR, 50%

dither) and for two such pulsers. The measured signal for two pulsers increased 2.6 dB over the

level for a single pulser. This falls within the precision of the measurement for the expected 

3-dB increase. 

Figure E.6 shows APDs measured in a 1-MHz bandwidth for a single pulser and two pulsers. 

Each pulser produced a signal with10-MHz PRR and 50% dither. The APDs for the individual

pulsers appeared Gaussian. The APD for the two pulsers also appeared Gaussian, but was raised

about 3 dB from the individual pulser APD, as theory predicts.

Figure E.7 shows APDs measured in a 1-MHz bandwidth for a single pulser and two pulsers. 

Each pulser produced a non-dithered signal with 100-kHz PRR. The two-pulser APD shows a

stepped high-amplitude plateau, where the lower step is equal in amplitude to the single pulser

APD, but with about 1.5-2 times the percentage duration (depending on what amplitude is used

to compare the duration). In addition, there is a very-small-percentage step that is about 6 dB

higher than the single pulser maximum amplitude, which is consistent with impulses from the

two pulsers occasionally overlapping and combining coherently. 

Figure E.8 shows a 1-MHz APD that was derived from the combination of one pulser with 

10-MHz PRR (dithered) and one pulser with 100-kHz PRR (non-dithered). The APD shows an

approximately Gaussian character, which should be expected considering that the non-dithered

100-kHz pulser produced only 1% as many impulses as the 10-MHz dithered pulser.

Figure E.9 shows APDs measured in a 1-MHz bandwidth for a single pulser and two pulsers. 

Each pulser produced a signal with 100-kHz PRR and 50% dithering. Since the UWB pulses

remain non-overlapping in the 1-MHz bandwidth, the resulting APDs are identical to the APDs

measured in Figure E.7. 

Table E.1 shows the detector values for the various APDs.
E-3

Table E.1 - Detector Values for Aggregate Tests

Figure Source PRR Dither Avg Log Avg volt RMS Peak

Figure

E.6

 #1 10 MHz 50% -49.2 -47.9 -46.9 -39

#2 10 MHz 50% -49.2 -47.9 -46.9 -39

#1 & #2 - - - - - - -46.5 -45.1 -44.1 -36.5

Figure

E.7

#1 100 kHz none -87.2 -76.6 -67.9 -54

#2 100 kHz none -87.2 -76.6 -67.9 -54

#1 & #2 - - - - - - -84.1 -72.1 -65.2 -49

Figure

 E.8

#1 10 MHz 50% -49.2 -47.9 -46.9 -39

#2 100 kHz none -87.2 -76.6 -67.9 -54

#1 & #2 - - - - - - -49.2 -47.9 -46.9 -39

Figure

E.9

#1 100 kHz 50% -86.9 -76.6 -67.9 -54

#2 100 kHz 50% -86.9 -76.6 -67.9 -54

#1 & #2 - - - - - - -84.0 -72.1 -65.2 -49

The measurement results can be summarized as follows:

1. Noise-like signals with Gaussian APD characteristics (10-MHz PRR, 50% dither) add together

to give noise-like signals with Gaussian APD characteristics (Figure E.6). All detector values

increased by approximately 3 dB when two equal UWB Gaussian signals were added.

2. A noise-like signal with Gaussian APD characteristics added to a weaker (20 dB weaker)

impulsive signal produced a signal with a Gaussian APD characteristic (Figure E.8). The

difference in detector values was not apparent, though this may have been caused by limited

measurement system resolution.

3. Impulsive signals added to impulsive signals (Figures E.7 and E.8) produced APDs that were

less impulsive that the original signals. Dithering of signals in an impulse environment (i.e.,

measurement bandwidth greater than the combined PRR) produced similar results to nondithered signals. The combined signals produced APDs with approximately twice the total

percentage pulse duration as the original pulses at the same amplitude, as well as a small

percentage of pulses with amplitudes as much as 6 dB higher than the original pulses. The

detector values were generally about 3 dB higher for the combined signals (except 6 dB increase

for peak).
E-4

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

500 1000 1500 2000 2500

10 kHz

30 kHz

100 kHz

300 kHz

1 MHz

3 MHz

f2r2-7.ep

Frequency (MHz)

Coupled Power (dBm)

Figure E.2. Spectrum analyzer emissions spectra from 100-kHz PRR, 

50% dither pulser.

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

500 1000 1500 2000 2500

f3r7-12.ep

These features due to

dither sequence length

3 MHz

1 MHz

300 kHz

100 kHz

30 kHz

10 kHz

Frequency (MHz)

Coupled Power (dBm)

Figure E.3. Spectrum analyzer emission spectra from 10-MHz PRR, 50%

dither pulser.
E-5

-60

-40

-20

0

0 20 40 60

f1r3.ep

100 Hz

300 Hz

1 kHz

3 kHz

10 kHz

30 kHz

100 kHz

300 kHz

1 M Hz

3 MHz

Dimensionless Units

Peak Relative to 3 MHz IF Bandwidth (dB)

Figure E.4. Peak bandwidth progression stairstep for 10-MHz PRR, 50%

dither pulser.

-53

-50

-47

0 0.005 0.010 0.015 0.020

Single 10 MHz dithered pulser

Pair of 10 MHz dithered pulsers

f1r4-5.ep

Time (seconds)

Received Signal Level (dBm)

Figure E.5. Video signal from single and double pulsers, each at 10 MHz

PRR, 50% dither.

 
E-6

-100

-80

-60

-40

-20

0

.001 .1 1 5 10 20 35 50 70 80 90 95 99

Sum of 2 sources

Single source

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure E.6. 1-MHz APD for single and double 10-MHz, 50% dither pulser.
E-7

-120

-100

-80

-60

-40

-20

.001 .1 1 5 10 20 35 50 70 80 90 95 99

Sum of 2 sources

Single source

Percent Exceeding Ordinate

P

o

w

er (d

B

m

B

Figure E.7. 1-MHz APD for single and double 100-kHz PRR, non-dither

pulsers. 
E-8

-100

-80

-60

-40

-20

0

.001 .1 1 5 10 20 35 50 70 80 90 95 99

10 MHz source (50% dither) +

100 kHz source (sans dither)

Percent Exceeding Ordinate

P

o

w

er (d

B

m

B

Figure E.8. 1-MHz APD for a 10-MHz PRR, 50% dither pulser and a 

100-kHz, non-dithered pulser.

 
E-9

-120

-100

-80

-60

-40

-20

.001 .1 1 5 10 20 35 50 70 80 90 95 99

Sum of 2 sources

Single source

Percent Exceeding Ordinate

P

o

w

er (d

B

m)

Figure E.9. 1-MHz APDs for single and double 100-kHz PRR 50%

dithered pulsers.