NBSIR 73-304

REFERENCE-WAVEFORM GENERATION USING DEBYE

DIELECTRIC DTSPERSIDN

N.S. Nahman

R.M. Jickling

D.R. Holt

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

December 1972

Final Report

Prepared for:

Department of Defense

Calibration Coordination Group 69-33

U. S. Army Metrology & Calibration Center

Redstone Arsenal, Alabama 35809

NBSIR 73-304

REFERENCE-WAVEFQM GENERATION USING DEBYE

DIELECTRIC DISPERSION

N.S. Nahman

R.M. Jickling

D.R. Holt

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

December 1972

Final Report

Prepared for:

Department of Defense

Calibration Coordination Group 69-33

U. S. Army Metrology & Calibration Center

Redstone Arsenal, Alabama 35809

u s. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS. Richard W Roberts Director

CONTENTS

Chapter Page

Abstract 1

1. INTRODUCTION 2

1. 1 Definition of Reference-Waveform. Generation 2

1.2 Definition of Available-Waveform 2

1.3 NBS Reference-Waveform Generator Characterization 2

1. 4 Determination of the Available-Waveform 3

2. DEVELOPMENT AND CONSTRUCTION 8

2, 1 Uniform Line Parameters 8

2. 2 Uniform Line Design and Parameter Characterization 11

2. 3 Coaxial Connector/Adapter Design and Parameters 14

2. 4 Liquid Dielectric Preparation and Parameter

Measurements 19

2. 5 Available-Waveform Computation/ Evaluation 23

3. OPERATING SYSTEM 29

3, 1 Electrical Network Physical Structure 29

3, 2 Waveform Data Acquisition System 30

4. SUMMARY 31

REFERENCES 32

ILLUSTRATIONS 33

APPENDIX A-1 - TIME DOMAIN REFLECTOMETRY 61

ILLUSTRATIONS FOR APPENDIX A-1 7 8

APPENDIX A-2 - WAVEFORM DATA FOR FIGURES 86

2. 15 and 2. 16

iii
ILLUSTRATIONS

Page

Figure 1.1 Reference waveform parameters. 33

Figure 1. 2 The available waveform e (t) across a 50 ohm load. 34

3. Figure 1. 3 The defining network for the available waveform e (t). 35

ct Figure 1.4 The generated waveform ^^(t). 36

Figure 1. 5 (A) Squared difference of the output voltage ^^{x) com- 37

pared to the defined available waveform e (x)

(B) The output voltage eQ(x) overlayed on the defined

available waveform e (x) a Figure 1. 6 Time domain insertion method of calibration 38

Figure 2. 1 The equivalent circuit per meter for the uniform 39

transmission line.

Figure 2. 2 TDR signature of the nominally uniform 4. 65 m trans- 40

mission line filled with 1. 0 molal solution of 2-Heptanone in normal heptane.

Figure 2,3 Dielectric support PTFE, r =2.38 mm, r = 4.76mm, 41

-I- w r^ 9. 97 mm, t = 3. 18 mmi.

Figure 2. 4 TDR signature of the nominally uniform 1. 55 m trans- 42

mission line filled with 1.14 molal solution of 2-Heptanone in normal Heptane.

Figure 2. 5 Modified and NBS adapters, external view. 43

Figure 2. 6 Modified commercial and NBS adapters, internal view. 44

Figure 2. 7 NBS adapter, engineering drawing. 45

Figure 2. 8 TDR signature of the connector used with the 4. 65 m 46

line filled with 1. 0-molal solution of 2-Heptanone in

n-Heptane.

Figure 2. 9 TDR signature of the connector used with the 1. 5 mm 47

or 3. 10m line filled with 1. 14-molal solution of 2-Heptanone in n-Heptane.

Figure 2. 10 Lumped circuit equivalent networks for connector/ 48

adapters.

iv
ILLUSTRATIONS -continued Page

Figure 2. 11 Interpolation determination of the static dielectric con- 49

stant parameters e and a of n-Heptane.

r Figure 2, 12 Digitized observed driving waveform ej,(t), 50

dl

Figure 2. 13 The observed insertion voltage e (t) overlayed on the 51

d^ computed insertion voltage e (t) for 7 = 5. 52 ps. d2

Figure 2. 14 (A) Squared difference between the observed insertion 52

voltage e (t) and the computed insertion voltage "S" (t).

d2 d2

(B) The observed insertion voltage e (t) overlayed on

d2

the computed insertion voltage e" ,„(t) for T = 3, 52 ps, d2

Figure 2. 15 The generator output voltage e^(x) overlayed on the 53

defined available waveform e (x). a Figure 2. 16 The squared difference of the output voltage ©^(x) 54

compared to the defined available waveform e (x) for

a

the waveforms shown in Fig, 2. 15,

Figure 3. 1 Liquid-dielectric filling system. 55

Figure 3.2 A view of the liquid-filled transmission lines installed on 56

the supporting tower.

Figure 3. 3 The tunnel-diode mount attached to the lower end of a 57

liquid-filled transmission line.

Figure 3, 4 The electrical waveform sampler attached to the upper 58

end of a liquid-filled transmission line.

Figure 3, 5 Overflow venting, 59

Figure 3. 6 Block diagram of the waveform data acquisition system.

v
ILLUSTRATIONS IN APPENDIX

Pag

Figure A-1 The input equivalent circuit for a uniform lossless trans- 7 8

mission line terminated in an impedance Z(s) and driven

by a bandlimited generator E^(s). R^^ is the transmission line characteristic impedance.

Figure A-2 The bandlimited driving voltage, e (t), 79

Figure A-3 The TDR equivalent circuit for a series inductive dis- 80

continuity sL between two uniform transmission lines of

- characteristic impedances R and R respectively.

Figure A-4 Qualitative time domain responses for the total inductive 81

load voltage. A delay line of time delay t^/2 and characteristic impedance R^^ is used to isolate in time the

observation point and the discontinuity.

Figure A-5 The input equivalent circuit for a uniform lossless trans- 82

mission line termination in an admittance Y(s) and driven

by a bandlimited generator I (s) . G is the transmission line characteristic admittance.

Figure A-6 The bandlimited driving current, i (t). 83

Figure A-7 The TDR equivalent circuit for a shunt capacitive discon- 84

tinuity sC at the junction of two uniform transmission

lines of characteristic admittances G^^^ and G^^, respectively.

Figure A-8 Qualitative time domain responses for the total capacitive 85

load voltage.

vi
LIST OF TABLES

Table Number T^age

Table 2. 1 Transmission Line Parameters 25

Table 2. 2 Connector Parameters 26

Table 2. 3 Relative 1 kHz Dielectric Constants of Polar

Solutions and Nonpolar Solvents as 23°C 27

Table 2. 4 Summary of Electrical Characteristics for

4. 65 m Reference Waveform Generator 28

vii

REFERENCE-WAVEFORM GENERATION USING DEBYE

DIELECTRIC DISPERSION

by

N. S. Nahman, R. M. Jickling and D. R. Holt

ABSTRACT

This report discusses the theory, construction, and operation of

Reference-WaveforrQ Generators using a tunnel diode transition-waveform generator driving 4. 65 meter (15 foot), 3. 10 meter (10 foot), and

1. 55 meter (5 foot) liquid-dielectric uniform lossy coaxial lines to

produce known 0. 2 volt transition waveforms across 50 ohms with

(10-90%) transition times from 205 to 560 picosecond. Each resultant

Available -Waveform is characterized in terms of its departure from

the step response of the uniform lossy coaxial line operating into a 50

ohm load. The liquid dielectric solutions are dispersive with relaxation times of the order of 4 picoseconds in which heptane is the solvent

and the ketones, butanone, heptanone and octanone are the solutes in

concentrations ranging from 0. 25- to 2-molal.

Key words: Pulse distortion in transmission lines; pulse techniques;

reference waveform generation; time domain measurements; transient

response Debye dielectric.
1. INTRODUCTION

1. 1 Definition of Reference-Waveform Generation

Reference -Waveform Generation is the production of an electrical

waveform of known mathematical form with a known source impedance. --^ A Reference -Waveform Generator may be completely characterized in

terms of its open- circuit voltage in the time domain e (t), source img

pedance (in the frequency domain) Z (s) and a time window (interval)

over which e (t) andZ (s) are valid, Fig. 1.1 [ 1] . g g

1 . 2 Definition of Available -Waveform

A Reference-Waveform Generator may be characterized by its

Available -Waveform e (t). The Available- Waveform is defined as the

a

voltage e (t) produced by the Reference-Waveform Generator across a

a

50 ohm load, Fig. 1.2. In practice the Available-Waveform is a well

defined mathematical expression.

1. 3 NBS Reference-Waveform Generator Characterization

For the NBS Reference-Waveform Generators the mathematical

form and source impedance of the generated waveform is primarily determined by the bandwidth limitation produced by a lossy uniform coaxial

transmission line. The transmission line loss is produced by filling the

line with a liquid polar dielectric which introduces Debye dispersion.

The Available -Waveform of the NBS generator is produced as the

step response of the lossy transmission line terminated in 50 ohms and

driven by a 50 ohm source, Fig. 1.3. In practice, the actual GeneratedWaveform e (t) does depart from the defined value; this departure can

o be characterized and is the fundamental error in generating the known

waveform.

Note that the objective here is to generate a waveform of defined

mathematical form; the objective is not to generate the shortest

possible transition (rise) time step-like waveform of unknown shape.

2
Each Generated-Waveform ^^(t) is produced by driAring a length

of lossy transmission line with a 50 ohm, ultra-fast tunnel-diode transition waveform generator. Connectors at each end couple the line to the

tunnel-diode generator and to the 50 ohm load, Fig. 1. 4. Imperfections

in the nominal 50 ohm terminations are considered negligible, and the

two connectors are assumed identical. Therefore, the Generated-Waveform e (t) does depart from the defined Available -Waveform e (t). The

o a departures are directly traceable to the three factors: (1) the physical

impossibility of generating a perfect step function as the driving function

e^(t), Figure 1.4, (2) the presence of non-uniform connectors (M networks Figure 1. 4) at the ends of the uniform liquid filled transmission

line, and (3) our inability to separate the driving waveform ej(t) from

that of the observed system response used to characterize the driving

waveform. The departure may be characterized by the squared error

2

A (t) between the defined Available -Waveform e (t) and the Generateda

Waveform e^lt), Fig. 1.5.

1. 4 Determination of the Available -Waveform

The Available- Waveform is calibrated by the insertion method

shown in Fig. 1. 6; the voltages and parameters are defined as follows:

e (t) The recorded sampling-os cillodl ~ scope analog output voltage when

the 50 ohm transition generator

^j^(t) is connected directly to the

5 0 ohm sampling head.

ej-(t) = The recorded sampling-os cilloscope analog output when the

lossy transmission line with the

M connectors is inserted between

3
the transition generator and the

sampling oscilloscope.

Z (s), Z (s), Z (s) = Lumped impedance parameters

^ ^ characterizing an M-connector. ''''

^ N(s) = The input port to analog-output

transfer function for a sampling

oscilloscope having a 50 ohm

input port impedance,

y(s), Z^(s), I = The propagation function, characteristic impedance, and length,

respectively, of the lossy uniform

transmission line.

In terms of the defined parameters, the frequency domain voltages

corresponding to e ..(t) and e (t) are given by

d 1 cl^i E (6)

E^l(s) = i[e^i(t)] = ^^^N (1.1)

- iy

50 Z e

= E,(s)N °

^ {[50(1 + Z^/Z^) + Z^](l + Z^/Z^) +(1 + 50/Z2)Z^}^

(1.2)

where Z , Z , Z , Z , N, and ^ are functions of s. ^ ^[E,„(s)] is o Z 3 4 d2

the initial (direct) waveform appearing at the oscilloscope output terminals and is valid for the time interval 0 <t < 3 T where

* Although a connector is a distributed network, it may be considered

as a network of lumped impedances if its transmission time is sme ll compared to the transition time of a pulse passing through it.

4
T =

I Imaginary Part of ^y(j CO)

| 3^

This assumes that the transmission time through the connectors is

negligible in comparison to T. From (1.1) we have

Ej(s)N = 2 E^j(s) (1.4)

which when put into (1.2) obtains the output voltage E.^^{s) in terms

of the observable voltage E (s) , dl

50 Z e E (s) = 2E (s) r

{[50(1 + Z/Z) + Z 1(1 + Z/Z) +(1 + 50/Z.)Z } * 3 c 3 o 4 2 o

and (1.5)

50 Z e"

e (t) = i!~ 2E (s) 2

{[50(1 + z^/z^) + z^Ki + z^/z^) +(1+ 50/Z2) zj

0 < t<3T (1.6)

Equation (1.6) provides the basis for calibrating the Generated - Waveform. The calibration procedure consists of comparing the experimentally observed generated-waveform e (t) with a computed

value "e^^TO fr om (1, 6), The quantities within (1. 6) are determined

by independent experiments; consequently, agreement between the

observed ^^g^^^ computed waveform establishes that the

transmission line/ connector voltage transfer function

E , (s) 100 Z e

^ ^, . d2 o G(s) = ^dl^^^ {[50(1 + Z^/Z^) + Z^Kl + Z^/Z^) +(1 + 50/Z2)Z^}^

(1.7)

5
is valid. It is then possible to consider the departure between the

Generated-Waveform

e (t) = S,~ [E,(s)G(s)] , 0< t< 3T

o i (1.8)

and the ob served-waveforra e ,„(t) dZ

e^^it) = =£"^[E^^(s) G(s)] , 0<t<3T (1.9)

Clearly, the departure between (1.8) and (1.9) is caused by E j( s)

being different from E (s) where E ( s) and E ( s ) are related by

dl 1 d 1

Ej(s) = N(s)

(1. 10)

that is, the oscilloscope used to observe e^{t) transforms (distorts)

e^(t) into ®^j(^). Consequently, due to the uncertainty with which e^(t)

is known, e (t) is bounded by the time domain response (1.9). Because the

o Reference-Waveform Generator is employed without the specific oscilloscope used for calibration, all of the uncertainty due to the oscilloscope,

N(s), has to be transferred to Ej(s), that is, ( 1 . 9 ) is used in place of

(1.8) in computing the uncertainty in the Available -Waveform.

It is then possible to compare the Generated-Waveform e^(t) with

the defined Available-Waveform

e (t) = Z

-1 50 Z e o (50 + Z ) o

0 < t < 3T (1. 11)

which is the step response of the lossy transmission line driven from a 50 ohm source and terminated in 50 ohms.

6
e (t) and e (t) are compared in terms of the square

o a difference between them

A^x) = [ e^(x) - e^^lx)]^

Note that e (t) is used in place of e (t) so that the uncertainty due to

dZ o the oscilloscope is transferred to the driving generator e (t). The

2 independent variable x is a relative time variable. A (x) is minimized

by superimposing the waveforms e (x) and e (x) upon each other and

a cLl, aligning the waveforms by x-translation so that (1, 12) is minimized in

some meaningful way. For example, one choice could be to minimize

the quantity,

3T

(1. 13)

T

7
2. DEVELOPMENT AND CONSTRUCTION

A uniform transmission line filled with a (lossy) polar-liquid

dielectric and physically terminated in connectors forms an integral

part of the reference waveform generator. Under the current project,

4. 65 m ( 15 ft. ), 3. 10 m ( 10 ft. ) and 1.55 m (5 ft. ) lines have been constructed consisting of rigid sections of coaxial transmission line mounted

in a vertical position to simplify filling and draining of the liquid dielectric through special coaxial connectors/adapters.

2, 1 Uniform Line Parameters

The uniform transmission line is primarily bandwidth limited by

Debye dielectric loss and to a lesser degree by planar skin effect loss.

The transmission line equivalent circuit per meter is shown in Fig. 2. 1. The impedance per meter and the admittance per meter are given by

Z(s) and Y(s), respectively, [ 1] ,

Z(s) = sL+K/s, ohms/m ( 2. 1

)

sC^

Y(s) = sC, +

1 1 + sRC , mhos/m (2. 2)

L and K are respectively the external inductance (henrys/m) and the

1/2 planar skin effect coefficient (ohms/[ m (radians/sec) ] ). C^ is the

high frequency limit capacitance,

C = lim ^ ^ ^

, farads/m. (2,3)

1 I SI _ « s

While C + C is the low frequency limit capacitance

J- w

lim

s I -»

Y(s) farads/m. (2. 4)

8
Also, the time constant RC is defined as the Debye relaxation time,

Y , that is

T = RC. (2. 5)

The parameters L, K, C and C + C can be computed from the transmission line physical dimensions and material parameters ^ , cr , a.nd

C(s) as shown in [l] . The characteristic impedance Z^(s) and the propagation function

y (s) are given by

Z (s) = o

n/ Z(s)/Y(s)

( s L + K /s )

sC.

sC, + -; — 1 1 + s T

-1

(2.6)

and

7(s) = n/ Z(s) Y(s)

(sL + K /s) sCj +

sC.

1 + S T (2.7)

The admittance/m , Y ( s), can also be expressed in the form A ^(s)

where A is a constant and € (s) the complex dielectric function (see

Section E. 4). At low frequencies | K /s | is negligible compared to

|sL 1 . Setting K /s = 0 and taking the limit of (2. 6) and (2. 7) as

js 1 _» 0 , the low frequency limits for the characteristic impedance and

the propagation function are obtained

9
and

1/2

[z^(s); =

K/s= o

lim

s U o

1 + s T C^/(C^ + C^)"

1 + S T

(2.8)

s|_> o K/s=o

y(s)j = lim s /l](C~fCpr

s _ o

1 + stC^/(C^+ )

1 + s T

1/2

= s v/l(C^ + C^) (2.9)

In the high frequency limit, (2. 6) and (2, 7) yield

Z (s) o lim

s I «

L

-1

(2. 10)

and

= s (2. 11)

10
By virtue of the limiting values (2. 8) and (2. 10), it can be seen

that as the frequency is increased, the characteristic impedance

magnitude |z (s)| increases from \/ L/(C +C ) at low frequencies to

x/L/C^ at high frequencies. Also, from (2. 9) and (2. 11) it is seen

that as the frequency is increased, the time delay decreases from

y/ 140 ^ + C^) at low frequencies to y/ LC ^ at high frequencies.

2. 2 Uniform Line Design and Parameter Characterization

Commercial 50 ohm coaxial transmission lines in 4. 65 m (15 ft. ),

3. 10 m (10 ft. ) and 1. 55 m (5 ft. ) lengths of 2. 22 cm (7/8-inch) diameter

rigid copper with EIA standard flanges have been employed. The 4. 65

meter commercial line was directly filled with the liquid for the first

design. Consequently, the resultant (filled) characteristic impedance was

approximately 33 ohms. Subsequent designs for the 3. 10 m and 1.5 m

lines replaced the original 0. 866 cm (0. 341 inch) diameter center conductor in the commercial lines with a smaller diameter conductor

(0. 476 cm, 3/16 inch). This size for the new inner conductors was

selected from easily available stock tubing such that the low-frequency

characteristic impedance of the coaxial lines is approximately 50 ohms

when filled with a 2-molal solution of heptanone in heptane (g- 3 ) . The initial transmission line system design (4. 65 m) had three

objectives:

1. A free-draining coaxial transmission line

assembly.

2. A connector assembly providing a means for

filling and emptying the transmission line as sembly.

3. Minimization of the time for the design and

development of the transmission lines/connector

11
system in deference to the design of peripheral

equipment for filling and emptying the transmission line.

The unmodified commercial transmission line satisfied the first and

third objectives. The second objective was met by a slight modification of a commercial connector to eliminate liquid- trapping (see Sectio:

2. 2 for connector design).

The uniformity of the 4. 65 m transmission line is illustrated by

the time domain reflectometer (TDR) signature of the line filled with

a 1, 0-molal solution of 2-heptanone in normal heptane, Fig. 2. 2. Inspection of the TDR signature shows that the relative reflected voltage is -0. 2 which corresponds to a characteristic impedance of 32. 5

ohms referenced to 50 ohms. Static (1 KHz) measurements of the

line capacitance for a 1. 0-molal concentration yield a low frequency

relative dielectric constant e (o) of 2. 46 resulting in a low frequency

r characteristic impedance Z (o) of 32 ohms,

= 32 ^2

Also, the presence of periodic inductive reflections are clearly shown

due to the solid dielectric (TFE, = 2. 05) pins supporting the center

conductor. These reflections correspond to periodic inductive element

each being 0. 175 nanohenrys spaced 27. 5 centimeters apart. The time

separation of the reflections is 2. 88 nanoseconds which corresponds to

the physical separation d between the dielectric pins of 27. 5 cm; that

12
2. 88 X 10

-9

X 3 X 10

10

d =

t_2

2 y e^(o)

= 27. 5 cm.

Such inductive reflections may be minimized by using a smaller inner

conductor and then choosing the solution concentration so that the resultant low frequency liquid dielectric constant €(o) matches that of the

solid dielectric pins (c =2. 05). However, such an approach fixes the

r dielectric loss per unit length and requires that the overall dielectric

loss must be adjusted solely by the choice of the total length. Alternately, the inductive reflections can be minimized by using thin dielectric supports of small cross - sectional area.

The 1. 55 m and 3. 10 m transmission lines have identical crosssectional dimensions and dielectric supports. The inner conductor

diameter is 0. 476 cm (3/16 inch) which yields a characteristic impedance of 50 ohms when the relative dielectric constant is 2. 95. Using

a 1. 14 molal solution of 2-heptanone in heptane, results in a relative

dielectric constant of 2. 54 and a characteristic impedance of 53. 8 ohms.

The dielectric supports are thin (1. 59 mm, 1/16 inch) triangular shaped

TFE wafers, Fig. 2. 3. The uniformity of the resultant transmission

line is illustrated by the TDR signature of the line filled with a 1. 14

molal solution of 2-heptanone in normal heptane. Fig. 2. 4. Inspection

of the TDR signature shows that the relative reflected voltage is 0. 0385

which corresponds to a characteristic impedance of 53. 9 ohms. The

inductive reflections due to the dielectric supports are negligible.

The transmission line physical dimensions and equivalent circuit

parameters are summarized in Table 2, 1. The capacitance values are

given for air ( ^ =1) and for a 1. 0-molal solution of 2-heptanone in

normal heptane. The skin-effect metal loss coefficients are given for

the brass and copper conductors (1. 55 and 3. 10 meter lines) and for the

13
copper conductors (4.65 meter line),

2. 3 Coaxial Connector/Adapter Design and Parameters

For a vertically positioned transmission line physically terminated

in an unmodified commercial adapter (Female Type N to 7/8-incli rigid 50

ohm line), the lower adapter will trap a six millimeter column of liquid wh

the upper one approximately the same amount of air. The lower trapped

polar-liquids would contaminate subsequent solutions; the upper void

would present an undesirable transmission line section with a characteristic impedance higher than that of the liquid-filled section. Therefore,

special adapters from Type N (female) to 7/8-inch rigid line have been

designed and constructed for the 1. 55 m, 3. 10 m, and 4. 65 m transmission lines to allow complete filling and draining of the liquids.

The adapter for the 4. 65 m line consisted of a commercial adapter that had been mechanically modified to provide complete drainage

and venting of the transmission line. No modifications were made to

optimize the pulse response of the connector when filled with liquid.

A commercial adapter with a modified drainage path is shown on the

left in Fig, 2. 5 and again with the internal structure of this adapter

visible, in Fig. 2, 6A (note the two O-ring seals for inner and outer

conductors). A brass cube, silver- solde red adjacent to the Type N

female end, has been drilled for drainage and tapped to accept 1/8-

inch male pipe thread. The original vent for pressurizing the line now

sealed is shown in both photographs.

The adapters for the 1. 55 m and 3. 10 m transmission lines, in

addition to adequate drainage properties, are designed to confine the

liquids to the uniform line section only, thus improving the pulse re- sponse of the transition at either end between the 50-ohm external line

sections and the liquid-filled section. One of these adapters is shown

on the right in Fig. 2. 5 with the drainage vent plugged for shipment.

14
The adapter has been constructed frora a modified Type N (female)

threaded panel connector (UG-680/U), and a brass flange meeting EIA

standards except for thickness. The surface of this adapter facing the

polar-liquids in operation can be seen in Fig. 2, 6B. The drain plug

has been removed in this view. The two original flats on the Type N

connector designed for a 9/16-inch wrench now serve as the beginning

of the drain and fill apertures. An internal connection to the drain is

not visible. Fig. 2. 7 is an engineering drawing of the adapter.

The TDR signatures for the new connectors attached to their

respective liquid-filled transmission lines are shown in Figs. 2. 8 and

2. 9. The 4. 5 m line contains a 1. 0-molal solution of 2-heptanone in

heptane while the 1. 55 m or 3. 10 m line contains a 1. 14 molal solution.

The TDR* signatures can be characterized in terms of lumped inductive and capacitive elements, Figs. A-3 and A-7, by applying the following

equations:

^^01 ^ ^02^ m

2 R

01

m

(2. 12)

C = R

01

^01% 2

^Gl "^^02

m

m

(2. 13)

Equations (2, 12) and (2. 13) provide a means for estimating the

inductance or capacitance of a discontinuity at the junction of two transmission lines of different characteristic impedances, R^, and R^

01 02

being the characteristic impedances for the input and output transmission

lines, respectively, e is the peak value of the reflected voltage m ° measured from the steady state level of the reflected voltage e (<»). r

* See Appendix A. 1 for a complete description of time domain reflectometry (TDR) and definitions of the various parameters used in this TDR

discussion.

15
When e is greater than e (oo) , the discontinuity is inductive and m r

(2, 12) is used; for e < e , capacitance is present and (2. 13) is used. m r m is the slope of the incident voltage finite- ramp, e.(t). These eqs.

result from the application of the bandwidth limiting conditions,

and

(Rq^ +R^^)>> 1sL| (2.14)

(Gqj +Gq2)>> |sC| (2. 15)

respectively, to the general solution for the transmission line voltage in

the presence of an L or C discontinuity. The incident voltage is a finite

ramp of the form

f mt , 0 ^ t ^ T

In practice, m is the maximum rate of voltage change in the first

transition region of the incident transition function,

de. (t)

dt

= m, volts/sec, (2.17)

max

When ~ "^q 2

' "^^^ reduce to the usual TDR equations

for a transmission line of characteristic impedance R^ with a given L

or C discontinuity [ 2, 3] ,

2 R_ e

• L = ^—^

(2.18) m

and -2 e C = -^—2^ (2. 19)

. ..

.. Rq m

16
When there are two successive discontinuities, the TDR signature

in the S domain will be of the form

E (s)

E(s) = -V-

? = T 9 -2s(T +T ) 1 + e 1 + (1- ) e + . . .

(2.20)

where p , p , T , and T denote the first- discontinuity reflection

coefficient, the second- discontinuity reflection coefficient, the propagation time between the TDR reference plane and the first discontinuity,

and the propagation time between the first and second discontinuities,

respectively. Consequently, it is seen that the contribution from the

second discontinuity is weighted by the factor

W = (1 - p^) . (2. 21)

Inspection of the TDR signature for the 4. 65 m line connector,

Fig. 2,8, shows that three discontinuities are present; e ^ e and mO, ml

e _ correspond successively to a capacitive and two inductive discon- m2 J r

tinuities, respectively. The capacitive discontinuity is located at the

junction of a 50 ohm and a 32. 5 ohm transmission line; therefore (2. 13)

is used to compute C from the peak reflected voltage e mO

The subsequent discontinuities are seen through the first one

2 with the weighting factor of 1 ~ p^ • The first reflection coefficient is

bandlimited such that (G + G ) >> |sc |

; hence p is approximately,

1 33+50

17
which gives a weighting function of

I - pI

= 0.96.

Accordingly, the peak voltage values e , and e ^ produced in the

ral m2

32. 5 ohm line should be multiplied by 1/0. ^6 to remove the weighting

due to the first discontinuity. Similarly, there is a weighting by the

second discontinuity of the reflected voltage from the third discontinuity;

however, since the duration of the reflected voltage from the second

discontinuity is much shorter than that of the third, the weighting factor

of the second discontinuity is negligible. Because the inductive discontinuities generating e . and e ^ are located in the uniform trans- mi m2

mission line of = 32. 5 ohms, in principle, (2. 18) should be used

with R- = 32. 5 and the peak voltages modified to e ,/0. 96 and

0 ml

e^2/0-96. However, (2. 12) will give the same result. This can be

demonstrated by dividing e^ in (2. 18) and (2. 19) by the bandlimited

form of (2. 21 ); the results will be (2. 12) and (2. 13) , respectively.

The reason why these results are the same is that e in both (2. 12) m

and (2. 13) is referred to the steady state value of the reflected voltage.

Applying (2. 12) and (2. 13) to the TDR signatures shown in

Figs. 2. 8 and 2.9, yields the discontinuity capacitances and inductances

for the two connectors. Fig. 1.6; these values are given in Table 2. 2.

To construct equivalent networks for the connectors requires the

specification of the position of each discontinuity. This is done by considering the time delay between each reflection and putting a corresponding lossless transmission line length between each successive discontinuity element. However, when the discontinuities are very close to

each other in the sense that the propagation time between them is very

small compared to the over all system transition time, the transmission

line elements may be deleted for a first approximation. This yields a

18
lumped circuit approximation for the connector network. Fig. 2. 10

shows the lumped circuit equivalent networks for the 1. 55 m and 3. 10 m,

and 4. 65 m lines; the elements are denoted by the 77 -network parameters (Fig. 1.6) Z^, Z^, Z^ in Table 2. 2.

2. 4 Liquid Dielectric Preparation and Parameter Measurements

The mathematical form and source impedance of the generated

waveform is mainly determined by the bandwidth limiting properties of

the losses produced in the liquid polar dielectric which fills the dielectric space of the uniform coaxial transmission line.

Three different ketones were used as solutes with heptane as the

solvent. The ketones were 2-butanone, 2-heptanone, and 2-octanone.

Preparation and maintenance of these solutions require some care as

all four organic liquids are quite volatile and are excellent solvents.

To minimize evaporation errors, the molal solutions of 0. 25, 0. 50,

1. 0, and 2. 0 m 2-butanone, 2-heptanone, and 2-octanone were prepared directly into their containers on a laboratory single-pan balance,

first weighing out the required fractional gram-molecular-weight of

the ketone and adding a kilogram of heptane.

The first solutions prepared were stored in polyethylene containers which proved to be an unfortunate choice for the storage containers. Serious changes in the 1 kHz dielectric constants of the solutions were measured in the weeks following preparation. The changes

were apparently caused by a differential diffusion of solvents and solutes

through the polyethylene containers in which the newly prepared solutions were stored. Glass containers were not used and were ruled

out because of the safety hazard involved in breakage with flammable

liquids being present. By changing to metal storage containers the

evaporation induced changes in the dielectric constants of the stored

liquids were eliminated.

19
The static dielectric constant values were determined by 1 kHz

measurements. Since the Debye relaxation times of each resultant

solution is about 5 picoseconds, then at 1 kHz the relative dielectric

constant will be essentially equal to the static value.

Using a precision transformer ratio-arm bridge at 1 kHz, the

open-circuit capacitance of the 15-foot transmission line was measured

when filled sequentially with air, heptane, polar solutions, and benzene.

The relative static dielectric constants, e (o) , of the polar solutions

r listed in Table 2. 3 were computed from these measurements using

the dielectric constant of heptane as a standard reference, with benzene serving as a secondary reference. A schedule of rinsing the

transmission line with heptane and drying with forced air and dry nitrogen between different solutions was employed. The rinse and dry

schedule is necessary to prevent contamination of the heptane and benzene reference standards of capacitance as was noted by the continual

increase in dielectric constant of the heptane rinse solution.

Verification of the handbook [ 4 ] value for the dielectric constant of heptane was performed in two stages. First, an interpolation of c and its temperature coefficient Oi for each of five other

r alkanes (pentane, hexane, octane, nonane, and decane) gave a value

for C and OL for heptane. This interpolation was necessary because

of the unfortunate omission of heptane from the table of the dielectric

constants and their temperature coefficients of organic liquids in this

handbook [ 5 ]

. The temperature coefficient of f for heptane was of

r primary interest since the reference waveform generator is normally

used at a temperature other than 20*^0 for which the tables are given.

For a liquid dielectric consisting of non-polar molecules, the dielectric

constant decreases with an increase in temperature because of the decrease in the number of molecules per unit volume. Figure 2. 11 shows

20
the interpolated values of € and a for heptane; at 23 C, ^ = 1.919

-2 ^

^ and OL = -0. 148x10 . A negative temperature coefficient for the

polar solutions also was noted experimentally which is consistent with

the 1/T temperature dependence of the molecular polarization in the

Debye model for weak polar solutions [ 6] . Second, the above values were verified by using benzene as a

dielectric standard because e and a are well established ( C =2.278

-2

^ @ 23°C and a = 0. 2 x 10~ [ 4 ] ) . The verification was accomplished

by filling the line with benzene and measuring the resultant capacitance.

This capacitance value was compared with that obtained with heptane

and verified the values of € and a for heptane within 0. 3 percent.

r Direct measurements of ^ for heptane, benzene and the polar

r solutions were attempted on a precision 1 kHz bridge using a short section of air-spaced coaxial transmission line as a test

cell. The desired precision in these measurements was not achieved

because of evaporation problems with the small amounts of liquids

involved and the difficulty encountered in keeping the test cell connectors uncontaminated by the polar solutions.

In Section 2. 1 it was pointed out that the admittance/m Y(s) can

also be expressed in the form Ac (s) . Consequently, (2. 2) through

(2. 4) can be written as

Y(s) = Ae^c^(s) (2.22)

^1 = ^^o'r<"^ ^^-^^^

C, = Ac e (o) (2.24)

I c or

and ,

. , . e (o) - € (oo

) Y(s) = AC r r

e (a) ^— —

r^ ' 1 + s r (2.25)

where is the dielectric permittivity of free space, farads/meter.

21
Comparing (2. 22) with (2.25) yields the frequency dependent relative

dielectric function,

e (s) = € (co) +

r r

c (o) - c («)

r r (2.26)

1 + s T

For a given solution and solvent the 1 kHz capacitance measurements

provide the data for calculating c (o) and c (oo); the former is the

r r static relative dielectric constant of the binary solution while the latter

is that of the solvent.

The reason why the high frequency limit for the solution's relative

dielectric function (2. 26) is given by the solvent's static relative dielectric constant is that the induced molecular dipole orientation of the polar

solute molecules can not follow a high frequency electric field for frequencies much greater than 1/t . The major contribution from the solute

molecules to the dielectric polarization at high frequencies is their

electronic polarization. Accordingly, the relative dielectric constant of

the solute at very high frequency is about the same as that for the solvent

as the solvent polarization is totally electronic. Consequently, the

high frequency limit for the dilute solution dielectric polarization is

electronic and is essentially equal to that of the solvent. Because the

solvent molecules are non-polar, the solvent polarization is solely

electronic and frequency independent. Therefore, measurements at

1 kHz establish the value of the solvent's relative dielectric constant

which in turn is equal to the high frequency limit of (2. 26 ) , €

( co) . r The one remaining parameter to be determined is the Debye re- laxation time 7 . It is established by a computer program iteration

using (1. 6) which matches the predicted response with the observed

experimental response. Here, the overall system predicted response is

compared to the observed experimental response, Figs. (2. 13) and (2. 14);:

22
The value of r is selected which causes the predicted response to fit the

experimental data when the Debye relaxation model is valid, the value of

7* which establishes the fit to the experimental data is in fact the Debye

relaxation time, Fig. 2. 14.

2. 5 Available -Waveform Computation/Evaluation

The computation of the Available -Waveform and its inherent

squared- error is based upon the following assumptions:

1) The planar skin effect model accurately represents the

conductor surface impedance.

2) The Debye model accurately represents the dielectric

function c( s).

3) The high frequency limiting value of the relative dielectric function ^

(oo) equals 1.92, the static value for

r heptane.

4) The connector equivalent circuit is valid for the system

transition- times under consideration.

These assumptions if not valid can always be removed by using more

accurate models based upon experimental data. Consequently, they

offer no fundamental limitations to the methods used here. The procedure for computing the Available-Waveform and its inherent squarederror consists of the following steps:

1) Acquire and digitize the experimentally observed driving

function e,,{t), (1. 1) Fig. 2. 12.

di

2) For the given transmission line and connectors, acquire

and digitize the experimentally observed output voltage

e (t), (1.6) Fig. 2.13, dashed curve.

23
3) Using the numerical values for e^Jt), the applicable set of

transmission line and connector parameters (Tables 2. 1 and

2. 2), and estimated values of j in equation (1. 6), iteratively

determine 7 by repeatedly computing e ( t) until the computed

value of e ( t) over-lays the observed value e,-(t). The solid

, d2 d2

curve in Fig. 2. 13 is e^^l computed for T = 5. 52 picoseconds,

Fig. 2. 14 shows the resultant overlay of e~".(t) and e„(t), d2 d2

and the squared difference between the two curves, A^(t).

When 7 is finally determined, all the parameters of y(s) and

Z (s) are determined,

o

4) Compute the Available-V aveform e (t) , (1.11) and compare

it to ^Q^^) accordance with the instructions following (1. 12).

e (x) is the solid curve while e (x) is the dashed curve in

Fig. 2. 15.

2

5) Compute the squared- difference A {^) between e (x) and

3. eQ(x) , (1. 12).

In sumxaary, the above procedure is illustrated for the 4. 65 meter line

in Figs. 2. 12 through 2. 16. The data illustrated in Figs. 2. 15 and

2. 16 are the calibration data for the 4. 65 meter Reference-Waveform

Generator and are tabulated in Appendix A, 2. Table 2. 4 summarizes

the electrical characteristics of the 4. 65 m Reference Waveform

Generator.

24
TABLE 2. 1 TRANSMISSION LINE PARAMETERS

Pa. Ta.Tn pi'p t

Transmission Line

1. 55 m 3. 10 m 4. 65 m

i, Length of uniform section, m 1. 526 3. 050 4. 660

r , Outer conductor radius, cm 0. 997 0. 997 0. 997

r^^. Inner conductor radius, cm 0. 238 0.238 0. 433

L , External inductance, nH/m 286 286 166, 8

C , Capacitance, air- filled, pF/m

o

38. 43 38. 31 66. 32

C^, Capacitance, high frequencylimit (heptane), pF/m

73. 73 73. 51 127. 26

Cj + C2,Low frequency limit (1

molal solution) , pF/m

of 2-Heptanone in Heptane

94. 73 94. 44 163. 50

K, Skin effect coefficient, |ifi/m

( radians / sec)^/^

17. 5 17. 5 7. 86

Capacitance, benzene -filled, pF/m 87. 50 87. 22 151. 01

25
TABLE 2. 2

CONNECTOR PARAMETERS

Line Length and Solution Concentration

Network

1. 55 m 3. 10 m. 4, 6 5 m

Impedances (1 14 Molal) (1.14 Molal) ( 1 0 Molal)

00 00 0. 06 pF

h

0. 48 nH 0. 48 nH 0. 57 nH

0. 41 pF 0. 41 pF 00

26
TABLE 2. 3

RELATIVE 1 kHZ DIELECTRIC CONSTANTS OF POLAR

SOLUTIONS AND NONPOLAR SOLVENTS AT 23°C

Solution Concentration e (o)

r

2-butanone/heptane 0. 25 m 2. 04

0. 50 2.15

1.00 2.39

2. 00 2.92

2-heptanone/heptane 0. 25 2. 06

0.50 2.19

1.00 2.46

2.00 2.98

2 -octanone /heptane 0, 25 2. 06

0. 50 2. 19

1.00 2.46

2. 00 2.96

Heptane 1.92

Benzene 2. 28

27
TABLE 2. 4

SUMMARY OF ELECTRICAL CHARACTERISTICS FOR 4. 65 M

REFERENCE WAVEFORM GENERATOR

Polar dielectric 1, 0 molal concentration of 2-Heptanone in Heptane € (o) = 2. 46 , r

f (oo) = 1. 92 , T = 3. 52 ps.

r

Low frequency characteristic

impedance 32.5 ohms

Time window of evaluation 4 ns

10% -90% Transition times

Defined available waveform, ta 381 psec.

Generator output voltage, to 380. 2 psec.

Transition time difference %,

t - t ° ^ X 100 , t

- 0. 29%

a

Waveform uncertainty in a 4 ns

time window, peak value of the

squared difference 5. 76 X lO"'*

28
3. OPERATING SYSTEM

An operational Reference Waveform Generating System consists of two subsystems: (1) the electrical network for the waveform

generation and (2) a waveform data acquisition system for calibration

and evaluation of the generated waveform. The former subsystem is

the subject of this report while the latter one is reported elsewhere

[7 J. In this chapter the overall physical structure of the electrical

network will be presented along with a brief description of the waveform data acquisition subsystem.

3. 1 Electrical Network Physical Structure

For operating convenience, the transmission-line sections of

the waveform generators have been mounted vertically on a 24- foot

(antenna) tower, their lower ends accessible for pressure -filling with

the polar-liquid on one floor, their upper ends adjacent to the data

acquisition equipment on the second level. The arrangement for

filling the transmission lines with the polar solutions is diagramed

in Fig. 3. 1. A photograph of the tower from near the lower-floor

level. Fig. 3. 2 , shows the 15-foot line just visible on the right. Fig.

3. 3 shows a tunnel-diode pulse generator attached to the lower end

of the transmission line; Fig. 3. 4 shows a sampler for data acquisition

attached to the upper end. Of course, the pulse generator and sampler

may be interchanged, the transmission-line section is symmetrical.

A polar-liquid dielectric is placed within an adjacent steel paint

tank, the tank is then pressurized with dry nitrogen gas at 5 to 10 psi

forcing the polar liquid through the connecting tubing, special adapter,

uniform line- section, into the overflow bottle. The pressurizing

system (three tanks) can be seen in Fig. 3. 3. The overflow bottle

29
when approximately half- full, closes a micro switch indicating to the

operator at the lower end by a panel light and buzzer that the transmission-line section is completely filled and the generator is ready

for operation. The overflow bottle and micro switch are shown in

Fig. 3.4.

Exterior venting of the heptane- and ketone-laden fumes during

the drying procedure described in Section 2. 3 is necessary for safety.

The 3/4-inch copper pipe visible just inside the left tower leg in Fig,

3. 5 ventilates both the 15 -foot transmission line through its plastic

overflow bottle and the paint tanks at the base of the tower through

their common manifold. The venting manifold valves for the tanks

can be seen in Fig. 3. 2. The 5- and 10-foot generators can easily

be filled visually without an electrical overflow -indicator; outside

venting, however, is necessary.

3. 2 "Waveform Data Acquisition System

The data acquisition system is simply a sampling oscilloscope

interfaced to a data storage system, A block diagram of the present

operational system is shown in Fig, 3. 6, [7] . This particular system

can acquire and store 1000 sampled data values. The stored waveform

is displayed on a CRT display unit; the data can be read out for processing on a time share computer or a general scientific computer.

30
4. SUMMARY

The work reported here has for the most part answered the

question as to how to utilize the step response of a band-limited network as a reference waveform.

Because perfect step generators and non-bandlimited connectors

and oscilloscopes are not physically realizable, a priori knowledge of

the shape of the reference waveform will be uncertain within definable

limits over the waveform time window.

Accordingly, the defined reference waveform is given as the

step response of a characterizable bandlimited network; its mathematical form and time domain response are known. The generated

reference waveform (output waveform across the specified load)

departs from the defined waveform. This departure is characterized

by a squared- difference curve.

In this report, the reference-waveform generator was charac2

terized in terms of the two quantities e (t) and ^{t) over the time

3. window, e (t) is the defined available waveform based upon the step

response of a Debye Dielectric bandlimited transmission line operating into a 50 ohm load and being driven by a perfect step generator

2

of 50 ohm impedance, ^(t) is the departure between the generated

waveform and the defined available waveform including the uncertainty

due to oscillographic measurements.

31
REFERENCES

[ 1] McCaa, Jr. , W. D. , and N. S. Nahman, Generation of reference

waveforms by uniform lossy transmission lines, IEEE Trans.

Instrum. Meas. , IM-19, No. 4, 382-390 (Nov. 1970 ).

[ 2] Strickland, J. A, , Time-Domain Reflectometry Measurements,

1st Ed. Tektronix, Inc., Beaverton, Ore., (1970).

[3] Time Domain Reflectometry, Application Note No. 62, HewlettPackard Co. , Palo Alto, Calif., (1964).

[4] American Institute of Physics Handbook, 2nd Ed. McGraw-Hill

Co., Inc., New York, N. Y. , (1963).

[5] Handbook of Chemistry and Physics, 53rd Ed. , The Chemical

Rubber Co. , Cleveland, Ohio, (1972).

[6] Debye, P., Polar Molecules, Dover Publications, New York,

N. Y. , (1929)

[7] Gans, W. L. , Block diagrams, schematic circuit diagrams, and

operating instructions for the time domain measurement system.

(To be published. )

32
gure 1, 1 Reference waveform parameters.

33
Figure 1. 2 The available waveform e (t) across a 50 ohm load.

34
Figure 1. 3 The defining network for the available waveform e^(t).

35
50

TIME

I

Figure 1.4 The generated waveform e_(t).

36
0. 5-

(Uu O1—

1

(U

>s

• I-l Q

X)

(U

X , 200 ps/division

Figure 1. 5A Squared difference of the output voltage ^^(x)

compared to the defined available waveform e (x), a

1.0

o>

<0

SI

•r-( r—

I

S

uo

0. 5

e (x)

a

e (x) . . . o

X , 200 ps/divi sion

Figure 1. 5B The output voltage e^(x) overlayed on the defined

available waveform e (x). a

37
50

AAAr

e. (t) 0 50 a

50 Z3(S)

e.lt) 0 Z2ls)< Z^(s)

V V y

M

Figure 1. 6 Time domain insertion method of calibration.

38
Z(s)

rrr\

sL

sC. ^Y(s)

J

sC,

Figure 2. 1 The equivalent circuit per meter for the uniform

transmission line.

39
Aelt) = 0.

1.15x2.5 = 2.88 ns

02 V

/) = -0.2, 32.5 /D = 0, 50n

J II T I I I I I I 11 J I I I 1^

(t) TIME, 2.5ns/DlVISI0N

TDR signature of the nominally uniform 4. 65 m transmission line filled with 1. 0 molal solution of 2-Heptanone in

normal heptane.

40
Figure 2.3 Dielectric support PTFE; r^ = 2. 38 m, r^ = 4.76 mm,

r^ = 9. 97 mm, t = 3. 18 mm.

41
e(t)

CO

o

> 1.0

o

UJN

o

/) = 0,50ii /) = 0.0385, 53.911

J L J L J L J L

(t)

TIME, 1.0 ns/DlVISION

Figure 2. 4 TDR signature of the nominally uniform 1. 55 m transmission

line filled with 1. 14 molal solution of 2-Heptanone in normal

Heptane.

42
Figure 2. 5 Modified and NBS adapters, external view.

43
44
45
Figure 2. 8 TDR signature of the connector used with the 4. 65 m line

filled with 1. 0-molal solution of 2-Heptanone in n-Heptane.

46
Figure 2. 9 TDR signature of the connector used with the 1. 55 m or 3. 10 m

line filled with 1. 14-molal solution of 2-Heptanone in n-Heptane.

47
r

0.16 nH

rrrx

0.41 nH

rrr\

±l0.06pF

0.48 nH

rrr\

0.2pF=Z =:0.2lpF

Figure 2, 10 Lumped circuit equivalent networks for connector/adapters.

48
49
1. 0

CO

-)-> rHO

>

<D

•i-i 1—4

B 0. 5 uo

-» I I » T »— t —1 1 » » 1 f > » »

t , 200 ps/division

Figure 2. 12 Digitized observed driving waveform ^^j^^^)-

50
t , 200 ps/division

Figure 2. 13 The observed insertion voltage ^^^(t) overlayed on

computed insertion voltage e (t) for T = 5. 52 ps.

51
o

u

<0

0. 5

Q

^

CO

0

Figure 2. 14A

t , 200 ps/division

Squared difference between the observed insertion voltage

ej_(t) and the computed insertion voltage e^,_(t), dc dZ

o>

0)

1.0

03 0.5-'

S

u

oZ

T = 3,52 ps,

t , 200 ps/division

Figure 2. 14B The observed insertion voltage ^^^2^^^ overlayed on the

computed insertion voltage e" (t) for T = 3. 52 ps.

CI w

52
Figure 2. 15 The generator output voltage e^(x) overlayed

on the defined available waveform e (x).

53
1.0 T

0)

(J (M

CJ O

(U .-H

is in S >^ 0.5-

Figure 2. 16 The squared difference of the output voltage e^(x)

compared to the defined available waveform e (x) a

for the waveforms shown in figure 2. 15.

54
Resistive Termination

Overflow

Bottle

Nitrogen Gas

To Data

Acquisition

Equipment

Oscilloscope

Sampler

Uniform

Transmission Line

Modified Adapter

Tunnel Diode

Pulse Generator

Tunnel Diode Bias

and Triggering

Polar Liquid

Figure 3. 1 Liquid-dieiectr ic fiiimg system,

55
Figure 3. 2 A view of the liquid-filled transmission lines installed on

the supporting tower.

56
r

' Figure 3. 3 The tunnel-diode mount attached to the lower end of a

liquid-filled transmission line.

57
58
59
RE ut: <;

1—

1

H

CO

1—I >- I— llj ct: uj q: o >— z: o s:

C3 O UJ <: 2: rr_ 1

a:LU

I—

<: en \ LU Q >

O

I—I O

Q CD CO T

I—

(—1 Q 1—

1

Q

CO

\ LUo

>-

_j Q q:

CO LU LU <C >- CD

H-. =a; o

d; _i I—

I

ct LU > Q I—

03

I—

I

_i

CQ

CI. X LU

oo

00

Q-0

^1—

1

SC

_J 0

Q_ _I

_J

< 1—

1

00

osc

QO

LU >- LU Q _J Q 0 Ou 0 1—< Q. I—

1

Q ZD Q

00

_l _l

LU 00 LU Z <=C »—

1

ID CQ ID(—

5:q;0 on

u_ 0

LU 1— >

< cr: 3 LU

• LU

U. CD

LU

•a; CO

C3

C3

3 on o o

00

00

O

>—' Q

—I <

Q_ LU

s: in <c

oo

o

I—

CQ>>

COO

cro

a

o

>

03

o

r—

I

CO

0)

60
APPENDIX A -1

TIME DOMAIN REFLECTOMETRY

1 . Fundamental Equations

Consider the circuit shown in Fig. A-1, Here, E (s) and

"^01 ^^P^^^^^t ^ lossless transmission line of characteristic impedance R^j^ being driven by a bandlimited generator K^{s) and

terminated in an impedance Z(s). The TDR signature is the voltage

E(s). The fxindamental TDR equations are

E(s) = E (s) - I(s) Rq^ (A-1. 1)

E(s) = E.(s) + E^(s) (A-1. 2)

where E (s) and E (s) are the incident and reflected components of

i r E(s). Equating (A- 1. 1 ) to (A- 1 . 2) obtains

E (s) = E (s) - E (s) - I(s) R (A-1. 3)

r 2 1 ^ ^

Since the incident voltage E^(s) is the voltage when Z(s) = R^^ , i. e,, E^(s) = 0 , then ^

E.(s) = —5 (A-1. 4)

1 2

which when put into (A-1. 3) to eliminate E (s) obtains

E (s) = E.(s) - I(s) R . (A-1. 5) r 1 01

61
The inverse Laplace transformation of (A-1. 5) yields the time domain

reflected voltage e (t) r

e^(t) = e.(t) - i(t) (A-1. 6)

Similarly, the total time domain voltage of the TDR signature follows

from (A-1. 1). _

(A-1. 7)

(A-1. 6) is useful for interpreting the reflected voltage while (A-1. 7)

establishes the absolute levels of the TDR signature. The nature

of Z(s) determines the properties of i(t) under the excitation of

2. The excitation e (t)

For the cases analyzed here, e (t) will be assumed to be a finite

ramp voltage as shown in Fig. A-2 , that is

at, 0 ^ t ^ T

aT , T ^ t ^co

(A-1. 8)

62
3. The current for an Inductive Z(s)

Consider Fig. A- 3 which shows the TDR equivalent circuit fo a series inductive discontinuity sL between two uniform lossless

transmission lines of characteristic impedances R and ^^.^ , respectively. The current I(s) is given by

E (s)

I{s) = i (A-1

where

^OT " ^01 "^^02

Now

e (t) = at u(t) - a(t-T) u(t-T) (A-1

g

where u(t) is the -unit step function. The Laplace transform of

(A-1. 10) E (s) is given by

g

£ e (t) = E (s) = -f- - e"^"^-—; (A-1.

§ ^ s^ s

therefore,

63
I(s) = Ij(s)

^2 (R,^+SL) — e sT a

s (R^^+sL)

(A-1. 12)

In the time domain we have

y + j

1 f st^

(s) d s 7 -J

St

Residues of

2

S (s+Sq)

where s = R.^/L. Continuing

o OT

a

L \ ds (s

St -| J +

r St e

s

s = 0

3 = S^-"

at a L

R

OT R

OT

1 - e ) u (t) (A-1. 13)

Since

ys) = e"^"^ I^(s)

64
^2^^^ is equal to - i ^^(t) delayed T seconds in time and multiplied

by the delayed unit step function u(t-T). Consequently, we have

0 ^t^ T .

(A-1. 14)

and

i(t) =

R

OT

a t a L

R

OT R

OT

R

R

OT

a L

2 R

OT

(t-T)

OT

T ^00 (A-1. 15)

From (A-1. 14) or (A-1. 15) for t = T, we obtain

i(T) = (A-1. 16)

Upon combining terms and rearranging (A-1. 15) can be written in terms

of (A-1. 16) ,

R

OT

i(t)J = T ^ t ^ 00

a T

R

OT

i(T) - aT

St

(t-T)

(A-1. 17)

65
4. The Reflected Voltage for an Inductive Z(s)

The reflected voltage is given by putting (A-1, 14) and (A-1, 17)

into (A-1. 6) :

e^(t)

0 ^ t ^ T

at / ^02 "-^01 \

a L R

+

01

R

OT (

R

1 - e

OT

L

>

(A-1. 18)

e^(t)

T < t

a T

2 (^) -

(

i(T) -

a_T

R'-)

OT/

R

OT,(t-T)

(A-1. 19)

Fig. A -4 qualitatively illustrates (A-1. 18) and (A-1. 19).

The reflected voltage can be normalized relative to the incident

voltage steady state level, ,

E

a T

(A-1. 20)

Consequently,

2 E. a = (A-1. 21)

Upon replacing "a" by ( A- 1 . 2 1 ) in ( A- 1 . 1 8) and ( A - 1 . 19 ) and then

writing e (t)/E^ as R (t) obtains

r 0

66
R(t)

0 ^ t ^ T

^OT

^ t ^ T

(A-1, 22)

R

R(t)

T < t <

OT

R

01 R

OT J

(t-T)

(A-1. 23)

For t -» 03 , R(oo ) approaches the dc value of the reflection

coefficient p (0).

R(oo) = p(0) = ^02 ~ ^01

^02 + ^01

(A-1. 24)

Recall that R(t), ( A- 1 . 22) and ( A- 1 . 23 ), is the reflected voltage

normalized to the steady state value of the incident voltage e.(oo) = This normalized reflected voltage R(t) is not equal to the impulse

response of the reflection coefficient. Since,

-1

it is clear that

p(t) = Z p(s)

p(t) + R(t)

-1 Z(s) - R

01

Z(s) + R

01

(A-1. 25)

except in the limit as t approaches infinity.

Therefore, the designation of the scale for R(t) in terms of resistive

reflection p units should not be interpreted to mean that R(t) = P(t).

The basis for using resistive reflection p-units stems from (A-1. 24)

which is a dc relationship.

67
5. The Calculation of L from e (t)

Consideration of (A-1, 18) and (A-1. 19) leads to the conclusion

that L can be determined from e^(t) in either of two ways:

(a) By measuring the peak value of e (t) which

r occurs for t = T and computing L from

(A-1. 18) with t = T.

(b) By measuring the time required for an e

^ magnitude change in the exponential trailing edge

waveform of (A-1. 19) and computing L from

the exponential time constant r = L/R^^ .

For small reflections, i. e. , small values of L and subsequent small

peak values of e (t) , the reflected voltage peak value is more visually

r discernable in wide-band sampling system noise than is the exponential

decay. Consequently, for visual measurements the method of (a) is

more effective. On the other hand, for systems in which signal

processing methods are applied to the sampled-data analog signal, the

method of (b) tould be more appropriate.

We now turn our attention to the determination of L from peak

reflected voltage measurements as described in (a). Consider Fig. A-4

which shows the total voltage e(t) = e^(t) + e^(t). Since the zero

level of the reflected voltage e (t) is the steady state value of the

r incident voltage, measurement of the difference between the peak value

of the total voltage waveform and the steady state value of the incident

waveform yields the peak value of the reflected voltage. Such a measurement is easily accomplished with a sampling oscilloscope by

offsetting the steady state incident voltage level to the display zero

68
level and using the high gain of the sampled-data amplifiers to enlarge

the reflected waveform. The maximum reflected voltage occurs for

t = T/'' From (A-l. 18) we have

R

e^(T) = a T / ^02-^01 \ ^01 /

a L R.

OT

T

)

(A-l. 26)

For small reflections, that is, for small values of L, the network

bandwidth limitations would be such that R >> jsL |

; consequently.

R

the exponent

OT

T would be very large, and exp

r R

OT

T would

be essentially zero. Under such conditions, e (T) is given by

r

e (T) =

r

aL R

01

^OT

r R

Here e (T) denotes e (T) when exp

OT

L

T

(A-l. 27)

is essentially zero. Upon solving for the inductance L we obtain

When Rq2 = Rq^ , Rq^ = 2 R^^ , and (A-l. 28) becomes

4^01 -

L = e (T) (A-l. 29)

a r

If one considered eq. A-l. 18 to hold for all time and

"^^qI' ^^^^

the maximum value of e would occur at t = - —

r max R

If this t is sufficiently less than T, then the following equations max

and conclusions are no longer applicable.

69
This result is identical to the band- limited case (2 R^^ >> sL) results

given by [2, 3] ; it can be seen to be identical by putting it into the

form

L = "^1 -

e (T)

a \ r

[ maximum voltage referred to e.(oD)

] L = —F r- X 2 R-

[ slope of the incident voltage ramp J ^

(A-1. 30)

The general result for L when R^^ t given by (A-1. 28)

requires that e (T) be measured from its inherent zero level which is ^ a T

absolutely equal to the steady state incident voltage E = . If

the peak value of the voltage is measured from the steady state value

of the refle

with t CO

,

of the reflected voltage e^('») , i. e. , from the value given by (A-1. 19)

a T

e (") = —rr c.

then we have

a L R

-^(T) - e^M = — 01

R

OT

(A-1. 31)

(A-1. 32)

Defining

e (T) = [-e (T) - e (-)] m

(A-1. 33)

70
we can then write

a L R

e (T) = r- m _ Z

and

R

L = OT

a R

01

01

R

OT

(A-1. 34)

or

[ maximum voltage referred to e (oo)] R

OT

[ slope of the incident voltage ramp] 2 R^^^

(A-1. 35)

This last result is the most practical one. Comparison of (A-1. 32)

with (A-1. 28) shows that to use (A-1. 28) one would in fact have to

first determine e (oo) to compute L. Consequently, use of (A-1. 32),

r

i. e. , (A-1. 35) includes e (oo) automatically.

r

6. Dual Equations for Capacitive Loads

Capacitive reflections are conveniently viewed in terms of admittance parameters and the node voltage E(s) due to a current

generator. Fig. A-5.

Here I (s) and G.. represent a lossless transmission line of

g 01

characteristic admittance G being driven by a bandlimited generator

71
I (s) and terminated in an admittance Y(s). The fundamental TDR

g

equations in terms of incident and reflected currents are

I(s) = ys) - E(s)

I(s) = I.(s) +1 (s)

1 r

(A-1. 36)

(A-1. 37)

Since the incident current I.(s) is the current when Y(s) = G , 1 01

(I (s) = 0) , then

r

(A-1. 38)

which when put into (A-1. 36) to eliminate I (s) yields

I (s) = I (s) - E(s) G . (A-1. 39)

r 1 U

1

The inverse Laplace transformation of (A-1. 39) yields

i (t) = i (t) - e(t) G

r 1 o 1 (A-1. 40)

Similarly the total TDR time domain current follows from (A-1. 36)

i(t) = i (t) - e(t) G

01

(A-1. 41)

These are the dual equations to ( A - 1 . 6 ) and ( A- 1 . 7 ).

7. The Excitation i (t)

For the cases analyzed here, i (t) will be assumed to be a finite

g

ramp current as shown in Fig. A-6, that is,

72
i (t) - btu(t) - b(t) u(t-T) (A-1.42)

where u(t) is the unit step function.

8. The Voltage for a Capacitive y(s).

Consider Fig, A- 7 which shows the TDR equivalent circuit for a

shixnt capacitive discontinuity sC at the junction of two uniform lossless

transmission lines of characteristic admittances G and G , respectfully. The voltage E(s) is given by

I (s) ^^^^ = + .r (A-1.43)

where

^OT = ^01 +^02

Since (A-I. 42) and (A-1. 43) are the duals of (A-1. 10) and (A-1. 9),

respectively, the voltage

-1 y^'

= ^ G +sC (A-1. 44)

OT

is the dual of the current i(t) given by (A-1. 14) and (A-1. 15). Consequently, we can immediately write down e(t) by inspection of

(A-1. 14) and (A-1. 15) through the dual relationships. Hence we have

from (A-1. 14) and (A-1. 17)

e(t) = bt bC

G 2

L OT G (

^t

0 ^ t ^ T

(A-1. 45)

73
and

e(t) = b T

G

+ e(T) - OT

b T

T < t <

9 . The Reflected Voltage for a Capacitive Load

Recalling that the total voltage is equal to

e(t) = e.(t) + e (t)

1 r

we can write

e (t) = e (t) - e .(t) r 1

Also, from Thevinin's theorem we have that

Therefore,

which yields

b = a G

01

74
Upon putting (A-1. 48) into (A-1.

(A- 1. 47) we obtain

45) and (A-1. 46), and the results into

G

a G^, t

OT

e.(t) ^ Si ^ OT

G

OT

1 - e )

0 ^t ^ T (A-1. 49)

and

e^(t)

OT

e.(t) + e(T)

^ Si ^ St

T ^ t ^00 ,

'

OT (t-T) ;

(A-1. 50)

Since

e.(t)

0 ^ t < T

a t 0 ^ t < T

e.(t)

1 T ^ t ^

R

a T

2

'

1

R

OT

1 01

T ^ t ^

^01 ^02

^01 +S2

01

We can write for (A-1. 49) and (A-1. 50)

2

e^(t) = at / ^02-%l \ \ /

^ iSl+S2/ " Si \

1 - e R C

P

)

0 ^ t ^ T ,

(A-1. 51)

75
and

e^(t) =

I- -

aT/ ^02-%l \

2 i ^^01+^02/

+ e(T) -

T ^ t ^0=

R C

P

(t-T)

(A-1. 52)

Fig. A-8 qualitatively illustrates (A-1. 51) and (A-1. 52),

10. The Calculation of C from e (t) r

The comments given in Section 5 also apply here. One can use

the exponential decay for t >T or can use the peak value of e (t). We

r now develop the formulae for small C from the peak value of e (t).

The peak value occurs at t = T ; consequently we have from

(A-1. 51) or (A-1. 52)

R a C ^ '1- e R C

P

R

01

(A-1. 53)

We again invoke a bandwidth limitation such that for small values of c, G = r >> |s C| ; consequently exp (-T/R C) is essentially OT

zero,

R.

e^(T) = a T ^02~^01

^0l"^^02

R^ a C

R

(A-1. 54)

01

Upon referring the peak value of the total load voltage to the steady

state value of the reflected voltage, we obtain

76
e (T) - e ( = ) r r

e (T) m

R a C

_-E

R

01

and

C = a R

C = [maximum voltage referred to e (-) 1 R^^

r 0

1

slope incident voltage ramp] 2R

R

When = R^^ , R

01

and

(A-1. 55)

C = [maximum voltage referred to e 12( = )

[ slope incident voltage ramp] R

01

(A-1. 56)

which is the usual formula [2, 3] for C when R = R

01 02

77
Figure A-1 The input equivalent circuit for a uniform lossless transmission line terminated in an impedance Z{s) and driven by

a bandlimited generator E (s). R ^ is the transmission

line characteristic impedance.

78
Figure A-2 The bandlimited driving voltage, e (t).

79
AAA/-

E(s)

sL

rrr\

I (s)

Ejs) 0 02

X

Figure A-3 The TDR equivalent circuit for a series inductive discontinuity

sL between two uniform transmission lines of characteristic

impedances and R respectively.

80
TIME

Figure A-4 Qualitative time domain responses for the total inductive

load voltage. A delay line of time delay t^/Z and characteristic impedance R^^ is used to isolate in time the observation

point and the discontinuity.

81
Figure A- 5 The input equivalent circuit for a uniform lossless

transmission line termination in an admittance Y(s)

and driven by a bandlimited generator I (s). is

the transmission line characteristic admittance.

82
;ureA-6 The bandlimited driving current, i(t).

83
Figure A -7 The TDR equivalent circuit for a shunt capacitive discontinuity

sC at the junction of two uniform transmission lines of characteristic admittances G and G , respectively.

84
e(t)'

Figure A-8 Qualitative time domain responses for the total capacitive

load voltage.

85
APPENDIX A -2

WAVEFORM DATA FOR FIGURES 2. 15 AND 2. 16

T(PSEC.) EA(T) EO(T) T (PSEC. ) EA(T) EO(T)

0 .5000 . 5000 -260 . 0329 . 0501

-10 . 4727 . 4487 -270 . 0279 . 0449

-20 . 4455 . 4296 -280 . 0235 . 0405

-30 . 4185 . 4044 -290 . 0197 . 0366

-40 . 3917 . 3787 -300 . 0164 . 0334

-50 . 3653 . 3547 -310 . 0136 . 0301

-60 . 3395 . 3305 -320 . 0113 . 0271

-70 . 3144 . 3072 -330 . 0093 . 0249

-80 . 2901 . 2846 -340 . 0076 . 0231

-90 . 2666 . 2623 -350 . 0061 . 0210

-100 . 2444 . 2423 -360 . 0051 . 0193

-110 . 2224 . 2245 -370 . 0040 . 0176

-120 . 2020 . 2055 -380 . 0032 . 0162

-130 . 1827 . 1866 -390 . 0025 . 0149

-140 . 1645 . 1702 -400 . 0020 . 0143

-150 . 1474 . 1551 -410 . 0016 . 0137

-160 . 1317 . 1396 -420 . 0012 . 0129

-170 . 1171 . 1265 -430 . 0009 . 0118

-180 . 1035 . 1147 -440 . 0106

-190 . 0912 . 1035 -450 . 0095

-200 . 0800 . 0942 -460 . 0083

-210 . 0698 . 0849 -47 0 . 0073

-220 . 0606 . 0764 -480 . 0068

-230 . 0524 . 0693 -490 . 0062

-240 . 0451 . 0627 -500 . 0056

-250 . 0386 . 0563 -510 . 0050

86
WAVEFORM DATA FOR FIGURES 2. 15 AND 2. 16 ( Cont. )

T(PSEC. ) EA(T) EO(T)

-520 .0044

-530 . 0039

-540 . 0033

-550 . 0027

-560 .0021

-570 . 0016

-580 .0013

-590 .0010

87
WAVEFORM DATA FOR FIGURES 2. 15 AND 2. 16

T(PSEC.) EA(T) EO(T)

0 . 5000 . 5000

10 . 5272 . 5250

20 . 5541 . 5553

30 . 5808 . 5805

40 . 6069 . 6051

50 . 6324 . 6316

60 . 6573 . 6567

70 . 6814 . 6810

80 .7 047 .7031

90 . 7269 . 7266

100 . 7482 . 7508

110 . 7685 . 7717

120 .7877 . 7920

130 . 8057 . 8105

140 . 8227 . 8281

150 . 8386 . 8459

160 . 8534 . 8625

170 . . 8670 . 8772

180 . 8796 .8915

190 . 8912 . 9048

200 .9019 .9147

210 .9115 . 9248

220 . 9203 . 9348

230 . 9282 . 9434

T(PSEC. ) EA(T) EO(T)

240 . 9354 . 9508

250 . 9419 . 9576

260 . 9478 . 9635

27 0 . 9527 . 9689

280 . 9573 . 9744

290 . 9613 . 9788

300 . 9649 . 9824

310 . 9679 . 9853

320 . 97 07 . 9876

330 . 9731 . 9888

340 . 9752 . 9904

350 . 9770 . 9923

360 . 9787 .9934

37 0 . 9800 . 9945

380 . 9812 . 9953

390 . 9823 .9963

400 . 9832 . 9972

410 . 9840 . 9974

420 . 9847 . 9977

430 . 9853 . 9979

440 . 9859 . 9983

450 . 9863 . 9988

460 . 9867 .9992

47 0 . 9871 . 9997

88
T(PSEC. EA(T) EO(T) T(PSEC. ) EA(T)

480 . 9874 1. 0000 740 .9913

490 . 9877 1. 0000 750 .9913

500 . 9880 . 998 760 .9914

510 . 9882 . 9992 770 .9915

520 . 9884 . 9986 780 .9916

530 . 9886 . 9982 790 . 9917

540 . 9888 . 9972 800 . 9917

550 . 9890 . 9977 810 .9918

560 . 9892 . 9975 820 .9919

570 . 9893 . 9972 830 . 9920

580 . 9895 . 9971 840 .9921

590 . 9896 . 9972 850 . 9922

600 . 9898 . 9974 860 . 9922

610 . 9899 . 9977 870 . 9922

620 . 9900 . 9979 880 . 9923

630 . 9901 .9981 890 . 9924

640 9903 . 9985 900 .9924

650 . 9904 . 9990 910 .9925

660 . 9905 . 9996 920 .9926

670 . 9906 . 9990 930 . 9926

680 99 07 1. 00 00 940 9927

690 . 9908 950 . 9927

700 . 9909 960 . 9928

710 .9910 970 . 9929

720 .9911 980 .9929

730 . 9912 990 . 9930

EO(T)

1. 0000

1. 0000

89
T(PSEC.) EA(T) EO(T) T(PSEC.) EA(T)

1000 .9930 1. 0000 1260 .9942

1010 . 9931 127 0 .9942

1020 .9931 1280 . 9943

1030 . 9932 1290 . 9943

1040 . 9932 1300 . 9943

105 0 . 9933 1310 . 9944

1060 . 9933 1320 . 9944

107 0 . 9934 1330 . 9944

1080 .9934 1340 . 9945

1090 .9935 1350 . 9945

1100 .9935 1360 . 9945

1110 .9936 137 0 . 9946

1120 .9936 1380 . 9946

1130 . 9937 1390 . 9946

1140 .9937 1400 .9947

1150 . 9937 1410 .9947

1160 . 9938 1420 . 9947

1170 . 9938 1430 . 9948

1180 .9939 1440 . 9948

1190 . 9939 1450 . 9948

1200 . 9940 1460 . 9949

1210 . 9940 147 0 . 9949

1220 . 9940 1480 . 9949

1230 .9941 149 0 . 9949

1240 .9941 1500 . 9950

1250 .9941 1. 0000 1510 . 9950

EO(T)

1. 0000

1. 0000

90
T (PSEC. ) EA(T) EO(T) T(PSEC.) EA(T)

1520 . 9950 1. 00 00 1780 . 9957

1530 . 9950 1790 . 9957

1540 . 9951 1800 . 9957

1550 . 9951 1810 . 9957

1560 • 9951 1820 . 9958

1570 . 9951 1830 . 9958

1580 . 9952 1840 . 9958

1590 . 9952 1850 . 9958

1600 . 9952 1860 . 9958

1610 . 9952 1870 . 9959

1620 . 9953 1880 . 9959

1630 . 9953 1890 . 9959

1640 . 9953 1900 . 9959

1650 . 9954 1910 . 9959

1660 . 9954 1920 . 9960

1670 . 9954 1930 . 9960

1680 9954 1940 9960

1690 9955 1950 . 9960

1700 9955 I960 . 9960

1710 . 9955 1970 . 9961

1 ^7 O A

. 9955 1 n Q n

. 99d 1 1730 . 9956 1990 . 9961

1740 . 9956 2000 .9961

1750 . 9956

1760 . 9956

1770 . 9956 1. 0000

EO(T)

1. 0000

1. 0000

91
FORM NBS-114A (1-71)

u..',. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession

BIBLIOGRAPHIC DATA mSlR 73- 304

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

REFERENCE-WAVEFORM GENERATION USING DEBYE

DIELECTRIC DISPERSION

5. Publication Date December 1972

6. Performing Orgasizatioo Ca4«

7. AUTHOR(s) N. S. Nahman, R. M. Jickling and D, R. Holt 8. Performing OrgaoizadoB

rCKr L'KMllNLj UKOAIN IZjA 1 lUIN INAMr, AINU AUUKCOO

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

10. Project/Task/Work Unit No. 2725390

11. Contract/Grant No.

12, Sponsoring Organization Name and Address Department of Defense

Calibration Coordination Group 69-33

U.S. Army Metrology & Calibration Center

Redstone Arsenal, Alabama 35809

13. Type of Report & Period Covered Final

14. %>onsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factua 1 summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) This report discusses the theory, construction, and operation of ReferenceWaveform Generators using a tunnel diode transition-waveform generator driving

4. 65 meter (15 foot), 3. 10 meter (10 foot), and 1, 55 meter (5 foot) liquid-dielectric

uniform lossy coaxial lines to produce known 0. 2 volt transition waveforms across

50 ohms with (10-90%) transition times from 205 to 560 picosecond. Each resultant

Available -Waveform is characterized in terms of its departure from the step

response of the uniform lossy coaxial line operating into a 50 ohm load. The liquid

dielectric solutions are dispersive with relaxation times of the order of 4 picoseconds in which heptane is the solvent and the ketones, butanone, heptanone and

octanone are the solutes in concentrations ranging from 0. 25- to 2-molal.

17. KEY WORDS (Alphabetical order, separated by semicolons) PulsB distortion in transmission lines;

pulse techniques; reference waveform generation; time domain measurements;

transient response — J, — — Debye dielectric.

—

r—j— v.wv^ — 18. AVAILABILITY STATEMENT 19. SECURITY CLASS

(THIS REPORT)

21. NO. OF PAGES

HKl UNLIMITED. UNCL ASSIFIED

1 1 FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

20. SECURITY CLASS

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22. Price

USCOMM-DC 66244.P7I

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