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NBS TECHNICAL NOTE 699

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and

technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to pro- mote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Institute for Computer Sciences and Technology, the Office for Information Programs, and the

Office of Experimental Technology Incentives Program.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consist- ent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scientific community, industry,

and commerce. The Institute consists of the Office of Measurement Services, and the following center and divisions: Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Center for Radiation Research — Laboratory Astrophysics 2 — Cryogenics 2 — Electromagnetics 2 — Time and Frequency 2

. THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized materials needed by industry, commerce, educational insti- tutions, and Government; provides advisory and research services to other Government agencies; and develops, produces, and

distributes standard reference materials. The Institute consists of the Office of Standard Reference Materials, the Office of Air and Water Measurement, and the following divisions:

Analytical Chemistry — Polymers — Metallurgy — Inorganic Materials — Reactor Radiation — Physical Chemistry.

THE INSTITUTE FOR APPLDZD TECHNOLOGY provides technical services developing and promoting the use of avail- able technology; cooperates with public and private organizations in developing technological standards, codes, and test methods; and provides technical advice services, and information to Government agencies and the public. The Institute consists of

the following divisions and centers: Standards Application and Analysis — Electronic Technology — Center for Consumer Product Technology: Product

Systems Analysis; Product Engineering — Center for Building Technology: Structures, Materials, and Safety; Building

Environment; Technical Evaluation and Application — Center for Fire Research: Fire Science; Fire Safety Engineering.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research and provides technical services designed to aid Government agencies in improving cost effectiveness in the conduct of their programs through the selection, acquisition, and effective utilization of automatic data processing equipment: and serves as the principal focus wthin the executive branch for the development of Federal standards for automatic data processing equipment, techniques, and computer

languages. The Institute consist of the following divisions: Computer Services — Systems and Software — Computer Systems Engineering — Information Technology.

THE OFFICE OF EXPERIMENTAL TECHNOLOGY INCENTIVES PROGRAM seeks to affect public policy and process

to facilitate technological change in the private sector by examining and experimenting with Government policies and practices in order to identify and remove Government-related barriers and to correct inherent market imperfections that impede

the innovation process. THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS: promotes the development of the National Standard Reference Data System and a system of in- formation analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services

to ensure that the NBS staff has optimum accessibility to the scientific information of the world. The Office consists of the following organizational units:

Office of Standard Reference Data — Office of Information Activities — Office of Technical Publications — Library —

Office of International Standards — Office of International Relations.

1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C 20234.

3 Located at Boulder, Colorado 80302.
DEC 2 1977^ ace.- Ro

SPECTRUM AMPLITUDEDefinition, Generation and Measurement

C\OQ

©153

111

James R. Andrews

M. Gerald Arthur

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

* W 'ft

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued October 1977
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 699

Nat. Bur. Stand. (U.S.), Tech. Note 699, 100 pages(October 1977)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1977

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-01865-1 Price $2.75 (Add 25 percent additional for other than U.S. mailing)
CONTENTS

Page

1 . INTRODUCTION 1 Background 2 2. FOUNDATIONS FOR THE DEFINITION OF SPECTRUM AMPLITUDE 4

2 . 1 Fourier Transform Fundamentals 4

2 . 2 Fourier Transform, a Complex Quantity 6

2 . 3 Fourier Transform Dimensional Units 8

2 . 4 Fourier Transform, a Continuous Function 11

2 . 5 Use of the Fourier Transform 13

2 . 6 Summary 18

2.7 Derivation of V (f) 19

r

3

.

SPECTRUM AMPLITUDE GENERATION 21

3 . 1 Amplitude Spectrum of Common Waveforms 21

3.2 Mercury Switch Impulse Generator 25

3.3 Avalanche Transistor Impulse Generator 27

3.4 NBS Step Recovery Diode Impulse Generator 30

3.5 RF Pulse Generator 33

3.6 Microwave Impulse Generator 37

4

.

SPECTRUM AMPLITUDE MEASUREMENT TECHNIQUES 41

4.1 Standard Transmission Line Method. . . . T 41

4 . 2 Harmonic Measurement 41

4 . 3 Energy Method 4 2 4.4 Sum and Difference Correlation Radiometer 44

4 . 5 Dicke Radiometer 4 7 4.6 Video Pulse — Mil. Std. 462 48

4 . 7 Spectrum Analyzer 50

4.8 Standard Pulse Comparison 52

4.9 Time Domain Measurement/Fourier Transformation Computation... 55

5. EXPERIMENTAL COMPARISON OF VARIOUS S(f) MEASUREMENT TECHNIQUES 58

5 . 1 Standard Transmission Line Experiment 58

5.2 Sum and Difference Correlation Radiometer Experiment 58

5.3 Experiments with Commercial Mercury Switch

Impulse Generators 60

5.4 Experiment with Step Recovery Diode Impulse Generator 63

6. ERROR ANALYSIS OF S(f) MEASUREMENT USING TD/FFT 66

6 . 1 Sampling Oscilloscope Errors 66

6 . 2 Computer Errors 67

6 . 3 Nonrepeatability 69

6 . 4 Error Tabulation 69

6 . 5 Comparison with Other Measurement Techniques 71

6 . 6 Calibration of Other Components 71

iii
CONTENTS (Cont)

Page

7. NBS IMPULSE GENERATOR SPECTRUM AMPLITUDE CALIBRATION SERVICE 72

7 .

1

Spectrum Amplitude Definition 72

7.2 NBS S(f) Measurement Technique 73

7.3 Limitations and Capabilities of S(f) Measurement Service 73

7.4 Calibration Report 78

APPENDIX A — NBS IMPULSE GENERATOR SPECIFICATIONS, CIRCUIT

DESCRIPTION AND SCHEMATICS 7 9 REFERENCES 91

IV
SPECTRUM AMPLITUDE — DEFINITION, GENERATION AND MEASUREMENT

James R. Andrews and M. Gerald Arthur

This technical note is a detailed discussion of the electromagnetic quantity, spectrum amplitude, which is used to characterize

broadband signals and noise. The definition of spectrum amplitude

is presented in detail. Several practical means of generating

electrical signals with broadband spectrum amplitudes are included.

Various techniques for the measurement of spectrum amplitude are described along with experimental comparisons. The NBS measurement

service for the calibration of impulse generator spectrum amplitude

is described along with an error analysis.

Key words: Electromagnetic interference; Fourier transformation;

impulse; impulse generator; spectrum amplitude.

1. INTRODUCTION

In EMC work, and in the EMC literature, one often encounters an electromagnetic quantity that has the dimensional units of volts per hertz, or more

commonly, microvolts per megahertz. However in reading the literature, one is

sometimes puzzled or confused by the variety of names that this quantity is

given, or may become suspicious that the way in which this quantity is being

used is somehow different from the way that someone else has used it. This

technical note addresses this quantity with the purpose of clarifying what

some of its important characteristics are, and to attempt to reduce some of

the large amount of confusion, half truths, and whole untruths about it. The

most official name given to this quantity is found in the IEEE Dictionary [1]

and IEEE Std. 376-1975 [2]. That name is Spectrum Amplitude. Spectrum amplitude, S (f ) , is defined in terms of the magnitude of the Fourier transform,

V(f), of a time-domain signal function, v(t).

S(f) = 2|V(f)

|

(1-1)

where

oo V(f) = / v(t)e" j2Trft dt. (1-2)

—00 Other names that can be found in the EMC literature are Impulse Spectral Intensity, Spectral Intensity, Spectral Density, Voltage Spectrum, Impulse Strength

and Interference Intensity. All of these names have been applied to quantities

that have dimensional units of volts per hertz or its mathematical equivalent,

volt-seconds. The unit in common usage is microvolts per megahertz (yV/MHz)

.

Also in common usage is a decibel expression, decibel microvolts per megahertz

(dByV/MHz) , above 1 yV/MHz.

S <*» = 20 ^10 (B^ (1-3)
Background

Impulse generators are widely used as transportable field calibration

instruments for the calibration of field intensity meters (FIM) , spectrum

analyzers, and receivers. FIM's are the basic instruments for measuring electromagnetic (EM) fields and the spectrum amplitude, S(f), of broadband impulsive noise.

The area of electromagnetic field (EM) measurement is of considerable

importance. It is relevant to the broad area of interference described

variously as RFI (radio frequency interference) , TVI (television interference)

,

and EMI (electromagnetic interference) . It is the measurement base for frequency allocations based on EMC (electromagnetic compatibility) . In national

security electronic espionage and electronic warfare countermeasures , radiated

impulse measurements (RIM) are very critical.

Present FIM calibration techniques utilize CW signal generators for narrow- band measurements and impulse generators for broadband measurements. The CW

signal generator presents no problem as its calibration is directly traceable

to NBS. Impulse generators have been an entirely different matter in that

tneir calibration has not been traceable to NBS. Users of impulse generators

nave had to rely upon the manufacturer's calibrations. There are discrepancies

between various commercial impulse generators, as many users have discovered.

As a result of several years of effort dating back to 1966, NBS has developed

a measurement service for the calibration of the spectrum amplitude output of

impulse generators. This service was publicly announced in the Fall 1976

Appendix to NBS SP-250, "Calibration and Test Services of the National Bureau

of Standards." This Technical Note summarizes the research and development

effort at NBS necessary to establish this measurement service.

Funding for establishing NBS standards and traceability for impulse

generator spectrum amplitude has come from both internal NBS funds and various

contracts from the U.S. Department of Defense. The various DoD contracts were

as follows

:

1. U.S. Army Electronics Command, Ft. Monmouth, N.J. , contract No.

67-95896, Dec. 1966 tq, Sept. 1971.

2. Army/Navy/Air Force Calibration Coordination Group (CCG) , project

CCG 69-26, FY 1969.

3. Army/Navy/Air Force Calibration Coordination Group, project CCG 72-

70, FY 72.

4. Army/Navy/Air Force Calibration Coordination Group, project CCG 72-

71A, FY 72.

5. Army/Navy/Air Force Calibration Coordination Group, project CCG 75-

97, FY 75-76.

In addition to the above contracts, funding was received from the CCG for work

in the related area of picosecond pulse measurements. As it turned out, a
great deal of this work was directly applicable to the impulse generator

problem. In particular, the calibration console currently used for impulse

generator calibrations was originally developed as a Time Domain Automatic

Network Analyzer under CCG 72-68. Other related CCG projects were: 71-50,

71-52, 72-65, and 72-66. This Technical Note serves as part of the final

report on tne most recent contract CCG 75-97.

This Technical Note is organized in seven chapters and one appendix.

Tne first chapter is this introduction. Chapter 2 discusses the definition of

spectrum amplitude along with its mathematical and physical concepts. Chapter

3 discusses practical means of generating electrical signals with broadband

spectrum amplitudes. Chapter 4 describes various techiques for the measurement

of spectrum amplitude. Chapter 5 presents a summary of results obtained from

experiments to compare the various measurement techniques of Chapter 4.

Cnapter 6 is an error analysis of the time domain measurement/Fourier transform

computation technique of determining spectrum amplitude. Chapter 7 describes

tne NBS measurement service for impulse generator spectrum amplitude. An

appendix describes in detail an impulse generator developed at NBS which

produces an 8 V, 100 ps impulse with a spectrum useful to beyond 5 GHz.

Cnapter 2 was contributed by M.G. Arthur and the subsequent chapters were written by James R. Andrews.
2. FOUNDATIONS FOR THE DEFINITION OF SPECTRUM AMPLITUDE

This chapter deals with certain characteristics of the Fourier transform

[3], upon which is based the spectrum amplitude S(f). Because many workers

who deal with impulsive signals appear to have misunderstandings about this

quantity, a review of certain of its more important characteristics may be

helpful.

Every physical signal has an amplitude spectrum [4]; that is, every physical

signal can be described in both the time domain and the frequency domain. One

mathematical way of expressing this physical duality is by means of the Fourier

transform pair of algebraic equations. It is certainly possible to postulate

mathematical waveforms for which the Fourier transform, and hence the amplitude

spectrum, does not exist [5] . However, because every signal which we might

generate and every signal sample which we might extract from some arbitrary

generating system is finite in both duration and amplitude, and hence has

finite energy, the conditions for the existence of their Fourier transforms

are always met.

Three major points will be emphasized concerning the Fourier transform

as follows: (1) In the general case, it is mathematically a complex quantity

having botn magnitude and phase. (2) Its dimensional units are different

from tnose of the waveform function being transformed. (3) It is a continuously

defined function of frequency, and not a discontinuous, discrete function of

frequency. After these points are discussed, we will point out that the

magnitude of the Fourier transform appears explicitly in many signal equations,

tnus leading naturally to the definition of spectrum amplitude, S(f).

2 . 1 Fourier Transform Fundamenta ls

This section very briefly presents the basic information that will be

needed in the following sections. More thorough treatments of the Fourier

transform are available in the open literature.

The Fourier transform pair of equations are the following:

00 V(f) = / v(t)e" j27Tft dt (Fourier transform) (2-1)

—00

00 v(t) = / V(f)e j2ljft df (inverse Fourier transform) (2-2)

— 00

This pair of equations can be used to mathematically represent a physical

signal which is labeled v(t) in the time domain and V(f) in the frequency

domain. Equation (2-1) transforms the time domain quantity, v(t), into the

frequency domain quantity, V(f); and conversely for eq. (2-2). The physical

signal itself is not transformed by the Fourier transform; it is a physical

entity that exists in both the time and frequency domains. Transformation is

a mathematical operation on the equations that algebraically represent the
signal. However, a graphic plot of the signal's time domain waveform, v(t),

will in general have a different shape than a plot of its frequency domain

waveform, V(f), because the two algebraic equations are usually different.

(The single Gaussian pulse is an exception to this statement.)

To be transformable as indicated above, the algebraic time domain function, v(t), must satisfy the three Dirichlet conditions; viz.:

v(t) must be absolutely integrable; that is,

oo

/ |v(t) | dt < ». (2-3)

2. v(t) must have a finite number of maxima and minima in any finite

interval of time.

3. v(t) must have a finite number of discontinuities in any finite

interval of time.

We will use the single rectangular baseband pulse shown in figure 2-1 as an example to illustrate the characteristics of the Fourier transform that we are emphasizing. This waveform has an amplitude of A from t = to t = x , and

is zero elsewhere. Although this idealized waveform cannot be generated as

a physical signal, it satisfies the Dirichlet conditions, and its mathematical

representations are easy to work with and comprehend. All of the observations

and conclusions we will make from this example generally apply to any physical

signal, regardless of whether it is a single pulse of arbitrary shape, a series

of pulses repeated at perfectly regular intervals, a series of pulses repeated

at irregular intervals, or continuous-type signal functions of regular,

irregular, or random shape.

v p (t)

Figure 2-1. Single rectangular baseband pulse.
2. 2 Fourier Transform, a Complex Quantity

The time domain representation, v (t) , of the waveform of figure 2-1 is

v (t) = A, < t < T p

= elsewhere. (2-4)

The Fourier transform, V (f ) , of v (t) is obtained by substituting eq. (2-4)

hr hr into eq. (2-1)

.

V (f) = A /V^ 2TTft dt (2-5)

= j~y [sin(2iTfT) - j2 sin 2 (iTfT)] (2-6)

Equation (2-6) shows that V (f) is a complex quantity having both a real and an imaginary part. This is true in general of any v(t), although some signal

representations, depending upon their waveform and the choice of time origin,

may have only a real or an imaginary part.

The purpose of emphasizing the complex nature of V(t) is the following:

Spectrum amplitude, which is twice the magnitude of V(f), may not, in general,

be sufficient to adequately describe the signal. Phase information may be

needed, depending upon the application (for example, when predicting the

effect of changing the measurement bandwidth of an EMI receiver). However,

for many purposes found in EMC work, the magnitude, |v(f) | , is a very useful

quantity, as is discussed later.

V (f) may also be written in polar form in which the magnitude and phase

ir are explicit.

V

p

(f) = |V

p

(f)|e^p (f) (2-7)

where

V (f)

27Tf { I sin(2Trfx)] 2 + [-2 sin 2 (TTfx)] 2

}

1/2 (2-8)

and

= At sin(TTfi)

Trf x (2-9)

4(f) = tan

ir -1 1 -2 sin 2

(-rrf x)

sin (2-rrf t)

-1

= tan [-tan(T7f t) ] .

(2-10)

(2-11)
The interpretation of the multivalued arctangent function can be obtained by

plotting V (f) from eq. (2-6) in the complex plane as a function of frequency.

Figure 2-2 shows such a plot from f = to f = 2/t . For positive frequencies,

V (f) occupies only the third and fourth quadrants. Thus the phase, <£ (f ) , is written as

(f) = -irfi + m\ (2-12!

where n=0, ±1, ±2, ... Substituting eqs. (2-9) and (2-12) into eq. (2-7) gives

V (f) = Ax

P

sin (irfx)

TTf T

j (-Trfx+nTi) (2-13;

A quasi-polar form for V (f) is

V (f ) = AT 5in ^

fT) e-^fT

p ufx (2-14)

since, for the baseband pulse of figure 2-1,

At

sin (irf t)

TTf T e

JnTr _ At sinUfx)

TrfT (2-15)

Equation (2-15) can also be gotten directly from eq. (2-6)

IraV p (f)

» ReV

p (f)

INCREASING FREQUENCY

Figure 2-2. The locus of V (f) for positive frequency.
2 . 3 Fourier Transform Dimensional Units

The dimensional units of the Fourier transform are different from those of

the signal waveform which is being transformed; specifically, they are the units

of the signal waveform multiplied by time (dimensional unit of seconds) . The

purpose of emphasizing this characteristic is to distinguish the Fourier transform representation of the signal from the Fourier series representation [3]

.

In the latter case, the spectrum is a discrete spectrum, the components of which

are eternal sinusoids whose amplitudes have the same dimensional units as those

of the physical signal. In the former case, the time domain function is transformed into an entirely different function with a different set of dimensional

units. These different units warn us that we are dealing with a "transformed"

function that may have different properties from the Fourier series components.

To illustrate how the Fourier transform differs from the Fourier series

representation, we will make use of geometrical interpretations of the algebraic

equations. Consider again the waveform given in figure 2-1. As before,

-£ V (f) = / Ae~ l2lTft dt. (2-5)

P o The integrand, y, of eq. (2-5) is

. -j2iTft

y = Ae J

= A cos(2irft) - jA sin(2TTft), < t < t

= elsewhere. (2-16)

The function y is a function of both frequency and time; it is also complex.

The real part of y in this example is

Re[y] = A cos(2iTft), < t < x (2-17)

and the imaginary part is

Im[y] = -A sin(2irft), < t < x. (2-18)

Figure 2-3 shows a portion of a three-dimensional plot of the real part of y.

It is three dimensional because y is a function of both frequency and time.

The result is a wavy surface with a cosinusoidal variation in both directions

.

Because V(f), in general, is an integral [see eq. (2-1)], it is geometrically

an "area." The real part of the Fourier transform, Re [V (f ) ] at a specified

XT frequency, f, is the area under the cosine curve of figure 2-3 at frequency f

in the time direction. For example, figure 2-4 shows four "slices" through

this wavy surface parallel to the time-axis and perpendicular to the frequencyaxis. The value of Re [V (f ) ] at frequency f is the area marked "c." The

imaginary part of V (f) can be found in a similar way. V (f) is the vector sum

of the real and the imaginary parts (see the vector diagram at frequency f, ) .
4-+

-P

CNWo

o<

>1

Pi

o

+JOH

ft

(0coH

enc

aiSH

t3

I(U

cu

I CM

a)

•H

7i*-a©6
>1 &C

CDQ)

-P

CD X)

•HWcoH

4J

fd .H

ajn

QJ X!

-P • r—i S M-l •H

•P

td

J-i -P

CO3 aC

id i CM

CD

C7> •H

10
Being an area, V(f) has dimensional units which are the product of the

units of its constituent parts, height (ordinate) and base (abscissa) . If

v(t) is a voltage, then V(f) has the units of volt-second. From this we can

see that V(f) is not the amplitude per se of sinusoidal voltages that are com- ponents of the physical signal in the frequency domain. It is neither a voltage, a power, or an energy. Rather, because its dimensional units, voltseconds, are mathematically equivalent to the units "volts per hertz," we see that spectrum amplitude, S(f), is a voltage density quantity, or, mathematically,

a type of weighting function. It is a measure of the "strength," in voltseconds or volts per hertz, of the physical signal.

There is a strong possibility for confusion and misapplication if the

units of volts per hertz are used for V(f) rather than volt-seconds. It is

true that mathematically they are equivalent. From a physical standpoint,

volts per hertz suggests a density function whereas volt-seconds does not. No

engineering justification can be found for using one set of units in preference

to the other. However, the units, volts per hertz, can mislead one into

thinking that he can simply integrate V(f) over a finite interval of frequency

and obtain a voltage that has some useful physical meaning. Such may not be

the case. What does have useful meaning, as was seen in eq. (2-2), is the

integral of the product of V(f) with an (eternal) exponential function, which,

for the infinite integral, yields the complete time-domain signal representation v(t). Incidentally, the infinite integral of just V(f) over the entire

frequency interval is the value of the time-domain signal function at time

t = 0. This is a basic theorem of Fourier transforms. Thus the integral of

V(f) over a finite frequency interval yields the part of v(t) at t = con- tributed by the frequency-domain signal in that band of frequencies. But these

quantities are normally of limited interest, and most EMC instruments do not measure them.

2. 4 Fourier Transform, a Continuous Function

Another important characteristic of V(f) is that it is a continuously

defined function of frequency. Again, the purpose of emphasizing this characteristic is to distinguish it from the discrete spectrum of the Fourier series

representation. Although there may be specific frequencies where the Fourier

transform, V(f), is zero, it is generally true that there are no frequencies

where V(f) is undefined. This is not the case with the Fourier series

representation. There the spectrum is defined only at discrete frequencies.

A plot of |v (f ) | and <j> (f) for the waveform of figure 2-1 is given in

IT ir figure 2-5. |v (f)| has the familiar "absolute sine x over x" shape and cj> (f)

is a linear sawtooth, as given by eqs . (2-9) and (2-12), respectively. Note

that these plots are for the single rectangular pulse, figure 2-1.

11
>1uC

CDO1 <DM

14-1

COw>

4-1

-e- G

IW

a

iwow

+>

in1 CN

0) H

12
The Fourier transform, V(f ) , of a finite train of repeating pulses can appear experimentally to be a discrete line spectrum such as would be given by

the Fourier series representation. Actually, the spectrum is not a true line

spectrum, but only appears to be so because of the sensitivity and resolution

characteristics of our test equipment. This can be shown as follows.

The Fourier transform of a regularly repeating rectangular function, such

as the one illustrated in figure 2-6 (a), which is of finite duration T (as all

physical signals are) , is a sum of terms given by the equation

V

r

(f) = ATfQT

n=°° sin(iTnf x) sin|>(f-nf )T]

Y o t __J__ o

' -rrnf t TT(f-nf )T

n=-oo o o (2-19)

where f is the repetition rate of the physical signal (see section 2.7). Each

term of this sum can be plotted as an individual spectral amplitude distribution centered at frequency f = nf . Three such terms are shown in figure

2-6 (b) for n = and n = ± 1. As the time interval T becomes longer and longer,

the amplitude distributions become more and more compact in the frequency

dimension, and, as T approaches infinity, the total amplitude distribution

approaches a line spectrum. However, in the regions between the frequencies

where the amplitude distribution is bunched up in narrow clumps, V (f) is not

zero but only extremely small. Because of this limiting form, which is what

is observed in practice, many investigators have the erroneous impression that

the spectrum amplitude for a finite periodic signal is a line spectrum. More

importantly, through confusion with the Fourier series line spectrum, this can mislead one into thinking that these "lines" represent the amplitudes of

sinusoid voltages at specific frequencies. Such is not the case, as was shown

in section 2.3.

Note from figure 2-4 that V (f) is not constant with frequency. This is

true for any physical signal. Thus, spectrum amplitude, S(f), is not constant

with frequency, but varies in a manner that is determined by the signal waveform. Often an impulse generator will be specified by its spectrum amplitude

at very low frequency, and it is then tacitly assumed that this value is

applicable up to a frequency where S(f) is 3 dB below this value. It must be

emphasized, however, that no physical signal is truly "flat" over all frequencies since this, of course, would require that -it contain an infinite

amount of energy.

2. 5 Use of the Fourier Transform

The discussion thus far has focussed on three characteristics of the Fourier

transform, V(f), that are often not understood. This section will give some examples of how V(f) occurs in equations relating to electromagnetic measurements,

First, consider the inverse Fourier transform, eq. (2-2) , by which a physical signal can be described in the time domain when the frequency domain

quantity V(f) is known. For the signal given by eq. (2-5), which originated

from eq. (2-4) , the inverse Fourier transform yields the expression (see

13
hh|cm o

h|cm

U

rH

CnC

4-> U

(1) o6

ftO

iwwCM

+J

ft

0) •HMOo

fa c

•H

+J

0)

Q)

v

ft

>i • H C

o3 id 3 +> Cn

0) QJ M ffl -3 0)

0) o,

w

+Jc c

•h rd Cm XJ

0) ^ W

id iCQ — XI «j I 3

0u

0)>o

d)

5-1

tn H

fa

14
section 2.8)

00 v (t) = At /

si"^fT) cos[2Trf (t-T/2)]df. (2-20)

tr —oo

Note that, in general, the value of v(t) at any time t is an integral over frequency of a function of frequency. Thus, v

f

(t) is also an area which, in this

example, has the dimensional unit of volts.

Figure 2-7 shows a portion of a three-dimensional plot of the integrand,

z(f,t), of eq. (2-20), where

z(f,t) = At S±"^fT) cos[2Trf (t-T/2)]. (2-21)

This wavy surface has a "sine x over x" shape in the frequency direction at

time t = t/2 and a cosine shape in the time direction. The surface extends to

plus and minus infinity in both the time and frequency domains . The area under

the function z(f,t), at a specified time t, is the value of v (t) at that

time (see figure 2-8) . Because v(t) for every physical signal is a purely real function of time,

v(f) is Hermitian, and therefore its real part is alway an even function, its

imaginary part is always odd, and

V(f) = V*(-f)

(2-22)

Using this mathematical property, eq. (2-2) can be written

00 v(t) = 2 / |v(f)| cos[2wft + <Mf)]df, (2-23) o where $ (f ) is the phase of V(f). Equation (2-23) applies to all physical

signals. This form of mathematical representation has the engineering merit

that the integral is over the positive frequency domain only.

The spectrum amplitude

S(f) = 2|v(f)

(2-24)

thus appears explicitly in eq. (2-23) as the amplitude of a cosine function.

The quantity 2|v(f)| also appears in other working equations where a spectrum

amplitude is involved.

Three examples where S(f) is used are as follows:

1. If v(t) is applied to a two-port network which has an impulse response

h(t), the network response, r(t), is given by the equation

OO r(t) = / S(f) •

| H (f ) | • cos[2iTft + <Mf) + 6(f)]df (2-25)

o where |H(f) | and 8(f) are the magnitude and phase of the transfer function of

the network. It is this application for which the knowledge of spectrum amplitude

has its greatest practical use, namely, for the calibration of Field Intensity

Meters and Noise Meters.

15
p

M-lN

-Po

(0ao

•HwCe

•H

'di<u

<du

Xi

Enl

•H

Pm

16
N

az. LUQ

m

CD

-p

CD .Qa

-H

X!

COo

•H

+J

CD

CD X!

+J&c

•H

-P

rfl

S-) -PW . 3H >

00I CN

CDM

Cn H

Cm

Du

17
2. Another example is the measurement of the impulse bandwidth, IBW, of an idealized bandpass filter [2] using the equation

X _. T7 (max) IBW = STfJG (2-26) o

where R, .is the maximum value of the envelope of the network response r(t),

(IHdX J and G is the network maximum gain.

o

3

3. The total energy, E , delivered by v(t) to a resistance R is given by

the equations

OO 00 Et

= I

/ v

2 (t) dt = | / |V(f)| 2 df (2-27)

= i=- / S

2 (f)df 2R 2-2!

The part, E, , of E, , that lies in the frequency band from f, to f_ is given by

the equation

E

b

= 5r / s2 ( f ) df - (2-29)

f l The total energy, E , due to the output signal from a two-port network is given

by the equation

OO E

n

= JR $ S ' (f) '

l H(f) I' df * (2-30)

o Signal power can be derived from these energy equations.

2 . 6 Summary

In summary, we have emphasized the following points:

First, the frequency-domain representation of a physical signal is a complex mathematical quantity with both a magnitude and a phase.

Second, this complex quantity, the Fourier transform, has dimensional

units (e.g., volts per hertz) that are different from those of the time domain

representation (e.g., volts) of the physical signal. Thus it is a type of

density function that describes how the strength of the signal is distributed

with frequency.

Third, the Fourier transform of every physical signal is continuously

defined throughout the entire frequency domain. It is not a discrete or true

line function of frequency.

13
Fourth, twice the magnitude of the Fourier transform is defined as the

spectrum amplitude, and is a useful engineering quantity because it appears in

tnis form in many useful algebraic relationships. Like the Fourier transform,

it is a continuously defined function in the frequency domain, and not a discrete line spectrum nor a single-valued quantity independent of frequency.

It may not of itself be sufficient to adequately describe a physical signal in

tne frequency domain. One may also need to know the phase of V(f).

Finally, the dimensional units of spectrum amplitude are both voltseconds and volts per hertz, equivalently . However there may be practical

reasons for using one set of units rather than the other.

2.7 Derivation of V (f) r For the finite regularly repeating function shown in figure 2-6 (a), v (t)

is the convolution of the eternal periodic function, v (t) , and a gate function,

g(t),

v (t) r v

e

(t) g(t) (2-31)

wnere

v

e

(t) A, - J

< t < J

= 0,

= A,

T „ 1 T — < t < 2 f o

2 1 T T + 7T < f 2 2 o

1 T 1

< t

f 2 f o o

1 T < t < - - f 2 o

= 0, o o 2_ + I< t <_I _ 1

f 2 r

f 2 o o

(2-32)

and

etc . ,

g(t) = 1, - 2< t < |

= elsewhere

19

(2-33]
From tne time-convolution theorem,

v

e

(t) * g(t; V

e (f)G(f) (2-34)

where V (f) and G(f) are the Fourier transforms of v (t) and g(t), respecp e tively, and tne symbol (<--»-) reads "is the transform of" in both directions

The Fourier transform of v (t) is [6]

n=°° sin(imf x)

V (f) = Axf y 2

-— • 6(f-nf ) e o L Trnf t o n=-°o o wnere 6 is the unit impulse function. The Fourier transform of g(t) is

sin (irfT)

(2-35)

G(f) = T

TTfT (2-36)

which is similar to eq. (2-14) except that in this case the imaginary part is zero because of the choice of time origin. Therefore, the Fourier transform of v (t) is

r V

r

(f) = V

e (f)G(f)

, , m , n=°° sin(Trnf t) smUfT) y o_ . O TTfT TTnf O

n=-°° o

Axf T

o

n=°° sin(Trnf x) sin[-rr(f-nf )T]1

y o , o

1 ' Trnf x TT(f-nf )T n=-°° o o (2-37)

2.8 Derivation of v (t)

P

For the baseband pulse, figure 2-1, we use eqs. (2-2) and (2-14) to obtain

00 v (t) = / V (f)e j2 ^ ft df

oo = At , sin(TTfx)

e J(2wft-TTfx)

J df

TTfT —oo

oo sin (TTft) At / TTfT cos[2rrf (t-x/2) ]df

,

(2-38)

since

sin (TrfT) AT / »-";j; rT| sin[2TTf (t-x/2)] =

20
3 . SPECTRUM AMPLITUDE GENERATION

This chapter deals with the techniques commonly used to generate electrical

signals which have a broadband spectrum amplitude. The first section presents

a tabulation and figures of S(f) for various common waveforms. Section 3.2

describes mercury switch impulse generators while section 3.3 describes similar

generators which use avalanche transistors. Section 3.4 describes a new solid

state impulse generator developed at NBS which produces a useful spectrum to

6 GHz. Section 3.5 describes a useful technique for generating rf pulses.

Finally, section 3.5 describes a broadband microwave impulse generator.

3 . 1 Amplitude Spectrum of Common Waveforms

In EMC pulse measurements, a limited number of waveforms are commonly

encountered. They are the step, truncated ramp, impulse, rectangular pulse,

triangular pulse, sine squared pulse, and the rf pulse. These waveforms are important because they can be described mathematically and their spectra can

be readily calculated. Actual generators are capable of closely approximating

these idealized waveforms.

Table 3-1 lists these various waveforms, their mathematical equations in

the time domain, and the equations for their amplitude spectrum, S(f). Figures

3-1 through 3-6 show the waveforms and their respective S(f).

The unit step, figure 3-1, and the truncated ramp, figure 3-2, are power

signals and as such do not possess Fourier transforms as defined earlier.

They are not absolutely integrable as they do not satify the Dirchlet conditions

The spectral equations given in table 3-1 were obtained from the more general

unified Fourier transform by deleting the delta functions [7] . For example,

the unified Fourier transform of the unit step is

F[u(t)] =^77+ tt6(cj) (3-1)

|F[u(t)] | = i, us > 0. (3-2)

The spectrum of the ideal step, figure 3-1, is inversely proportional to

frequency. It is thus characterized by a constant slope of -20 dB/decade. The

truncated ramp's spectrum, figure 3-2, is identical to that of the ideal step

for low frequencies. However as the frequency increases and approaches 1/t , S(f) departs from the -20 dB/decade slope and assumes more the characteristic

of the triangular pulse, figure 3-4.

The rectangular pulse, figure 3-3, is seen to have a sin(x)/x variation

(see also Chapter 2) . A distinguishing feature of this pulse and most other

impulsive shaped pulses, such as the triangular pulse, figure 3-4, and the sine

squared pulse, figure 3-5, is the fact that the spectrum amplitude approaches

a constant value 2 v t at low frequencies. v t is simply the area under the

o o

^ o o v(t) curve and is defined as the "Impulse Strength" [2] . The shape of the

21
Table 3-1. Amplitude Spectrum of Common Waveforms

Waveform

Step

V(t)

V u(t)

S(f)

V /(ir£)

Truncated Ramp ^ [t u(t) - (t-t

Q )u(t-to

)] o

o o /I TT

[1 - cos(2TrftJ] 1/2

(t f) 2

Rectangular Pulse V

Q [u(t) - u(t-t )] 2V

^o o

sinfrrft ) o

firft )

Triangular Pulse ^ [t u(t) - 2(t-t

o )u(t-tQ

) o

+ (t-2t

o )u(t-2tQ

)]

2 V^o no

sinfirft v ) o

I (Hft )

Sine Squared Pulse in'(ii-)uCt)

11 O^

.in»[j|-)»(t.t )

2V

^o o

sin(2Trft ) (2Kft

o )[l-(2fto

) 2

]

RF Pulse V [sin(2Trf

c t)u(t + t o /2)

sin(2irf

c t)u(t-to /2)]

Vo

sin(TtAft ) sin[iT(2f +Af)t ] v O CO

(irAft ) [ir(2fc+Af)t ]

where Af = f - f

22
v(t)

Figure 3-1. Step,

s(f)/S(£

o

)

dB

-*- t

-40-

0.1

> f/f

100

v(t)

A

S(f)/(V t //T If)

dB.

->» t *o ° Figure 3-2. Truncated ramp.

SC£)/2v t

dB

-20-

*.t -40

Figure 3-3. Rectangular pulse.

(\f\., ,,t .

i >£-t

23
S(£)/Zv v J t #

dB

>t *- f«t

Figure 3-4. Triangular pulse.

S(f)/2v

o

t o

dB

o o Figure 3-5. Sine squared pulse

k

dB

*-t

20

-40

A A

Figure 3-6. Rectangular rf pulse.

-v f/f

24
spectrum for the triangular pulse, figure 3-4, is identical to that of the rec- tangular pulse except that S(f) of the triangular pulse drops faster with

frequency. Note that the vertical scale is 20 dB/div. instead of 10 dB/div.

The sine squared pulse, figure 3-5, has its first spectrum zero at 1/t like

earlier pulses. Its higher order zeros occur twice as often.

A special case of the rectangular pulse is the true impulse or as it is

called in mathematics, the Dirac delta function, 6 (t) . It is defined as

6(t) = lim u(t) - u(t-a)

a+0 a

OO / 5(t) = 1 (3-4)

—OO

This is seen to be a rectangular pulse of width a and height 1/a with a constant

unit area. Its spectrum is like that of the rectangular pulse except that its

first sin(x)/x zero occurs at infinity. In other words its spectrum amplitude

is constant for all frequencies.

In practice a narrow rectangular pulse is often referred to as an impulse.

This is done with the implicit understanding that its spectrum amplitude is

essentially constant for all frequencies of interest.

The spectrum of the rectangular rf pulse, figure 3-6, is seen to be simply

that of the rectangular pulse transposed in frequency by the carrier frequency, f . However, the sidebands are not symmetrical. The dissymmetry is

caused by the second term involving (2f + Af ) . This second term accounts for

the aliasing caused by the transposition of the rectangular pulse spectrum to

both +f and -f . When the rf pulse contains an integer number of cycles,

i.e., t = N/f , then the number of zeros of S(f) between zero and f are equal to N. For frequencies near f (i.e., Af - 0) , S(f) is essentially

constant and approximately equal to v t .

3. 2 Mercury Switch Impulse Generator

Most of the impulse generators used in the field for broadband calibration

of field intensity meters (FIM) are of the mercury switch variety. They are attractive for several reasons including (1) low cost, (2) reasonably predictable output, and (3) easily adjustable output.

A mercury switch impulse generator is an extremely simple circuit, figure

3-7 [8]. It consists of a dc voltage source, V,,, a charging resistor, R , a short coaxial transmission line of impedance R and length I, and a mercury

wetted mechanical switch. Initially with the switch open, the transmission

line appears as a capacitor and is charged up to the supply voltage, V, , ,_ through the charging resistor, R . When the switch is closed the transmission

line discharges into the load R^. During discharge the line appears as a source of voltage V, , and internal resistance R . If the load is matched to DO O

25
the line,

*L

= R

o

(3-5)

Then the output voltage, V , is simply

o bb

(3-6)

and the output pulse duration, t , is fixed at twice the electrical transit

time of the line.

t = 21 /v , o ' p

(3-7)

v is the velocity of light in the line (v ^ 3 * 10 8 m/s in air) . Thus a P P

30 cm length of air line will produce a 2 ns pulse.

This generator thus produces a rectangular pulse of amplitude, V , duration, t , impulse strength, V t , and at low frequency, its spectrum amplitude

is

S(f) = 2V

o

t Q

, f << F

(3-8)

If the supply voltage is adjustable then S(f) may also be varied.

R >> R

c o rj^V^I

V

bb'

T.

v

1 (t)

V

->-t 1/t 2/t 3/t ' o o o ^f

Figure 3-7. Mercury switch impulse generator.

26
For proper functioning the load resistance must equal the line impedance.

To insure that this condition is met some manufacturers permanently install a coaxial attenuator between the switch and the output connector.

Typical pulse transition times (rise and fall times) are of the order of

0.5 ns. However, with microminiature mercury switches, transition times of

40 ps have been achieved [9] . Pulse amplitudes as large as 2 kV are possible

with pressurized mercury wetted switches. Even higher voltages are possible

if the mercury switch is replaced with a spark gap. Some spark gaps are triggered externally with a laser pulse.

Equation (3-7) is quite accurate for HF IG's with 10 ns or longer pulses.

Its accuracy suffers for t < 1 ns, because the waveform is no longer rectangular.

The transition (rise and fall) times are comparable to the duration. It also

becomes difficult to model or measure accurately the actual time delay of the

charge line and the switch.

The major disadvantage of the mercury switch is its mechanical nature which

inherently limits its switching repetition rate to a few hundred hertz at

most. Also due to its mechanical inertia, friction, etc., it is not possible

to trigger the switch closure with better than a few hundred microseconds

precision. This triggering uncertainty leads to much phase jitter.

3. 3 Avalanche Transistor Impulse Generator

The trigger uncertainty and the low repetition rate disadvantage of the

mercury switch can be eliminated by replacing the mercury switch in an impulse

generator, figure 3-7, with an avalanche transistor. Trigger jitter of less

than 10 ps and repetition rates of several MHz are possible. This section

briefly describes an inexpensive, simple impulse generator developed at NBS

several years ago [10] . The major disadvantage is its lower voltages compared

to mercury switches (50-100 volts are typical)

.

Avalanche multiplication in reverse-biased pn junctions is a result of

impact ionization produced by mobile charge carriers. If the electric field

in the depletion region of the pn junction is large enough, an electron moving

through the crystal lattice gains sufficient energy to release an additional

electron and hole when it collides with an atom in the lattice. The two free

electrons may then cause additional ionizations and an ever-growing cascade,

or an avalanche of ionization occurs.

In transistors the avalanche breakdown [11] may be controlled through the

injection of carriers by the base current, figure 3-8. Normal transistor

operation lies in the region of collector-emitter voltages between and BV„„_ CEO

and forward base currents. BVCE0 is tne breakdown voltage from the collector

to the emitter with the base open circuited. If a reverse base current is

applied, then the collector-emitter voltage may be increased above BV.,.^ before CEO

an avalanche breakdown is reached. The upper voltage limit BV^Dr, is reached CBO

when I b

= lc

. BVCB0 is the breakdown voltage from the collector to the base with

27
the emitter open circuited. The avalanche region of the transistor lies between BV_ and BV"C

. An important item to notice in figure 3-8 is the negative slope of the constant I, curves in the avalanche region. The negative

slope means that the small-signal resistance, r = AV/Ai, is negative. A negative resistance implies unstable operation. Thus the avalanche transistor is

useful as an oscillator or switching element. The switching speeds that can be

obtained are quite fast because of the multiplying effect of the avalanche

breakdown. Transition times of 500 picoseconds have been obtained.

• TRIGGER

bvceo

D,CER e

Figure 3-i Transistor V-l

characteristic

curves including

the avalanche

region.

Figure 3-9, Typical avalanchetransistor switching

circuit.

A typical avalanche transistor switching circuit is shown in figure 3-9.

The large supply voltage, V , and dc load resistor, R, , of figure 3-9 place

the transistor at the stable operating point A, figure 3-8. The positive trigger

pulse injects an additional quantity of base current causing the collector cur- rent to move along the ac load line, R , to operating point B. Point B is in

the negative resistance region and is an unstable point. Thus the operating

point rapidly switches along the ac load line to the next stable location,

point C.

Many transistors are capable of avalanche operation although very few are actually specified as avalanche transistors. If the specification sheet for a given transistor says the BVPDn is greater than BV^„^, it is probable that

the transistor will avalanche, although the switching characteristic may not be

fast. Very few pnp transistors have been found that will avalanche.

An impulse generator that will produce a usable frequency spectrum to

beyond 1 GHz is shown in figure 3-10. The circuit is an avalanche transistor

adaption of the classical mercury switch -- charged transmission-line pulse

generator [12]. Charge line, DL1, is charged through R4 to BVC of Ql . When

a positive trigger pulse is coupled through CI and Rl into the base of Ql,

28
avalanche breakdown is initiated. Ql rapidly switches to its lower breakdown

voltage BV _ and allows the charge line, Dll, to discharge into R3 and the

external 50-ohm load. A square pulse is generated with transition times of

the order of 500 picoseconds. The pulse duration is fixed at twice the electrical transit time of the charge line, DLL An impulse can be formed byshortening the charge line until the desired impulse width is obtained. As soon

as the charge line is discharged Ql reverts to a low current state. The output delay line, DL2 , is included so that reflections from the external load do

not arrive back at £1 until it has switched off. R3 is included to provide a 50-ohm reverse termination for reflections. This impulse generator is designed

to be driven directly by TTL pulses. Ul is included to demonstrate this fact.

It can be driven at repetition rates up to 1.5 MHz.

100 kft 1.5 nF

R4 C2

_n_n_ input

Figure 3-10. Avalanche transistor impulse generator,

Figure 3-11 shows the impulse output measured with a 50-ohm sampling

oscilloscope with a 10- to 90-percent transition time of approximately 28 picoseconds. The impulse has a peak amplitude of 14 volts and an impulse duration

of 420 picoseconds. Figure 3-12 shows the impulse spectrum as measured on a spectrum analyzer over the frequency range of 500 kHz to 1250 MHz. The spectrum

is approximately 10 dB down at 1250 MHz. Usable 10-kHz markers were measured

up to 1250 MHz. The amplitude of the 10-kHz markers was approximately 80 microvolts at 150 MHz, 64 microvolts at 450 MHz, and 30 microvolts at 1250 MHz.

29
I i r I

i

i

: .'__!

|

Figure 3-11. Avalanche transistor impulse generator output.

Figure 3-12. Avalanche transistor impulse generator spectrum.

3 . 4 NBS Step Recovery Diode Impulse Generator

Extremely fast transition times of the order of 100 ps can be obtained

using step recovery diodes (SRD) to shape the output pulses from avalanche

transistors. Voltage amplitudes of 10-30 volts are possible. Impulses with

durations of 100 ps produce a useful spectrum well into the microwave region.

This section describes a baseband impulse generator recently developed

at NBS [13]. The generator is completely solid-state. It uses avalanche

transistors and step recovery diodes to generate a 100 ps duration impulse of

8 volts amplitude into 50 ohms. The spectrum amplitude of the impulse is

greater than 6 dByV/MHz at frequencies up to 5 GHz. The generator source impedance is a well matched 50 ohms. The repetition rate of the generator is

controlled by a quartz crystal oscillator and is adjustable in a 1,2,5 sequence

from 50 Hz to 100 kHz.

30
Ext. 10 MHz

Xtal Clock

Power Supplies

High-Pass

?X Filter

Figure 3-13. Block diagram of the NBS SRD impulse generator.

Figure 3-13 is the basic block diagram of the NBS impulse generator,

series 3-75-X. The internal repetition rate is derived from a 10 MHz crystal

controlled oscillator. The 10 MHz frequency is divided into lower frequencies

from 100 kHz down to 50 Hz using TTL, t 2, t 5, and t 10 dividers. The internal

or external repetition rate source is used to trigger the driving pulse

generator. This generator develops a 50 volt, 0.7 ns transition time pulse in

a 25 ohm circuit using avalanche transistors and a step recovery diode. This

pulse is driven through a diode gate onto two 50 ohm circuits in parallel. The

first is a 30 dB attenuator the output of which is used as the trigger output.

The second is an 80 ns coaxial delay line. At the output of the delay line is an extremely fast step recovery diode (SRD) which sharpens the leading edge of

the driving pulse to a transition time less than 100 ps. Bias current for the

SRD is supplied at the input to the delay line. This sharpened pulse is then

differentiated in an R-C high pass filter and by passing it through a 4-8 GHz,

3 dB directional coupler, thus producing the desired output impulse. The

purpose of the directional coupler is twofold. In addition to providing the

necessary differentiation of the fast step from the SRD it also provides an excellent 50 ohm generator source impedance.

31
The primary purpose of the impulse generator is as a source of broadband

impulse noise with as flat a spectrum as possible. To achieve the flat spectrum objective the output should be a pure impulse with no other spurious

pulses present. Low-level, wide-spaced pulses will distort the spectrum

particularly at low frequencies. To achieve this objective calls for design

compromises that would not be made if the objective were simply to generate the

highest amplitude, narrowest impulse possible.

To insure that only a single impulse is obtained, the driving pulse is

shaped to be an exponential pulse with a fast leading edge transition time of

0.7 ns and an exponential decay time constant of 15 ns. After sharpening by

the SRD, the differentiating action of the high pass filter and the directional

coupler produce an impulse only on the fast rising leading edge of the driving

pulse. A portion of the driving pulse incident upon the SRD is reflected back

toward the driving pulse generator. If a portion of this reflected signal were allowed to eventually escape from the instrument through the impulse output port it would have the effect of distorting the impulse generator's spectrum

particularly at low frequencies. The 30 dB trigger output attenuator is used

to internally absorb this reflected signal. This reflection from the SRD is

delayed in time by the delay line so that it arrives at the diode gate 160 ns after the driving pulse passed through the gate traveling in the opposite direction. The decay time of the driving pulse and the reverse bias on the gate are chosen so that the gate is nonconducting when the reflection arrives thus

forcing the reflection to be absorbed in the 50 ohm, 30 dB attenuator.

The 80 ns delay line also serves an auxiliary purpose in providing an extremely stable time delay between the trigger and impulse outputs for

sampling oscilloscope measurements of the impulse output.

Complete circuit description and schematic diagrams are found in appendix A,

Figure 3-14 is a typical waveform into a 50 ohm load from this generator.

The impulse consists of a small precursor pulse, the main impulse, a negative

undershoot and finally some low level damped perturbations on the baseline that

last approximately 2 ns after the main impulse. There are no other signals

emanating from the generator earlier or later in time than those shown with

the exception of two low level impulses -36 dB and -46 dB below the main

impulse occurring 80 ns and 160 ns respectively after the main impulse. The

impulse amplitude is 8 volts and its 50% level duration is 100 ps.

32
WW

r

1 I—

M

\4-[-----~:

/- a

Figure 3-14, Typical output waveform

of an NBS SRD impulse

generator. Vertical:

50 mV/div. X 30 dB,

Horizontal: 200 ps/div.

S(f) in dByuV/MHz

70 - .—•. .. 60 H

50

40

30

Figure 3-15,

Frequency in GHz

Typical spectrum amplitude

of an NBS SRD impulse

generator.

10

The spectrum amplitude, S(f), of the impulse is shown in figure 3-15.

S(f) is seen to be relatively flat at approximately 62 dByV/MHz out to 5 GHz

with a +3 dB, -2 dB ripple. The peak in the ripple occurs at 0.75 GHz while

the minimum occurs at 1.6 GHz. Beyond 6 GHz S(f) drops very rapidly at approximately 30 dB per octave. Due to the ac coupling inherent in the directional

coupler, the spectrum amplitude is not flat to dc . It rolls off at frequencies

below 2 MHz.

3 . 5 RF Pulse Generator

Potentially the most accurate method of generating a known spectrum amplitude at a particular frequency is the rf pulse technique [14] . The technique

is quite simple. A cw signal generator provides a stable sine wave of known

frequency and constant level. An rf switch is driven by a baseband pulse

generator and is used to gate on and off the cw sine wave thus producing an rf

pulse. This is the classical case of amplitude modulation. The spectrum of

the modulation waveform is translated from a distribution about zero frequency

to a distribution about the carrier frequency, f . As seen earlier, a rec- tangular pulse produces a sin(x)/x spectrum. Thus a rectangular pulse modulated rf burst produces a sin(x)/x spectrum centered at f . This technique has

an advantage over baseband impulses in that it can concentrate most of the

energy in the signal uniformly in the frequency region where a receiver to be

calibrated is tuned.

33
As shown in table 3-1 the exact expression for S(f) contains two terms

s < f > v t

sin(TiAft )

(TTAft )

sin[TT (2f +Af ) t ] c o

[7T(2f +Af)t ] c o

(3-9)

where

Af = f - f (3-10)

The first sine (sin(x)/x) term contributes most of the expressions value near

the carrier, f , while the second sine function, which is sometimes called the

phase correction, will become significant at frequencies far removed from the

carrier. The second sine term becomes important if the rf pulse is short,

i.e., if it only contains a small number of rf cycles. The example of figure

3-6 was for an extremely short pulse of only four cycles. For that case the

sidebands were quite unsymmetrical. Reeve [14] has made calculations of the

importance of the phase correction. For long rf pulses of fifteen or more

rf cycles the spectrum amplitude may be approximated as

S(f) V t o o

sin(TrAft ) o

(TTAft

(3-11)

In the immediate vicinity of f

S (f ) = S = V t , Af %

o o o (3-12:

As can be seen from eqs. (3-11) and (3-12), S(f) can be completely characterized by knowing the amplitude, V , and the duration, t . These values can

be obtained by direct measurement. The amplitude can be obtained by measuring

the output power, P, with the rf switch in the ON state.

V = /2PR. (3-13; o

R is the input impedance (typically 50 ohms) of the power meter. The duration,

t , can be measured by using a calibrated oscilloscope. An alternate technique

is to use a spectrum analyzer or receiver to determine the frequency, f ,,, at which the first null occurs in the rf pulse spectrum. From eq. (3-11) t is

given by

t = o null c

(3-14)

The most critical component in the rf pulse generator is the rf switch.

Of utmost importance is its on-off ratio. If the leakage in the off state is

too large, then the continuous presence of the carrier will give undesirable

results. For carrier suppression of 20 dB below S the rf switch on-off

isolation must be

isolation (dB) > -20 log(t 3 f ) + 20 dB

o o

(3-15!

34
where t is the pulse duration and f is the pulse repetition rate. As an example using typical numbers of 100 ns pulse duration and 100 Hz pulse

repetition rate, a switch isolation in excess of 120 dB is required.

Another important parameter of the rf switch is its switching speed.

Ideally, it would have zero switching times. In practice the switching times

are limited, and they thus introduce some uncertainty in the pulse duration, t . PIN diodes provide excellent rf switches. They are capable of quite high

isolation (90 dB) with switching times of the order of 5-50 ns . Another excellent rf switch is a Schottky diode balanced modulator. Switching times of the

order of 1 ns are possible. Below 1 GHz balanced modulators are available with

excellent isolation (60 dB) . Quite fast balanced modulators are also available

in the microwave region, but they typically have poor isolation of 20-30 dB.

P. Simpson of NBS has recently built a microwave pulse generator for

calibrating microwave receivers [15] . A PIN diode modulator was used as the rf

switch. This generator has the characteristics listed in table 3-2.

Table 3-2. NBS microwave pulse generator characteristics.

Frequency Bands:

Max. cw Output Power into 50 Ohms:

Pulse Duration:

On and Off Transition Times:

Max. Spectrum Amplitude into 50 Ohms

Output Step Attenuator:

Pulse Repetition Rate:

1-2 GHz

2-4 GHz

4-8 GHz

8-12.4 GHz

tunable

1 mW, except . 1 mW for

8-12.4 GHz

^ 20 ns 2-5 ns

^ 7 6 dByV/MHz

except ^66 dByV/MHz

for 8-12.4 GHz

to 99 dB in steps of

1 dB

10 Hz to 10 kHz

In addition to the microwave pulse generator [15] , NBS has also built an

rf pulse generator to cover the frequency range of 5 MHz to 500 MHz. Figure

3-16 is the block diagram of this generator, and table 3-3 lists the characteristics of this generator. An external signal generator is used to provide

the cw sine wave. A low level signal of only -27 dBm is required. Broadband

amplifiers Al and A2 amplify the cw sine wave to +3 dBm to drive the double

balanced mixers, DBM 1 and 2. Al and A2 also provide isolation between the

signal generator and the mixers. The mixers function as an rf switch. They

are driven by simultaneous baseband pulses to turn on the sine wave. The

baselines of the pulse generator outputs are independently adjusted to

35
15 dB 15 dB dBm -1 dBm -2 9. dB 0-81 dB

RF Pulse

Output

Figure 3-16. NBS rf pulse generator block diagram.

Table 3-3. NBS RF pulse generator characteristics.

Frequency Range:

Max CW Output Power into

50 Ohms for linear Operation:

On-Off Isolation:

Pulse Duration:

On and Off Transition Times:

Output Step Attenuator:

Pulse Repetition Rate:

5-500 MHz

determined by ext. signal gen,

+ 5 dBm

115 dB @ 100 MHz

set by baseband pulse gen.

^ 1 ns

to 81 dB in steps of 0.1 dB

set by baseband pulse gen.

36
optimize the on-off isolation of the mixers. By careful adjustment, isolations

in excess of 115 dB have been achieved. The output of the second mixer is

-5 dBm in the on state. Amplifier A3 is used to raise this level to +6 dBm.

A3 also provides a well matched constant output impedance regardless of the

state of the mixers. A set of 50 ohm step attenuators are provided on the

output to allow precise setting of the output level. Figure 3-17 is the time

domain waveform of a 100 ns, 100 MHz, rf pulse. Figure 3-18 is the spectrum as observed on a spectrum analyzer.

Figure 3-17. RF pulse generator

output waveform.

100 ns, 100 MHz

rf pulse.

Peak power is

+4 dBm.

Figure 3-li Spectrum of dBm,

100 ns, 100 MHz rf

pulse. Horizontal

scan from to

200 MHz.

3 . 6 Microwave Impulse Generator

The NBS microwave pulse generator built by P. Simpson [15] is an excellent

source of relatively narrowband (< 10 MHz), known, impulsive noise. However,

there are some microwave applications such as time domain antenna testing that

require a very broadband (several GHz), high power, impulsive noise source. In

these cases none of the previously described generators are adequate.

NBS has found that a useful technique of generating broadband, high power

impulsive noise is to shock excite a high power traveling wave tube amplifier

(TWTA) . The TWTA is driven by an extremely narrow (< 100 ps) baseband impulse,

such as the output of the NBS SRD impulse generator (section 3.4). The TWTA

acts as both a wide bandpass filter (typically octave bandwidths , i.e., 1-2 GHz,

2-4 GHz, etc.) and a high gain amplifier. The output is a short rf pulse of a few rf cycles with a frequency near the low end of the TWTA pass band. Peak

power comparable to the output power rating of the TWTA can be obtained. A

broadband, adjustable, coaxial attenuator is required between the impulse

generator and the TWTA to avoid driving the TWTA into saturation.

37
With the extremely short pulse duration of this type of generator, it is

not possible to use the calibration technique employed for the rf pulse generators of section 3.5 to determine the spectrum amplitude. For this generator

the time domain technique described later in section 4.9 is recommended.

Figures 3-19 and 3-20 show waveforms and spectra obtained from several

pulsed TWTA's covering C, X and Ku bands, i.e., 4-8 GHz, 8-12.4 GHz, and 12.4-

18 GHz. The TWTA's were driven by the NBS SRD impulse generator, figure 3-19 (a) , The variable attenuator was adjusted to drive the TWTA just below the saturation level. Saturation was evidenced by an abrupt change in the output waveform. The spectrum amplitudes of the TWTA's outputs were measured by the APMS

(see section 4.9). As can be seen in figure 3-20, broadband spectrum amplitudes

of the order of 80 dByV/MHz can be obtained. The C band TWTA output is useful

(20 dB range) from 2 GHz to 13 GHz. The X band TWTA useful range extends from

4 GHz to 15.5 GHz with the exception of a sharp notch at 9.4 GHz. The Ku band

TWTA appears to be useful from approximately 10 GHz to 16 GHz.

38
(a)

(d)

Figure 3-19. Impulse response of TWTAs . Vertical: 10 V/div. except

(a") which is 3.2 V/div. Horizontal: 200 ps div. (a) NBS

SRD impulse generator (SN 3-75-3) used as input to TWTA.

(b) C band, 3 dB, 10 W TWTA. Input impulse attenuated

15 dB. (c) X band, 30 dB, 20 W TWTA. Input impulse

attenuated 16 dB. (d) Ku band, 30 dB, 2 W TWTA.

39
90 -

80

70- >

3- 60.

a

•H

iww 50-

40-

30

impulse

10

-T"

14

-T12 16 l£~~ ~?c

f in GHz

90-

80-

N£

70 >

60

eH

^.

IH

co 50

40,

30' "i—i—

r

16 IE i—

r

20

i—i—i—

r

«—

r

10

i—

r

12

i—

r

14

f in GHz

Figure 3-20. Spectrum amplitudes of TWTA impulse responses.

40
4 . SPECTRUM AMPLITUDE MEASUREMENT TECHNIQUES

This chapter discusses the various techniques that have been used to

calibrate impulse generators and to measure spectrum amplitude. The techniques

included are (1) standard transmission line method, (2) harmonic measurement,

(3) energy method, (4) sum and difference correlation radiometer, (5)Dicke type

radiometer, (5) video pulse, Mil Std. 462, (7) spectrum analyzer, (8) standard

pulse comparison, and (9) time domain measurement with Fourier transformation

computation. Advantages and disadvantages of each technique are discussed.

4 . 1 Standard Transmission Line Method

This method is only applicable to the calibration of mercury switch impulse

generators, such as discussed in section 3.2. As shown there the spectrum

amplitude is given by eq. (3-8)

S(f) - 2V t , f

• 2V t , (4-1) o o f«|-

o into eq

.

(3-8) gives

V,,£/v , bb pf«2-

O

Substituting eqs. (3-6) and (3-7) into eq

S(f) = V ,£/v i f (4-2]

' y o where V,, is the dc supply voltage, I is the transmission line physical length,

and v is the propagation velocity of light in the transmission line.

V, , can be measured quite accurately. More uncertainty exists in the

measurement of v and I because the actual generator structure includes not

P

just a piece of uniform transmission line, but also the left half portion of

the switch, figure 3-7. Rather than determining t from I and v it can also

be found from R and the total line capacitance, C , . o

^ t

t

Q

= 2R

Q

C

t (4-3)

R can be determined either from the geometrical dimensions of the charge line

O

3 = or from time domain ref lectometry (TDR) measurements. C can be measured on a capacitance bridge. It is also possible to determine t directly from TDR mea- surements .

4 . 2 Harmonic Measurement

If one has an extremely narrow bandwidth receiver, an impulse generator

can be calibrated by measuring a single spectral line in the impulse generator's

spectrum, figure 4-1, and comparing it against a known CW voltage standard. The

spectrum amplitude is then given by

f :(f,k) = -^ , (4-4) o where

kf

Q

(4-5)

41
and f is the pulse repetition rate of the impulse generator. V, is the voltage

+ v» amplitude L of the k harmonic of f . f can be measured very accurately with a o o

2 J digital frequency counter. V, can also be measured accurately if the pulse

repetition rate is much greater than the receiver bandwidth, BW.

f >> BW

o

(4-6)

If this condition is not met then the bandpass characteristics of the receiver

must be well known. Palladino [16] has given a good discussion of this mea- surement technique along with an error analysis.

^1-

-A^Y-

> f

Figure 4-1. Harmonic measurement.

4 . 3 Energy Method

R. B. Andrews [17] has developed a spectrum amplitude measurement technique

based upon the measurement of spectrum intensity. Spectrum intensity is defined [2] as the ratio of the power contained in a given frequency range to the

frequency range as the frequency range approaches zero. This technique re- quires a power meter and a bandpass filter centered at the frequency of interest

between the impulse generator and the power meter, figure 4-2.

Radio

Receiver

Impulse

Gen. Bandpass

Filter

IFUt Amp

Power

Meter

Figure 4-2. Energy method,

42
The energy relations derived in chapter 2 are used here. The total energy

delivered to a load resistor, R , was given by eqs. (2-27) and (2-28). The

average power delivered to the resistor by a series of impulses, v(t), periodically applied at the repetition rate f and period T = 1/f is given by

1 T

P = -=- ! v

2 (t)dt (4-7)

TR o and also

f P = — / S

2 (f)df (4-8)

2RT o

Li

If the impulse is applied to a bandpass filter with a voltage transfer function

H (f ) , the avera

from eq. (2-30)

H(f), the average power delivered to a resistor R at the output is obtained

f P = — / S

2 (f) |H(f)

|

2 df (4-9)

2R

L

o

If the spectrum amplitude is flat over the bandwidth of the filter then

f S

2 (f) P - — / |H(f)| 2 df (4-10)

2R

L

o

The power bandwidth, PBW, of the filter is given by

i °° PBW = ±

/ |H(f) | 2 df (4 " l;L > H

2 (f .) o

o cf

where H (f ,.) is the maximum gain of the network which occurs at the center

o cf ' frequency, f

f

. From eqs. (4-10) and (4-11) the spectrum amplitude is obtained.

'1/2

s(fcf ) = 2RT P

f PBW H

2 (f _) o o cf

(4-12)

This technique has the advantage that it uses ordinary metrology lab

equipment to measure frequency and power. The bandpass filter commonly used is

a radio receiver. The major disadvantages are: (1) the necessity of measuring

Af and H at each frequency of interest which can be a laborious procedure,

(2) the power meter must be able to respond accurately to waveforms having a high peak to average ratio and the low repetition rate of the impulse generator,

and also (3) the background noise from the receiver between pulses may drastically corrupt the measurement of the pulse power. Receiver gating can be

used to reduce the effect of this last item.

43
4 . 4 Sum and Difference Correlation Radiometer

In the late 1960's, NBS developed a sum and difference correlation radiometer (SDCR) to calibrate impulse generators [18,19,14]. The SDCR is similar to

the previously described energy method in that S(f) is obtained by measuring the

spectrum intensity (watts/hertz) . The unknown impulse is compared against a known thermal white noise source. The SDCR basically measures the available power spectrum intensity, P (f )

,

a of a Thevenin equivalent generator of internal source generator voltage, V (t)

,

and internal source resistance R . The maximum available power is obtained

from this generator when the external load resistance R

? matches the internal source resistance.

RT = R (4-13)

L S For this case the output voltage, v , across the load is

a R v (t) v (t) = 2 v (t) = — . (4-14)

a R + RT S

2 s L

The available average power, P , of an impulse generator of pulse repetition

rate f and period T = 1/f is (see eqs. (2-27) and (2-28))

o o

1 T

P = -i- / v (t) 2 dt (4-15)

a TR oa

s Using the Fourier integral theorem P is also given by

a

f 2 oo p = _P_ / V (f) 2 df (4-16)

R o

s

or

f P = _°_ f s

2 (f)df (4-17)

2R o

where

S (f) = 2|V (f)

|

(4-18)

3. a

is the available spectrum amplitude. Equation (4-17) can also be written in

terms of the available power spectrum intensity, P (f ) . a

CO P = / P (f)df (4-19]

a

; a o

f

Z S

2 (f

)

P ( f , = -°_5

(4 _ 20)

2R

s

44
Input*-

fUS UUP » UCTWnDK UHANNCl. n mmunn

HYBRID

JUNCTION

'180"

PRECISION

ATTENUATOR

-4- STABLE CW

GENERATOR

ANALOG

MULTIPLIER

CHANNEL B NETWORK K fr

AVERAGING NETWORK

OUTPUT

INDICATOR

Figure 4-3. Sum and difference correlation radiometer,

The spectrum amplitude, S (f )

, can be obtained from eq. (4-20)

s (f)

cl

2R P (f)

s a 1/2

(4-21)

To determine S (f) from eq. (4-21) the source resistance, R , is measured

a s with an impedance bridge or other suitable means, the pulse repetition rate,

f , is measured with a frequency counter, and the available power spectrum

intensity, P (f) is measured with the sum and difference correlation radiometer

a (SDCR) . Figure 4-3 is the block diagram of an SDCR [20,21], The impulsive signal

is applied to the SDCR input through a narrow bandpass filter to reduce the

peak amplitude of the pulses, and to increase the duration of each pulse. This

allows the SDCR to operate within its linear range.

The SDCR is designed so that a null voltage output is obtained from the

system when the power from an external signal generator, connected to the input

port of the SDCR, is balanced against the power from internal sources within

the SDCR. The internal sources of the SDCR consist of a) a stable cw generator

and b) the unavoidable internal noise sources of the networks within the system.

The power level of the cw generator is adjusted by a calibrated precision

attenuator that is a part of the SDCR.

When the impulse generator under test is connected to the input port of

the SDCR, the precision attenuator is adjusted to obtain zero output voltage

from the system (null condition) . The attenuator dial reading is recorded for

45
this condition. Then the impulse generator is disconnected, and a thermal

noise generator of known noise temperature, T , is connected to the input port

of the SDCR. The precision attenuator is readjusted to obtain a null condition,

and its reading is recorded.

Arthur has shown in a lengthy derivation in reference [19] , that the

impulse generator available power spectrum intensity, P (f ) , is given by

10 AA

TO AA

P a

(f) = kT

n

10 1U- kT

e

(l - 10 iU

) (4-22)

-23 where k is Boltzmann's constant (1.38 x 10 watt-second per degree kelvin)

,

T

n is the noise temperature of the calibrated noise generator, and AA is the

difference, in dB, between the precision attenuator settings that produce the

two null conditions stated above. T is the effective input noise temperature

of the SDCR. The procedure for measuring T has been described by Arthur,

et al. [21]

.

The SDCR technique measures the composite spectrum intensity of the

impulse generator under test which includes both impulsive noise and Johnson

thermal noise. To separate the two noise contributions, it is necessary to measure the Johnson noise alone with the impulse generator's impulse output

turned off, but with the generator still connected to the SDCR.

Two SDCR radiometers for impulse signals have been built [14]. Their

operating frequencies are 30 MHz and 1 GHz, and the impulse bandwidth is 30 kHz

for each system. The measurement uncertainties of these instruments appear to

be no greater than approximately 1 dB. The measurement uncertainty depends upon

the spectrum amplitude level and the pulse repetition rate. Figure 4-4 shows

the ranges of these two quantities within which the 30 MHz system can be used

with stated accuracy. For levels less than the values along the bottom edge of

the "band of operation," the system performance becomes poor because of the

small signal-to-noise ratio of impulse power to system noise power. For levels

greater than the values along the top edge of the "band of operation," the

system performance becomes poor because of non-linear amplification in the

system. However, levels greater that those bounded by the "band of operation"

can be measured by attenuating the impulsive signal before applying it to the

SDCR system. The 1 GHz system has a similar "band of operation," except that

the lower edge of the band is raised approximately 10 dB because of the larger

internal noise level.

The SDCR radiometer technique has the potential of great accuracy. In

addition it does not require a precise measurement of the SDCR impulse bandwidth and bandpass characteristics as this parameter doesn't appear directly in

the relevant equations (4-21 and 4-22). There are however several major disadvantages. First it provides data at a single fixed frequency. Second, the

SDCR is a quite sophisticated and expensive instrument. Its primary usefulness

is as an independent measurement technique in a national standards laboratory.

Third, eq. (4-21) requires that the impulse generator source impedance be

46
Pulse Repetition Rate, pps

Figure 4-4. Useful range of operation of 30 MHz SDCR.

measured. This is not always an easy task as the source impedance of some generators is a time varying quantity. The simple mercury switch impulse

generator (see section 3.2 and figure 3-7) is the worst case. During the

initial pulse generation time (0 < t < t ) the generator can be represented as

a Thevenin source voltage V, , and source resistance R . However, after the ^ bb o transmission line is discharged (t > t when R = R ) the generator's equivalent circuit is a source voltage V, , and source resistance R which is much ^ bb c larger than Z . Even later in time when the switch opens, the generator's

equivalent circuit is simply an open circuit. Some manufacturers attempt to

reduce this problem by installing a coaxial attenuator (typically 6 dB) between

the switch and the output connector.

4 . 5 Dicke Radiometer

In 1974, Oranc [22] proposed using a Dicke radiometer [23] to calibrate

impulse generators. The Dicke radiometer measures the noise temperature of

an input broadband signal. It is a linear radio receiver in which the input

is switched alternately between the unknown signal source and a known thermal

noise source. A synchronous detector locked to the input switching frequency

is used to detect the difference between the two input noise temperatures.

47
For this radiometer measurement the equivalent circuit of an impulse

generator consists of the internal impulse voltage source, v . (t) , the internal

source resistance, R , and a Johnson thermal noise source, v (t) , associated s sn with the resistor, R •

Impulse

Gen.

"cf

_4~_

°^>

©-*

o

•WWV (rms)

Tuned

Radio

Receiver

cf

Video

output Oscilloscope

area A

Figure 4-5. Video pulse - Mil. Std. 462.

4. 6 Video Pulse — Mil. Std. 462

The video pulse technique, figure 4-5, is the one currently accepted by

the U.S. military for the calibration of impulse generators [24]. The IEEE

also recognizes it as a valid measurement technique [2] . The technique consists essentially of connecting the impulse generator to a narrowband filter

(such as a radio receiver) and observing with an oscilloscope the envelope

response (i.e. video pulse) of the filter output and comparing the peak amplitude to that obtained from a known cw sine wave signal generator. The impulse

bandwidth, IBW, of the filter must also be known and there are several measure- ment techniques to determine IBW [25,26].

U.S. Military Standards 461, 462, and 463 set forth the specifications,

definitions, and calibration procedures for impulse generators. Those portions

pertinent to this topic are reproduced here.

Mil-Std-461A, 1 Aug. 1968, p. 11

5.4 Impulse Generators . -- Impulse generators shall conform to the following

requirements

:

(a) Calibrated in terms of output to a 50 ohm load.

(b) Spectrum shall be flat ± 2 dB over its frequency range.

(c) Amplitude accuracy shall be ± 2 dB.

48
Mil-STD-462, 31 July 1967, p. 4 4.2.3.6 Impulse Generators . — Impulse generators shall be calibrated as follows:

(a) Apply the output of an impulse generator to the input of an amplitudelinear receiver having synchronously tuned, less than critically

coupled circuits. EMI receivers are satisfactory for this purpose

if their impulse bandwidth is at least five times the repetition

rate of the impulse generator. Any AGC system, shall be disabled and

the AGC line firmly referred to ground with a low impedance voltage

source of appropriate value.

(b) Obtain an oscilloscope pattern of the overall receiver response at

the IF output. The oscilloscope controls shall be so adjusted that

the pattern is as large as possible within the calibrated area on the face plate. Either photograph or trace the pattern. Record the

oscilloscope sweep speed setting. (The sweep speed shall be calibrated

accurately.

)

(c) Use a planimeter or other integrating device to determine the area of

the pattern. This operation shall be carried out at least 10 times and

the average of the readings taken as the area.

(d) Calculate the impulse bandwidth of the receiver in accordance with the

following formula:

TT, T7 . TT (Pattern height in cm) IBW in Hz = i a (Pattern area in cm2

) (Sweep speed in sec/cm)

(e) Connect a sinewave generator to the receiver and at f and adjust the

output until the peak pattern height is the same as that obtained with

the impulse generator.

(f) Connect an r.f. power meter to the signal generator and measure the

power output. Calculate the r.m.s. voltage on the sinewave signal.

(g) The output of the impulse generator is now calculated by taking the

r.m.s. voltage calculated in step (f) divided by the impulse bandwidth

determined in step (d)

.

Mil-Std-462, Notice 2, 1 May 1970, Appendix A

30. Impulse Generators

30.1 By definition, the calibration for broadband measurements is referenced

to the RMS value of an equivalent sine wave. Correct calibration of

impulse generators is subject to verification by witnessing officials,

in accordance with Mil-Std-462.

Mil-Std-463, 9 June 1966, p. 5

4.18 Impulse Bandwidth . The peak value divided by the area of the

impulse response envelope.

49
4.20 Impulse Strength . The rms unmodulated sine wave voltage required to

produce in a circuit a peak response equal to that produced by the

impulse in question, divided by the impulse bandwidth of the circuit.

For the purpose of this standard it is expressed in terms of yV/MHz

or dByV/MHz.

The video pulse method is probably the most widely used due to the fact

that is is specified by Mil. Std. 462 and because it uses common laboratory

instruments such as a calibrated cw signal generator, a tunable receiver, and

an oscilloscope. There are however several difficulties associated with this

technique. The major problem lies in the determination of the narrowband

filter impulse bandwidth. E.B. Larsen [2 5] of NBS has written an exhaustive

report on the many problems that are encountered in accurately determining the

impulse bandwidth of a radio receiver. He reports that the results can vary

widely depending upon the actual shape of the filter passband, both in amplitude and phase. Overcoupled or stagger tuned networks or mechanical filters

are definitely undesirable for this purpose. Problems also arise in trying

to determine the impulse bandwidth from the envelope response area per

Mil. Std. 462 due to noise distortion of the envelope response and accuracy

problems in measuring the area. Larsen [2 5] and Simpson [15] have recommended that the most accurate

method of determining impulse bandwidth is to use a known rf pulse. Their

recommended procedure is listed in table 4-1.

As can be seen from eq. (1) in table 4-1 under No. 8, only two parameters

affect tne accuracy of measuring the impulse bandwidth by this standard pulse/cw

signal generator method. They are the pulse duration t and the difference in

two attenuator settings.

4 . 7 Spectrum Analyzer

A spectrum analyzer is perhaps the easiest instrument to use for making

broadband spectrum amplitude measurements. It gives an immediate visual

display of relative spectrum amplitude versus frequency. Some spectrum

analyzers of recent design are also capable of making quite accurate S(f)

measurements [14]. Of major importance is that the input impedance, gain,

and bandwidth of the instrument be constant and not a function of frequency.

It must also be free of spurious and image responses. Reeve [14] has found

tnat some FIM and EMI receivers currently in wide use are not suitable because

of impedance, gain, and bandwidth variations with frequency.

To use a spectrum analyzer, it must first be calibrated as a tuned voltmeter at several selected frequencies using a standard cw sine wave generator

of known output. The impulse bandwidth must also be calibrated at the same frequencies. The technique described in table 4-1 is recommended.

50
Table 4-1. Impulse bandwidth calibration procedure for field intensity

meter receivers.

1. Assemble a standard pulsed/cw signal generator consisting of a cw

sine wave generator, baseband pulse generator, modulator, and a calibrated attenuator. See section 3.5 for complete description.

2. Set the standard signal generator controls as follows:

a. mode -- pulse

b. carrier frequency, f -- same as FIM

c. repetition rate, f -- as desired, with the restriction

BW

f < =— , where BW is the nominal 3 dB bandwidth of the FIM O 3 d. rf pulse duration, t — as desired with the restrictions [11]

15

< t < X

f o 10 BW

c

e. duty cycle — t f < 0.05.

3. Set the FIM controls as follows:

a. amplifier mode — linear

b. AGC — off

c. detector — peak

d. video filter -- off

e. frequency tuning -- centered on f , the standard signal generator

frequency

f. bandwidth — as desired.

4. Connect the standard signal generator output to the FIM antenna

input.

5. Adjust the attenuator to obtain a reading on the FIM peak detector

that is near full scale and well above the FIM noise level. Check

that the FIM is operating in the linear region by increasing and

decreasing the input signal to the FIM by several dB and noting

whether the peak detector follows linearly the input variation.

Reset the attenuator to the desired level and record the attenuator

setting, A, , in dB and the peak detector reading, PD,

.

6. Set the standard signal generator mode control to cw.

7. Adjust the attenuator to obtain the same peak detector reading, PD, , as obtained in step 5. Record the attenuator setting, A~ .

8. Calculate the impulse bandwidth, IBW, from the following equation:

[(A -A )/20]

IBW = 1/t 10 (1) o

51
Spectrum amplitude can then be measured directly from the CRT display using

S(f) = V

± (f)/IBW (4-23)

where V. (f) is the equivalent input voltage as indicated on the spectrum

analyzer CRT screen. Most spectrum analyzers use a peak detector to determine

V. ; however, the CRT display is usually calibrated in terms of rms volts for

sine wave measurements. Thus S(f) from eq. (4-23) is a root mean square spectrum amplitude. To convert to standard spectrum amplitude the results from

eq. (4-23) should be multiplied by /2 or if S(f) is given in dByV/MHz, 3 dB

should be added.

Below 1 GHz there are several excellent spectrum analyzers commercially

available that are capable of making accurate spectrum amplitude measurements.

However above 1 GHz the currently available spectrum analyzers' performances

are not as good as the < 1 GHz models. If an analyzer is to be used above

1 GHz for S(f) measurements, considerably more care must be exercised in the

measurement.

A major problem in using a spectrum analyzer for S(f) measurements is its

susceptibility to overload. Most modern spectrum analyzers apply the input

signal directly to the input mixer. If the peak input voltage exceeds 150-

200 mV, signal compression occurs, while voltages in excess of a volt will

destroy the mixer diodes. This poses a severe limitation when attempting to

measure an extremely narrow (< 1 ns) impulse of several tens or hundreds of

volts. If the impulse is attenuated to the 150 mV peak level by a broadband

attenuator then the resultant spectrum amplitude is found to be comparable to or below the noise level of the spectrum analyzer. The solution lies in the use of preselector bandpass filters between the impulse generator and the input

to the mixer. The filter acts to reduce the peak voltage applied to the mixer

without reducing the spectrum amplitude at the measurement frequency. It is

good practice to use broadband attenuators of typically 6 to 10 dB on either

side of the filter to provide proper impedance matching. The preselector

filter bandwidth should be at least ten times larger than the spectrum analyzer's

impulse bandwidth. Otherwise the impulse bandwidth of the preselector/spectrum

analyzer combination must be calibrated at every measurement frequency. The

attenuation of the preselector and the external attenuators must be included in

the measurement calculations.

4 . 8 Standard Pulse Comparison

Reeve [14] has proposed a sophisticated scheme for automatically calibrating an impulse generator using a comparison against a known standard pulse

such as an rf pulse. His proposed system would use a programmable spectrum

analyzer, a tracking cw generator, a network analyzer, a standard pulsed/cw

signal generator, and a minicomputer to control all the various instruments to

perform the measurement and the necessary computations. Such a system would

52
e

fd

J-4 tn

to •H^OOH

X!OW

•H

(daeoo

CJw

rH

5-1 fdc

fd -Pwi

Cn H

fa

53
incorporate the best features of modern measurement technology and probably

offers the ultimate in precision and accuracy. The cost of such a system would

be quite high and for this reason it has not been built.

The basic ideas of Reeve's system can be incorporated in a manually

operated standard pulse comparison system. Such a system is shown in figure

4-6 which uses ordinary instruments normally found in a calibration laboratory.

Basically, the technique involves adjusting the level of the rf pulse from the

standard pulsed/cw signal generator until the same video pulse output is obtained from the narrow band filter (a spectrum analyzer or FIM) as is obtained

when the unknown impulse generator is connected to the narrow band filter

input.

A phase lock amplifier/detector may also be used in conjunction with a peak sample/hold and delay circuit to recover very low level video pulses from

the spectrum analyzer's peak detectors that would otherwise be buried in the

system noise. This permits a considerable increase in dynamic range of S(f)

measurements over simply using the spectrum analyzer's CRT display. A variable

delay circuit is triggered by a sync pulse from the impulse generator. The

delay is adjusted to correspond to the delay in the spectrum analyzer between

the impulse input and the peak of the output video pulse. The peak sample/

hold circuit is gated to sample and hold the peak value of the video pulse.

The sync pulse is used as a reference signal and the peak sample/hold output is

the unknown input to a phase lock amplifier. The standard pulsed/cw signal

generator is externally triggered by the impulse generator to establish its

repetition rate, f . In this manner by using the impulse generator to establish f it is possible to directly intercompare the two generators without

readjusting any of the phase lock video pulse detector circuits. The load

impedance is fixed at 50 ohms by using a fixed coaxial attenuator of at least

10 dB at the spectrum analyzer input. A preselector filter is used as discussed previously. The oscilloscope and frequency counter are additional

instruments required for setting and calibrating the equipment.

In operation the impulse generator is first connected to the spectrum

analyzer. All of the controls of the analyzer and phase lock detector are optimized to obtain a maximum indication on the phase lock detector meter.

This meter reading is recorded. The standard pulse/cw signal generator is then

connected to the spectrum analyzer and the amplitude of the rf pulse is adjusted with the calibrated attenuator until the same phase lock detector meter

reading is obtained as previously with the impulse generator. The attenuator

setting in dB, A, , is recorded. In this setting the rf pulse spectrum amplitude, S

f

(f ), is equal to the impulse generator spectrum amplitude S . (f ) . W = ^V (4 " 24)

S

f is given in dByV/MHz by

S rf (f c

) = SQ

(f c

) - A

1 (dB) . (4-25)

S (f ) is determined with the attenuator set to dB and measuring the cw

o c

r output power and the rf pulse duration, t , as described in section 3.5.

54
4 . 9 Time Domain Measurement/Fourier Transformation Computation

With the exception of the standard transmission line method (section 4.1)

the previous techniques for measuring spectrum amplitude have all been some variation of a frequency domain measurement using a narrow bandpass filter.

An alternate technique is to measure the time domain waveform, v. (t) , of the

signal to be measured. From v. (t) the spectrum amplitude, S. (f ) , can then be

computed using the basic definition of spectrum amplitude, eqs. (1-1) and (1-2).

S

±

(f) = 2|v

i

f)

|

(4-26)

oo V

±

(f) = / Vi (t)e" D2lTft dt (4-27)

—oo

This technique has been known for a long time, but it has not been widelyused because it has been very time consuming. It has required photographing

an oscilloscope CRT display of the signal to be analyzed. Many data points

must then be read by eye from the photograph, typed onto paper tape or computer

cards, and then processed (eqs. (4-26) and 4-27)) on a time share or large

central computer. The process easily consumed an entire working day.

With the advent of inexpensive (< 10 K$) minicomputers, this has all

changed. The cost of computing capability is now comparable to that of a high

performance oscilloscope, and it is now cost-effective to dedicate a minicomputer to be hard-wired to an oscilloscope. In addition, sampling oscilloscopes are commercially available with bandwidths as great as dc-18 GHz which

permit v(t) and hence S(f), via eqs. (4-26) and (4-27), to be measured over

this very broad range with a single instrument.

In 1974, NBS built such a time domain measurement system. It is called

the Automatic Pulse Measurement System (APMS) . As shown in the block diagram

of figure 4-7, the APMS consists basically of a dc-18 GHz sampling oscilloscope

directly interfaced with and controlled by a minicomputer. The APMS is described in full detail in NBS Tech Note 672 [27] . it was originally developed

as a Time Domain Automatic Network Analyzer (TDANA) [2 8] but has several other

capabilities as tabulated below:

1. Acquisition and storage in memory of a time domain waveform. Data

arrays as large as 2048 points can be accommodated.

2. Signal averaging for greatly improved signal to noise ratio and

the recovery of low level signals buried in the noise.

3. Spectrum analyzer using the Fast Fourier Transformation (FFT) of

time domain waveforms.

4. Computation of time domain waveform parameters such as pulse

amplitude, risetime, overshoot, duration, distortion, etc.

55
14-

Impulse

Gen.

6 dB

if—\w^C 75ns, 50 n >H> Sampler

dc-18 GHz

50 fi

Y sync

L

^/^30 dB

Optional

30 dB

or

g'ii— in

Sampling

Oscilloscope

in

-<>

D/A

2^:

y

out

A/D

r> s r

Minicomputer

Trigger

CRT

TTY

Terminal

Figure 4-7. NBS automatic pulse measurement system,

56
5. Network analyzer measurements of the S parameters (transmission and

reflection) , in both magnitude and phase, of rf and microwave networks. Present limits are a dynamic range of 40 dB and frequency

coverage from dc to X band but will be increased in the future.

6. Availability of a minicomputer within the laboratory with both BASIC

and FORTRAN capability for solving many mathematical problems.

When the APMS is used to measure the spectrum amplitude of an impulse

generator, it gives excellent results. Chapter 5 presents the results of the

APMS with other measurement techniques. In operation, the impulse to be measured is applied to the input of the sampler. If the impulse amplitude is

greater than ± 400 mV then broadband coaxial attenuators must be used between

the impulse generator and the sampler. The impulse generator must also supply

a suitable stable trigger pulse to the sampling oscilloscope approximately 75

to 100 ns prior to the impulse. Some electronic impulse generators normally

supply such a trigger pulse. However the vast majority of impulse generators

use mercury switches or spark gaps and are not capable of being triggered

reliably. The sync pulse from these generators cannot be used. For these

generators a trigger pick off and coaxial delay line, figure 4-7, must be used

to provide the necessary trigger for the sampling oscilloscope.

When a delay line is necessary the overall system bandwidth is degraded

below the sampler 18 GHz bandwidth. The major limitation is due to skin effect

in the coaxial delay line. With ordinary coaxial cables the arrangement of

figure 4-7 is useful only up to 1 or 2 GHz. For higher frequencies and

impulse durations less than 250 ps a superconducting coaxial delay line is

'used [9,29]

.

The APMS time domain method of calibrating impulse generators has the

advantages of: (1) very broad frequency coverage (dc-18 GHz) , (2) rapid

measurement time of typically two minutes, and (3) providing a large amount

of data (typically several hundred data points) . It does have some disadvantages however. The major one is that it cannot measure v(t) over the

complete interval -°° < t < +°°. It can only acquire a limited finite amount

of data points. Thus a time window of finite extent is used to observe the

impulse. Any signals emanating from the impulse generator other than the

main impulse and positioned in time outside of the time window are ignored.

Their contribution to the composite spectrum amplitude is not accounted for

in the FFT computation. Another problem which arises when either external

attenuators and/or a trigger pick off delay line arrangement is used, is the

necessity to also calibrate the attenuation versus frequency of these additional

components to provide correction factors for the measured S(f). This is not

a major problem however because the APMS can also be used as a TDANA to determine

the "S" parameters of these components. The major effect is a reduction in the

overall accuracy.

57
5. EXPERIMENTAL COMPARISON OF VARIOUS S(f) MEASUREMENT TECHNIQUES

This chapter presents the results of a set of experiments to compare the

various spectrum amplitude measurement techniques that were discussed in

chapter 4. The energy method and the Dicke radiometer techniques were not

used. The other techniques were investigated and were found to all give

consistent results.

5. 1 Standard Transmission Line Experiment

A mercury switch impulse generator was constructed consisting of a small

mercury switch mounted in a 3 mm coaxial housing; a 5 ns, 50 ohm, 3 mm semirigid coaxial cable; a stable dc voltage supply; and a digital voltmeter.

The transition time (10%-90%) of the mercury wetted reed switch was 0.21 ns

[9]. The exact value of t was determined from eq. (4-3) using a TDR measure- ment of R and a capacitance bridge measurement of C

T

. R was 50.5 ohms and

C was 102.33 3 pF.

With a supply voltage of 1.6 volts and an impulse duration of 10.336 ns,

the low frequency spectrum amplitude, S , is 84.37 dByV/MHz. Being almost a perfect rectangular pulse, the spectrum should theoretically follow the

sin(irft )/(irft ) equation. For a 10.336 ns pulse the first zero in the spectrum

occurs at 96.749 MHz.

Table 5-1 is a comparison of the theoretically predicted spectrum for this

generator and measurements made on the NBS APMS using the time domain measurement/

fast Fourier transform computation (hereafter abbreviated as TD/FFT) technique. There is agreement within ± 0.6 dB over the low frequency portion of

the spectrum up to 8 5 MHz which covers a 15 dB range. The spectrum nulls

near the frequencies f = n-l/t are extremely sharp and as expected the

agreement between theory and experiment is very poor. However, good agreement

is obtained for the peaks on the higher order lobes of the spectrum.

5. 2 Sum and Difference Correlation Radiometer Experiment

Experiments were performed in 1972 by Reeve [14] to measure spectrum amplitude using the NBS sum and difference correlation radiometer (SDCR) . He used

an NBS step recovery diode impulse generator develped in 1970 by Ondrejka [30] as the broadband impulsive noise source to be tested. The same generator was measured in 1976 using the TD/FFT technique using the NBS APMS. The results are compared in table 5-2. At 30 MHz the results obtained by the two techniques

differed only by 0.35 dB. At 1 GHz the agreement was not as good. G. Reeve [31]

cautions that the 1972 SDCR results are not to be considered as an absolute

calibrated measurement as a complete error analysis of the SDCR has never been

made. However, he feels that the 3 MHz SDCR is much more accurate than the

1 GHz instrument. The 1 GHz SDCR was plagued with a reduced sensitivity and a phase instability. Thus considerable doubt exists concerning the validity of

the 1 GHz measurements.

58
Table 5-1. Comparison of S(f) measurement using TD/FPT technique versus standard transmission line theory.

S(f) in dBuV/MHz

Frequency Std. Line

in MHz TD/FFT Theory Difference

9.96 83.87 84.22 0.35

19.92 83.32 83.76 0.44

29.88 82.44 82.96 0.52

39.84 81.20 81.80 0.60

49.80 79.59 80.19 0.60

59.76 77.46 78.00 0.54

69.72 74.77 74.99 0.22

79.68 70.69 70.54 -0.15

89.64 63.87 62.28 -1.59

99.56 40.65 53.37 12.7

119.5 67.34 69.16 1.82

139.4 69.90 71.10 1.20

159.4 68.71 69.13 0.42

179.3 63.31 62.05 -1.26

199.2 38.21 53.45 15.2

259.0 64.39 64.46 0.07

Table 5-2. Comparison of S(f) measurements using the SDCR and TD/FFT

techniques

.

S(f) in dBuV/MHz

Frequency

in MHz SDCR

37.15

TD/FFT

37.5

Difference

30 -0.35

1000 35.35 33.9 1.45

59
5 . 3 Experiments with Commercial Mercury Switch Impulse Generators

Four different measurement techniques were used in experiments to measure

the spectrum amplitude of two commercial* mercury switch impulse generators.

The techniques were: (1) TD/FFT; (2) standard pulse comparison; (3) video

pulse -- Mil. Std. 462; and (4) spectrum analyzer. The first generator produced a 10 ns impulse with a spectrum amplitude specified by the manufacturer

to be flat within + 1 dB from 500 Hz to 35 MHz. The output was adjustable

from to 121 dByV/MHz (RMS) in 0.25 dB steps. The second generator was specified by the manufacturer to produce a spectrum output flat within i 1 dB

from 60 kHz to 1000 MHz. The output was adjustable from 10 to 101 dByV/MHz

(RMS) in 0.25 dB steps. The results of these experiments are summarized at

a few representative frequencies in tables 5-3 and 5-4.

Table 5-3. Comparison of S(f) measurements on a commercial mercury

switch HF impulse generator.

S(f) in dBiiV/MHz

Frequency

in MHz

Manufacturer

Spec. d)

s TD/FFT

83.1

Std.

Pulse

83.1

Mil. Std.

462

Spectrum

Analyzer

5 83.0 (1) 83.8 82.8

10 83.0 83.0 82.6 83.3 83.5

20 83.0 83.0 82.8 83.4 83.2

40 NA (2) 82.3 82.3 82.8 82.5

60 NA 78.9 79.0 79.7 78.9

(1) Output amplitude controls set at +80 dByV (RMS) /MHz

.

(2) Output specified flat within ± 1.0 dB maximum from 500 Hz to 35 MHz

*It is NBS policy not to mention manufacturers nor commercial products in its

publications. This is done to avoid giving unfair economic advantage to any

manufacturer which might occur through a real, implied, or imagined endorsement,

60
Table 5-4. Comparison of S(f) measurements on a commercial mercury

switch UHF impulse generator.

S (f ) in dByV/MHz

Frequency

in MHz

Manufacturer '

s

Spec

.

TD/FFT

(2)

83.9

Std.

Pulse

83.4

Mil. Std.

462

Spectrum

Analyzer

20 83.0 (1) 83.9 82.8

60 83.0 83.6 83.8 84.4 83.5

100 83.0 83.6 84.0 84.2 82.7

200 83.0 83.4 83.5 84.0 84.0

500 83.0 82.3 83.2 83.2 82.7

1000 83.0 82.0 84.4 85.1 84.8

(1) Output amplitude controls set at +80 dByV(RMS) /MHz.

(2) Output amplitude controls set at +50 dByV(RMS) /MHz for measurement,

Data corrected to +80 dB level.

The TD/FFT measurement of S(f) was performed by the NBS APMS . These

mercury switch impulse generators did not supply the necessary trigger pulse

for the oscilloscope. Thus the arrangement shown in figure 4-7 was used to

obtain the necessary trigger signal. A broadband (dc-18 GHz) 6 dB coaxial

power divider is used as a trigger pick-off. The power divider is impedance

matched, i.e. when its two output ports are terminated in 50 ohms it presents a

50 ohm load to the impulse generator. The trigger input of the sampling

oscilloscope is only nominally matched to 50 ohms. The VSWR is high enough

to upset precision measurements if the output of the 6 dB power divider were connected directly to the trigger input. To provide impedance matching and

VSWR isolation a broadband (dc-12 GHz) , 30 dB, 50 ohm attenuator terminates

the trigger output port of the power divider. To compensate for the trigger

signal amplitude loss due to the attenuator, a broadband (5-500 MHz) 30 dB

amplifier is used. The other output of the power divider is connected to a

75 ns , 50 ohm coaxial delay line, which in turn is connected to the remote

sampler. The delay line has a 3 dB bandwidth of 3 GHz. The actual waveform

measured by the APMS is the input to the remote sampler. This waveform is

attenuated and distorted due to transmission through the power divider and

the delay line. Thus, the APMS measurement must be corrected for the insertion loss versus frequency of the power divider and delay line to give the

correct spectrum amplitude of the impulse generator under test. The necessary

correction factors are obtained by operating the APMS as a TDANA to measure

S„, of the power divider/delay line network.

61
The frequency domain measurements, namely the standard pulse comparison,

the video pulse, and the spectrum analyzer all used a commercial spectrum

analyzer as the measuring instrument. It tunes from 100 kHz to 1250 MHz with

a specified flatness of ± 1 dB. The bandwidth is adjustable from 300 Hz to

300 kHz in a 1,3 sequence. There is no preselector in this instrument. The

input signal is applied directly to the first mixer through an adjustable

input attenuator. Prior to making any measurements the spectrum analyzer was calibrated against cw signal sources of known power and frequency.

The impulse bandwidth of the spectrum analyzer was measured at 30 MHz using

several different methods that have been reported in the literature [25] . This was done to compare the relative accuracies of the various methods. The results

are tabulated in table 5-5. The nominal bandwidth is the value engraved on the

front panel of the instrument. The standard pulse impulse bandwidths were determined as described in section 4.8 and table 4-1. The difference between

the two measurements was the output indicator which was the spectrum analyzer

CRT display in one case and an external oscilloscope display of the video output

pulse in the other. The video pulse impulse bandwidth is determined from the area under the video output pulse time domain response as described in section

4.6. The 6 dB bandwidth is simply the bandwidth between the -6 dB points on

the frequency response curve. The area bandwidth is that of an equivalent

rectangular frequency response with an area equal to the area under the linear

frequency response curve. The power bandwidth (sometimes called random noise

bandwidth) is that of an equivalent rectangular frequency response with an area equal to the squared voltage frequency response curve. In the 100 kHz and

lower positions the frequency response appeared to be almost perfectly gaussian

while the video pulse response was also gaussian-like . In the 300 kHz position

the frequency response was slightly nonsymmetrical and the video pulse response

included a minor secondary pulse 4 ys after the primary pulse. For the 100 kHz

position with its gaussian-like response, extremely good correlation was obtained between the video pulse IBW, standard pulse IBW, and the area BW.

For the non-gaussian 300 kHz position the correlation between various bandwidths was not as good. The difference in the two standard pulse measurements

illustrate some of the problems that can be encountered in making measurements

at two supposedly identical measurement ports. The difference noted here is

attributed to the video signal output amplifier bandwidth. The video pulse

technique correlates within 1 dB of the standard pulse method. The 6 dB bandwidth also gave good agreement for this set of measurements, however, Larsen

[25] cautions that it is subject to large errors for extremely non-gaussian

responses. The area bandwidth gives a good correlation for a gaussian response

but introduces a large error for a slightly non-gaussian response. The power

bandwidth should not be used for the impulse bandwidth.

62
Table 5-5. Comparison of various impulse bandwidth measurement methods,

300 kHz Nominal 100 kHz Nominal

Bandwidth Bandwidth

Impulse Bandwidth IBW IBW-IBW(std) IBW IBW-IBW(std)

Measurement Method kHz dB MHz kHz dB MHz

-0.73 158 0.05

-0.22 144 -0.75

2.11 158 0.05

-1.99 106 -3.41

Standard Pulse per

Table 4-1 (CRT Display) 371 157

Standard Pulse per

Table 4-1 (video

signal output) 360 -0.26 152 -0.28

Video Pulse per

Mil. Std. 462 341

6 dB Bandwidth 362

Area Bandwidth 473

Power Bandwidth 295

5. 4 Experiment with Step Recovery Diode Impulse Generator

A set of experiments were also run to measure the spectrum amplitude of

a step recovery diode impulse generator using five different measurement

techniques. The techniques were: (1) TD/FFT; (2) standard pulse comparison;

(3) video pulse -- Mil Std. 462; (4) spectrum analyzer; and (5) harmonic measurement. The results are tabulated at a few representative frequencies in

table 5-6. The generator used was NBS impulse generator S/N 3-75-1. It is

identical to the one described in section 3.4 and appendix A with the exception that the RC high-pass filter is not included in the SRD module as was done with later models.

The TD/FFT measurement of S(f) was performed by the NBS APMS . The

generator impulse output was connected directly to the sampler through a broadband (dc-12 GHz), 30 dB, 50 ohm, coaxial attenuator. The sampling oscilloscope

was triggered directly from the trigger output from the generator. The APMS

S(f) measurement was corrected for the attenuation versus frequency characteristic of the 30 dB attenuator which was obtained by a S~, measurement using

the APMS as a TDANA.

The frequency domain measurements all used the same commercial spectrum

analyzer described previously in section 5.3 with the exception that the

measurements at 1, 2, and 5 GHz were made with a different rf tuning unit plugin. Various combinations of attenuators and low-pass or band-pass filters were

used at different frequencies. The standard rf pulse generators used were previously described in section 3.5 and tables 3-2 and 3-3. The standard pulse

comparison, video pulse, and spectrum analyzer measurement techniques used

are the same as used in the previous section. In addition to these it was

63
also possible to use the harmonic measurement technique as this impulse generator was capable of operating at high repetition rates up to 100 kHz. A 300 Hz

bandwidth was used for this measurement and the harmonic amplitude was read

directly from the spectrum analyzer CRT.

The results of this experiment, table 5-6, all show good agreement. The

worst case difference is 2.1 dB at 500 MHz. The frequency domain measurements

at 500 MHz had the poorest accuracy due to the 700 MHz preselector low pass

filter used which resulted in a poor signal to noise ratio. The spectrum

analyzer detected a small 1 dB, 3 MHz ripple in the spectrum at frequencies

up to 200 MHz. This was due to a small 60 mV secondary pulse 330 ns after

the main impulse. This secondary pulse was not included in the TD/FFT

measurement time window which helps explain part of the differences noted at

low frequencies. Particularly encouraging were the mirowave results between

2 and 5 GHz. For these measurements the impulse generator was applied directly

to the spectrum analyzer through a tracking YIG preselector with a 70 MHz

bandwidth.

The results of the experiments on the two mercury switch impulse generators are listed in tables 5-3 and 5-4. The frequency domain measurements were made using the 300 kHz bandwidth of the spectrum analyzer and 10 dB of input

attenuation. For the Mil. Std. 462 data the impulse bandwidth used was 341 kHz.

For the spectrum analyzer results the spectrum amplitude was obtained from

the peak deflection noted on the calibrated CRT screen divided by an impulse

bandwidth of 371 kHz. The data was corrected for a 3 dB difference due to the

RMS calibration of the spectrum analyzer. The standard pulse data was obtained

by adjusting the output attenuator of the standard rf pulse generator (see

section 3.5 and table 3-3) to obtain the same peak deflection on the CRT as from

the unknown impulse generator. The majority of these tests were made using a 0.5 ys rectangular rf pulse. The maximum cw output was +4 dBm. The unknown

generator's spectrum amplitude was obtained directly from the attenuator setting

in dB, A, and the following equation

S = 108 - A dByV/MHz. (5-1)

For the tests with the 10 ns, HF generator, a 6 dB attenuator was used at

the input to the spectrum analyzer to provide a dc return for the impulse generator. The insertion loss of the attenuator was calibrated at each measurement

frequency and was used as a correction factor. For the UHF impulse generator

various attenuators, low pass or band pass filters, and generator output amplitudes were used to obtain the optimum peak impulse amplitude into the spectrum

analyzer. The insertion loss of the various external components and the output

amplitude change are all included as correction factors to normalize the data

to the nominal 83 dByV/MHz level. The measurements at 500 and 1000 MHz have the

poorest accuracy due to a poor signal to noise ratio.

64
The measurements on the 10 ns, HF impulse generator all show excellent agreement. The worst case is 1 dB between the Mil. Std. 4 62 and the spectrum analyzer

at 5 MHz. Between the TD/FFT and the standard pulse the largest difference is

0.4 dB at 10 MHz.

The results of the measurements on the 1/2 ns, UHF impulse generator showed

a fair amount of spread. The large spread in the results at 500 and 1000 MHz

is attributed to the poor signal plus noise to noise ratio of 14 dB in the

frequency domain measurements. In other words the random noise on the spectrum

analyzer CRT display was 20% of the signal level. This made it difficult to

make precise measurements within closer than + 1 dB at best. These problems

could have been alleviated if narrowband preselector filters had been available at the time of the measurements. At 500 MHz, a 700 MHz loss pass filter

was used, while at 1000 MHz a 900 to 1200 MHz bandpass filter was used. At

frequencies up to 200 MHz the agreement between the TD/FFT and the standard

pulse measurements was quite good. The largest difference was 0.5 dB at 20 MHz.

Table 5-6. Comparison of S(f) measurements on an NBS step recovery

diode impulse generator (S/N 3-75-1) .

S (f ) in dByV/MHz

Frequency

in GHz

TD/FFT

(1)

72.9

Std.

Pulse

72.1

Mil. Std.

462

Spectrum

Analyzer

71.8 (2)

Harmonic

0.05 72.4 71.2

0.10 72.2 72.4 73.2 71.6 (2) 71.8

0.20 71.6 72.5 73.1 72.9 (2) 72.3

0.50 70.7 68.9 68.6 70.4 70.7

1.0 68.7 68.7 69.2 69.6 68.3

2.0 68.4 68.1 68.8 68.9 68.4

5.0 58.6 58.0 58.6 59.0 57.8

(1) TD measurement made using a 30 dB external attenuator.

(2) One dB, 3 MHz ripple noted in spectrum due to small secondary

pulse 330 ns after main impulse.

65
6. ERROR ANALYSIS OF S(f) MEASUREMENT USING TD/FFT

NBS calibrations of the spectrum amplitude output of impulse generators

are made on the NBS Automatic Pulse Measurement System (APMS) using the time

domain measurement/Fourier transformation computation (TD/FFT) method described

previously in section 4.9. It is the purpose of this chapter to discuss the

various sources of errors in this method.

An impulse can be characterized to the first order by (1) its peak amplitude, V , ; (2) its duration, t; and (3) its low frequency spectrum amplitude, pK

S = 2V , t . Thus the two major sources of error in S(f) are uncertainty in the

o pk J measurement of voltage and time.

6 . 1 Sampling Oscilloscope Errors

The vertical, voltage axis of a typical sampling oscilloscope can be calibrated using accurately known dc voltages to a typical uncertainty of ± 3% for

full scale (or 10 cm) deflection on the CRT. The vertical linearity is quite

good (< ± 1%) over the normal range of operation. The major nonlinearity is severe signal compression for amplitudes greater than + 0.7 V [32]. ± 4%

vertical uncertainty contributes + 0.36 dB.

The time base in a typical sampling oscilloscope can be calibrated to

within + 4% uncertainty for a 10 cm horizontal deflection. The time base may

have a nonlinearity of + 6% within any one cm. Thus a time base uncertainty

of + 10% contributes ± 0.92 dB.

The voltage and time uncertainties in an ordinary calibrated sampling

oscilloscope are unacceptable for accurate impulse generator calibrations.

Thus prior to each IG calibration the APMS sampling oscilloscope is calibrated

on the particular vertical and horizontal scale factors actually used in the

S(f) measurement. Typically the impulse amplitude is adjusted to be approximately 300 mV and the 50 mV/cm vertical scale is used. Under control of a computer program an accurately known dc voltage is applied to the sampler and

incremented in 50.00 mV steps. The computer determines the resultant oscilloscope deflection and computes the average scale factor. For a 0.5 ns impulse

the 5 ns/cm time base is used. The time base is calibrated by applying an accurately known 200.00 MHz sine wave. The computer analyzes the resultant

displayed waveform and determines either the positive or negative slope zero crossing intercepts of the sine wave. From this data it then prints out a scale

factor for each centimeter of horizontal deflection along with the average

sweep rate. In a typical IG calibration, the operator selects for later

computational use the scale factor of the particular centimeter in which the

impulse waveform under test is located. Using these computer assisted calibrations, it is possible to reduce the vertical and horizontal uncertainties

to less than + 1% each, or ± 0.09 dB.

In addition to the error contribution to the value of S(f), the time base

uncertainty of ± 1% translates directly to a ± 1% uncertainty in the actual

frequency, f . . 66
The calibration of an impulse generator is in terms of the voltage

delivered to a resistive 50 ohm load. Any deviations in the actual load

impedance from 50 ohms are an additional source of error. The maximum measured

VSWR over the frequency range . 1 to 6 GHz for the APMS sampler is 1.278 at

4.6 GHz [33]. For this VSWR the uncertainty contribution is ± 1.13 dB . Another

source of uncertainty is the frequency response of the sampling gate. Based

upon risetime measurements the -3 dB bandwidth of the sampling gate is of the

order of 18 GHz. Frequency domain measurements on similar samplers tend to

confirm this value [32,33,34]. Thus at 6 GHz an error of 0.33 dB would be

contributed.

A source of random error is the sampling oscilloscope noise. There are

two distinct types, namely vertical amplitude fluctuations and horizontal

timing jitter. Noise experiments [27] on the APMS have determined that the

short term noise has a normal distribution with a standard deviation of 1.9 mV

(3a = 5.7 mV) . For a single measurement of a 300 mV impulse this gives a signal to noise ratio (V v /3a) of 34.4 dB or an error of + 0.17 dB. With the

px

computer it is possible to do digital signal averaging to improve the signal

to noise ratio. For a typical mercury switch IG calibration 50 waveforms are measured and averaged which gives a 17 dB improvement in signal to noise ratio

reducing the vertical noise error contribution to ± 0.023 dB.

The short term timing jitter was also found to have a normal distribution

with a standard deviation of 3 ps under the most optimum conditions. When

additive vertical signal averaging is used on a signal with time jitter, the

effect is the same as passing the signal through a low-pass filter [27] . Three

picoseconds of jitter is equivalent to a 44 GHz low-pass filter. Thus the

effective -3 dB bandwidth is reduced from a nominal 18 GHz to 16.7 GHz.

6 . 2 Computer Errors

The APMS computer interface is another potential source of errors. The

X coordinate or point in time of a measurement is determined by the computer.

The computer generates a digital X address which is then converted to an analog

voltage via a 14 bit D/A. This analog voltage drives the X axis of the

sampling oscilloscope. The sampling oscilloscope then samples the input signal

at the addressed position in time, t.. The sampled value, V (t.), is an analog

voltage. It is then converted into a digital number via a 14 bit A/D for

storage and later processing in the computer. Thus the A/D and D/A conversions

are performed with a precision of 1 part in 16384. For a typical calibration

the 50 mV/cm and 5 ns/cm scales are used. Thus the vertical precision is 30 yV

and the horizontal precision is 3.1 ps. For a 300 mV, 0.5 ns impulse these

amount to uncertainties of ± 0.001 dB and ± 0.054 dB, respectively.

For machine computation purposes, errors may be thought of as being

inherent errors, truncation errors, or roundoff errors. Inherent errors in

data are errors introduced into the data before it reaches the computer. These

data errors may be caused by such things as systematic and random measurement

67
errors, measurement recording errors, and data input errors (caused by a faulty

papertape reader, for example) . Truncation errors are caused by the necessity

of truncating an infinite series representation of a function for computational

purposes. For example, calculation of the sine of x from the infinite series,

3 5 7 sin x = x-jr+^ir-yj-+ ... (6-1)

leads to truncation errors because an exact answer can be obtained only by

computing the values of an infinite number of terms.

Roundoff errors are caused by memory limitation in the computer. Depending

on the machine design, only so much memory is allocated for storage of a number.

Also, arithmetic processes are limited in the size of numbers upon which they can operate. Thus, only an approximation for such irrational numbers as tt and

e may be stored and used in a computer. The APMS system minicomputer, operating

in FORTRAN, is capable of storing and operating upon numbers up to seven decimal

digits in length. Remaining least significant digits are simply discarded.

It is known that both truncation and roundoff errors are generated by an FFT computation, but an exhaustive attempt to establish bounds on these errors remains for necessary future work.

Another source of computational error that must be considered is the error introduced by the FFT algorithm. Use of this algorithm not only generated

errors of truncation and roundoff, as mentioned above, but also errors due to

aliasing and windowing may be introduced.

As discussed in reference [27] aliasing errors occur whenever the frequency

content of the acquired time domain waveform exceeds l/2At where At is the time

sampling interval. For the most part, these errors may be effectively eliminated

by use of bandpass or low-pass filters, either analog or digital, that remove

any frequency components of the time domain waveform at or above the Nyquist

or folding frequency, or by a proper selection of At relative to the waveform

under test. In a typical measurement of a 0.5 ns triangular impulse the 5 ns/cm

time scale is used. One thousand twenty four data points are acquired over the

50 ns time window. Approximately 20 data points describe the major features

of the impulse. The sampling interval At is 48.8 ps . Thus the Nyquist frequency is 10.24 GHz. The first zero in the spectrum of a 0.5 ns impulse is

in the vicinity of 2 GHz which is approximately a factor of 5 below the

Nyquist frequency. Thus the maximum aliasing overlap into the first spectrum

lobe (dc-2 GHz) is 67 dB below S . This contributes 0.004 dB error. The

o FFT computes the spectrum at harmonics of the reciprocal of the time window,

T . For a 50 ns time window the results are given at harmonics of 20 MHz. w

3 Errors introduced by windowing are more difficult to resolve. The problem

faced is that leakage errors will occur in the FFT computation if the time

domain waveform to be transformed does not start and stop at exactly the same value of amplitude. This primarily requires the operator to select an appropriate time window to insure that the impulse waveform has returned to

68
the zero baseline. It also requires that the time window be wide enough to

include all secondary pulse emissions or reflections from the impulse generator. This does not pose a problem with mercury switch impulse generators.

This is a problem with many solid-state generators which often produce spurious

low level secondary pulses. If the secondary pulse problem is too severe,

the TD/FFT cannot be used to determine S(f).

6.

3

Nonrepeatability

Another uncertainty introduced into an impulse generator calibration is

the nonrepeatability of the measurement. The effects of long term drift,

particularly in the vertical and horizontal axis of the sampling oscilloscope,

greatly influence this. In a normal IG calibration the APMS is programmed to

automatically repeat the measurement several times. The final output listing

is a tabulation of the mean and standard deviation of S(f) versus frequency.

This allows the operator to maintain statistical control of the calibration.

For an extremely stable impulse generator that can be operated at a high

repetition rate, such as the NBS step recovery diode generator, standard

deviations of 0.06 dB are obtained over the frequency range of 1.3 to 4.4 GHz.

The worst cases are at the low and high frequency end of the calibration, with

0.34 dB at the lowest frequency, 50 MHz. A similar effect is also noted with

mercury switch impulse generators; however, the standard deviation is 0.15 dB over the middle portion of the main spectrum lobe. The higher standard

deviations obtained at low frequencies are attributed to slow drift in the

vertical axis, while the high frequency effect is attributed to timing drift.

6 .

4

Error Tabulation

The results of the error analysis in the previous sections is summarized

in table 6-1. The results are tabulated in columns according to frequency

band. The VSWR, bandwidth, and measurement standard deviation are the

frequency dependent error sources. The uncertainty associated with the

measurement consists of two parts: (1) the total systematic error obtained

by taking the root sum of the squares of the various systematic errors; and

(2) the measurement standard deviation. The total uncertainty is obtained

by taking the root sum of the squares of the total systematic error and

three times the measurement standard deviation (3a)

.

69
Table 6-1. Uncertainties in spectrum amplitude measurement,

(TD/FFT Method)

Frequency Range in GHz

Type of Error Common

0.087 dB

.005-1 1-2 2-3 3-4 4-5 5-6

DC Voltage Calib.

Time Base Calib. 0.087 dB

VSWR (dB) 0.12 0.61 0.68 0.69 1.13 1.11

Sampling Gate Band- 0.02 0.05 0.10 0.17 0.26 0.39

width & Averaged

Jitter (dB)

Averaged Vertical

Noise

A/D Quantization

D/A Quantization

FFT Aliasing

Total (RMS) Systematic Error (dB)

Measurement Standard Deviation (dB)*

Total (RMS)

Uncertainty (dB)

0.023 dB

0.001 dB

0.054 dB

0.004 dB

0.18 0.63 0.70 0.72 1.17

0.48 0.66 0.72 0.74 1.11

1.11

0.15 0.06 0.06 0.06 0.06 0.20

1.32

*The measurement standard deviation in the .005 to 1 GHz range is for a typical mercury switch IG, while the remaining values are for a solid-state

ps IG.

70
6 . 5 Comparison with Other Measurement Techniques

Chapter 5 gave the results of a set of experiments designed to compare

the results obtained with the TD/FFT and various other S(f) measurement techniques. They were: (1) standard transmission line; (2) sum and difference

correlation radiometer; (3) standard pulse comparison; (4) video pulse — Mil.

Std. 462; (5) spectrum analyzer; and (6) harmonic measurement. From this set

of experiments and the previous error analysis, conclusions were reached

regarding the total uncertainty that should be assigned to the NBS calibration

service for IG's. In weighing the results from the various experiments, the

heaviest emphasis was given to the differences between the standard pulse

comparison and the TD/FFT. From this analysis the total uncertainty assigned

to the NBS IG calibration service is as listed in table 6-2.

Table 6-2. Uncertainties for the NBS Impulse Generator

Spectrum Amplitude Calibration Service.

Frequency Range S(f) Total Uncertainty

5 MHz 1 f 1 1 GHz ± 0.6 dB

1 GHz < f <_ 4 GHz ± 1.2 dB

4 GHz < f < 6 GHz ± 2.0 dB

6 . 6 Calibration of Other Components

For some impulse generator calibrations it is necessary to use additional

components to attenuate the amplitude and/or to provide the necessary trigger

signal. For amplitude attenuation, broadband, 50 ohm coaxial attenuators are

used. To obtain a trigger signal a power divider and delay line are used.

In either case it is necessary to calibrate the attenuation versus frequency

characteristic of the components used in a particular measurement. The

uncertainty of this attenuation calibration must then be added to the uncertainty of the APMS S(f) measurement to arrive at the final uncertainty assigned

to an impulse generator calibration. The attenuators, power divider, and delay

line used in IG calibrations are calibrated for S^, with the APMS operating in

the TDANA mode. The uncertainty, U, of the TDANA S-, measurements has been

evaluated by a set of comparisons with other standards and measurement techniques [24] . The uncertainty equation is

U(dB) = 0.02 + 0.015 A + 0.0015 Af (6-2)

where A is attenuation in dB and f is frequency in GHz. For example, the 6 dB

power divider and delay line combination has an attenuation of 6.24 dB at dc

and 8.43 dB at 2 GHz with respective uncertainties of 0.11 dB and 0.14 dB.

A 30 dB attenuator will have uncertainties of 0.47 dB at dc and 0.74 dB at

6 GHz.
7. NBS IMPULSE GENERATOR SPECTRUM AMPLITUDE CALIBRATION SERVICE

In response to calibration needs from the electromagnetic interference

(EMI) community, NBS has developed a measurement service to calibrate the

broadband spectrum amplitude output from impulse generators. Such a generator

can then be used as a transfer standard of broadband impulsive noise for field

calibration of spectrum analyzers and field intensity meters (FIM) . This

chapter describes the currently offered NBS measurement service for calibrating

the spectrum amplitude output of impulse generators. It includes NBS definitions, measurement technique, and a tabulation of the capabilities and limitations of the service.

7 . 1 Spectrum Amplitude Definition

Spectrum Amplitude, S(f), is defined by NBS and the IEEE [2] as two times

the magnitude of the Fourier transform, |v(f) | , of a time domain signal function, v (t) .

oo V(f) = / v(t)e" j2TTft dt, (7-1)

— OO

S(f) = 2|V(f) | . (7-2)

The unit of S(f) is volt-second or equivalently volts per hertz. The unit in common usage is microvolts per megahertz (yV/MHz) . Also in common usage is

a decibel expression, decibel microvolts per megahertz (dBMV/MHz) , above

1 yV/MHz.

S(dB) = 20 log 10

SJjjV/MHz)

1 yV/MHz

(7-3)

In the time domain voltages are measured in terms of absolute SI volts. In

the frequency domain however power is usually a major consideration and as a result voltages are usually expressed in RMS voltage. For a sine wave the peak

voltage is /2~ times the RMS voltage. On a power basis where the voltages are squared this becomes a factor of 2 or expressed in dB, 3 dB. When a peak

responding receiver that has been calibrated in terms of the RMS value of a sine wave is used to measure S(f) the measurement results will be 3 dB lower

than if it were calibrated in terms of the peak value.

The NBS and IEEE definition of S(f), eqs . (7-1) and (7-2) uses absolute SI

volts and seconds with NBS measurements expressed in dByV/MHz, eq. (7-3). NBS

customers using peak responding, RMS calibrated receivers to measure S(f) are cautioned to apply the 3 dB correction factor to their measurements.

72
7 . 2 NBS S(f) Measurement Technique

Several techniques are available for measuring spectrum amplitude. They were discussed in detail in chapter 4. They are also summarized in a paper

[35] presented at CPEM-76 by J. R. Andrews entitled "Impulse Generator Spectrum

Amplitude Measurement Techniques." It was published in the December 1976 issue

of the IEEE Transactions on Instrumentation and Measurement.

The NBS calibration service uses the time domain measurement/Fourier

transformation computation (TD/FFT) method for calibrating of impulse generators

This is done using the NBS Automatic Pulse Measurement System (APMS) , figure

7-1. The APMS consists of an 18 GHz bandwidth, 20 ps risetime, 50 ohm sampling

oscilloscope directly interfaced with and controlled by a minicomputer. The

APMS measures an impulse generator's time domain waveform which is digitized

and stored in the minicomputer memory. By acquiring an ensemble of many

waveforms it is possible to perform signal averaging within the minicomputer

to improve the signal to noise ratio in the measurement. The minicomputer

then computes the spectrum amplitude from the digitized, averaged waveform

using the Fast Fourier Transform (FET) and eqs. (7-1), (7-2) and (7-3). As a matter of policy, the spectrum is also checked on a spectrum analyzer to

detect any gross anomalies which might be caused by small secondary pulses

that were not included in the APMS measurement time window. Depending upon

the severity of the secondary pulses either the calibration error limits are expanded or the generator is rejected as unsuitable for calibration.

7 . 3 Limitations and Capabilities of S(f) Measurement Service

The APMS sampling oscilloscope imposes some requirements on the impulse

to be measured. Peak voltages in excess of ± 3 volts will destroy the

sampling diodes. Severe waveform compression occurs in the region + 1 volt.

Best results are obtained with peak voltages of ± 300 mV. The high level

signal compression is minimized while maintaining a good signal to noise ratio.

Impulses with peak voltages greater than ± 400 mV are attenuated to this

level using broadband, coaxial, 50 ohm attenuators. There are also peak

voltage limitations on the coaxial attenuators. Therefore, NBS will not accept

any impulse generator with an output greater than ± 1.2 kV.

m The APMS sampling oscilloscope time base must be triggered at least

75-100 ns in advance of the impulse to be measured. It is preferable if the

impulse generator itself provides a stable trigger pulse. When this is not

possible then the oscilloscope will be triggered from the impulse itself using

a coaxial, 6 dB, 50 ohm power divider tee. One output of the tee connects to

the trigger input of the oscilloscope. The other output of the tee is con- nected to a 50 ohm coaxial delay line, the output of which is connected to

the sampling head. A time window of 200 ns is the broadest that can be used

with this arrangement. This sets the 5 MHz lower limit on the advertised IG

calibration service. This limit can be extended to broader time windows and

73
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74
lower frequencies if the generator is an electronic generator with a suitable

trigger pulse and adjustable delay.

When it is necessary to use external attenuators for peak voltage reduction and/or the 6 dB tee and delay line for obtaining a trigger pulse, then

these components must also be calibrated for wideband attenuation over the same frequency range that the impulse generator is calibrated over. The total

external attenuation in dB is added to the spectrum amplitude computed from

the measured waveform to give the actual spectrum amplitude of the generator's

impulse output. Likewise, the uncertainty of the attenuator calibration is

added to the basic uncertainty of the actual waveform measurement and S(f)

computation. The attenuators, tee and delay line are calibrated by operating

the APMS in the TDANA mode [2 7,28].

The following table along with qualifying notes lists NBS ' s current

capabilities for impulse generator spectrum amplitude calibration. Table 7-2

lists the wide band attenuation capability.

Table 7-1. Impulse generator spectrum amplitude measurement service

capabilities.

Parameter

Maximum Impulse Amplitude

without attenuators

Maximum Impulse Amplitude

with external attenuators

Limits

+ 400 mV

± 1.2 kV

Spectrum Amplitude

S(f) Uncertainty

Frequency Range

f <_ 1 GHz, ± 0.6 dB

1 GHz < f <_ 4 GHz, ± 1.2 dB

4 GHz < f <_ 6 GHz, ± 2.0 dB

5 MHz to 6 GHz

Notes

1,2,3

3,4

-15 dBuV/MHz < [S(f)-S ] < ± 5 dBpV/MHz 5,6,7

5,6,7,8&9

5,6,7,&10

Frequency Spacing

Frequency Uncertainty

Load Impedance

Load Impedance Uncertainty

Trigger Pulse Magnitude

Trigger Pulse Transition Time

Trigger to Impulse Delay

Trigger to Impulse Jitter

Af = 5,10,20,50, or 100 MHz

± 1%

50.0 ohms

± 0.1 ohm at dc

VSWR < 1.3 up to 6 GHz

> 10 mV

< 5 ns

75 ns < t < 100 ns

< 20 ps

5,10

7

8,11

12

12

12

12

75
Table 7-1. Continued.

Notes

1. The impulse generator is characterized by its impulse output

waveform into 50 ohms of peak amplitude (V , )

, 50% level duration pK

(t), and low frequency spectrum amplitude (S ^ 2 V v t).

o P-K 2. Impulse generator with an adjustable amplitude impulse output

will be calibrated with the generator adjusted to give a peak amplitude

in the range of 200 mV to 400 mV.

3. Impulse generators with fixed outputs greater than ± 400 mV

must have the impulse attenuated to the 200 mV - 400 mV level by 50

ohm wideband coaxial attenuators

.

4. Either customer supplied or NBS attenuators may be used.

5. Depends upon actual generator characteristics.

6. Data will not be given in the first spectrum null or at frequencies above. Typically 100 data points are supplied.

7. Subject to revision.

8. Only for impulse amplitudes less than + 400 mV.

9. If external attenuators and/or a 6 dB tee and delay line are used then the uncertainty associated with the attenuator calibration

is added to these values.

10. Lower frequencies (< 5 MHz) are available as a special test.

11. Depends upon input impedance of external attenuators when used.

12. If the impulse generator does not supply a trigger output or if

the trigger output does not have the proper characteristics then a 6 dB tee and a delay line will be used to provide a suitable trigger

pulse

.

76
Table 7-2. Wide band attenuation/gain measurement service capability.

Parameter

Attenuation/Gain

Attenuation/Gain

Uncertainty

Frequency

Frequency Uncertainty

Frequency Range in MHz

Source and Load Impedance

Connectors

Limits Notes

or

40 dB 1

U = 0.02 + 0.015 A 1,2,3

+ 0.0015 Af in dB

< 12.5 GHz 1

± 1% 1

+ i x 100, < i < 124 1,4,5

i x 50, 1 < i < 120

50 ohms , nominal

Coaxial 6

Notes

1. Subject to revision.

2. A is attenuation in dB, f is frequency in GHz.

3. Applies only for APC-7 sexless connectors.

4. Lower frequency ranges are also available.

5. Lower frequencies and smaller frequency spacing is also available.

6. All measurements are made by the substitution method, which requires

that the connectors used be sexless or that the network under test have a male connector at one port and a female connector at the other. If an adapter is required to comply with the foregoing, it must be supplied with

the network. The combination will be calibrated as one unit.

77
Many of the limitations concerning the frequency range and spacing are related to the FFT. With an oscilloscope it is not possible to observe waveforms from t = -°° to + oo. One can only observe a waveform within a limited

time window. For this particular measurement service time windows of 10 ns,

20 ns, 50 ns, 100 ns and 200 ns are available. Within the time window the

sampling oscilloscope measures 1024 separate uniformly spaced, values of the

waveform. This sampled data is then transformed to the frequency domain using

the FFT. Due to the mathematics of the FFT, the lowest frequency resulting

from the computation is the reciprocal of the time window (i.e., 50 ns * 20 MHz),

The other frequency components are harmonics of the fundamental (i.e., 20,

40, 60, 80 MHz ...). The highest frequency component is l/(2At) where At is

the time domain sample c spacing c 3 and At = T , /N. For the 50 ns window At window

is 48.8 psc and f is 10.24 GHz. Due to various accuracy considerations the max J time window is chosen such that at least ten data points are obtained on the

major feature of the impulse waveform. Fewer data points rapidly introduce

significant errors in the computations. As an example an impulse of 500 ps

duration would be measured over a 50 ns time window with a At of 48.8 ps and

a resulting spectrum amplitude data table starting at 20 MHz. Another significant limitation on the choice of the time window is the requirement that

no other spurious pulses occur outside of the window and that the waveform be

completely relaxed and resting on the baseline at the beginning and end of

the time window. If these criteria cannot be met then the generator is rejected

for calibration.

Eighty percent of the impulse generators calibrated at NBS are of the

mercury switch variety with an impulse duration of 1/2 ns and adjustable

amplitude. For this type of generator the calibration fee at the time of

publication of this technical note was $475 for a single unit and $385 for

additional identical items. The current fee schedule can be determined by

consulting the most recent appendix to the NBS SP-250 [36] . Generators with

different characteristics are not covered by this fee schedule. Individual

fee quotations are given for these generators.

7 . 4 Calibration Report

A "Report of Calibration" is furnished to a customer upon completion of

calibration of his impulse generator. A typical report includes: (1) spectrum

amplitude definition, (2) a description of the calibration procedure, (3) the

specific control settings and operating conditions of IG at the time of calibration, (4) a computer generated plot of the IG's waveform, (5) a table listing

the spectrum amplitude, S(f), versus frequency, (6) a statement regarding the

standard deviation of the particular calibration, (7) a statement of the total

uncertainty, including the standard deviation, associated with the particular

calibration, and (8) a list of pertinent references.

78
APPENDIX A — NBS IMPULSE GENERATOR SPECIFICATIONS, CIRCUIT DESCRIPTION

AND SCHEMATICS

This appendix describes in more detail the NBS Impulse Generator, series

3-75-X, that was discussed in section 3.4 in the main text. Figure A-l is

a photograph of the actual instrument. Specifications, circuit descriptions

and schematics are included in this appendix.

Impulse Output

Source Impedance

:

Impulse Amplitude;

Polarity:

Baseline:

Impulse Duration (50%)

:

Spectrum Amplitude, S(f)

Frequency Range for S(f) Spec.

:

Repetition Rate, Trigger and Timing

Internal Rep. Rate:

External Rep. Rate Input:

Frequency:

A-l. Specifications

50 ohms, ± 1 ohm at dc . ± 0.1 p maximum

reflection as measured by a 30 ps risetime

TDR.

8 volts, ± 25%, into 50 ohms.

Positive.

volts.

100 ps, + 25%.

> 60 dByV/MHz.

20 MHz to 3 GHz.

Pulse Required:

Polarity:

Input Loading:

Delay:

Trigger Output Pulse:

Source Impedance

;

Amplitude:

Polarity:

Baseline:

Risetime:

50 Hz to 100 kHz in a 1,2,5 sequence.

Quartz crystal controlled. (± 0.001%.)

DC to 100 kHz max. Repetition rates in excess of 100 kHz may damage the impulse

generator

.

Standard TTL pulse

0V< "0" < 0.8 V

2 V < "1" < 5 V.

Triggering occurs on positive going

transition.

Single TTL 74H00 gate.

Nominal 25 ns lag at trigger output port

referred to the external input port.

50 ohms

.

1.5 volts, ± 25%, into 50 ohms.

Positive

.

volts.

0.7 ns, ± 25%.

79
Duration (50%;

Timing:

Jitter:

Note: Second pulse of + output pulse.

10 ns, + 25%.

Leading edge of trigger pulse is

80 ns, ± 5 ns, in advance of impulse

output

.

< 5 ps jitter in the delay between the

trigger output pulse and the impulse

output.

V amplitude occurs 160 ns after the main trigger

117 volts, ± 10%, 60 Hz.

30 watts, nominal.

43 cm x 45 cm x 26.5 cm. 11.8 kg • Less Accessories.

General

Supply Voltage:

Power Consumption:

Size:

Weight:

Accessories Furnished

1. Power cord, 2.4 m.

2. Output cable, 1 m, RG-9B/U, type N male connectors.

3. BNC, 50 ohm termination for trigger output.

4. Mounting hardware for standard 48 cm relay rack.

5. Operating and service manual.

6. Calibration certificate.

A-2 . Circuit Description

Figure A-2 is the chassis wiring schematic. Practically all of the electronic circuits are on printed circuit cards which are described below.

Card 1 - Low Voltage

Printed circuit card number 1 contains the low voltage power supplies.

Figure A-3 is the schematic diagram. +15 V, +5 V, -15 V, and -18 V are supplied by this card. Most components are mounted directly on the card with

the exception of the power transformer, the -15 V regulator and the +5 V pass

transistor. Integrated circuit voltage regulators are used throughout with

the exception of the -18 V which is obtained using a zener diode.

Card 2 - High Voltage

Figure A-4 is the schematic for the high voltage power supply. The high

voltage transformer is mounted on the chassis. The circuit is quite conventional. With the resistor combination the output voltage is nominally 240 to

250 V at normal line voltage. The zeners are not used for regulation but are included to limit the maximum output voltage to +25 V under conditions of high

line voltage. This is done to protect the transistors in the high voltage

regulator, card 3.

80
Figure A-l. NBS impulse generator exterior and interior view,

81
Card 3 - High Voltage Regulator and SRD Bias Current Regulator

Printed circuit board 3, figure A-5, contains two separate circuit functions, namely the high voltage regulator and the SRD bias current regulator.

The driving pulse generator requires well-regulated +100 V and +200 V for its

avalanche transistor circuits. The +250 V raw dc from the high voltage card

is dropped to +200 V by the series pass transistor Q2 . R4 , R7 , and R8 provides

a sample of the +200 V output to the (+) input of the operational amplifier ICl.

A fixed +6.8 V reference voltage is supplied to the (-) input by the zener

diode, CR2 . ICl, Q4 , Q3, and Ql form the feedback error amplifier to drive

the series pass transistor Q2 . R3 and Q5 are used to provide current limiting

protection. The +100 V is obtained from the +200 V by the 2:1 divider, R9-R10,

and the emitter follower Q6

.

The remaining components of board 3 are the SRD bias current regulator.

The collector of Q8 acts as a high impedance current source for the SRD.

Operational amplifier, IC2 , and Q7 function as the feedback error amplifier

for Q8 to regulate the SRD bias current. The emitter current of Q8 , which

is approximately the same as its collector current, is regulated by IC2 by

comparing the voltage drop, across R12 with the adjustable reference voltage

set by R13 and zener diode CR3 . By connecting Q7 in a Darlington configuration with Q8 , a super-high beta transistor results so that the SRD bias cur- rent is essentially identical to the emitter current of Q8 which is regulated

by IC2. The diodes CR4-7 are included to provide an alternate path for the

SRD bias current in the event that the SRD is not connected. They also provide

overvoltage limiting protection for the SRD.

Card 4-10 MHz Clock

Printed circuit card 4, figure A-6 , contains the 10 MHz crystal controlled

oscillator and the -r 1, r 2, t 5 frequency divider for the internal repetition

rate source. Ql is the oscillator. Q2 is a high input impedance FET buffer

amplifier, while Q3 is an overdriven squaring amplifier to provide a TTL logic

level, 10 MHz square wave to the TTL frequency dividers. The 7400 quad, dual

input NAND gate is included to allow digital selection of either the internal

10 MHz source or an external clock. This feature is not used in this impulse

generator. The card was designed for some previous NBS pulse generators which

used this feature. For this generator the INT line, pin 25, is permanently

connected to the +5 V while the EXT line, pin 5, is grounded. The 7490 is

connected to function as independent t 2 and t 5 frequency dividers driven by a common 10 MHz clock. Thus from the 7490 three frequencies, namely 10 MHz,

5 MHz, and 2 MHz, are available. The 7454 functions as a digitally controlled

switch to select one of these frequencies. "Cold" switching is used, i.e.,

only dc control voltages are selected by the repetition rate switch, figure A-7,

with the actual signal switching being performed on the circuit board. +5 V is

required to activate the desired switch.

82
Card 5 - Frequency Divider

Printed circuit card 5, figure A-8 contains a chain of TTL frequency

dividers. IC1-5 are 7490, * 10 dividers connected in series to reduce the frequency from the clock card in steps of 10. The 7454 and 7451 are used for

"cold" switch selection of the desired frequency in the same manner as on the

clock card. The 7402 is used as an OR gate to combine the outputs of the

7454 and 7451.

Card 6 - Driving Pulse Generator

The driving pulse generator circuit is found on card 6, figure A-9. The

rep. rate pulse, either internal or external, from the rep. rate switch is

applied to two 74H00 NAND gates to sharpen up the positive going transition.

The positive going pulse from the output of the second 74HO0 gate is differentiated by C3 and is then used to trigger the first avalanche transistor,

(jl. When Ql avalanches, it very rapidly discharges C4 through pulse transformer

Tl. The output of Tl provides a large pulse to trigger Q3 into avalanche breakdown. Q2 is connected in series with Q3 and it also goes into avalanche breakdown simultaneously. The breakdown of Q2 and Q3 discharges a short 25 ohm transmission line, DLl, and C5 and C6 which had previously been charged to +200 V.

The output of Q3, i.e., the emitter, is connected to a 25 ohm transmission line

circuit, DL2 . Thus when Q2-Q3 breakdown a high amplitude, fast rising, positive going pulse is launched onto DL2

.

The pulse from the avalanche transistors Q2-Q3 has its leading edge

sharpened by the step recovery diode, CR7 . CR7 is normally forward biased by

the -15 V supply and R9 . The positive pulse from Q2-Q3 attempts to reverse

bias CR7 . However, CR7 continues to conduct in the reverse direction until

its stored charge is depleted. At the instant when all the stored charge has

been removed CR7 switches rapidly to a nonconducting state. It is this fast

transition that decreases the rise time of the pulse.

The fast rising pulse from CR7 is then passed through the diode gate

consisting of CR5 and CR6 in parallel. CR5-6 are reverse biased at -15 V.

The pulse from CR7 is large enough to forward bias the gate and pass through

it. On the other side of the gate the pulse encounters two 50 ohm circuits in

parallel which provide a 25 ohm load to match the 25 ohm impedance of the

driving pulse generator. The generator is also backmatched to 25 ohms by

resistors R6 and R7 to absorb internal reflections. The purpose of the gate and

the two paralleled 50 ohm circuits was discussed earlier. Bias current for the

external, ultra-fast SRD module is inserted through L8 . Cll provides a dc

block.

83
SRD Module and Impulse Forming Network

Figure A-10 is the schematic diagram for the ultrafast step recovery diode

and the impulse forming network. The leading edge of the driving pulse after

transmission through the delay line is sharpened to less than 100 ps risetime

by the ultrafast SRD. The SRD is a special device consisting of two separate

identical step recovery diode chips connected in series and mounted in the same package. This allows the device breakdown voltage to be twice that of an individual chip while maintaining essentially the same step recovery transition

time of a single chip. The ultrafast step transition from the SRD is formed

into an impulse by the 3 dB directional coupler. Rl-Cl form a high pass filter

to provide additional pulse shaping for the purpose of giving a flat spectrum.

It is possible to obtain a larger amplitude impulse without Rl-Cl in the circuit but the penalty paid is a nonuniform spectrum. The circuit requires micro- wave construction techniques and is built in a 3 mm, 50 ohm coaxial housing,

figure A-ll. The SRD package has been modified by cutting off a portion of the

cathode stud with a fine jewelers saw.

84
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85
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Figure A-3. Card 1 - low voltage.

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Figure A-4. Card 2 - high voltage.

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Figure A-9. Card 6 - driving pulse generator.

Pr>'vi'r

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Figure A-10. SRD module and impulse forming networks. (D\A.i~*3*.f~

89
(d) (e)

Figure A-ll. SRD module and impulse forming network,

(a) SRD module and directional coupler

installed in generator and connected to

coaxial delay line. (b) SRD module

assembled. (c) SRD module, disassembled,

(d) Close-up showing placement of SRD,.

CI, and Rl. (e) Modified SRD package and

mounting screw.

90
REFERENCES

[I] IEEE Standard Dictionary of Electrical and Electronics Terms , IEEE Std.

100-1972, p. 549 (John Wiley & Sons, Inc., New York, 1972).

[2] IEEE Standard for the Measurement of Impulse Strength and Impulse Bandwidth , IEEE Std. 376-1975 (IEEE, New York, 1975)

.

[3] Westman, H.P. (editor) , Reference Data for Radio Engineers , Fifth Edition,

Chapter 42 (Howard W. Sams & Co., Inc., New York, 1968).

[4] Bracewell, R. , The Fourier Transform and its Applications , pp. 8-13

(McGraw-Hill Book Company, New York, 1965)

.

[5] Middleton, D. , An Introduction to Statistical Communication Theory , pp. 88-90 (McGraw-Hill Book Company, New York, 1960) .

[6] Lathi, B.P., Signals , Systems and Communications , p. 130 (John Wiley

& Sons, Inc., New York, 1965).

[7] Cooper, G.R. and McGillem, CD., Methods of Signal and System Analysis , sec. 5-10, (Holt Rinchart & Winston, Inc., New York, 1967).

[8] Millman, J. and Taub, H. , Pulse, Digital and Switching Waveforms , pp. 101-

104 (McGraw-Hill, Inc., New York, 1965).

[9] Andrews, J.R. , Picosecond pulse generators using microminiature mercury

switches, NBSIR 74-377, NBS, Boulder, Colo. (1974).

[10] Andrews, J.R. , A frequency calibrator for UHF using an avalanche transistor, QST, 16-18 (May 1972) . [II] GE Transistor Manual, 7th Edition, pp. 516-620 (1964) . [12] Millman, J. and Taub, H., op. cit. [8], pp. 510-512.

[13] Andrews, J.R. and Baldwin, E.E., Baseband impulse generator useful to

5 GHz, 1975 IEEE Electromagnetic Compatibility Symposium Record, 6BIdl-4

(Oct. 7-9, 1975)

.

[14] Reeve, G.R., Calibration of impulse noise generators, NBSIR 73-343,

NBS, Boulder, Colo. (Oct. 1973).

[15] Simpson, P. A., Broadband pulsed/cw calibration signal standard for field

intensity meter (FIM) receivers, NBSIR 74-371, NBS, Boulder, Colo. (June

1974) . [16] Palladino, J.R., A new method for the spectral density calibration of

impulse generators, IEEE Trans. EMC, Vol. EMC-13, No. 1, 2-7 (Feb. 1971) . [17] Andrews, R.B., Jr., An impulse spectral intensity measurement system,

IEEE Trans, on I&M, Vol. IM-15, No. 4, 299-303 (Dec. 1966).

[18] Arthur, M.G., Impulse spectral intensity calibration at the National

Bureau of Standards, Proc. 1969 Dept. of Defense Electromagnetic

Compatibility Symposium, 133-138 (1969) . [19] Arthur, M.G. , Standards and measurement of impulse spectral intensity,

unpublished NBS report to sponsor (196 9)

.

[20] Allred, CM., A precision noise spectral density comparator, J. Res.

NBS, 66C, 323-330 (Oct. -Dec. 1972)

.

[21] Arthur, M.G. , Allred, CM., and Cannon, M.K., A precision noise power

comparator, IEEE Trans, on Instr. & Meas., IM-13, 301-305 (Dec. 1964).

91
[22] Oranc, H.S., Calibration of impulse generators by using Dicke-type

radiometers, IEEE Trans. Instr. & Meas., Vol. IM-23, No. 3, 232-234

(Sept. 1974)

.

[23] Dicke, R.H., The measurement of thermal radiation at microwave frequencies, Review of Scien. Instru., Vol. 17, No. 7, 268-275 (July 1946).

[24] Mil. Std. 462.

[25] Larsen, E.B., Calibration of radio receivers to measure broadband interference, NBSIR 73-335, NBS , Boulder, Colo. (Sept. 1973).

[26] EMI measurement procedure, HP-Appl. Note 142, Chapter II and Appendix A

(July 1972)

.

[27] Gans, W.L. and Andrews, J.R., Time domain automatic network analyzer for

measurement of RF and microwave components, NBS Tech. Note 672, NBS,

Boulder, Colo. (Sept. 1975).

[28] Andrews, J.R. and Gans, W.L., Time domain automatic network analyzer,

Proceedings of the Colloque International sur 1 ' Electronique et la Measure,

Paris, France, 258-267 (May 26-30, 1975) and also L'Onde Electrique,

Vol. 55, No. 10, 569-574 (Dec. 1975) . [29] Andrews, J.R., Precision picosecond pulse measurements using a high quality

superconducting delay line, IEEE Trans, on I&M, Vol. IM-23, No. 4, 468-

472 (Dec. 1974)

.

[30] Ondrejka, A.R., Development and evaluation of a solid state impulse

generator, unpublished NBS Report to Sponsor (1970).

[31] Reeve, G.R., private communication.

[32] Nahman, N.S. and Jickling, R.M. , Frequency domain measurement of baseband

instrumentation, NBSIR 73-330, NBS, Boulder, Colo. (1973).

[33] Andrews, J.R., Whittemore, T.R., and McCaa, Jr., W.D., Survey of present

waveform sampling system limitations, unpublished NBS Report to Sponsor

(1972)

.

[34] Lennon, C, Measurement of Microwave Sampling Gates , M.S. Thesis, Univ. of

Toledo, Toledo, Ohio, 1975.

[35] Andrews, J.R., Impulse generator spectrum amplitude measurement techniques,

IEEE Trans, on Instr. and Meas., IM-25 , 4, 380-384 (Dec. 1976).

[36] Calibration and Test Services of the National Bureau of Standards,

NBS Special Publication 250, Office of Measurement Services, NBS, Wash.

D.C., 20234. An updated appendix is issued in April and Oct. of each year.

92
»ff

w

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUT ATION OR REPORT NO.

NBS TN 699

2. Gov't Acces

No.

3. Recipient's Accession No.

L TITLE AND SUBTITLE

Spectrum Amplitude -- Definition, Generation

and Measurement

5. Publication Date October 1977

6. Performing Organization Code

276.00

AUTHOR(S)

James R. Andrews and M. Gerald Arthur

8. Performing Organ. Report No.

PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. tlZS 21&SAQA

11. Contract/Grant No. CCG-75-97

2. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Department of Defense, Calibration Coordination Group

c/o Mr. Claude Moss, Chairman

Aerospace Guidance § Metrology Center

Newark, OH 43055

13. Type of Report & Period Covered

Final for FY 75

14. Sponsoring Agency Code

5. SUPPLEMENTARY NOTES

S. 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 technical note is a detailed discussion of the electromagnetic

quantity, spectrum amplitude, which is used to characterize broadband

signals and noise. The definition of spectrum amplitude is presented in

detail. Several practical means of generating electrical signals with

broadband spectrum amplitudes are included. Various techniques for the

measurement of spectrum amplitude are described along with experimental

comparisons. The NBS measurement service for the calibration of impulse

generator spectrum amplitude is described along with an error analysis.

7. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Electromagnetic interference; Fourier transformation: impulse; impulse

generator; spectrum- amplitude.

8. AVAILABILITY £2? Unlimited

1 2 F°r Official Distribution. Do Not Release to NTIS

lx [ Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13« 46:699

I ! Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

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