NTIA Technical Memorandum 10-464

CORRECTION FACTORS AND 

MEASUREMENT PROCEDURE TO 

ASSESS THE INTERFERENCE

IMPACT OF LINEAR SWEPT 

FREQUENCY SIGNALS ON

RADIO RECEIVERS

technical memorandum series

U.S. DEPARTMENT OF COMMERCE  National Telecommunications and Information Administration
NTIA Technical Memorandum 10-464

CORRECTION FACTORS AND 

MEASUREMENT PROCEDURE TO

ASSESS THE INTERFERENCE

IMPACT OF LINEAR SWEPT 

FREQUENCY SIGNALS ON

RADIO RECEIVERS

 Edward F. Drocella

David S. Anderson

U.S. DEPARTMENT OF COMMERCE

Gary Locke, Secretary

Lawrence E. Strickling Assistant Secretary

for Communications and Information

December 2009
ii

ACKNOWLEDGMENTS

The authors wish to thank Brent Bedford of the National Telecommunications and Information Administration’s Institute for Telecommunication Sciences, for his support and work in 

performing the measurements that were fundamental to the completion of this technical memorandum.
iii

EXECUTIVE SUMMARY

The National Telecommunications and Information Administration (NTIA) is developing 

a handbook documenting the best practices in spectrum engineering. This technical memorandum provides a methodology to determine the average and peak power level at the output of a 

filter with a linear swept frequency pulse train input to the filter. Using this method, NTIA calculated two correction factors necessary to accurately compute the interference power level of a 

system that employs linear swept frequency signals. The two correction factors enable the conversion of the peak power at the filter input to the peak power or average power at the output. 

These correction factors cover the case where the peak input power is stated in dB relative to a 

reference power (e.g., dBW). NTIA also carried out, as part of this technical memorandum, 

measurements of linear swept frequency signals at the input and output of a variety of filter 

bandwidths. A comparison of measured and calculated correction factors showed the values to 

be in good agreement. The measurements carried out in this technical memorandum resulted in 

the development of a general procedure for measuring the emissions of a system employing linear swept frequency techniques. This method enables an accurate measurement of the emissions from which to assess compatibility with other radio services. The correction factors and 

the measurement procedure described in this technical memorandum will be used in the development of the Best Practices Handbook.
iv

TABLE OF CONTENTS

EXECUTIVE SUMMARY ..................................................................................................... iii

TABLE OF CONTENTS .........................................................................................................iv

GLOSSARY OF ACRONYMS AND 

ABBREVIATIONS ...................................................................................................................v

SECTION 1.0 INTRODUCTION ........................................................................................ 1-1

1.1 BACKGROUND .................................................................................................. 1-1

1.2 OBJECTIVE ......................................................................................................... 1-3

1.3 APPROACH ......................................................................................................... 1-3

SECTION 2.0 ANALYTICAL APPROACH....................................................................... 2-1

2.1 INTRODUCTION ................................................................................................. 2-1

2.2 PEAK POWER CORRECTION FACTOR ........................................................... 2-1

2.3 AVERAGE POWER CORRECTION FACTOR.................................................... 2-2

SECTION 3.0 ANALYSIS OF MEASUREMENTS ........................................................... 3-1

3.1 DESCRIPTION OF MEASUREMENTS ............................................................. 3-1

3.2 DISCUSSION OF MEASUREMENTS ................................................... 3-1

3.2.1 Peak Power Measurements ..................................................................... 3-1

3.2.2 Average Power Measurements ................................................................ 3-4

3.2.3 Applications of Linear Swept Frequency Correction Factors ................... 3-8

SECTION 4.0 GENERAL MEASUREMENT PROCEDURE FOR LINEAR 

SWEPT FREQUENCY SIGNALS.......................................................................4-1

4.1 GENERAL MEASUREMENT PROCEDURE ..................................................... 4-1

4.2 DESCRIPTION OF GENERAL MEASUREMENT PROCEDURE ..................... 4-1

SECTION 5.0 CONCLUSIONS .........................................................................5-1

5.1 CONCLUSIONS .................................................................................................. 5-1
v

GLOSSARY OF ACRONYMS AND ABBREVIATIONS

AWG Arbitrary Waveform Generator

Bt Extent of Frequency Sweep

BW Bandwidth

BWCF Bandwidth Correction Factor

BW3dB 3 dB Filter Bandwidth

CFA Average Power Correction Factor

CFP Peak Power Correction Factor

EIRP Equivalent Isotropically Radiated Power

IF Intermediate Frequency 

ITS Institute for Telecommunication Sciences

kHz Kilohertz 

LNA Low Noise Amplifier 

MHz Megahertz

msec Millisecond

NTIA National Telecommunications and Information Administration

OSM Office of Spectrum Management

PAO Average Power at the Output of Filter

PPi Peak Power at the Input of Filter

PPO Peak Power at the Output of Filter

PRT Pulse Repetition Time

PW Pulse Width

RBW Resolution Bandwidth

RF Radio Frequency 

RMS Root Mean Square

SR Sweep Rate

τi Input Pulse Width

UFS Unit Under Test Frequency Sweep

UUT Unit Under Test

μsec Microsecond
1-1

SECTION 1.0

INTRODUCTION

1.1 BACKGROUND

The National Telecommunications and Information Administration (NTIA) Office of Spectrum Management is examining best practices in spectrum management for 

use by regulators, technology developers, manufacturers and service providers. This effort includes the development of a Best Practices Handbook that will aggregate a common set of approaches for conducting engineering analyses and will assemble a common 

set of criteria for performing technical studies to evaluate emerging technologies. NTIA 

will prepare a series of technical memorandums on various topics related to performing 

engineering analyses and will use the results of the individual technical memorandums to 

develop the Best Practices Handbook. This technical memorandum is one in a series addressing specific topics related to spectrum engineering. 

An increasing number of federal and non-federal systems being developed employ linear swept frequency techniques. For compliance purposes the emissions from 

these devices are typically measured in a reference bandwidth (e.g., 1 MHz). To assess 

the compatibility of systems employing linear swept frequency techniques with other radio receivers, both average and peak power levels at the victim receiver intermediate frequency output are required. To perform this assessment, it is necessary to develop a 

means of converting the power (peak or average) of a linear swept frequency signal as 

measured in one bandwidth (e.g., reference bandwidth) to what would be expected in 

another bandwidth (victim receiver bandwidth). To perform this conversion, equations 

referred to as correction factors can be developed. In addition to providing a conversion 

for determining the peak or average power in different bandwidths, the correction factor

can also be used to convert between peak and average power levels within the same 

bandwidth.

1.2 OBJECTIVE

The objective of the measurements and analyses described in this technical memorandum is to develop peak and average power correction factors for linear swept frequency signals. To accomplish this objective, NTIA conducted a series of tests providing 

measured data to support the understanding of the signal at the output of a filter over a 

range of filter bandwidths that results from each of a variety of input linear swept frequency signals. The measurements carried out in this technical memorandum will be 

used to develop a general procedure for measuring the emissions of a system employing 

linear swept frequency techniques. 

1.3 APPROACH

The NTIA Institute for Telecommunication Sciences (ITS), in conjunction with 

the NTIA Office of Spectrum Management, performed the measurements described in 

this technical memorandum.
1-2

During the initial phase of the program, NTIA developed a linear swept frequency 

signal source. The swept frequency signal source was capable of generating a constant 

amplitude signal that swept across a range of at least 15 MHz with sweep rates of 0.005, 

0.05, 0.5, 5, 50 and 500 kHz per microsecond (μsec). The carrier frequency was not a 

critical parameter in this measurement program. 

The swept frequency signals were input to a spectrum analyzer. With the spectrum analyzer in a zero span mode at a frequency that is at the mid-point of the 15 MHz 

sweep range of the swept frequency signal generator, signals were measured in the spectrum analyzer with resolution bandwidths (RBWs) of 3 MHz, 1MHz, 300 kHz, 100 kHz, 

30 kHz, and 10 kHz for each of the sweep rates. 

The signal was measured using the root-mean-square (RMS) average and peak 

detectors. The peak and average power levels were measured using the maximum hold 

feature of the spectrum analyzer for approximately ten scans of the source signal. These 

multiple scans were performed for each of the sweep rates. The average power using the 

RMS average detector was measured over a 1 millisecond (msec) time interval. The peak 

power for each input signal was obtained. 

In addition, similar spectrum analyzer measurements of peak and average power 

were carried out with the swept frequency held constant at 500 kHz/μsec and the pulse 

repetition time varied (600 μsec, 1.1 msec, and 6 msec). These additional measurements 

show the impact of duty cycle on the average power.

NTIA then analyzed the measured data along with certain analytical representations to develop a methodology to convert the peak power at a filter input to the peak or 

average power at the filter output.
2-1

SECTION 2.0

ANALYTICAL APPROACH

2.1 INTRODUCTION

This section presents the development of the analytical expressions to determine 

the peak and average power correction factors for linear swept frequency signals. The 

correction factors are used to determine the peak and average power expected at the output of a filter with a linear swept frequency pulse train at the filter input. 

2.2 PEAK POWER CORRECTION FACTOR

The input pulse train considered in this analysis is characterized by the following 

parameters:

▪ PPi is the peak power of a rectangular pulse at the filter input (Watts);

▪ τt is the pulse width of the rectangular pulse (μsec);

▪ Bt is the extent of the linear frequency sweep during the pulse on-time (τt) 

(MHz); and

▪ PRT is the pulse repetition time, the time from the start of one pulse to the start 

of the next pulse (μsec).

The sweep rate (SR) of the pulse (with units of MHz/μsec) is determined by:

SR = Bt/τt (2-1)

The filter is characterized by its 3 dB bandwidth (B3dB) in MHz. For the analysis 

presented in this technical memorandum to be applicable, Bt must be greater than B3dB. If 

Bt is less than B3dB, the total frequency sweep falls within the filter bandwidth and is not 

addressed in this technical memorandum. 

The reduction in peak power, as the input pulse passes through the filter, is determined by the ratio of the time the swept frequency signal is within the filter bandwidth 

(i.e., B3dB/SR) to the response time of the filter. The response time of the filter is 1/B3dB. 

Thus, the peak power at the output of the filter (PPo in Watts) is:

PPo = PPi [(B3dB/SR)/(1/ B3dB)] = PPi [(B3dB)

2

/SR] (2-2)

This result can be expressed as a peak correction factor (CFP) in dB, which provides a method to correct the peak power of the input pulse to account for the filter 

bandwidth effect. Expressing Equation 2-2 in logarithmic form results in:

10 Log (PPo) = 10 Log(PPi) + 10 Log [(B3dB)

2

/SR] (2-3)

The term 10 Log [(B3dB)

2

/SR] is CFP. If the peak power at the input is expressed in units 

of dB relative to a reference power (in dBW), the CFP can be applied to determine the 
2-2

output in the same power units. There is, however, a limit on the range of applicability of 

CFP = 10 Log [(B3dB)

2

/SR]. The peak correction factor cannot exceed 0 dB or (B3dB)

2

/SR 

cannot exceed one. That is, if (B3dB)

2

/SR is greater than one, it should be set equal to one 

to determine CFP. If CFP where allowed to have a value greater than 0 dB, the peak power out of the filter would be greater than the peak power into the filter, which is not possible. 

2.3 AVERAGE POWER CORRECTION FACTOR

Once the peak power at the output of the filter has been determined, the average 

power at the output (PAo in Watts) of the filter can be determined by taking into account 

the duty cycle of the output pulse train:

PAo= PPo (τo/PRT) (2-4)

where τo is the pulse length at the filter output. This is also the response time of the filter:

τo = 1/B3dB (2-5)

Combining Equations 2-2 and 2-4 results in:

PAo= PPi [(B3dB)

2

/SR] [1/(B3dB x PRT)] = PPi [B3dB/(SR x PRT)] (2-6)

This produces a correction factor (in logarithmic form) for average power (CFA) 

in the same units as that of the peak power (e.g., dBW or dBm):

CFA = 10 Log [B3dB/(SR x PRT)] (2-7)

 
3-1

SECTION 3.0

ANALYSIS OF MEASUREMENTS

3.1 DESCRIPTION OF MEASUREMENTS

In order to confirm the analytical results presented in Section 2, NTIA ITS performed a series of measurements. The measurements initially involved configuring a 

signal generator to linearly sweep from 92.5 to 107.5 MHz. The linearity of the sweep 

was confirmed using a vector signal analyzer. The slowest sweep rate used was 5 

Hz/μsec and the fastest was 500 kHz/μsec. NTIA ITS used a spectrum analyzer to measure the peak and average power at the output of the RBW filter. These RBW filters are 

incorporated in the spectrum analyzer and have a Gaussian selectivity characteristic. The 

average power measurements were made using a RMS detector with an integration time 

of 1 msec for the initial measurements.

The pulse-on time of the pulse train was established by the sweep rate selected for 

the specific measurement and the extent of the frequency sweep (92.5 to 107.5 MHz). 

The off-time between pulses was very short initially such that the difference between total peak and average power at the filter input was less than 3 dB. The spectrum analyzer

was operated in the zero-span mode with maximum hold and tuned to the center frequency of the frequency sweep of the pulse. 

3.2 DISCUSSION OF MEASUREMENTS

3.2.1 Peak Power Measurements 

Table 3-1 provides a summary of the peak power measurement results. As shown 

in Table 3-1, the measured peak power at the output of the RBW filter relative to the input of the filter is a function of the bandwidth and sweep rate. The quantity measured is 

the difference between maximum peak power at the filter input and the measured peak 

power at the filter output for a combination of sweep rate and filter bandwidths, CFP = 10 

Log [(B3dB)

2

/SR]. 

Table 3-2 shows a comparison of measured and calculated CFP values. As shown 

in Table 3-2, the calculated CFP values are higher in magnitude than the measured CFP

values. This indicates that the analytical expression developed in Section 2 provides an 

overestimate of the actual CFP. Thus, it is necessary to modify the equation for CFP developed in Section 2. Including a factor of 1.6 in Equation 2-3 results in CFP values in 

better agreement with the measurements as shown in the last column in Table 3-2. 
3-2

Table 3-1. Measured Peak Power Correction Factors for Various Sweep Rates

Sweep Rate

(kHz/μsec)

RBW Measured CFP

(dB)

5x10-33 MHz 0

5x10-23 MHz 0

5x10-13 MHz 0

5 3 MHz 0

5x1013 MHz 0

5x1023 MHz 0

5x10-31 MHz 0

5x10-21 MHz 0

5x10-11 MHz 0

5 1 MHz 0

5x1011 MHz 0

5x1021 MHz 0

5x10-3300 kHz 0

5x10-2300 kHz 0

5x10-1300 kHz 0

5 300 kHz 0

5x101300 kHz -1

5x102300 kHz -5

5x10-3100 kHz 0

5x10-2100 kHz 0

5x10-1100 kHz 0

5 100 kHz 0

5x101100 kHz -5

5x102100 kHz -15

5x10-330 kHz 0

5x10-230 kHz 0

5x10-130 kHz 0

5 30 kHz -5

5x10130 kHz -15

5x10230 kHz -25

5x10-310 kHz 0

5x10-210 kHz 0

5x10-110 kHz -4

5 10 kHz -15

5x10110 kHz -24

5x10210 kHz -32
3-3

Table 3-2. Comparison of Measured and Calculated Peak Power Correction Factors 

for Various Sweep Rates 

Sweep 

Rate

(kHz/μsec)

RBW Measured 

CFP

(dB)

Calculated CFP

10 Log [(B3dB)

2

/SR]

(dB)

Calculated CFP

10 Log 1.6 [(B3dB)

2

/SR]

(dB)

5x10-33 MHz 0 0 0

5x10-23 MHz 0 0 0

5x10-13 MHz 0 0 0

5 3 MHz 0 0 0

5x1013 MHz 0 0 0

5x1023 MHz 0 0 0

5x10-31 MHz 0 0 0

5x10-21 MHz 0 0 0

5x10-11 MHz 0 0 0

5 1 MHz 0 0 0

5x1011 MHz 0 0 0

5x1021 MHz 0 0 0

5x10-3300 kHz 0 0 0

5x10-2300 kHz 0 0 0

5x10-1300 kHz 0 0 0

5 300 kHz 0 0 0

5x101300 kHz -1 0 0

5x102300 kHz -5 -7.4 -5.4

5x10-3100 kHz 0 0 0

5x10-2100 kHz 0 0 0

5x10-1100 kHz 0 0 0

5 100 kHz 0 0 0

5x101100 kHz -5 -7 -4.9

5x102100 kHz -15 -17 -14.9

5x10-330 kHz 0 0 0

5x10-230 kHz 0 0 0

5x10-130 kHz 0 0 0

5 30 kHz -5 -7.4 -5.4

5x10130 kHz -15 -17 -15.4

5x10230 kHz -25 -27 -25.4

5x10-310 kHz 0 0 0

5x10-210 kHz 0 0 0

5x10-110 kHz -4 -7 -4.9

5 10 kHz -15 -17 -14.9

5x10110 kHz -24 -27 -24.9

5x10210 kHz -32 -37 -34.9
3-4

NTIA ITS carried out additional peak power measurements with the sweep rate 

held constant at 500 kHz/μsec and the PRT varied (600 μsec, 1.1 msec, and 6 msec). The 

data set previously discussed included data for a sweep rate of 500 kHz/ μsec and a PRT 

of 60 μsec. Table 3-3 shows these data sets and peak power correction factors. As 

shown in Table 3-3, the peak power correction is not dependent on the PRT.

Table 3-3. Comparison of Measured and Calculated Peak Power Correction Factors 

(Sweep Rate of 500 kHz/600 μsec)

Spectrum 

Analyzer

RBW

PRT Measured 

CFP

(dB)

Calculated CFP

10 Log [(B3dB)

2

/SR]

(dB) 

Calculated CFP

10 Log 1.6 [(B3dB)

2

/SR]

(dB)

3 MHz 60 μsec 0 0 0

3 MHz 600 μsec 0 0 0

3 MHz 1.1 msec 1 0 0

3 MHz 6 msec 1 0 0

1 MHz 60 μsec 0 0 0

1 MHz 600 μsec 0 0 0

1 MHz 1.1 msec 0 0 0

1 MHz 6 msec 0 0 0

300 kHz 60 μsec -5 -7.4 -5.4

300 kHz 600 μsec -5 -7.4 -5.4

300 kHz 1.1 msec -5 -7.4 -5.4

300 kHz 6 msec -5 -7.4 -5.4

100 kHz 60 μsec -15 -17 -14.9

100 kHz 600 μsec -14 -17 -14.9

100 kHz 1.1 msec -14 -17 -14.9

100 kHz 6 msec -14 -17 -14.9

30 kHz 60 μsec -25 -27.4 -25.4

30 kHz 600 μsec -25 -27.4 -25.4

30 kHz 1.1 msec -24 -27.4 -25.4

30 kHz 6 msec -24 -27.4 -25.4

10 kHz 60 μsec -32 -37 -34.9

10 kHz 600 μsec -34 -37 -34.9

10 kHz 1.1 msec -34 -37 -34.9

10 kHz 6 msec -34 -37 -34.9

3.2.2 Average Power Measurements 

Table 3-4 provides a summary of the average power measurement results. The 

table shows that the measured average power at the output of the RBW filter relative to 

the peak power at the filter input as a function of RBW and sweep rate. The quantity of 

interest is CFA = 10 Log [B3dB/(SR x PRT)], which is the difference between the peak 

power at the input of the filter and the average power at the output. However, this formula for CFA assumes the integration time for the average power measurement is long 

enough to include at least one full pulse repetition period at the filter output. If a full 
3-5

pulse repetition period is not included in the integration time, a true average power measurement for the pulse train cannot be obtained. For most linear swept frequency signals, 

the integration time will be sufficient. However, for some of the measurements presented 

here this was not true and for those cases the formulation CFA = 10 Log [B3dB/(SR x 

PRT)] is not applicable. This does not mean the average power cannot be calculated for 

these special cases, but a slightly different approach must be employed. The first such 

case occurs when the integration time (1 msec for these measurements) is less than the 

time the swept frequency signal is within the RBW. The time the swept frequency signal 

is within the RBW is B3dB/SR. For this case, the pulse is present for the full integration 

time and there is no interpulse period in the integration time. The output will be equal to 

peak power at the input. This results in CFA = 0 dB. These cases are denoted by a single 

asterisk accompanying the CFA entry in Table 3-4. The second case occurs when the 

swept frequency signal spends less time in the filter than the integration time, but the 

PRT is longer than the integration time. For this case, the average power is measured for 

a condition where only a portion of the interpulse period is considered in the averaging. 

The correction factor is calculated by the ratio of the time the signal falls within the filter 

to the integration time, CFA = 10 Log [(B3dB/SR)/1x103]. These cases are denoted by a 

double asterisk accompanying the CFA entry in Table 3-4. For the third case, the formulation CFA = 10 Log [B3dB/(SR x PRT)] applies. These complications requiring special 

consideration can be overcome by the judicious selection of the integration time for the 

specific signal and filter bandwidth being measured. The measurements that are the subject of this technical memorandum includes a range of sweep rates that covered five orders of magnitude and filter RBWs that covered two orders of magnitude. This wide 

range of parameters made it difficult to select an integration time. The determination of 

CFA requires values of PRT. Table 3-5 contains these PRT values for each value of SR 

that was analyzed in Table 3-4.

Additional average power measurements were carried out with the sweep rate 

held constant at 500 kHz/μsec and the PRT varied (600 μsec, 1.1 msec and 6 msec). The 

data set that was discussed previously included data for a sweep rate of 500 kHz/sec and 

a PRT of 60 μsec. Table 3-6 provides these data sets and the average power correction 

factors. The Table 3-6 data was for an integration time of 1 msec. These additional measurements were performed to examine some of the Case 1 and Case 2 data in Table 3-4. 

This did not eliminate all of the “special” cases. As shown in Table 3-6, there are some 

Case 2 conditions where the integration time for the determination of overall average 

power was too short. Measurements were then performed for the twelve Case 2 entries in 

Table 3-6 with an integration time of 30 msec. This integration time exceeds the longest 

PRT of 6 msec and thus the overall average should be realized. The results of these measurements and calculations are shown in Table 3-7. 
3-6

Table 3-4. Comparison of Measured and Calculated Average Power Correction 

Factors for Various Sweep Rates

Sweep Rate

(kHz/μsec)

RBW Measured CFA

(dB)

Calculated CFA

(dB) 

5x10-33 MHz 0 0 *

5x10-23 MHz 0 0

*

5x10-13 MHz 0 0

*

5 3 MHz -3 -2.2**

5x1013 MHz -9 -10***

5x1023 MHz -10 -10***

5x10-31 MHz 0 0

*

5x10-21 MHz 0 0

*

5x10-11 MHz 0 0

*

5 1 MHz -7 -7

**

5x1011 MHz -14 -14.8***

5x1021 MHz -15 -14.8***

5x10-3300 kHz 0 0

*

5x10-2300 kHz 0 0

*

5x10-1300 kHz -2 -2.2**

5 300 kHz -12 -12**

5x101300 kHz -19 -20***

5x102300 kHz -20 -20***

5x10-3100 kHz 0 0

*

5x10-2100 kHz 0 0

*

5x10-1100 kHz -6 -7

**

5 100 kHz -17 -17**

5x101100 kHz -24 -24.8***

5x102100 kHz -24 -24.8***

5x10-330 kHz 0 0

*

5x10-230 kHz -3 -2.2**

5x10-130 kHz -12 -12.2**

5 30 kHz -22 -22.2**

5x10130 kHz -29 -30***

5x10230 kHz -29 -30***

5x10-310 kHz 0 0

*

5x10-210 kHz -6 -7

**

5x10-110 kHz -16 -17**

5 10 kHz -27 -27**

5x10110 kHz -33 -34.7***

5x10210 kHz -32 -34.7***

* Case 1 – Time in filter longer than integration time: CFA = 0 dB

**Case 2 – PRT longer than integration time: CFA = 10 Log (Time in Filter/Integration Time)

***Case 3 – PRT less than integration time: CFA = 10 Log [B3dB/(SRxPRT)]
3-7

Table 3-5. Summary of Sweep Rates and Pulse Repetition Times

SR

(kHz/μsec)

PRT

(μsec)

5x10-32.97x106

5x10-2319x103

5x10-150.6x103

5 6x106

5x101600

5x10260

Table 3-6. Comparison of Measured and Calculated Average Power 

Correction Factors 

(Sweep Rate of 500 kHz/μsec)1

Spectrum 

Analyzer

RBW

PRT Measured 

CFA

(dB)

Calculated CFA

10 Log [B3dB/(SR x PRT)]

(dB) 

3 MHz 60 μsec -10 -10

3 MHz 600 μsec -19 -20

3 MHz 1.1 msec -22 -22.2*

3 MHz 6 msec -22 -22.2*

1 MHz 60 μsec -15 -14.8

1 MHz 600 μsec -23 -24.8

1 MHz 1.1 msec -26 -27*

1 MHz 6 msec -26 -27*

300 kHz 60 μsec -20 -20

300 kHz 600 μsec -29 -30

300 kHz 1.1 msec -32 -32.2*

300 kHz 6 msec -32 -32.2*

100 kHz 60 μsec -24 -24.8

100 kHz 600 μsec -33 -34.8

100 kHz 1.1 msec -36 -37*

100 kHz 6 msec -36 -37*

30 kHz 60 μsec -29 -30

30 kHz 600 μsec -39 -40

30 kHz 1.1 msec -42 -42.2*

30 kHz 6 msec -42 -42.2*

10 kHz 60 μsec -32 -34.8

10 kHz 600 μsec -43 -44.8

10 kHz 1.1 msec -46 -47

*

10 kHz 6 msec -46 -47

*

* Case 2 – PRT longer than integration time: CFA = 10 Log(Time in Filter/Integration Time)

 

1. An integration time of 1 msec was used to determine the RMS. 
3-8

Table 3-7. Comparison of Measured and Calculated Average Power 

Correction Factors 

(Sweep Rate of 500 kHz/μsec)2

Spectrum 

Analyzer

RBW

PRT Measured 

CFA

(dB)

Calculated CFA

10 Log [B3dB/(SR x PRT)]

(dB) 

3 MHz 1.1 msec -22 -22.6

3 MHz 6 msec -29 -30

1 MHz 1.1 msec -27 -27.4

1 MHz 6 msec -33 -34.7

300 kHz 1.1 msec -32 -32.6

300 kHz 6 msec -39 -40

100 kHz 1.1 msec -37 -37.4

100 kHz 6 msec -43 -44.7

30 kHz 1.1 msec -42 -42.6

30 kHz 6 msec -49 -50

10 kHz 1.1 msec -47 -47.4

10 kHz 6 msec -54 -54.7

3.2.3 Applications of Linear Swept Frequency Correction Factors

For many applications of the linear swept frequency analysis, the peak and/or average power will be referenced in a specific bandwidth (e.g., Y dBm/MHz). The CF equations, CFP =10 Log 1.6[(B3dB)

2

/SR] and CFA = 10 Log [B3dB/(SR x PRT)], show that 

CFP varies as 20 Log (B3dB) and CFA varies as 10 Log (B3dB). This lends itself to the concept of a bandwidth correction factor (BWCF). Thus, where an average power level referenced to a certain bandwidth (B1) needs to be converted to another bandwidth (B2), the 

factor 10 Log(B2/B1) must be added to the reference power to determine the average 

power in B2. Similarly, to convert the peak power in a reference bandwidth (B1) to that 

in a bandwidth (B2), 20 Log (B2/B1) must be added to the reference power level. It is also 

possible to convert the peak power in a given bandwidth (B1) to the average power in the 

same bandwidth by adding -10 Log (1.6 x B1 x PRT) to the peak power. Similarly, the 

average power in a given bandwidth can be converted to the peak power in the same 

bandwidth by adding 10 Log (1.6 x B1 x PRT) to the average power.

All these bandwidth corrections are subject to the limitation that the peak correction factor CFP = 10 Log [1.6 x (B3dB)

2

/SR] cannot exceed 0 dB. If the correction factor 

exceeds 0 dB, CFP should be set equal to 0 dB. 

 

2. An integration time of 30 msec was used to determine the RMS. 
4-1

SECTION 4.0

GENERAL MEASUREMENT PROCEDURE FOR 

LINEAR SWEPT FREQUENCY SIGNALS

4.1 GENERAL MEASUREMENT PROCEDURE

The Federal Communications Commission Part 15 Rules permit devices that employ swept frequency techniques. The Commission’s Rules require that the compliance 

measurements for swept frequency devices be performed with the frequency sweeping 

turned off.3 Performing the compliance measurements with the frequency sweeping 

stopped ensures that the maximum emission levels generated by the device are captured. 

However, performing the compliance measurements with the frequency sweeping turned 

off may tend to overestimate the emissions generated by the device. Performing the compliance measurements with the frequency sweeping active could provide a more accurate 

representation of the emissions generated by the device while in its operational mode. 

Also, measuring emissions with the frequency sweeping turned off would require a special test mode be added to the device. Altering the device strictly for this purpose could 

produce measurement results that may not accurately represent the emissions generated 

while the device is operating as intended. The challenge is to develop a general compliance measurement procedure that is applicable to the different implementations of a 

swept frequency system (e.g., sweep rates, sweep frequency ranges). The measurement 

procedure would also have to provide an accurate measurement of the emissions so that 

they can be used to assess compatibility with other radio services. This section provides 

a description of a general measurement procedure for measuring the emissions of a linear 

swept frequency system with the frequency sweeping active. 

4.2 DESCRIPTION OF GENERAL MEASUREMENT PROCEDURE

The measurement techniques employed in this technical memorandum can be 

used to develop a general procedure for measuring the emissions of systems employing 

linear swept frequency signals. These measurements are applicable to linear swept frequency systems where the extent of the frequency sweep is at least 3 MHz. All the measurements will be made with the unit-under-test (UUT) operating in the swept frequency 

mode.

The measurement approach requires the measurement of radiated measurements 

and should be carried out in a shielded enclosure. If a shielded enclosure is not available, 

a test site should be selected where the background radio-frequency (RF) environment is 

fairly quiet in the range of frequencies of concern. This background RF environment 

should be monitored periodically through the test period and this data must be included in 

the test report.

 

3. 47 C.F.R. Section 15.31(c).
4-2

The required test equipment includes a spectrum analyzer with a peak and rootmean-square detector and maximum hold capability, a reference measurement antenna 

(for the frequency range of interest), a wide-band detector, an oscilloscope, and suitable 

cables to connect the test equipment. A low-noise amplifier (LNA) should be used to 

maximize the dynamic range of the measurement system. The LNA should be connected 

directly to the output of the measurement antenna. In addition, a separate variable frequency generator (or suitable substitute) is required to calibrate the measurement system.

The test description reported here is based on a UUT antenna that is not an extensive array. An extensive array would have at least one dimension greater than one-third 

the distance separation from the UUT antenna to the reference measurement antenna. If 

the array is extensive, the test procedure would need to be repeated for various measurement antenna placements that result in a meaningful sample of the emissions from the 

UUT.

The reference measurement antenna is to be positioned at a level and orientation 

to be within the mainbeam of the UUT antenna. The reference antenna is to be separated 

from the UUT antenna by a minimum distance for far-field antenna conditions and close 

enough so that the received signal is strong enough to carry-out the required measurements. However, the final measurements will need appropriate adjustments to determine 

UUT equivalent isotropically-radiated-power (EIRP) values.

The first series of measurements requires the spectrum analyzer to be connected 

to the measurement antenna through appropriate cables and the LNA, if required. The 

spectrum analyzer is to be operated in the frequency sweep mode with the frequency span 

of the spectrum analyzer frequency sweep set to be slightly greater than the UUT frequency sweep. With the spectrum analyzer in the maximum hold mode and using the 

peak detector, the UUT signal is to be measured over many scans until the individual 

peak power values no longer increase with each scan. Measurements are made for resolution bandwidths of 1 and 3 MHz. These measurements will show the extent of the 

UUT frequency sweep (UFS).

The second series of tests requires the wide-band detector and oscilloscope to be 

placed in the test setup as a substitute for the spectrum analyzer. The time waveform of 

the UUT pulse train is to be measured to determine the pulse width (PW) and pulse repetition time (PRT) of the UUT signal.

The third series of measurements requires the spectrum analyzer to be placed in 

the test setup as a substitute for the detector/oscilloscope and operated in the zero span 

mode with maximum hold. These zero span measurements should be performed at frequencies corresponding to 10 percent, 50 percent, and 90 percent of the UUT frequency 

sweep. The time per division setting of the spectrum analyzer should be such that many 

frequency sweeps of the UUT are measured in one sweep of the spectrum analyzer and a 

line is traced across the spectrum analyzer display. At the 10 percent frequency with the 

peak detector selected, the peak power is to be measured for resolution bandwidths of 3 

MHz, 1 MHz, 300 kHz, and 100 kHz. The spectrum analyzer should then be tuned to the 
4-3

50 percent frequency and the above measurements repeated. The spectrum analyzer

should then be tuned to the 90 percent frequency and the measurements repeated. Then 

the RMS detector should be selected and the average power measured for each of the 

conditions established above in this paragraph. The integration time for the average 

power measurements should be at least 5 to 10 times the PRT. The distance between the 

UUT antenna and the reference measurement antenna should be measured and recorded. 

The gain of the measurement antenna, preferably across the frequency range of the UUT 

swept frequency, but at least at the 10 percent, 50 percent, and 90 percent test frequencies, should be determined from manufacturer specifications or from antenna gain measurements. The gain (loss) from the measurement antenna output through the spectrum 

analyzer must be measured, preferably across the frequency range of the UUT swept frequency, but at least at the 10 percent, 50 percent, and 90 percent test frequencies. This 

can be determined by connecting the variable frequency generator to the cable or LNA 

that was connected to the test antenna output with the generator set to a known peak 

power output level and then sweeping the generator across the frequency range of interest 

while measuring peak power at the spectrum. The difference between power in and power out expressed in decibel is the required calibration factor.

The average EIRP in a 1 MHz bandwidth can be determined by adjusting the average power levels (measured in the third series of tests in a 1 MHz bandwidth) to account for propagation path loss at the measurement distance, measurement antenna gain, 

and the gain (loss) measured for the cables and the LNA used in the measurement system. 

The average EIRP is to be determined at each of the test frequencies used in the third series of tests.

The peak EIRP must be determined for the bandwidth stipulated in the certification requirements. For example, the certification might stipulate the peak EIRP in a 50 

MHz bandwidth or the total peak EIRP. For the peak EIRP determination, the peak power measured in 3 MHz (from the third series of tests) will be the basis. The measured 

peak power must be adjusted for propagation loss, measurement antenna gain, and the 

cable/LNA gain (loss). This yields the EIRP in a 3 MHz bandwidth. To determine the 

peak EIRP in any bandwidth, a limiting bandwidth (B) must be determined,

B UFS/(1.6PW)

(4-1)

where:

UFS is the extent of the UUT frequency sweep (MHz); and

PW is the UUT pulse width (microseconds).

At this limiting bandwidth, the total peak power will be realized at the filter output and 

thus increasing the bandwidth beyond B will not increase the peak power observed.

If the certification stipulates a bandwidth less than B, then the EIRP in 3 MHz is increased in decibel by 20 Log (reference bandwidth (MHz)/3). If the reference bandwidth 

is greater than or equal to B or if the total power peak EIRP is needed in a 3 MHz bandwidth, then the EIRP in 3 MHz is increased in dB by 20 Log (B/3).
5-1

SECTION 5.0

CONCLUSIONS

5.1 CONCLUSIONS

This technical memorandum develops a methodology to determine the average 

and peak power level at the output of a filter with a linear swept frequency pulse train 

input to the filter. The correction factors are necessary to accurately compute the interference power level of a system that employs linear swept frequency signals. Two correction factor equations were developed to correct the peak power at the filter input to the 

peak power or average power at the output. These correction factors are used for the case 

where the peak input power is stated in dB relative to a reference power (e.g., dBW). 

The correction factor to yield the output power is:

CFP = 10 Log 1.6[(B3dB)

2

/SR] (5-1)

The peak output power is PPi + 10 Log 1.6[B3dB

2

/SR]. The CF for average power is:

CFA = 10 Log [B3dB/(SR x PRT)] (5-2)

The average output power is PPi + 10 Log [B3dB/(SR x PRT)]. 

This technical memorandum defines the terms in these equations and the limits to 

which the equations are subject. NTIA performed measurements of swept frequency signals at the input and output of a variety of filter bandwidths as described in this technical 

memorandum and developed a general procedure for measuring the emissions of a system employing linear swept frequency techniques to provide an accurate measurement of 

the emissions. This is necessary to assess compatibility with other radio services. The 

correction factors and the measurement procedure described in this technical memorandum will be used in the development of the Best Practices Handbook.