NBSIR 73-325

PULSE TESTING OF RF AND MICROWAVE COMPONENTS

William L Gans and N. S. Nahman

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

July 1973

Interim Report

Prepared for:

Department of Defense

Calibration Coordination Group

72-68

NBSIR 73-325

PULSE TESTING OF RF AND MICROWAVE COMPONENTS

William L. Gans and N.S. Nahman

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

July 1973

Interim Report

Prepared for:

Department of Defense

Calibration Coordination Group

72-68

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W Roberts Director

CONTENTS

Page

1. INTRODUCTION 2

2. COAXIAL MICROWAVE DEVICE EXPERIMENT 3

2. 1 Theory 3

2. 2 Experimental Test Setup 7

2. 3 Experimental Data and Results 8

2. 3.1 4. 1 GHz Low Pass Filter 8

2. 3. 2 10 dB Coaxial Attenuator 9

2. 3, 3 20 dB Coaxial Attenuator 9

2. 3. 4 40 dB Coaxial Attenuator 10

3. AC ELECTRONIC VOLTMETER MEASUREMENTS 11

3.1 Experimental Purpose 11

3.2 Frequency Domain Tests 11

3.3 Time Domain Tests 12

3.4 Conclusions 13

4. REFERENCES 15

iii
LIST OF FIGURES

Figure Page

2-1 Diagram of circuit used to obtain G^j^(t) 16

2-2 Diagram of circuit used to obtain e ,_(t) 17

d2

2-3 Complete time domain data acquisition system

block diagram ...18

2-4 Photograph of e^^(t) and e^^{t) for the 4. 1 GHz

low pass filter as seen on the sampling

oscilloscope 19

2-5 Photograph of e „(t) and e ,^(t) for the 4. 1 GHz

dl d2

low pass filter after signal averaging 19

2-6 Computer plot of the amplitude frequency response

of the 4, 1 GHz low pass filter 20

2-7 Photograph of e^Jt) and e,^(t) for the 10 dB

dl dZ

attenuator as seen on the sampling oscilloscope 21

2-8 Photograph of e (t) and e (t) for the 10 dB

attenuator after signal processing 21

2-9 Computer plot of the amplitude frequency response

of the 10 dB attenuator 22

2-10 Photograph of e^^(t) and e^^^*) for the 20 dB

attenuator as seen on the sampling oscilloscope 23

2-11 Photograph of e,,(t) and e,^(t) for the 20 dB

dl d2

attenuator after signal averaging 23

2-12 Computer plot of the amplitude frequency

response of the 20 dB attenuator 24

2-13 Photograph of e (t) and e (t) for the 40 dB

CLX dud attenuator as seen on the sampling oscilloscope 25

iv
List of Figures (Con't)

Figure Page

2-14 Photograph of e^^(t) and e^^{t) for the 40 dB

attenuator after signal averaging 25

2- 15 Computer plot of the amplitude frequencyresponse of the 40 dB attenuator 26

3- 1 Simplified block diagram of ac VTVM tested 27

3-2 Block diagram of system used to perform ac VTVM frequency domain measuronents 28

3-3 Graph of amplitude frequency response of ac VTVM using the 50 Cl termination 29

3-4 Graph of amplitude frequency response of ac VTVM with 50 Cl termination removed 30

3-5 Photograph of ac VTVM meter amplifier response

waveform after being made periodic and smoothed. ... 31

3-6 X-Y recording of ac VTVM meter amplifier

frequency response. 32

V
I

i
ABSTRACT

This interim report is concerned with the application

of time domain measurements to the determination of

frequency domain parameters. The theory is developed

for the calculation of the parameter (w) from time ^ 21

domain insertion measurements. Experimental results

are presented for a 4. 1 GHz low pass filter and coaxial

attenuators of 10 dB, 20 dB and 40 dB. Also presented

is an experimental justification showing the lack of

feasibility of applying time domain techniques to the

frequency response calibration of certain ac VTVMs.

Key Words: Fast fourier transform; frequency response;

microwave; pulse; S-parameter; time domain; transfer

function.
1. INTRODUCTION

This report is an interim report to the sponsor containing a condensed description of work accomplished through fiscal 1973. Upon

completion of the overall project objective a comprehensive final report

shall be published. The overall project objective is to develop the

capability at NBS to rapidly measure and process time domain data

such that new advances in time domain instrumentation can be accurately and efficiently analyzed.

Specifically, this interim report is concerned with the application of time domain measurements to the determination of frequency

domain parameters as functions of frequency. Such an application of

time domain measurements is intimately related to the processing of

time domain pulse data.

The report is divided into three chapters, the first being the

present introduction. Chapter 2 of this report contains the development

of a model used for the computation of the frequency domain parameter

S (s) from time domain measurements. In addition, this chapter contains the description and results of experimental time domain insertion

measurements for a coaxial low-pass filter and three coaxial attenuators.

S^jlJco) is computed for each component.

Chapter 3 consists of a description of experiments using both

frequency domain and time domain techniques aimed at determining the

feasibility of calibration of certain ac VTVM's using time domain

measurement methods. The conclusion drawn from these experiments

is that although time domain techniques are quite powerful, their use

for this purpose is unfeasible.

2
2. COAXIAL MICROWAVE DEVICE EXPERIMENT

The general goal of this experiment was to determine the frequency response characteristics of four coaxial microwave devices

from measured time domain data. [ 1]. The commercial devices tested

were a 4. 1 GHz low pass filter, a 10 dB attenuator, a 20 dB attenuator

and a 40 dB attenuator.

2. 1 Theory

These measurements were actually time domain insertion loss

measurements for the computation of the transfer insertion parameter,

S^jljoo) > where (j) is the angular frequency variable. [2] . A circuit

model analysis justifying the experimental measurement technique now

follows

.

The circuit used to obtain the incident voltage waveform at the

plane of insertion is shown in Figure 2-1. E (s) and Z (s) represent

the voltage source transition waveform generator where s is the complex frequency variable, jjj , ^2 ' 3.nd are three sections of precision coaxial airline of impedance R . The box labeled T(s) represents the sampling oscilloscope with an input impedance of Z(s) across

the line and a transfer function T(s). observable voltage;

it is the insertion plane transition waveform as seen through the transfer properties of jj^ and the oscilloscope. Z^(s) is a termination

whose impedance is very close to R^. For this analysis, it is assumed

that all connectors are ideal.

Since the generator impedance, Z^(s), may not be equal to R^ , and since the presence of the sampling oscilloscope at the end of line

I certainly changes the load impedance as seen by line 2 _ to some

value other than R , the reflections caused by these two discontinuities

o

3
will invalidate this analysis after some time T . The available time

window in which this measurement is valid is determined by the lengths

of the two lines, H and ji . The time delays for reflections from the

-L w generator and the oscilloscope, respectively, are

= 2 y LC

(2-1)

= 2 ^2 v/ LC .

Thus T , the available time window, will be either t , or r , which

ever is smaller.

The displayed initial input transition voltage waveform, ^^^(t) , may be expressed as

dl

(t) = Z j E (s)

[

'^1 ^2

(2-2)

where £

^ denotes the inverse Laplace transformation operator, and

where -^^^^(s) given in terms of the complex frequency variable s as

= E (s)

R e oZ (s) + R

Z(s) R

o Z(s) + R

Z(s) R

o

y T(s) .

^o Z(s) + R J o

(2-3)

4
For purposes of clarity and precision, the word "initial" used

above refers to the waveform present at the insertion plane only during

the inverval 0 to —^ + T • the generator and load impedances

2i were both equal to the line impedance R , then one could refer to the

o waveform at the insertion plane as an "incident" waveform, the distinction being that the incident waveform would exist over the time interval

(o , 03 ). By using two different terms, a clearer distinction is made

between the generator waveform over all time, and that part of the

generator waveform undistorted by reflections from either the source

or the oscilloscope impedance discontinuities within the time window.

Furthermore, the term "initial" can be used to describe waves arriving

or departing from a given port. For example, E^.(s) is the initial

waveform arriving at the insertion plane while

-^2t^^^

will designate the

initial waveform departing (or transmitted) from the output port of the

network under test.

Writing (2-3) in terms of E (s),

r 2^^)

o Z(s) + R

-s I.

R +

Z(s) R

o Z(s) +R

T(s:

(2-4)

Referring to Figure 2-2, with the addition of the device under

test into the 50 ohm system, the initial transmitted voltage waveform

E (s) may be expressed in the complex frequency plane as

^t(^^ = ^li^^^ ^21^^) (2-5)

5"
The displayed initial transmitted voltage waveform e (t) is

dZ

d2^

(t) = i:"^

j £^^(3) [ o<t<-^ "f '^d ^'^ ^^"^^

where

r Z(s) R

Z(s) + R

Z(s) R

R +

o Z(s) + R

o

T(s)e

-s JTC

(2-7)

T is the additional time delav introduced by the device under test,

d

From equations (2-5) and (2-7) E (s) is given by

Z(s) R

Z(s) + R

Z(s) R

R +

o Z(s)+R^j

^ T(s) e

-s /lc"

(2-8)

The quotient of E (s) and E ^(s) will yield the following result:

d2 dl

^ - s r ) E^^(s) - ^21^"^ • (2-9)

Thus, for the two time domain waveforms actually observed, in terms

of Laplace transforms,

6
£ je (t)l

or, replacing s by j co , we arrive at the final Fourier transform

equation

2. 2 Experimental Test Setup

The basic test configuration consisted of a 20 ps. 10%-9 0%

transition time voltage step generator, a 28 ps. 10%-90% transition

time sampling oscilloscope and a 1000 point local digital memory.

Precision 7 mm coaxial air lines were used for discontinuity reflection

isolation. The available time window j was 1 ns. The complete

system block diagram is shown in Figure 2. 3. [ 3] . With the device under test removed from the system, the time

domain waveform from the tunnel diode pulse generator was sampled

and recorded as a 1 000-point waveform. The device under test was

then placed in the line as shown in the block diagram and another 1 000-

point waveform was recorded. The first waveform,

initial waveform in the 50 ohm system while the second waveform,

^joC^) is the initial transmitted waveform from the network under test.

d2

Due to an excessive amount of noise in the system, some waveform signal averaging was necessary. This averaging was accomplished by taking several hundred voltage samples at each of the 1000

incremental time divisions. All the voltage samples taken at a given

point in time were then averaged through a simple R-C averaging

circuit and the resultant averaged voltage value was stored in memory.

7
This technique, in effect, is similar to averaging several hundred

1000-point time domain waveforms. The primary difference is that

averaging is done prior to storage in memory, so that the required

memory size is minimal.

Once the insertion waveforms were acquired and stored, they

were punched onto teletype paper tape. These records were then read

into an in-house computer where they were processed using a Fast

Fourier transform (FFT) subroutine.

The output of this subroutine consists of a set of complex frequency domain coefficients for each transformed time domain waveform. The amplitude frequency response of the test devices may then

be obtained by computing the ratio of the magnitude of the output and

input frequency domain coefficients for each frequency point of interest.

The resulting amplitude frequency response characteristics for

each device were then plotted as graphs of gain in dB versus frequency.

2. 3 Experimental Data and Results

2. 3.1 4. 1 GHz Low Pass Filter

The 4. 1 GHz low pass filter tested had a nominal impedance of

50 Q. It was equipped with type N connectors, one male and one female.

Filter insertion loss was rated at ^ 1 dB below . 9 x cut off frequency

and rejection was rated at 2: 50 dB above 1, 25 x cut off frequency.

Figure 2. 4 contains photographs of the insertion time domain waveforms obtained on the sampling oscilloscope., In this case, as well as

the following three cases, the transmitted initial waveform, e^-(t) , d2

is delayed from the initial 50 ohm system waveform, e (t). Thus, in

dl

the photographs, the output waveform transition occurs to the right of

the input waveform transition. The sampling oscilloscope was sampling

8
at a rate of 91. 6 kHz. Figure 2. 5 is a photograph of these same waveforras as observed on a monitor oscilloscope after signal averaging was

done. These were the waveforms actually stored in local memory for

computer processing.

Figure 2. 6 is a computer plot of the frequency response of the

low pass filter as calculated using the fast Fourier transform.

2. 3. 2 10 dB Coaxial Attenuator

The 10 dB attenuator tested was a dc to 18 GHz device with a rated maximum deviation from nominal attenuation of ± 0. 5 dB. The

connectors were both type N, one male and one female. The attenuator's nominal impedance was 50 ^,

Figure 2. 7 is a photograph of both input and output time domain

waveforms as seen on the sampling oscilloscope. The sampling oscilloscope sampling repetition rate was 24 kHz. Figure 2. 8 is a photograph

of both waveforms after signal averaging. Figure 2. 9 is a computer

plot of the frequency response of the 10 dB attenuator,

2. 3. 3 20 dB Coaxial Attenuator

The 20 dB attenuator was the same type as the 10 dB attenuator.

Figure 2. 10 is a photograph of the unaveraged input and output waveforms. Figure 2. 11 is a photograph of both waveforms after signal

averaging. Figure 2. 12 is a computer plot of the frequency response of

the 20 dB attenuator.

9
2.3.4 40 dB Coaxial Attenuator

The 40 dB attenuator was, again, the same type as the 10 dB

attenuator with the single exception that its rated maximum deviation

from nominal attenuation was ±1.0 dB.

Figure 2. 13 is a photograph of the unaveraged input and output

waveforms for the 40 dB attenuator. Figure 2. 14 is a photograph of

both averaged waveforms. Figure 2. 15 is a computer plot of the

frequency response of the 40 dB attenuator.

10
3. AC ELECTRONIC VOLTMETER MEASUREMENTS

3. 1 Experimental Purpose

The purpose of this experiment was to determine the feasibility

of utilizing time domain waveform measurement techniques for calibration of certain electronic ac voltmeters suitable for measurements

in the 20 Hz to 4 MHz frequency range.

One particular model was selected to represent this class of

test instrument and was subjected to both frequency domain and time

domain testing. A simplified block diagram of the VTVM is shown in

Figure 3-1.

Using twelve steps of attenuation, this meter measures ac voltage from 0.001 to 300 volts RMS full scale. The instrument is an

RMS indicating, average responding voltmeter with a frequency bandwidth from 10 Hz to 4 MHz. Instrument accuracy varies from ± 1% to

± 5% of full scale, the larger errors appearing at the extreme low and

high frequency regions of the rated bandwidth.

3. 2 Frequency Domain Test s

In order to provide a basis for verification of the time domain

tests which follow, frequency domain measurements of the VTVM's

amplifier frequency response were first conducted. Figure 3-2 is

a block diagram of the system used to perform these measurements.

Briefly, the measurements were conducted as follows. With the

system set up as depiected in Figure 3-2, and with the VTVM attenuation switch set to 0. 3 V full scle, the CW generator frequency was

set at 500 kHz. The amplitude of the generator sine wave was then

adjusted to 0. 3 V as observed on the reference RF voltmeter. The

voltage observed on the measurement voltmeter was then recorded.

11
This procedure was then repeated in steps of 200 or 300 kHz over the

range of frequencies from 500 kHz to 12 MHz. A graph of the resulting

VTVM amplifier frequency response scaled in dB versus frequency is

shown in Figure 3-3.

Since the manufacturer of this particular VTVM states that the

meter frequency response may vary as a function of the load impedance

across the OUTPUT terminals, the entire measurement described

above was repeated with the output termination removed. The

results of this test, again in dB versus frequency, are shown in

Figure 3-4.

The important feature to be noticed in both of these graphs is the

-3 dB point; in both cases, the meter amplifier gain, as measured at

the OUTPUT terminals, drops by 3 dB at approximately 9 MHz. The

instrument as a whole, however, has a rated upper band limit of only

4 MHz. Thus, these measurements appear to indicate that the frequency response of the meter amplifier and frequency response of the

whole instrument are not identical. This observation was substantiated

by the fact that the meter needle indication indeed dropped rather abruptly as the test signal frequency increased above 4 MHz.

3.3 Time Domain Tests

The time domain tests conducted on the ac voltmeter were performed on the same system as was used in the microwave experiments

described in Chapter 2. (See Figure 2-3), The only change to the

system was the substitution of a lower speed (350 ps 10%-90% transition time ) sampling head for purposes of noise reduction.

As in Chapter 2, with the voltmeter removed from the system,

the time domain waveform from a voltage step waveform generator

was sampled and recorded as a 1000-point waveform. The voltmeter

12
was then inserted into the system, and the initial transmitted meter

amplifier response waveform was sampled and recorded as another

1000-point waveform.

These two waveforms were then made periodic, smoothed and

processed using a fast Fourier transform subroutine [4] . The meter

amplifier response waveform, after being made periodic and smoothed,

is shown in Figure 3-5. The meter amplifier frequency response was

then plotted on an X-Y recorder in decibels versus frequency as shown

in Figure 3-6.

Observation of this figure along with Figures 3-3 and 3-4 will reflect the close correlation between meter amplifier responses obtained by

frequency domain and time domain techniques. As in the frequency domain case, the time domain techniques yielded a -3 dB point close to

9 MHz.

3. 4 Conclusions

In Chapter 2, a method was derived to obtain time domain insertion data. Using the time domain data, S (j CO) was computed for

w 1 several microwave devices. Although much work remains in the areas

of pulse generation, oscillographic techniques and data acquisition and

reduction, this method appears quite promising as a calibration technique.

On the other hand, the experiments conducted in Chapter 3 show

quite decisively that time domain measurement techniques, like their

frequency domain counterparts, cannot be applied blindly to all areas of

frequency response measurements. In particular, the feasibility of

using time domain techniques to measure the frequency response of

this type of ac VTVM is considered poor.

13
Both the time domain and frequency domain data closely agree

that the meter amplifier half power point lies near 9 MHz. However,

the meter indication, as read from the meter face, drops rapidly

above 4 MHz. It appears, then, that the network frequency response

of the meter amplifier and the frequency response of the indicating

meter itself are quite different. Although time domain calibration of

the meter amplifier is feasible, there is no justification that the

visually read meter would thus be calibrated. In short, there appears

to be no reliable correlation between the meter amplifier frequency

response and the visually read meter frequency response.

More generally, analog instruments that are visually read such

as oscilloscopes and VTVM's, should be visually calibrated. Unless a repeatable and reliable correlation can be established between the

instrument's visual indicator and measurable electronic properties,

any attempt to calibrate the instrument by purely electronic means

must be considered invalid.

14
4. REFERENCES

Nicholson, A, M. , "Broad-Band Microwave Transmission

Characteristics from a Single Measurement of the Transient

Response", IEEE Trans, on Instrumentation and Measurement,

Vol. IM-17, No. 4, pp. 395-402, December, 1968.

Ramo, S. , J. R. Whinnery, and T. Van Duzer, Fields and

Waves in Communication Electronics, John Wiley & Sons,

New York, 1965, pp. 603-609.

Gans, W, L. , "Block Diagrams, Schematic Circuit Diagrams,

and Operating Instructions for the Time Domain Measurement

System", NBSIR 73-321 (to be published).

Gans, W. L. and N. S. Nahman, "Fast Fourier Transform

Implementation for the Calculation of Network Frequency

Domain Transfer Functions from Time Domain Waveforms",

NBSIR 73-303, December, 1972.

15
INSERTION

PLANE

Figure 2-1* Diagram of circuit used to

Obtain e . ( t) . di

16
Zg(s) E^.(s)

n o- 4r M.H

DEVICE

UNDER

TEST

( s)

E2t(s)

Z(s)-

R

T(s) Z^(s)

~R

igure 2-2. Diagram of circuit used to obtain e (t) .

17
^ ui q:

LlJ O

Z O E

I— O U> UJ <: i:

2:

a

au

W)

ni

O

O

O CD

Q. <_)

a

-»-> COm

O

LkJ < (9 to HHi' i:

O 1-1

1-1 o

_l ct

CL. t-lJ

00

«t I—

c: — <

O X z in «t — o 2: o a:

LlI

cro

•rH(ta

o

0)a

•M

q; +j

<u

1—1a

a

oU

• CO

V

•IH

18
I * 4 nsec. ' I

Figure 2-4, Photograph of e (t) and e (t) for the 4. 1 GHz low pass filter as seen on the sampling oscilloscope.

time

Figure 2-5. Photograph of e^j{t) and e^^'^t) for the 4. 1 GHz low pass

filter after signal averaging.

19
1 J

/V-

—4—

iK

u

1

< . ..

-. ?

il L—

" * \

1

! 1 — V! J i 1

1

L

-i——

1

1

f

r

( i

5 6 7 8 9 GHZ

Low Pass Filter 4. 1

10 11 12 13 14 15

Figure 2-6. Computer plot of the amplitude frequency response

of the 4. 1 GHz low pass filter .

20
<^ pq

|-*——= 400 psec

Figure 2-7. Photograph of e,,{t) and e ,^(t) for the 10 dB attenuator

dl d2

as seen on the sampling oscilloscope.

time »

Figure 2-8. Photograph of e,T(t) and e,-(t) for the

dl d2

10 dB attenuator after signal processing.
6 7 8 9

GHZ

10 11 12 13 14 15

10 DB ATTENUATOR

Figure 2- 9. Computer plot of the amplitude frequency response

of the 10 dB attenuator.

22
400 psec.

Figure 2-10. Photograph of the e ^Jt) and e ,^(t) for the 20 dB

di d2

attenuator as seen on the sampling oscilloscope.

time

Figure 2-n. Photograph of e^^(t) and e^^{t) for the 20 dB

attenuator after signal averaging.

23
H

H

H

<

21. 7

21. 5

21. 3

21. 1

20. 9

20.7

20. 5

20. 3

20. 1

19.9

19.7

19. 5

19. 3

19. 1

18. 9

18. 7

—

-— J

—— / \

.

—

\ I

1 \ — V4

i\"J

L=_«

—

6 7 8 9 GHZ

20 DB ATTENUATOR

10 11 12 13 14 15

Figure 2-12, Computer plot of the amplitude frequency response of

the 20 dB attenuator.

24
as seen on the sampling oscilloscope.
41. 9

41. 5

41. 1

40. 7

40. 3

39.9

39. 5

H 39.1

H

H^ 38.

7

38. 3

37. 9

37. 5

37. 1

36.7

36. 3

35. 9

— \-A

1 /

T

1I—

GHZ

40 DB ATTENUATOR

Figure 2-15, Computer plot of the amplitude frequency response of the

40 dB attenuator.

26
3 UJ z

Ui i;: r3 o 1 CTCl. > LU OO ^

QC UJ O Lu OC O

G

— <.

Q- CO

- -« =

E >- T (_J LU

=3 O O era. ca

1^ ^ < o ®

®

-®

(S

O-Q.

Ui I/) UJ

u. on

UJ z: ^

=> O 1 O-Q- >

UJ ro

UJ o

u. cc o

O UJ z n

UJ z 5 =3 0 —

era.

UJ f

^

u. oc

-HI.

-<9

0)

>

>

o

ro

O

0)

I CO

27
<C I—

c: '-' <i: O X z

Lf) ct »—

t

o s:

et LU

C: '-' CQ = O X O H

LD <: q: = O a. o

q: u- ^

rD I—

—J

<: o

LU I—

O

PiV

cr

>

u

o

0)ft

01

:3

CO

U

O

1—

(

I COu

DC

iH

O

28
-H o (Mtn^iDvo 00 o r-i (M + I iiiii iri-^rt^^

gp UI UTBQ III,

29
o ^ pa m lOvo r~ oo o ^ <m«*» m sO + -i III II II I ^ 1-^ ^ II I I I I I

30
I- 2 fX sec.

Figure 3-5. Photograph of ac VTVM meter

amplifier response waveform

after being made periodic and

smoothed.

31
^ CO <M >-i O

I I I I gp UI UTljrj

32
FORM NBS-114A (1-71) U.S. DEPT. OF COMM. 1 . PU B LIC AT ION OR RE PORT NO. 2. Gov't Accession BIBLIOGRAPHIC DATA NBSIR 73-325

SHEET

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

PULSE TESTING OF RF AND MICROWAVE COMPONENTS

5. Publication Date July 1973

6, Performing Organization Code

7. AUTHOR(s) William L. Gans and N. S. Nahman 8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NAllONAL dUKEAU Or blANUARDs, iDOUiCler l_iaDS„

DEPARTMENT OF COMMERCE

kk3titfekkl^fekkKft3*ftkBoulder, Colorado 80302

10. Project/Task/ Work Unit No. 2725390

11. Contract/Grant No.

12. Sponsoring Organization Name and Address DoD/CCG

13. Type of Report & Period Covered mL c r 1 m rv e p o r x

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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

bibliography or literature survey, mention it here.) This interim report is concerned with the application of time domain measurements to the determination of frequency domain parameters. The theory is developed for the

calculation of the parameter ^^^(co) from time domain insertion measurements.

Experimental results are presented for a 4. 1 GHz low pass filter and coaxial

attenuators of 10 dB, 20 dB and 40 dB. Also presented is an experimental justification

showing the lack of feasibility of applying time domain techniques to the frequency

response calibration of certain ac VTVMs.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Fast fourier transform; frequency response; microwave; pulse; S-parameter;

time domain; transfer function

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(THIS REPORT)

UNCL ASSIFIED

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