NBSIR 73-334 i^)

A BROADBAND COAXIAL NOISE SOURCE

PRELIMINARY INVESTIGATIONS

W. C. Daywitt

L. D. Driver

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1973

Interim Status Report

Contract No. CCG/Navy Blanket

Program 73-78

Prepared for

Department of Defense

Calibration Coordination Group

Attn: Melvin L. Fruechtenicht, Chairman

Army Metrology and Calibration Center

Redstone Arsenal

Huntsville, Alabama 35809

CCG 73-78
I
NBSIR 73-334

A BROADBAND COAXIAL NOISE SOURCE

PRELIMINARY INVESTIGATIONS

W. C. Daywitt

L. D. Driver

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

October 1973

Interim Status Report

Contract No. CCG/Navy Blanket

Program 73-78

Prepared for

Department of Defense

Calibration Coordination Group

Attn; Melvin L. Fruechtenicht, Chairman

Army Metrology and Calibration Center

Redstone Arsenal

Huntsville, Alabama 35809

CCG 73-78

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

NATIONAL BUREAU OF STANDARDS. Richard W Roberts Director
i
CONTENTS

Page

INTRODUCTION 1

1. NOISE TEMPERATURE APPROXIMATION FOR A COAXIAL

NOISE STANDARD 4

2. RESONANCE TECHNIQUE (TEOl CIRCULAR MODE) FOR

MEASURING DIELECTRIC CONSTANT VS. TEMPERATURE 6

3. BROADBAND BEAD DESIGN 10

4. BROADBAND TERMINATION DESIGN . 24

5. . FIGURES 29

6 . APPENDICES

A. CCG Work Statement 48

B. Output Noise Temperature for a Coaxial Noise Source 52

C. Propagation Constant of a Coaxial Line 58

D. Design Formula for the TEOl Circular Mode

Resonance Measurement 61

E. Propagation Constant in a Lossy Dielectric 64

F. Dielectric Constant Measurement Using the

Automatic Network Analyzer 66

G. Curve Fitting Equation for Bead and Line Trimming "71

H. Step Capacitance 76

I. Effective Dielectric Constant and Face Compensation 77

J. Higher Mode Bead Resonances 82

iii
CONTENTS (Continued)

Page

K. TE 11 Cutoff Wavelengths 85

L. Termination Design Equations 86

7. REFERENCES 87

LIST OF FIGURES

Figure 1. TEOl Circular Mode Dielectric Measurement System 30

Figure 2. D-F Graph for TEOl Measurement 31

Figure 3. Table of TEOl Measurements for Various Materials 32

Figure 4. Bead Resonant Frequencies for TEll Circular Mode

in 14 mm Bead 33

Figure 5. Measurement Data for 14 mm Bead-Line Before

Compensation 34

Figure 6. 14 mm Bead and Line 35

Figure 7. Measurement Data for 14 mm Bead-Line After

Compensation 36

Figure 8. 7 mm Bead and Line 37

Figure 9. Measurement Data for 7 mm Bead-Line Before

Compensation 38

Figure 10. Measurement Data for 14 mm Bead-Line-Gap Before

Compensation ^9

Figure 11. Measurement Data for 14 mm Bead-Line-Gap After

Compensation 40

Figure 12. Resistive Cone and Cone Holder for 7 mm Termination 41

Figure 13. Resistive Cone : 42

Figure 14. Cone Holder 43

IV
LIST OF FIGURES (Continued)

Page

Figure 15. Equivalent Circuit for Derivation of Equation G. 11 44

Figure 16 . Profile View and Equivalent Circuit for Derivation

ofEquationI.il 45

Figure 17. Profile View for Derivation of Equation J. 6 46

Figure 18. Graph of (1 + k)X'll 47

v
ABSTRACT

This report describes investigations that were performed in fiscal year

1973, by the Noise and Interference Section of the Electromagnetics Division of

the Institute for Basic Standards of the National Bureau of Standards preliminary

to the design and construction of a coaxial thermal noise source in fiscal year

1974. The intent is to develop a coaxial thermal reference noise source that

will operate at nominally 1000°C and will have a low reflection coefficient from

0 . 1 to 12 GHz . /

Key words: Bead support; noise standard; resistive termination.

vi
A BROADBAND COAXIAL NOISE SOURCE

Preliminary Investigations

INTRODUCTION

This report is a report to sponsor of a number of investigations that were

performed during fiscal year 1973 in preparation for the design and construction

of a coaxial thermal reference noise standard. The sponsor is the Calibration

Coordination Group of the Department of Defense, and the task is designated

by either number CCG 73-78 or NBS 2726449. The proposed noise standard

is to have the following specifications:

(1) Noise temperature output is to be nominally

1273 K.

(2) Broadband characteristics require as low a reflection

coefficient as possible from 0.1 to 12 GHz.

In order to design and build this high temperature, broadband noise

standard four things are needed: 1) a method for calculating the noise

temperature of the coaxial noise source; 2) an accurate method of measuring

the dielectric constant of candidate inner conductor bead support materials

usable at elevated temperatures; 3) a means for designing broadband bead

supports for the inner conductor; and 4) a broadband termination design

that will withstand usage at elevated temperatures

.
In essence this year's work has bem aimed at developing needed

techniques and know how to accomplish the above. The following tasks

emerged as the most critical for the success of these objectives:

(1) to develop a technique for measuring dielectric constant

v-^ at high temperatures;

(2) to develop a predictaljle technique for designing low

reflection bead supports for the center conductor of

the noise source;

(3) to investigate and select the most workable thin-film

termination design;

(4) experiment to find a means for retaining a thin-film

on a ceramic substrate at or near 1000°C;

(5) to try to develop a technique for adjusting the termination

for a low reflection coefficient

.

These tasks can be recognized as being mainly concerned with achieving

a low reflection coefficient at high temperatures for the termination and

transmission line . For comparison the original CCG work statement is

included in its entirety as Appendix A

.

Section one of this report describes a method for calculating the

noise temperature output of a coaxial thermal noise source.

The first of the preceding five tasks has been completed and is discussed

in section 2 .

2
Task number two is 90% complete but was discontinued in this fiscal

year for lack of funds. It appears that about three weeks of the next fiscal

year effort will be needed for its completion . This task is discussed in

section 3.

Task number three is tentatively complete with the choice of a conical

termination design as discussed in section 4.

Task number four is approximately 50% complete and will be continued

into the next fiscal year. It is discussed in section 4.

Task number five was not started in order to allow sufficient funds

for task four and for writing this report. Some comments concerning this

task will be found in section 4 however

.

From the above it is apparent that task 2 was not completed, and

that task 5 was not begun because of insufficient funds . Sixty thousand

dollars was estimated to be needed to accomplish this year's work. Fiftyfive thousand dollars were received, and it is estimated now that an additional

six thousand dollars would have helped complete tasks two and five

.

3
1. NOISE TEMPERATURE APPROXIMATION FOR A COAXIAL NOISE STANDARD

An accurate calculation of the noise temperature from a waveguide ^"'^^

and a coaxial thermal noise standard differs in one important aspect. In a

waveguide standard a single temperature distribution along the length of the

waveguide is used. The coaxial standard in general has two such distributions,

one for the inner and one for the outer conductor . It is this difference that

prevents the direct use of previously developed equations for the calculation

of the noise temperature.

Equation (1.1) is the formula used to calculate the noise temperature

of a rectangular waveguide thermal noise source (Appendix B) .

^-T^OI, ^ jV^C^y ix (1-1)

The quantity ~"a~\^>'-o is the contribution toTfrom the termination, and the

integral term is the contribution from the waveguide itself. Clearly the waveguide contribution depends on only one temperature distribution ^ along its

length. This term can be rewritten as

where '^-/ is the real part of the propagation constant for the elemental

length c^i of line at position X along the waveguide and is defined in

Appendix B. It is significant that T"x and -^x appear as a product.

4
In a coaxial noise source there are two temperatures associated with

each point along the transmission line, one for the outer conductor and

one for the inner conductor. However, CLy does not allow a separate identification

of inner and outer conductor losses for the TEM wave. That is, does

not separate into the sum of two terms, one being solely identified with

the outer conductor and one with the inner conductor. Without this separation

the outer and inner conductor temperatures cannot be uniquely coupled

with the outer and inner conductor losses respectively. Therefore the

noise temperature of a coaxial thermal noise source cannot be calculated

exactly. However, for low loss lines an approximate separation of UL^

is possible and a first order approximation to the noise temperature is

obtained. This approximation is developed in Appendices B and C, and

it is shown there (Appendix B) that the resulting error in the noise temperature from using this approximation is negligible.

The result of this first order approximation for the noise temperature

is given by equation B . 9 of Appendix B .

A

T-= T^oL^ (T.^LL,,. +11, 0.,^ ) h±iVA'' \ Jx (1.3)

where Tf^ and T^g are the temperature distributions for the inner and

outer conductors respectively, and Ux; and ULxt, are the first order separated

real "propagation constants" for the inner and outer conductors respectively.

5
This result (eq 1.3) will be used to calculate the output noise temperature

of the thermal noise source and will be the basis for developing an error

analysis of the coaxial standard.

2. RESONANCE TECHNIQUE (TEOl CIRCULAR MODE) FOR MEASURING

DIELECTRIC CONSTANT vs . TEMPERATURE

In the design, testing, and troubleshooting of the coaxial noise standard

it will be necessary to identify and isolate reflections from a number of

sources. One source of reflection is an impedance mismatch between the

transmission line and the bead support(s) for the inner conductor. To

minimize this mismatch in the initial design of the bead support (s) an accurate

(i.e. , ± 5% or better) measurement of the dielectric constant of the bead

material is required at the working temperature. To this end the TEOl

(2) circular mode resonance technique was implemented, based on a brief

survey of candidate methods for measurements up to 1000°C.

The technique (Appendix D) involves resonating the TEOl circular

waveguide mode in a cylindrical dielectric sample that has been fitted

into a uniform diameter hollow cylindrical tube . The resonant frequency

satisfies the requirement that the TEOl mode propagates inside the sample

but is cut off outside of the sample . Since the electric field in the sample

vanishes at the inner surface of the tube, for this mode, a small air gap

between the sample and pipe does not greatly affect the dielectric constant

(2) measurement. This lack of sensitivity to such gaps allows the sample

to be heated with negligible error due to the gap produced by the heating.

6
The simplicity of the system can be explained with the aid of figure 1

.

RF energy is fed from the sweep generator into the coax-to-waveguide

adaptor at the right end of the X-band waveguide structure. The rf energy

proceeds through the isolated reaction cavity and directional coupler to

a wavegmde-to-3mm coaxial adaptor. The rf energy is coupled to the

sample residing in the circular tube through a small magnetic probe at

the end of the 3mm coaxial line . The reflected energy travels back through

the 3mm line , through the adapter and up the vertical arm of the directional

coupler to the tunable crystal detector . The detected signal is fed into

the vertical display of the oscilloscope whose horizontal axis is being swept

by the sweep output of the sweep generator . The oscilloscope display

shows two resonances. The right one in figure 1 is the sample resonance

and the left one is the resonance from the reaction cavity that is shown

for comparison. The sample material whose resonance is being displayed

is an isotropic pyrolytic boron nitride . A number of tubes and samples

used during these preliminary investigations are shown under and to the

left of the tube being used.

When a dielectric constant is to be measured at a high temperature

a tube of high temperature metal containing the sample will be placed in

an oven at the desired temperature. In this case a high temperature 3mm

coaxial line will be used to excite the sample. This high temperature line

is shown in the center of the figure leaning against the waveguide rail.

7
This technique requires that the product of the tube diameter D and

the resonant frequency f must lie between the values shown in figure 2

.

Then if the approximate value of the relative dielectric constant (Appendix

F) is known at the desired frequency an accurate value of at the same

frequency can be obtained by adjusting the sample length and diameter

with the aid of figure 2 and equations D . 2 and D . 3 of Appendix D .

To test the theory and the system a number of samples were measured

(3) and compared to measurements made using a slotted line technique

(4) that was adapted to measure at any given frequency. Figure 3

shows the results of these tests using two batches of boron nitride as the

sample material. In the first column Cu or Al indicate resonance measurements in which a copper or aluminum tube was used for the circular waveguide

.

"Coax" indicates that the measurement was performed with the slotted

line technique. The sample batch number indicates from which boronnitride batch the sample was cut . The frequencies given in the sixth column

are the measured resonance frequencies , or the frequencies at which the

measurements were performed with the slotted-line technique

.

By examining figure 3 the following conclusions and implications

can be drawn:

(1) Both the sets (coax and resonance measurements) have

a high internal consistency. For example, the relative spreads

in the value of Cp measured by the resonance (1"6) and coax

techniques (7, 8) about their average values are 0.24% and 0.07%

respectively.

8
(2) Although both sets of measurements are repeatable to a

fraction of a percent, they nevertheless differ by approximately

3% as evidenced by the average values of 4.632 and 4.490 measured

via the resonance and coax techniques respectively

.

(3) In the resonance measurements an air-gap does have

a negligible effect on the measured values as evidenced from

the small differences between the separate values and the

average value of 4.632 for the resonance measurements.

(4) Since the measurements using the Cu and Al tubes give

essentially the same results, the wall losses of the tubes have

a negligible effect on the measured dielectric constant.

(5) A number of resonance measurements not appearing in

this table were made with different sample loadings (different

separation distances between the rf probe and the sample face)

that indicate the results obtained to be free from excessive

coupling

.

The preceding results imply that the resonance technique is capable

of measuring dielectric constants at elevated temperatures quite precisely

although there is some question about the accuracy. Since there is a 3%

difference between the coax and resonance measurements, a maximum error

of 3% in the resonance technique will be assumed. This assumed error is not

crucial to the concerns of this report, but does allow some order-of-magnitude

9
estimates to be made in section 3 under the "Formula Test Results .

Due to the non-crucial nature of the assumed error no extensive effort

was used to track down the source of the discrepancy between the resonance

and coax values for .

Once the final bead material or materials are chosen a high temperature

tube or tubes of appropriate dimension will be purchased and the dielectric

versus temperature measurements performed. At present not enough is known

concerning the final design to allow this choice.

Another technique was partially investigated that may prove useful if

it becomes necessary to measure dielectric constant versus frequency. This

technique (Appendix F) utilizes an automatic network analyzer to measure

the scattering coefficients of a two-port comprised of a coaxial reference air

line filled with the dielectric material under question. From these measured

scattering coefficients the analyzer calculates and prints out the dielectric

constants for the frequencies of interest. This technique doesn't have a

high degree of accuracy, but could nevertheless be used to confirm or

eliminate the question of anomalous dielectric constant behavior should it

arise

.

3 . BROADBAND BEAD DESIGN

The principal mode characteristic impedance £o of a coaxial transmission

line is given by equations 3.1 or 3.2

10
= f X (3.2)

where and are the free space magnetic and electric permittivities

respectively, C^is the relative dielectric constant of the material filling the

line, Do is the inner diameter of the outer conductor and"I);k, is the outer diameter

of the inner conductor, and and are the inductance and capacitance per

vinit length respectively of the line . In constructing a transmission line using

bead supports for the inner conductor, must be the same for each point

along the length of line if the line is to be broadband, that is if the line is to

(5) have no reflections . For example, in the air filled region of a 50 ohm line

the diameter ratio i^£> in equation (3 . 1) must be chosen to make i-oequal

to 50 ohms with £p equal to unity. However, within the bead supports whose

relative dielectric constant might be 4 this ratio must be chosen to make 2.&

equal to 50 ohms with Coequal to 4. Therefore, at the interfaces between the

bead supports and the air the diameters of the inner an,d outer conductors

are abruptly changed to maintain the 50 ohm characteristic impedance. This

abrupt change or step in the conductors produces an anomalous increase

in the capacitance of the line at the step through the resulting fringing fields.

11
This step capacitance leads to a reflection since C in equation (3.2) is

increased by the step capacitance at the step and the resulting Zois less

than the desired 50 ohms. In order to decrease G back to the correct value

to make £o 50 ohms, some of the capacitance at the step is removed by

removing some of the material from the bead faces . This is usually accomplished by cutting a shallow toroidal groove in the bead faces concentric with

the conductors .

,

If the above is properly done , the line and bead supports will be

reflecti-onless from dc up to the lowest frequency at which the higher modes

begin to propagate within the bead, and it is therefore desirable to have

a formula for predicting the lowest frequency for the onset of these modes.

3 . 1 Bead Support Design and Trimming

The design, construction, and subsequent trimming of bead supports

to make them reflectionless is accomplished by the following procedure:

1. An accurate measurement (see Sec. 2) of the dielectric constant

of the bead material is obtained.

2. Equation (3.1) is used to determine the correct diameter ratio

for the conductors in the region of the bead support so that this

region will have the correct characteristic impedance, -?o , for the

relative dielectric constant ^pof the material measured in step 1.

3. An upper limit to the length of the bead is obtained from

the graph of the equation (J. 6) in Appendix J (Fig. 4). This equation

gives the frequencies at which the bead acts as a cavity at resonance for

12
the odd and even configurations of the TEll circular wavegmde

mode . The odd and even configurations appear alternately as the

frequency is increased, the first resonance to appear being that of

the even configuration . The details of this equation are explained

in Appendix J

.

4. The diameter of the outer conductor is increased and/or the

diameter of the inner conductor is decreased where the bead is to be

placed in accordance with the value of Do/JD;, calculated in step 2.

This increase and/or decrease in the diameters is not fully completed,

however, allowing for some inaccuracy in the measurement of Later

reflection measurements will indicate how much conductor trimming is left

to be done . The length of the bead and the changed diameter portions of

the line are determined in accordance with step 3, and a bead is cut to

press fit into the enlarged line.

A graph of equation (J. 6) for the first even and odd modes is

shown in figure 4 for a 14 mm line and bead. The resonant frequencies

for these modes are plotted horizontally for the bead lengths plotted

vertically . For example , for a 2 cm bead with a dielectric constant

equal to 4.56 with the dimensions given in the graph, the first resonance

occurs at about 5 .4 GHz. The next resonance to appear will be at about

6 .8 GHz and is due to the first appearance of the odd mode. As the

frequency is increased an infinite sequence of resonance frequencies

13
are encountered. The cutoff frequency for these TEll modes is 4.86

GHz for the dielectric constant in the figure and is a vertical asymptote for all the modes.

The actual bead length is then chosen to be less than that

length where the first even mode appears for the highest frequency

at which the bead and transmission line are to be used . For example

,

if the bead and line of figure 4 is to be used up to 9 GHz, the bead

length should be no greater than 0.1 cm where the first even configuration appears . After the bead is compensated for the step capacitance

it resonates at a frequency given by its original length minus the

length removed. For example, if 0.2 cm were cut into each face

of the 2 cm bead, its resonant length would be reduced to 1.6 cm

and the corresponding first resonant frequency would be increased

from 5 . 4 GHz to about 5 . 5 GHz .

5. The reflection coefficient magnitude (equation 3.3 below)

of the bead and line is measured as a function of frequency on the

automatic network analyzer, the data is plotted, and the constants D,

and X>2. are determined. The resulting plot of such a measurement

is shown in figure 5, where the dots represent measured data points.

The abscissa is the measurement frequency in gigahertz and the

ordinate is the reflection coefficient. The angles given under the

major frequency divisions are the electrical angles ( ZTT'-f /-f ^ )

14
corresponding to the given frequency, where "^o corresponds to

a full cycle or 360°. For example, 90° corresponds to 4.84 GHz

and is that point where only the first term or Di is present from

equation (3.3). The constants D, and of equation (3.3) for

the reflection coefficient (see Appendix G for a derivation of this

equation) are then chosen to make the equation fit the data points.

{V\ ^ \ T^,^ ZTV-P Dx-P C^m£\ (3.3)

where To is that frequency for which the electrical length of the bead

is one wavelength, and ''r is the measurement frequency . This equation

is a first order equation in J), and l^t-f /-f© . X>i is the reflection

coefficient caused by the characteristic impedance of the bead being

different from 50-n_, and 1^^. is the reflection coefficient caused by the

step capacitance

.

A nonvanishing ]I)| indicates that the diameter ratio in equation

(3. 1) was not properly chosen for the given dielectric constant of the

bead. If the outer conductor diameter -6- in the bead region is too

large by hiJ- , and/or if the inner conductor diameter a! in the bead

region is too large by ^0.' , and/or if is too large by <S£r , then the

resulting reflection Di is related to , (^G-' , and S^^^^ (see

Appendix G for details)

U / Ait ^^]-± ££c ^3.4)

SCj'-l Of J Z €r

15
In using equation (3.4) to determine what correction to the

conductor diameters or is needed to make IDi vanish, either

or any two of these cein be taken as zero and the

correction made entirely on only one of them

.

Before any compensation of the bead for the reflection caused by

the step capacitance is made will be nonvanishing . is related

to the step capacitance C (see Appendix I) through the relation

where

^D^^o-2Wo2,C (3.6)

(^z)o is the value of j>z before any compensating cuts ( dL= o ) are

made into the bead faces, d is the cutting depth, and Jo is that depth

of cut which perfectly nullifies (1^2.— <^ ) the reflection from the step

capacitance

.

A rough estimate of Jo (see Appendix I) is given by

d^o ^ "^o-z. a Cl>z.)o (3.7)

where

-7^ - ^ /<c (3.8)

16
^re. (see Appendix I) is the effective relative dielectric constant

in the portions of the bead where the compensating toroidal cuts

have been made, andJ^ is the bead length. Since this first measurement

is made before any bead compensating is done ( JL=o) , the value

of determined is the same as (Dz^o .

Equation (3.7) is now used to determine what approximate

depth of compensation of the bead will cancel the reflection from

the step capacitance.

6. After c^o is determined from step 5, a toroidal cut is

made into both faces of the bead to a depth that is some fraction of d?^

(e.g. 1/2 or 1/3), and another set of reflection measurements is

made and plotted. Again D, a.nd'J)^ are determined from the graph.

If Di agrees with the previous J), measured in step 5 , it is safe

to change the conductor diameters accordingly in the region of the

bead. If not, then enough care was not taken in fitting the bead

in the line and the process in the previous steps should be repeated

until agreement is obtained. Great care must be exercised in the

machining and fitting of the line and bead if the value measured

for is to be meaningful . The second measured value of X>^

should show some agreement with equation (3.5) .

7. Steps 5 and 6 are repeated until the bead-line reflection

coefficient is reduced to or below the desired value.

17
Formula Test Results

This first set of results is meant to show that the preceding formula and

ideas have sufficient validity to be gainfully used in the design and construction

of broadband bead supports .

The first group of results pertain to figures 4, 5, 6, and 7. Figure 6

is an exploded view of the 14 mm bead-line test apparatus, consisting

of an air line whose diameters have been changed in the bead region

.

The bead is made of boron nitride and is fitted onto the center conductor.

A compensation groove can be seen in the visible face of the bead. Figure 4

has been discussed and is used to predict the bead resonant frequencies

for the 14 mm bead and line . Before any compensation was performed

the predicted resonant frequency corresponding to the bead length of

0.725 cm was approximately 6.4 GHz. This prediction compares well

with the measured resonant frequency of 6 . 7 GHz indicated in figure 5.

After a 0.152 cm compensation cut was made into both faces the effective

length of the bead was reduced from 0.725 cm to 0.421 cm. The predicted

resonant frequency corresponding to this length is 7.2 GHz as obtained

from figure 4. This value compares well with the measured value of 7.6

GHz as shown in figure 7. The broad spike at 5 . 8 GHz in figure 7 is believed

to be generated in the network analyzer and is not a resonance. This coupled

with further experiments indicates that equation (J. 6) of Appendix J is quite

adequate for predicting the onset frequency for bead resonances, at least

for 14 mm and 7 mm lines with bead supports of moderate dielectric constant.

18
The calculation of the step capacitance of the 14 mm bead before

compensation using equation (H.l) of Appendix H gave 0.21 picofarads

for C . The measured value obtained from (D? through equation (3.6)

was 0.22 picofarads, in good agreement with the calculated value. The

second order value of 1.35 for was used in equation (3.6) although

the first order value, that obtained from equation (3.3), would also have

given good agreement . The second order value was obtained using a second

order equation for W\ analogous to the first order equation given by

(3.3) . This was done to better understand the data points and equation

(3.3), and to get a better expression for determining the value of the step

capacitance for cI.= c!Lo . and consequently the relationship (1.9) in Appendix I.

According to equation (3 . 3) the data points in figure 5 should pass through

zero at 4.84 GHz. The fact that they do not is due to the first order nature

of equation (3.3).

From figure 5 and the value of 1.35 for J)^ the depth of compensation

cut needed to nullify the reflection from the step capacitance is 0.153 cm

as calculated from equation (3.7) . After a cut of 0. 152 cm was made into

each face the resulting is + 0.0071 as seen in figure 7. The corresponding

calculated from equation (3.5) is + 0.009 in good agreement with the

measured value

.

The value of X>i obtained from figure 5 is approximately zero, showing

that the diameter ratio in equation (3.1) is apparently close to correct

19
for the value of CpTneasured for the bead. However, the value calculated

from equation (3.4) is - 0.046, taking ^Ol and S €.p to be zero. The

value obtained from figure 7 forX)| is - 0.045 in close agreement with

the calculated value of - 0.046. 3)i should be the same for both figures

5 and 7. The discrepancy implied by ^ from figure 5 can only mean

therefore that- S^r/'^ in equation (3.4) must have been approximately

equal to + 0.046 to offset the first term in equation (3.4), giving approximately

zero for . The only way this could have happened is for

to be approximately - 9.2%, a number three times larger than the maximum

measurement error of 3% for assumed in section 2 . This leads to the

conclusion that the outer diameter of the bead used for figure 5 was undersized

and that the bead used for figure 7 was a good fit. This was indeed the

case, and it points up the extreme care needed in fitting the bead into

the line

.

Figure 8 shows an exploded view of the 7 mm bead holder that was

constructed to further test the design formula. The bead is made from boron

nitride, and with the line is dimensioned such that at least two bead resonances

will appear in the 0 to 12 GHz frequency range. This picture was taken after

the bead had been partially compensated and the groove can be seen around

the center conductor of the line . The reflection coefficient measured on the

automatic network analyzer for this line and bead before the bead was compensated is plotted as a function of frequency in figure 9. Again the isolated

20
points represent the measured data and the solid curve represents the best

fit for equation (3.3) . At around 4.5 GHz the curve and data points begin to

diverge possibly owing to the first order nature of equation (3.3) . The sudden

jump in the data points at 9.5 GHz is apparently due to the measurement

apparatus since this jump is not explainable by the bead reflections or

resonances. The value for 3)2. implies a step capacitance of 0.26 picofarads,

while the value calcialated from equation (H.l) is 0.29 picofarads. Using

equation (3.4) , the value of D, indicates that the diameter of the outer conductor

is too small by 18 , or that the diameter of the inner

conductor is too large by 18%, or that €.r is too large by 20%. If the value

for^, is correct it indicates that the conductors should be changed accordingly

to reduce to zero, or in this case since S€r- is positive, could

be reduced to some effective value (Appendix I) 20% lower than its present

value to accomplish the same end . The ability to tune the bead by lowering

its dielectric constant through removing some of the bead material the

whole length of the bead should prove quite useful later on in the standard's

development. Two resonant frequencies in the 0-12 GHz range are predicted

for the bead by equation (J. 6) in Appendix J, the lower resonant being

that of the first even mode and the second being that of the first odd mode.

The values predicted for these resonant frequencies are 5.5 GHz and 8.3

GHz, both of which are 14% lower than the measured values of 6.4 GHz

and 9 . 6 GHz

.

21
Gap Experiment Results

Even if a bead and line are press fit together, when they are both heated

a small gap may appear between one of the outer conductors and the bead.

This gap will both change the bead characteristic impedance and its step

capacitance, causing the reflection coefficient to increase. The work of

(7) Cruz with effective dielectric constants implies that this gap problem

can be circumvented by inserting G^^ in place of in the design and

trimming formula, where is less than G^and accounts for the gap.

The expression for Gr-e ^^i^ case can be obtained from equation (1.2)

of Appendix I by using equation (I.l) and letting "6-" equal -6-'

, and <x"

equal the reduced bead outer diameter"(j--2^ where is the gap width

.

Then

G — €r i r- (3.9)

Although in reality the gap will not be concentric with the conductors , it is

expected that the eccentricity is a second or higher order effect and that

this treatment of the gap problem will still be useful. The experiment to be

described now supports this conclusion. It consists of constructing a bead

whose outer diameter is 5 mils (0.013 cm) smaller than the outer line diameter

of the 14 mm line. In other words the bead and line are the same as in figure 6

with the bead reduced by 5 mils in its outer diameter . The reflection coefficient

22
of the bead and line is then measured before and after compensation and

the measurement results compared with those predicted by equations (3.3),

(3.6), and (3.7), and equation (H.l) of Appendix H.

Figure 10 shows the measurement results before compensation.

The best fit for [PI is given by - 0.033 and + 0.859 forD, andt>a. respectively.

Equation (3.6) and the measured value of Dz. lead to a value of 0.14 picofarads for the step capacitance C. The value obtained forC from equation

(H.l) is 0.19 picofarads which compares favorably with the measured

value . The depth J^^ of cut to provide full compensation calculated

from equation (3.7) and equation (1.2) is 0.097 cm. The predicted TEll

resonant frequency using equation (J. 6) of Appendix J is 6.4 GHz compared

to a measured value of 6.9 GHz. The range of values obtained for "J),

is - 0.08 to - 0.04 using equation (3.4) with of equation (3.9) replacing

to account for the gap. The measured value forTj^ before and after

compensation is - 0.033 in good agreement with the calculated range of

values for J) I .

Figure 11 shows the measured reflection coefficient of the bead with

a 5 mil gap after a compensation cut to a 0.048 cm depth had been made.

In this case the bead length for the TEll resonance calculation is reduced

by 0.096 cm giving a resonant frequency of 6.6 GHz as compared to the

measured value of 7 . 1 GHz. i), is the same ,-0.0 33, as in figure 10 as

it should be since no changes to the bead or line diameters have been made.

The new measured value for is 0.431. The value calculated for

23
using equation (3.5) with d2o = 0.0<? 7 , cH = O • , and Cl)-z)o= 0,95^

is 0.434 which closely agrees with the measured value.

These results show that it is possible to trim a bead and line to achieve

a low reflection coefficient even though a gap is present. Although the

gap chosen for these measurements was between the outer diameters of

the bead and line, these results imply that the same trimming procedure

applies to a gap between the bead and line inner diameters.

As a bead and line are heated a gap may also appear between the

bead faces and the inner and outer conductor steps next to these faces.

This gap will modify the step capacitances which, hopefully, can still

be accounted for in the same manner indicated in equation (3.4) . However,

for lack of time no experiments were conducted to test this statement.

4 . BROADBAND TERMINATION DESIGN

Resistive Element Selection

In selecting an appropriate resistive terminating configuration

,

several different types were considered. Among these were various thin

film configurations such as the cylindrical center element with a tractorial

outer conductor, the conical center element with a cylindrical outer conductor

(5.8,9) and several strip line element types ' '

. Also, the solid lossy element

types were considered.

24

I
The conical center element of figure 12 was selected because of

the simplicity of design, ease of machining and greater predictability.

Also, another group in Division 272 has had considerable past experience

with this type of terminating element.

Materials Selection

The 12 GHz upper frequency limit and especially the 1000°C operating

temperature place very severe requirements on the materials to be used in the

terminating element. The conical substrate and the metallic resistive film

must maintain their mechanical and electrical properties up to these limits

as well as remain chemically and mechanically compatible with one another

.

A literature search for high temperature materials narrowed the choices

of suitable substrate materials to a very few . Certain types of boron nitride and

beryllium oxide appeared to have very good mechanical and electrical characteristics over the ranges of temperature and frequency of interest. Sapphire,

alumina, quartz and silica also seemed to be possible candidates. Samples of

pyrolytic isotropic boron nitride , hot pressed boron nitride and beryllium oxide

were obtained for initial testing

.

Some materials considered as possibilities for the resistive thin

film were platinum, rhodium, titanium, tantalum and tungsten. For the

first attempt, an alloy of 90% platinum and 10% rhodium was selected.

This material was selected because of high melting point, the excellent

chemical properties at high temperatures and the vast amount of published

25
material dealing with the mechanical and electrical characteristics of this

alloy. Also, this material has been used in previous high temperature

applications with good success.

High Temperature Materials Testing

Several samples each of pyrolytic isotropic boron nitride, hot pressed

boron nitride and beryllium oxide were sent out to a local firm for deposition

of thin films of the 90% platinum 10% rhodium alloy. The film on each sample

was deposited to produce approximately 30 ohms per square.

One sample of each type was subjected to 1000°C for several hours.

All three samples failed. Severe surface glazing was experienced with

both types of boron nitride. This glazing is believed to result from water

absorption by the material prior to film deposition . It has since been observed

at temperatures as low as 700°C. The beryllium oxide sample appeared

to withstand the temperature but resistance measurements of the film revealed

that it had become non-conductive

.

Boron nitride as a substrate material has been, at least, temporarily

set aside in favor of beryllium oxide . Samples of BeO with the Pt-Rh alloy

film have been run in an argon atmosphere and in a vacuum furnace in

an effort to determine the cause of the film failure at 1000°C . In all tests

the film failed in less than one hour when run at 1000°C. Also, the failure

takes place somewhere between 900°C and 1000°C. Samples have been

run at 900°C for several days without any sign of change or failure of

either the resistive film or the BeO substrate

.
Gold was deposited on two samples of BeO and tested at 900 C and

1000°C. These films failed also by becoming non -conductive . However,

since several hours were required at lOOO^C and two days at 900°C, it

is suspected that these failures resulted from sublimination

.

Resistive Element Design

Design equations for the tapered conical load are described in Appendix L.

A computer program utilizing these equations has been written to calculate

the various dimensional requirements (figure 12) for conical substrates

of different dielectric constants and for different coaxial line sizes . The

program was used to design a 7 mm conical termination to be used at room

temperature to gain insight into the characteristics of this type of termination.

This termination and its associated housing are shown in figures 13 and

14, respectively.

27
The authors gratefully acknowledge help from the following persons:

Dr. Howard E. Bussey, W. J. Foote, P. E. Werner, and other personnel

from Section .55 who helped with the use of the Automatic Network Analyzer.

.1 •

28
5 . FIGURES

1. TEOl Circular Mode Dielectric Measurement System

2. D'F Graph for TEOl Measurement

3. Table of TEOl Measurements for Various Materials

4. Bead Resonant Frequencies for TEH Circular Mode in 14 mm Bead

5 . Measurement Data for 14 mm Bead-Line Before Compensation

6. 14 mm Bead and Line

7. Measurement Data for 14 mm Bead-Line After Compensation

8. 7 mm Bead and Line

9. Measurement Data for 7 mm Bead-Line Before Compensation

10. Measurement Data for 14 mm Bead-Line-Gap Before Compensation

11. Measurement Data for 14 mm Bead-Line-Gap After Compensation

12. Resistive Cone and Cone Holder for 7 mm Termination

13. Resistive Cone

14. Cone Holder

15. Equivalent Circuit for Derivation of Equation G.ll

16. Profile View and Equivalent Circuit for Derivation of Equation 1. 11

17. Profile View for Derivation of Equation J.

6

18. Graph of (1 + k)X'll

29

(ZH9)i X (1^3)0

31
Tube

Tube

Diameter

(cm)

Sample

Batch

Number

Sample

Diameter

(cm)

Sample

Length

(cm)

Measured

Frequency

(GHz)

Relative

Dielectric

Constant

Loss

Tangent

Cu 2.007

Cu 2.007

2.007

2.007

0.828

0.808

9.827

9.917

4.635

4.632

0.0009

0.0009

Cu 2.007

Cu 2.007

2.007

1.999

0.726

0.726

10.110

10.115

4.630

4.625

Cu 2.007

Coax 14 mm

Coax 14 mm

2

1

2

2.007 0.772

5 cm

5 cm

10.016

8.486

10.000

4.634

4.489

4.492

Al 1.895 0.726 10.589 4.636 0.0013

*Diameter reduced by hand to fit tube

and tube

.

Bad job - visible air gap between sample

Figure 3. Table of TEOl Measurements for Various Materials.

32
VO

IS)

II

C_3 > o: z

(-!(—<:

H- o I—

ea; uj c/i _j _J z

LU LU

O

q; I—I o Q 1

LO

00 00 CVJ <c CO Ln 1^

UJ o

an 00 o o

LlJ oc o

UJ CVJ CM

z:

1—1

1—1

St _i

OE E o o

<a: =c E

1—(

1—1 u

QQ

zn

q: 1—

LU UJ cu

t—

Z3 UJ

t—1 O

CVJ m1

• oX

CVJ E 1 E u o

C\J in r—

in CVJ CVJ 1^ • • o o o

zn.

II II II CJJ

ZIZ z z

H- UJ o

Q. _j 1—t

UJ 1— o Q < z UJ z o CO UJ

l-H o. 1— UJ s: > o

(>1 1—1 o Z I— UJ on

o. UJ UJ

z: U_ H- o u. u. o UJ «=c

UJ

•a: CD

I—I

CD

>-

c_>

cr

UJ

a: EOu

•iH Uwo

0)uC

(Up

»^

4-»

nJO

(0(U OJ

-0

ni

0) m

00

•iH

LD ro CVJ

NI H19N31 av3a

33
/\ T n A 1 K BEAD

LINE RESONATOR BEAD

INNER DIA. (cm) 0 .620 0.281 0.281

OUTER DIA. (cm) 1 .429 1 .589 1 .589

LENGTH (cm) 0.725 0.725

0.5,-

e = 4.56

r f = 19.35GHz

0

360°

BEAD

RESONATOR

0.4 -

0.3 -

0.2 -

0.1 -

FIRST EVEN

TE^^ RESONANCE

0 1 2 3 4 5 6 7 (19°) (37°) (56°) (74°) (93°) (112°) (130°)

FREQUENCY IN GIGAHERTZ

Figure 5. Measurement Data for 14 mm Bead-Line Before Compensation

34
35
AIR BEAD COMPEN.

LINE RESONATOR BEAD TOROID

INNER DIA. (cm) 0.620 0.281 0.281 0.620

OUTER DIA. (cm) 1 .429 1 .589 1 .589 1 .429

LENGTH{cm) 0.725 0.725 0.1 52

e = 4.56, e =1.71

r

' re

fQ = 19.35GHz ~ 360°

CURVE

I r D, S 1 n

^ f,

D^f f

Cos

^

AIR

LINE

BEAD

RESONATOR

I

0 ' 0

BEST FIT: D^ ~ -0.045 , \)

'0

+0.0071

AIR

LINE

BEAD

COMPENSATION

re

FIRST EVEN

TE^^ RESONANCE

I 0 1 2 3 4 5 6 7 8

(19°) (37°) (56°) (74°) (93°) (112°) (130°)

FREQUENCY IN GIGAHERTZ

Fig ure 7. Measurement Data for 14 mm Bead-Line After Compensation.

36
37
1 .0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

AIR BEAD

LINE RESONATOR

INNER DIA(cm) 0.304 .304

OUTER DIA(cm) 0.701 1 .778

LENGTH (cm) 1.549

e = 4.695

r fg = 8.93GHz

CURVE

"in

(1)

(2)

D^STn ^

0

RES FREQS

MEAS CALC

— Cos — ^0 ^0

BEST FIT: 0.01 , 0.74

6.41GHz

9 . 60GHz

5.5GHz

8.3GHz

21 4

I 6

I 8

I 10

90° 180° 270° 360'

FREQUENCY IN GIGAHERTZ

1 2 90'

Figure 9. Measurement Data for 7 mm Bead-Line Before Compensation

38
BEAD

0.5

0.4

0.3

0.2

0.1

AIR

LINE

RESONATOR

CAVITY BEAD

INNER DIA(cm) .620 .302 1 .563

OUTER DIA(cm) 1 .429 1 .589

LENGTH (cm) .725

e = 4.695

fQ = 19.42

FIRST EVEN

TE^^ RESONANCE

2 3 4

FREQUENCY IN GIGAHERTZ

5 6 7 '-90°~4.93GHZ

Figure 10. Measurement Data for 14 mm Bead-Line-Gap Before Compensation

39
BEAD

AIR RESONATOR

LINE CAVITY BEAD

INNER DIA(cm) .620 .302 .302

OUTER DIA(cm) 1 .429 1 .589 1 .563

e = 4.695, e = 4.529, = 19.42GHz

r

' ero '0

CURVE:

|r| = D-| Si n -— X COS

0 ' 0

BEST FIT

f

0

—

n

7""////TK

A

629cm

.725cm

D^ = -0.033,

D2 = +0.431

FIRST EVEN

TE^^ RESONANCE

FREQUENCY IN GIGAHERTZ

Figure 11. Measurement Data for 14 mm Bead-Line-Gap After Compensation

40
41

43
44
Figure 16. Profile View and Equivalent Circuit for

Derivation of Equation 1. 11.

45
46
47
APPENDIX A

CCG Work Statement

A. Project Title: Reference Noise Standard Development

B. Objective:

1. General: To develop an excess noise reference standard

to provide a basis for support of waveguide and coaxial

noise sources in use within the Department of Defense.

design and development of a calculable reference

standard noise source meeting the following technical

requirements:

(1) , Output Level: Optimize for use with the AIL

type 82 system

.

(2) Frequency Range: At least 100 MHz to 12 GHz .

(3) Stability: Suitable for use as a primary reference

standard for eight years

.

(4) Output Connector Type: Selected to minimize

comparison errors when calibrating standards with

waveguide, 14 mm, 7 mm, 3.5 mm and type N precision

connectors

.

(5) Operation Requirements: Suitable for operation by

standards laboratory personnel.

2. FY 1973 Work Statement:

a. Investigate and establish the direction for the

48
(6) Physical Requirements: Suitable for operation in a

standards laboratory and capable of being transported

between laboratories,

b . Prepare a detailed report on the noise source requirements

and investigation results.

Background: The requirement exists within DOD to measure the

operating noise figure of RADAR, missile, ECM and communications

receivers using automatic noise figure meters and excess noise

sources. The reliability of these measurements depend, among other

things, upon the accuracy in the excess noise ratio value (dB) assigned

to the noise source by DOD calibration laboratories . Over the frequency

range of 0.5 to 7 GHz, these values are not tested due to the lack of a

primary reference within DOD and at NBS. The major thrust of this effort

is to provide the basis to fill this gap in our measurement system

.

Approach:

1 . Investigate and establish the direction for the design and

development of a calculable reference standard noise source

.

Prepare a report documenting the noise source requirements and

the investigation results.

2 . Develop and evaluate design approaches for a reference standard

noise source. Prepare a report documenting the design approaches,

test results and the proposed design for a prototype standard.

49
3. Develop and evaluate a prototype reference standard noise source

meeting stated technical specifications . Prepare a report including

a description of the development and evaluation of the prototype,

design drawings and test and operating instructions.

Milestones:

1 . Evaluate loss , VSWR and repeatability on required 3 Aug 72

coaxial connectors to determine the effects on

final accuracies and decide on transmission line

dimensions

.

2 . Estimate feasible temperature distribution for 30 Sep 72

transmission lines necessary to achieve reasonable

accuracy.

3. Complete accurate determination of dielectric 31 Oct 72

constants for proposed bead materials.

4. Establish feasible design of a broadband, low VSWR 31 Dec 72

transmission line using beads to support the inner

conductor.

5 . Determine feasibility of using heat pipes to 31 Jan 73

achieve required temperature distribution of

transmission line.

6. Complete investigation of tractrix design at room 28 Feb 73

temperature for a broadband low VSWR termination.

50
7. Complete evaluation of feasibility of the manner 30 Apr 73

of bead supporting the inner-conductor for 1000°C

application

.

8. Complete the determination of the design for the 30 Jun 73

termination required to achieve a broadband low

VSWR termination that will withstand temperature

cycling to 1000°C. Complete final report for this

phase of the project.

51
APPENDIX B

Output Noise Temperature for a Coaxial Thermal Noise Source

First Order Calculation

An approximate expression for the noise temperature of a coaxial

thermal noise source is developed in this appendix. This equation takes into

account the different temperature and resistivity distributions along the

inner and outer conductors respectively

.

The development starts from equation (N.2) of NBS Technical Note 615

which gives the output noise temperature, T, of a thermal noise source in

kelvins

.

where~r,^,is the physical temperature (in kelvins) of the resistive element

terminating the line; is the available power ratio (less than unity) of the

line from the termination at /= O to the output connector atX=--? » T/ is

the physical temperature (in kelvins) at x of the inner and outer conductor

of the line; and is the gradient at x of the available power ratio of the

line. The first term in equation (B.l) is the noise from the generating resistor

attenuated by the line arriving at the output connector from the termination,

while the second term is the noise generated by the line arriving at the output

connector. The line is assumed to be slightly lossy, but otherwise ideal.

The connector is assumed to be lossless and reflectionless

.

(B.l)

52
The second term can be rewritten as

(B.2)

where the parenthetical factor is the noise power generated in the elemental

piece of line ilX at x. This factor applies to the case where the inner

and outer conductor have the same temperature and resistivity distributions

as a function of x along their lengths. The purpose of this appendix is

to develop an approximation for this factor that applies to a coaxial line

where both distributions may be different.

The factor / '^-x will not in general separate into a sum of two

terms, one representing the inner conductor loss and one representing

the outer conductor loss. Therefore, it is not possible in general to determine

how much of the noise is generated in either conductor separately, a determination made important by the differing temperature distributions of the

inner and outer conductors. However, to first order in the propagation

constant (Appendix C) this factor is separable, allowing a separation of

the noise into a contribution from the inner and from the outer conductors.

From Technical Note 615

53
where

and where "-^^ is the real part of the propagation constant for the principle

or TEM mode. X'c^ is the reflection coefficient of the terminating element.

From (B . 3) it can be shown that

O^r. = ZUiJ i-HTxl" \ (B.4)

Since I / is the reflection coefficient looking toward the termination from

the elemental segment of line dx at x and does not involve dx itself, only [X^

characterizes the loss of dx and consequently the noise generated by it.

does not separate into a simple linear combination representing the inner

and outer conductor losses. However, to first order oly becomes (Appendix C)

54
in which case

Since the inner and outer conductor losses are now separate and

identifiable their separate noise contributions can also be identified.

Correspondingly, if the inner and outer conductors have temperature

distributionsTi?^ and Tx© respectively, the noise from dx is given by

This noise is attenuated by before it reaches the end of the line

at the output connector. Thus the total noise output from the line is

(B.8)

which is the sum of the attenuated noise contributions from each of the

elemental line segments

.

When the attenuated noise power i^^ OC^ from the termination is added

to (B.8), the noise output T from the source is

.JJ l^0(,«+^\ (Tx. Ur: i-T.r. a,..V \ g/. (B.9)

55
Error in the First Order Calculation

By assuming a single average temperature distribution for the inner

and outer conductors which is flat from the termination to some point where

the distribution goes through a transition to room temperature and is again

flat out to the output connector , an order of magnitude estimate of the relative

error (^T in the noise temperature T is obtained and is given by

,£T ^ KT. . LT^ (B.IO)

The first factor b>~\~\ / is the relative correction to the termination

temperature , and the second factor tTVi. I t~T\ is the relative error in

this correction . Using the above distribution an estimate for the factors

results in the following two equations:

Jill-. iLJL /.T^-T^^ (B.ii)

and

is the length of line from the start of the temperature transition to the

output of the source, R is the average resistance per unit length for the

length of line -3 , Tj^ is room temperature, 2.o is the characteristic line

impedance, and l_^,jis the line inductance per unit length.
For the standard envisioned in this report the relative error calculated

-7

from equation (B . 10) is of the order of 10 .

57
APPENDIX C

Propagation Constant of a Coaxial Line

The real part U of the propagation constant for the TEM mode in a

coaxial line is given by^"''^'^

where

and

X)r, = outer diameter of inner conductor,

•1^*1 = inner diameter of outer conductor,

"f = frequency in hertz

= resistivity of inner conductor in ohm-meters,

= resistivity of outer conductor in ohm-meters.

58
jU^ = magnetic permeability of the dielectric (air) between

conductors in henry/meter,

J-^"^'- = magnetic permeability of inner conductor in henry /meter,

J-^Qo - magnetic permeability of outer conductor in henry/meter,

^6 = dielectric constant of free space in farad/meter,

= relative dielectric constant of dielectric (air),

R = resistance in ohms/meter,

L = inductance in henrys/meter,

C = capacitance in farads/meter

,

G = conductance in mhos/meter ( zero for air dielectric)^

To second order in 1^/60) \_ a and (^/coi1^

U=. u^iuc/i^l^ s , m. V2_ \ (C.2)

For a line containing a perfect dielectric ( G = 0) , to second order in *c/coL,

which reduces to first order in tL/^'i^3^hen

]L<C<CoUo- (C.4)

When (C.4) holds, CL can be written as

59
where

(C.6)

and

Z CO Uo

(C.7)

60
APPENDIX D

Design Formula for the TEOl Circular Mode Resonance Measurement

(2) An intuitive picture of the relative dielectric constant measurement

using the TEOl circular resonance in a waveguide-below-cutoff cylinder

containing a sample of the material under consideration can be drawn as

follows . Consider a hollow air-filled cylinder which is below cutoff for

a particular waveguide mode, but which is above cutoff inside a dielectric

material sample located in the cylinder . Then for a particular length of

such a sample there exists a particular frequency for which the cylinder

and sample act as a resonant cavity at its resonance frequency. This frequency

is uniquely related to the sample length, the diameter of the cylinder,

and the dielectric constant of the sample. Therefore, if the length and

diameter are known , the measurement of the resonant frequency will yield

the dielectric constant of the sample . It will clearly work only when the

mode propagation constant is real inside the sample and imaginary outside.

From Appendix E it can be seen that this requirement implies that

where is the free space wavelength, /\^ is the cutoff wavelength in the

sample free part of the cylinder, and ^ r-is the relative dielectric constant

of the sample material. In terms of the frequencies corresponding to these

wavelengths

,

61
>-e>-f;C'" (D.i)

defines the range of frequencies over which a resonance can be expected

to work (figure 2) .

The circular TEOl mode is particularly useful in high temperature

measurements since its electric field vanishes at the cylinder walls. Therefore,

the resulting measurement of ^L^is much less susceptible to error from air gaps

between the sample and the cylinder, allowing the cylinder and sample to be

heated without introducing large errors. A useful expression for G^-is

(Appendix E with A = 1) ,

.

where }\aA is the guide wavelength in the dielectric.

(2) For the TEOl mode in a sample of length L to resonate is given by

^ ^L (D.3)

where y is a solution of the equation

L| ~fcsUvA„ — C

and

62
The cutoff wavelength for a partictilar diameter D is given by^'''''''^

C>,^ZC>J) (D.4)

for this mode

.

63
APPENDIX E

Propagation Constant in a Lossy Dielectric

This appendix contains an expression for the propagation constant

that is used in the two preceding appendices and is given here for convenient reference

.

The propagation constant for a particular mode in an ideal waveguide of

cylindrical symmetry filled with a lossy dielectric is given by^"'^'^'^

(E.l)

where

i/Zl l/Z.

In these expressions ~tA'^ ^ is the dielectric loss tangent, Gr-is the relative

dielectric constant (Appendix F), A is the free space wavelength,

64
guide wavelength in the dielectric, and '/^ is the cutoff wavelength for the

air filled guide. is infinite for the TEM mode of propagation

.

These expressions can be manipulated to give the following expression

for C : r

€r = ^ . A'A" (E.2)

where

For most cases ^^is given by equation (E.2) with A equal to one. For large

loss tangents however a better value for Gr- is given by equation CE.2) by

iteration, starting with A equal to one, obtaining the first approximation to

Q ^ , and proceeding to iterate using the resulting value of A.

65
APPENDIX F

Dielectric Constant Measurement Using the Automatic Network Analyzer

The complex relative dielectric constant of a dielectric material

(12, 13) completely filling a length of ideal waveguide is given by

and is obtained from the ANA data as:

where the S's represent the components of the 2x2 scattering matrix representing the length of dielectric filled waveguide section being measured

.

is the relative dielectric constant and is equal to ^ is the loss

tangent and is the ratio of C" to 6 ' . The last expression obtains where

the waveguide and material form a reciprocal junction.

These expressions are used in the following program written for

the automatic network analyzer^ \

66
ANA Program

5 DIM EC881^GC881

6 PRINT

7 PRim

10 pp. D I ELECTS. I C ANALYSIS

15 LET Q 1 =Q2=Q3=Q4=Q9=0

20 DIM SC32]^DC88>4]^MC88] ,FCBS] >ACS8],DCS3]

25 LET C9 = 2. ^965^^E-04

26 PRINT "AVERAGE DATA?

27 CALL (4 ULl ) 29 IF L1=C^ THEM 26

30 CALL (3^SC 1 1^ '1, 1 ) 40 LET F=SC27 1 50 FOR M = SC141 TO S C 1 4 ] + IMT ( ( S [ 3 ] - 1) /8 ) 60 LET Ml=S*(rJ-SC 14] ) + l 70 CALL CS^DTMU n , 0^M)

80 MEXT M

90 LET Ml = l +(SC 121-SC 1 1 1 )/SC 131

100 FOR M=l TO Ml

110 LET FCM1=SC 1 n+SC 131*(M- 1 ) 120 LET MCM1 = 1 +(FCM1 -SC 1 ] )/S[2]

130 MEXT M

150 REM CALC E PARAMETERS

155 CALL ( 14^ U0^C1 ) 156 IF Ll=l TKEM 3000

1 60 FOR M= 1 TO Ml

170 LET K=MCM1

1-75 IF S[3n = -1 THErj 210

1 80 LE*^ SI =DCK^ 1 1 185 LET S2=DCK^21

190 LET S3=DCK,21

1 95 LET S4=DCK, 11

200 GOTO 230

2 10 LET SI=DCX^n

215 LET S2 = DrK>2"!

220 LET S3=D[K>3]

225 LET S4=DCX^4]

230 CALL (12,S2>S3^C3)

235 CALL (12,SUS4^C4)

240 CALL (10^SUS4^C5)

245 CALL (10^CUC4>C4)

250 CALL ( 1 1 >C4, C3,C3)

255 CALL ( 13^C3, C5,C2)

260 CALL ( 1 1 >C2>C1 >C4)

265 CALL (10>C2>CUC5)

270 CALL ( 1 3^C4> C5^ G6)

230 CALL_ 115 , C6, EIM 1 > G CM 1 ) 2^)0 LET 3CM"!=-GCM]

3'^0 IF G!:mt>0 THEM 315

67
3 1 5 IF L 1 = 1 T H EN 4 00

32^) MEXT N

33?) PR INT

3 63 PPIMT " FUMCTIOM ";

365 INPUT J

37'7! IF J= 1 THEN 400

TIT 'r = P TUPTT 54 0

3 ?0 IF J=3 THEN 1000 / 335 IF J =4 THEN 9 000

39!^ GOTO 3 60

REN

40 1 PRINT "TITLE?**; ' _ - 402 CALL ( 4 1 ^ Q

)

4 0 3 T5 r? T f TT , 4 1 0 P^INT "FPEQ";T ABC 1 3

) "E* (NEAS ) "j TABC ^7

)

**E ' • C '!EAS ) " ; 4 1 3 PRINT TA3(4 1 ) **N"; TABC 53 ) '*K"

4 20 PRINT

425 IF Ll = l THBJ 44 5 • 440 FOR N=l TO Ml

44 5 IF E!:n]<1 then 50 6

450 GOSTTB 645

490 PRINT FCN 1 ; TABC 1 0 ) ; E CN 1 ; T A3 C 2 5 ) ; G CN] ; TABC 40) J D2;TA3C55 ) J Dl

500 ' GOTO 508

506 P^INT "BAD DATA**

5 0B IF Ll=l THEN 610 ^ 5 1 0 NEXT N

5 20 PRI'^IT

530 GOTO 3 60

5 40

550 PRINT "TITLE ?'*;

560 CALL C4U''^)

610 P^INT . 6 1 1 P^INT " LOSS REEL LOSS'*;

6 1 5 p^INT " RESlSTIUI'^v WAVELENGTH'*

620 PRINT "F'^.EO** ;TABC 1 4 ) "C DB/ IN ) ";TA3C 23 ) " CDE-NAX) ••; A o c O f- o PRINT TABC 4 1 ) " C OHN- CN ) " ; T A3 C 53 )

** C ) " 6 30 PR I ""IT 6 35 IF LI = 1 "^H EN 64 1 64 0 PO^ N= 1 TO N

1

64 1 IF ETN >< 1 THEN 7 40

64 3 GOSTIB 64 5

6 4 4 G 0 0 7 20

64 5 LPT X4 = S Q C E [ N It 2 +G C 3^2)

6 5^ LpT Dl =S0^C .5*CX4-F^N1)

)

6 60 LET D2 = 30^.C . 5*CK4 + E[N 1 ) ) 67 0 LF'^ D3 = 3 . 686*C9*D1 *FCN ]--te2. 54

6 ^

''^ LET D4=l 1802.3/CFC^n*D2)

6 90 LET D5=C C 1 +D2)T 2+Dl t 2)/C C 1-02:- " 2 + D1t 2)

695 LET D5 = D5yCD5-l)

7 0 0 LET D6=4 .3 43*L0G CDS)

704 IF GCNl>'''^ THEN 7 10

68
7r?6

7 1 '^ 7 15

7 20

730

74'?)

7A5

750

760

100 0

1020

1030

1040

1050

1 060

1 1 30

1 135

1 140

1 150

I 1 60

1 1 65

1 170

1 180

1 185

1 190

1195

1 20 0

1 260

1 262

1 265

1 27 0

1 27 5

1 28^^

1 290

1 300

1310

1320

133-^

1335

1 340

1350

13 60

1 37 0

1 380

1390

14 00

1410

1420

14 30

1 44 0

1 4 5 0

LET D7= 1 . 0 3000E + 20

GOTO 715

LPT D7= 1 . 8 0000E + 06/ (G CM ^ ^FCN 1

)

P E T

^

' ^I'J ?"IMT rem ."^ABc 1 0 ) ; D3; tabc 25 ) ; d6;tab(4 3 ) ; d7 ; A,nr

GOTO 745

P'^. IMT "BAD DATA"

IF Ll = l THET^I 9 00 0

MEXT N

GOTO 330

P. EM PLOT PO UT I r J E

PPINT "SET PAPE^ SCALE ?";

CALL (4UQ)

IF Q.= 1 THEM 1130

I

p- o = _ 1 T H EM 1 2 0 0

GOTO 10 10

CALL (40^15^J1)

MAIT (500)

IF Jl <0 THEM 1195

CALL (40,0^J2)

I F J2<0 THEM 1170

GOTO 1 1 85

CALL (43,255^255^1)

GOTO 1130

CALL (43>0>0W)

GOTO 1130

CALL (43,0,0, 1 ) P ^f"f CALL (43,255,0,1)

LET J8=2

^PIMT "PLOT TYPE, SCALE ",* IMPUT J9,J8

IF J9 = 1 0 THE!;- 3 60 . IF J9<1 THEri 1265

IF J9> 1 0 'f'HEM 12 65

FOP M= 1 TO

IF J9=l ^HEfJ 1400

IF J9=2 THEM 1420

IF J9=7 THEM 144 0

G0STT3 64 5

IF J9=3 THEM 15 00

T !-{ E'-J 15 20

THEM 1540

THEM 1560

THEM 1580

THEM 160 0

J9 = 4

J9 = 5 J? = 6

J 9 = 8

J9 = 9

IF

I F

I F

I F

IF

LFT v = t7^m;)

GOTO 170 0

LET Y = G!:m]

GOTO 17-^0

LET ^=ECM]/G[M1

GOTO 1700

69
1500 LET Y=D2

1510 GOTO I7d^

1520 LET Y=D1

;il53 0 GOTO 17-^0

1 540 LET ^ = D3

1550 GOTO 1700

1 560 LET Y = D6

1570 GOTO 170^

1580 LET Y=D7

1 5Q0 GOTO 1700

1600 LET Y=D4

1610 GOTO 17 0,0

1700 GOSTJB 2000

17 10 M EXT M

1720 GOTO 1260

2000 REM PLOT DATA POINTS

200 5 IF ECN3<1 TiiEM 23 SO

2010 LET X = 8 5* ( . 434*L0G (FCM 1

) - 2)

2020 LET Y=l 27. 5+( .434*L0G (Y)+2-JS

)

2030 IF Y>0 mm 2050

2040 LET Y=0

20 50 IFY<=255 THEM 207 3

2060 LET Y=255

2070 CALL (43^X^ Y^ 1

)

20 30 P-ETURM

3000 CALL (14>Mi^0,C8)

3010 LE'^ J=l

30 15 GOSUB 3 200

3 020 CALL ( 1 3^^.^C8,S1 ) 3025 LET J=2

3 03 0 GOSUB 3 200

3035 CALL (13,Z,C8,S2)

304 0 IF SC3n = -l THEN 3100

3'^45 LET S3 = S2

3050 LET S4=S1

3055 GOTO 3150

3100 LET J=3

3105 GOST^B 3200

3 110 CALL C13^Z^C8,S3)

3 115 LET J=4

3 120 G0STT3 3 20 0

3125 CALL ( 1 3>Z^C8^S4)

3 1 5-0 LET M = 1 3 160 LET FC 1 ]= (EC 1 ^+FCM1 ] )/2

3 170 GOTO 23''^ 3 20 0 CALL (14,0^0^7.)

3 210 FO" M=l TO

3220 LE*^ T^-•'^^]]

3 23 0 CALL ( 10^DrK, J] ^7^T)

3 24 0 MEXT n

3 25'^ ^ET'T'^.''T 9 00 0 CALL (2^F)

999 9 ENID

70
APPENDIX G

Curve Fitting Equation for Bead and Line Trimming

(5) MacKenzie and Sanderson give a formula for the imaginary part

of the impedance at the center of a dielectric bead in a coaxial line as a

function of frequency. They use this formula to determine the amount

of under and/or overcutting of the line, and beadface compensation necessary

to achieve a low VSWR for the bead support. Since they do not give a

derivation of this formula, this appendix is devoted to deriving a formula

for the reflection coefficient of the bead analogous to their formula for

the imaginary part of the impedance .

Figure 15 is a schematic representation for the TEM mode representation

for a bead in a coaxial line . The region between and including the step

discontinuity capacitances C (Appendix H) is the region in which the bead

support resides. The capacitances arise from the step introduced by overcutting

of the outer conductor and undercutting the inner conductor to make 2 , »

the characteristic impedance of the line in the bead region, the same as '^o >

the characteristic impedance of the normal air filled portion of the line.

The presence of the additional capacitances C introduces a lumped circuit

shunt reactance at the bead faces thus producing a reflection of the TEM

wave. In order to offset this additional capacitance and do away with the

reflection, some of the dielectric material is removed from the bead faces,

i.e., a groove is cut in each face

71
The impedance is the parallel combination of the capacitance C

and the characteristic impedance 2^ . This impedance will be more fullydiscussed later in Appendix I.

The impedance £3 is transformed through the bead region. For

the lossless bead

^..Z ^,4- (Z. ta^pO \ (G.l)

where ^is the imaginary part of the propagation constant in the bead, or

G,^ is the real part of the relative dielectric constant, and A is the free space

wavelength. Finally ^is the impedance at the other face of the bead consisting

of l/coC and H:^ in parallel, and is supposed to equal for reflectionless

bead design . ,

?.

^ - : X (G.2)

where l/O^C .

V is the reflection coefficient looking to the right into the bead and is

given by
When —j X is expressed in terms of and this equation can be written in

terms of » . ^ » and"6x^^2. . Since and will be close to "2.^ it is

convenient to write

2,= £.+

and

where ^"^ii and are small and vanish as the bead and line are trimmed.

When these are substituted into (G. 1) , and (G.3) is reduced to first order in

^2., and S £.i.the following expression for the magnitude of P results:

4

iru 1 8^, S^^pci-h&^^e^-ar^n (G.5)

where 8^ /and Si^^are the impedances and ^Z^divided by £0 , or the

corresponding magnitude of the reflections caused by ^1 being different from

, and C being nonzero, respectively.

Using the expression for 2^ given in Appendix I leads to

(G.6)

where

73
d is the depth of the compensation cut into the bead faces, A.o is the depth of

cut for full compensation , is the measured reflection from the bead

faces at ~Co where the bead is one wavelength in length, ^e> is the desired

characteristic impedance (50 ohms) , is the relative dielectric constant

of the bead material , is the effective relative dielectric constant

of the bead in the compensated region for which '^02. is the normalized

characteristic impedance, and X is the total bead length,

is given by

where <^ and ^are the inner and outer conductor diameter respectively in

the air-filled regions, and CX! and are the conductor diameters in the

bead region that have been chosen to make ^, approximately one. If O.' and

i-' have been chosen correctly for the given dielectric constant, then will

be unity. However, if (X' is too large by Sd} and "d-' is too large by ,

and too large by S , that is using

then using (G.7) and (G.8) and keeping only first-order terms in Sa.7<3L,

btr/'^ and /^r gives (for the 50 ohm line)

(G.9)

74
(5) The electrical phase shift can be interpreted in the following way :

(hi = e-n-c^i _ ;it4 _ zj^ (G.io)

where

Ae is the electrical length across the bead, ^ is the speed of light, and -^^

is the frequency for which J.^is one wavelength.

Equation (G.5) can now be rewritten as

irU ) "b, £;^2iif 1^ (W2irf \ (G.ii)

where

and

Equation (G.ll) is used in the bead and line trimming procedure for obtaining a low reflection coefficient.

75
APPENDIX H

Step Capacitance

Combining the equations given in Moreno ^

"'^ ''^ , the following

expression for the step capacitance in picofarads at the uncut face of the

bead support results:

(H.l)

where the first capacitance per \anit length J^^iis given by figure 6-21 in Moreno

and the second by figure 6-22. , A, "(r , A' , and are defined in

Appendix G. After some of the face material has been removed this capacitance

changes to C , where

C>C'>€.^C/€r (H.2)

and where &^^s the effective dielectric constant associated with the compensated part of the bead (Appendix I) .

The value for C given by (H. 1) should be multiplied by a frequency

factor ^^"'^^ when'}\, the free space wavelength, becomes an appreciable percentage

of^ -<X ; and should also be multiplied by a proximity factor accounting

for interactions between the fringing fields from the step discontinuities when

the bead length approaches

76
APPENDIX I

Effective Dielectric Constant and Face Compensation

In order to nullify the step capacitance and its resultant reflection

a toroidal groove is cut into each end face of the bead support. The depth

to which this groove is cut is determined by the amount of step capacitance

to be nullified, the dielectric constant, and the inner and outer diameter of

the toroid

.

An exact formula for the compensation depth can only be obtained by

a detailed consideration of the interaction between the evanescent modes , the

step, and the compensated bead. An investigation of this magnitude is

both beyond the scope and needs of this report. Therefore, the following

intuitive derivation is presented that gives an order-of-magnitude estimate of

the depth . It has proven quite useful and adequate for the purpose of trimming

beads

.

Figure 16 shows a profile section of one end of the bead support

and its equivalent circmt. The compensating toroidal region of length cH has

an effective dielectric constant €lr^ • is the capacitance per unit length

in the uncompensated bead region. Through this compensating region of

characteristic impedance the TEM wave travels with a propagation constant 3 • The magnitude of the step capacitance C' lies between C

and depending on the dimensions of the toroidal compensating

section where C is the step capacitance when cS.= C> or before any compensation

77
is effected. The diameters of the various regions are shown in the profile, and

are such that

(i.i)

which give a characteristic impedance of "2

(7) Using the equations given by Cruz the following relationships can be

derived for Ct< , andX*

4-

(1.2)

(1.3)

(1.4)

where Go is the free space dielectric constant.

The impedance 2'uis given by

(1.5)

where"£.is the parallel combination impedance of C and i.^

78
That is

,

^

f'X (1.6)

where

X ^ 1 /60 C'

and where'^is the radian frequency. The approximation in equation (1.6)

is quite adequate for the present needs

.

When equation (1.5) is reduced to first order in^/x the following expressions result:

where

where is the free space wavelength. Then S^-^can be reduced to

where is the free space speed of light and is the frequency.

(1.8)

79
The approximation"t(>A^il ^ has been used in arriving at equation (1.8)

and is in keeping with the approximate nature of the derivation. For the

experimental work it is convenient to define a measured parameter I^z which

represents the reflection coefficient caused by the uncompensated or partially

compensated step capacitance.

= ~ ^

4^:. (1.9)

where is frequency independent.

It has already been stated that the step capacitance C^is a function

of the dielectric configuration to the left of the step capacitance in figure 16

.

From what has been stated in Appendix H it is clear that C'^can vary from C given

by equation (H.l) for A~D , to G^^Cl when J.=-CO . There is some

depth (Jlc. where the compensating toroid just nullifies C causing the reflection

and to vanish. It has been found experimentally that C' is given approximately by CLQr^£x^ / when . That is, the value G.r of the

dielectric constant for C when the compensation depth is correct (no reflections) is given approximately by the geometric mean of and (£1-^ . Clearly,

Qx~ varies in some nonlinear fashion as is varied. However, for the estimate

here it is sufficient to assume that Gr varies linearly from (£k when cL= <0 to

C^r CviL^) when <^ = c^a . That is

Cr = Cr- -f £.r-a..^ri^\ & . (1.10)

80
When equations (1.8), (1.9), and (1. 10) are combined the following approximation

for the measured parameter results:

P^^Cl)^^oCl-i/Jo) (1.11)

Jio rr _Z.^ r'hA. d (1.12)

where (iD^^o is the value of ^-j^ when cll= £? ,and is the total bead length.

81
APPENDIX J

Higher Mode Bead Resonances

(14)

In an unpublished paper Bussey and Beatty show a way to calculate

higher mode bead resonances in a coaxial line that is not over or undercut.

They have indicated that, in the case of over or undercutting, their simple

approach must be modified in three essential ways: 1) the ^A-for the

appropriate regions, the uncut and cut region, must be used; 2) some account

for the step capacitance due to the cutting must be made; and 3) since the

two regions have different dimensions, the characteristic impedances for

the higher modes rather than their wave impedances must be used in the

impedance transformation formula.

Following is a derivation for the resonant frequencies of the TE modes

in a bead where the inner and outer conductors may be under or overcut

respectively. The derivation ignores modifications 2 and 3 above, but

follows the Bussey and Beatty derivation for the uncut line almost step for

step. The only justification offered for this procedure is that it has proven

useful in predicting the TEll resonant frequencies observed in the experiments.

Figure 17 shows a coaxial line in the region of a dielectric bead support.

2© and are the characteristic impedances (taken to be the wave impedances)

for the air and dielectric regions of the line respectively. and

are the propagation constants of the two regions, ( i£ understood)

and A^o and /\^^ are their cutoff wavelengths . The impedance i is

given in terms of by

82
where

,(14) and

^ = OQ for the even cavity modes

^ = 0 for the odd cavity modes,

is the radian frequency; JJ^ is the magnetic permeability of the dielectric

bead which is taken to be that of air

.

Further

,

^» = .4i^^ (J. 2)

The propagation constants are given by

and

The cutoff wavelengths for the TEml modes are^''^''^'^

1/^

83
where b is the inside diameter of the outer conductor, k is ratio of the outer

conductor inner diameter to the inner conductor outer diameter, and the

denominator is obtained either from tables, or graphically (see Appendix K)

(14) The condition for resonance is taken to be

(J. 5)

where the star signifies complex conjugate. This condition leads to the

following conditions for resonance

for the odd modes

(J. 6)

for the even modes

After a compensation cut into the bead faces has been made, is taken to b

the length of the uncut portion of the bead between the bead faces

.

84
APPENDIX K

TEll Cutoff Wavelengths

The cutoff wavelengths for the higher TEml modes in a coaxial

line are given by equation (J . 4) of Appendix J . The denominator of that

expression for the TEll mode can be obtained from figure 18 which is a graph,

of the denominator as a function of k . is a root of

Z'cfO Ni.'CW -HCh.%) = 0 (K. 1)

for a given value of k. J and N are Bessel functions of the first and second

kinds respectively . A table of values for x as a function of k extensive enough

for the present investigations was not found. Therefore a simple graphical

technique ^''"^'^ which only requires evaluating the ratio / was

employed to find the needed roots . This technique considerably reduces the

effort in finding x for equation (K.l), and provides sufficient accuracy for the

needs explained in Appendix I

.

85
APPENDIX L

Termination Design Equations

The resistance of a truncated cone of semi -angle© (figure 12) and jQ

(8) surface resistivity is given in the paper by Woods as

^= 0 .JL,-^/a. (L.i)

which reduces to the familiar equation

-^^L^irlcL (L.2)

where ^ is the wave impedance of the medium

.

Since the main field penetrates the film and sets up auxiliary fields

within the substrate, there are interactions which take place. The resulting

second order effects are handled by the following (figure 12)

-6; 4-

and

86
5. REFERENCES

(1) DayWitt, W. C. , Foote, W. J. , Campbell, E. , "WR15 Thermal Noise

Standard," NBS Technical Note 615, issued March 1972.

(2) Cohn, S. B., Kelly, K. C, "Microwave Measurement of High-Dielectric

Constant Materials, " IEEE Trans . on MTT, Vol. MTT-14, No. 9, Sept. 1966

(3,4) Bussey, H. E. , Private Communication, National Bureau of Standards,

Boulder , Colorado

.

(5) MacKenzie, T. E. , Sanderson, A, E., "Some Fundamental Design

Principles for the Development of Precision Coaxial Standards and

Components," IEEE Trans . on MTT, Vol. MTT-14, No. 1, Jan. 1966.

(6) Whinnery, J. R., Jamison, H. W., Robbins, T. E., "Coaxial Line

Discontinuities," Proc. IRE, Nov. 1944.

(7) Cruz, J. E. , "Experimental Verification of an Equation for Determining

the Effective Dielectric Constant of Center Conductor Supports in Coaxial

Transmission Lines," unpublished, NBS Report, March 1966.

(8) Woods, D. , "Improvements in Precision Coaxial Resistor Design,"

IRE Trans, on Inst., pp. 305-309, Dec. 1962.

(9) Harris, I. A. , "The Theory and Design of Coaxial Mounts for the

Frequency Band 0-4000 mc/s," Proc. lEE, Vol. 103C, Monograph

No. 132R, pp. 1-20, May 1955.

87
(10) Nelson, R. E., Coryell, M. R., "Electrical Parameters of Precision,

Coaxial, Air-Dielectric Transmission Lines," National Bureau of Standards

Monograph 96, issued June 30, 1966.

(11) Moreno, T. , "Microwave Transmission Design Data," Dover Publications

Inc .

,

New York , 1958. '

(12) Sucher, M. , Fox, J. , Eds. "Handbook of Microwave Measurements,"

Third Edition, Vol. II, Chapter IX, Polytechnic Press , New York, 1963.

(13) HoUey, A. , Private Communication, Hughes Aircraft Company.

(14) Bussey, H. E., Beatty, R. W., "Higher Mode Resonances of Dielectric

Support Beads in Coaxial Lines," unpublished, NBS Report,

June 1966.

II II

(15) Truell, R. , "Concerning the Roots of Jn(x)Nn(kx) - Ai(kx)Ni(x) = 0,"

J. of Appl. Phys., Vol. 14, p. 350, July 1943.

88
FORM NBS-n4A (1-71) U.S. DEPT. OF COMM. 1. PUBLICATION OR REPORT NO. 2. Gov't Accession

B'BLIOGRAPHIC DATA j^gglR 73-334

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

A Broadband Coaxial Noise Source

Preliminary Investigations

5. Publication Date October 1973

6. Performing Organization Code

7. AUTHOR(S)

W. C. Daywitt and L. D. Driver

8. Performing Organization

0 DCD IT r\D kilM/^ /^D 4 M I 7 A T'l/^M M A A MF^ A V\ VWi C CC PiiKr UKMINO UKLiAIn1Z,A1 IL/rsJ JNAMt, ANU AUUKr.c>c> NATIONAL BUREAU OF STANDARDS, Boulder Labs.

DEPARTMENT OF COMMERCE

Boulder, CO 80302

10. Project/Task/ Work Unit No. 2726449

11. Contract/Grant No,

Program 73-78

12. Sponsoring Organization Name and Address Department of Defense, Calibration Coordination Group

Attn: Melvin L. Fruechtenicht, Chairman

Army Metrology and Calibration Center, Redstone Arsenal

Huntsville. Alabama 35809

13. Type of Report & Period ^"""^'^ Interim Status

Report - FY 73

14. Sponsoring Agency Code

15, SUPPLEMENTARY NOTES

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

bibliography or literature survey, mention it here.)

This report describes investigations that were performed in fiscal year 1973, by

the Noise and Interference Section of the Electromagnetics Division of the Institute for

Basic Standards of the National Bureau of Standards preliminary to the design and

construction of a coaxial thermal noise source in fiscal year 1974. The intent is to develop a coaxial thermal reference noise source that will operate at nominally

1000 C and will have a low reflection coefficient from 0 , 1 to 12 GHz

.

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

Bead support; noise standard; resistive termination.

18. AVAILABILITY STATEMENT

r "1 UNLIMITED. ^

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

22. Pr

USCOMM-DC 66244.P71

ISCOMH EJU.