UNITED STATES EPARTMENT Of IOMMERCE

"UBLICATION NBS TECHNICAL NOTE 615

U.S.

:PARTMENT

OF

:OMMERCE

National

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QC

100

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WR15 Thermal Noise Standard
NATIONAL BUREAU OF STANDARDS

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•*mm bureau of simtm

JUN 8 1972 UNITED STATES DEPARTMENT OF COMMERCE

» (J 57 i Peter G. Peterson, Secretary

l)i$, NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

19>

NBS

•fc TECHNICAL NOTE 615

ISSUED MARCH 1972

Nat. Bur. Stand. (U.S.), Tech Note 615, 154 pages CODEN: NBTNA

WR15 Thermal Noise Standard

W. C. Daywitt, W. J. Foote, and E. Campbel

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

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

(Order by SD Catalog No. C13.46:615), Price $1.25

ERRATA

Page No

.

Line No. Erratum

17 15 "Silicon" to "Silicon carbide"

16 "Silicon" to "Silicon carbide"

last "beryllium" to "beryllia"

21 7 "varified" to "verified"

31 last "Si" to "SiC"

32 7,12,25 "Si" to "SiC"

33 2,6,9,10 "Si" to "SiC"

12,14,20

CONTENTS

Page

ABSTRACT 1

1. INTRODUCTION 1

2. ANALYSIS 4

2.1. Noise Temperature Output 4

2.2. Error Analysis 8

2.3. Critical Design Specifications 11

3. DESCRIPTION AND DESIGN 12

3.1. Internal Oven Components 15

3.1.1. High Temperature Resistive Generator-- 16

'3.1.2. High Temperature Waveguide 18

3.1.3. Heat Distributor Assembly 20

3.1.4. Thermocouples 22

3.2. External Oven Components 24

3.3. Auxiliary Components 26

3.3.1. Temperature Measurement System 26

3.3.2. Heating Control System 27

3.3.3. Cooling System 29

4. MEASUREMENTS AND OBSERVATIONS 29

4.1. Internal Oven Components 31

4.1.1. Thermocouple Accuracy 31

4.1.2. Lossy Termination Materials 31

4.1.3. Reflection Coefficient of the

Termination and Waveguide 32
CONTENTS (Continued)

Page

4.1.4. High-Temperature Waveguide Loss 34

4.1.5. Thermocouple Insertion Distance 34

4.1.6. Inconel Heating Test 35

4.1.7. Heating Coil Resistances 36

4.2. External Oven Components 36

4.2.1. Zirconium Oxide Insulation 36

4.3. Auxiliary Components 36

4.3.1. Residual Thermal EMF 36

4.3.2. Copper Lead Resistance and Resulting

Measurement Error 37

4.3.3. Water Temperature Control and

Measurement 37

4.4. System Performance 38

4.4.1. The Termination Temperature 38

4.4.2. Determination of the Waveguide

Temperature Distribution 38

4.4.3. Temperature Measurement Repeatability- 41

4.4.4. Wall Temperature Distributions 42

4.5. Additional Measurements 43

4.5.1. Oven Power Consumption 43

4.5.2. Laboratory Environment 43

IV
CONTENTS CContinued)

Page

4.6. Possible Improvements 44

4.6.1. Thermocouple Grooves 44

4.6.2. Isolation between Heating Coils -- 45

4.6.3. Diameter of the Heat Distributor 45

4.6.4. Different Wall Temperature

Distributions 46

5. ACKNOWLEDGMENTS 47

6. REFERENCES 48-50

7. FIGURES 51-105

8. DRAWINGS 106-109

APPENDICES

A. The Output Equation 110

B. Quantum Correction 114

C. Error Calculation 116

D. Computer Calculation of AT and 6AT 119

E. The Thermocouple Rod Expansion Program 121

F. Termination Formula 122

G. The Minimum Termination Length- 123

H. Waveguide Reflections 127

I. Atmospheric Attenuation 128
CONTENTS (Continued)

Page

J. Support Spider 129

K. Thermocouple Rod Expansion 130

L. Lead Resistance Error 132

M. Oven Temperature Control 133

N. Derivation of the Output Equation 137

VI
WR15 THERMAL NOISE STANDARD

W. C. Daywitt, W. J. Foote, and E. Campbell

ABSTRACT

This note describes the design and construction

of a WR1 5 thermal noise power standard. The standard is designed to operate around the Silver Point

Temperature (963.19°C) with a noise temperature output accurate to approximately ± 2 K.

Complete details of the theory, design, con- struction, and performance tests are given.

Key Words: Noise; Thermal noise standard; Millimeter wave; Error analysis; Nyquist's theorem.

1. INTRODUCTION

This note describes the analysis, design, construction,

and performance tests of the NBS WR15 Thermal Noise Power

Standard. This standard consists of a 0.148" x 0.074" I.D.

rectangular waveguide that is terminated by a well matched

load. The load and waveguide are heated to approximately

962°C in a specially designed oven. The noise temperature

output of the standard is approximately 1235 K and is known

to an accuracy of approximately ± 2 K. A sample of the output

temperature T as a function of frequency is shown in

figure 1.1.

The description of the standard is divided into three

parts: The internal oven components; the external oven
components; and the auxiliary components. The internal

components include the high temperature resistive generator

or termination, the inconel heat distributor and heating coils,

the high temperature platinum 101 rhodium waveguide, and the

thermocouples . The external oven components include the oven casing and the cooling coils. The auxiliary components

include the control rack containing the oven temperature

monitor and controlling circuits, and the recirculating cooling system. Photographs of the total system are shown in

figures 1.2, and 1.3.

Before the design and construction were begun, a thorough error analysis of the proposed standard's noise

temperature output was performed to determine the necessary

design specifications for holding the error to approximately

± 2 K. This error analysis along with the noise output

calculation were computerized and used to determine the final

error estimate.

The rest of the report is divided into three sections,

each with a number of subsections. Where necessary they are liberally augmented by appendices to avoid destroying con- tinuity, and a large amount of cross-referencing to avoid

excessive repetition. The figures and drawings are labled

alphanumerically , where the number or letter before the

decimal point indicates in which section or appendix the

principle discussion of the figure is to be found.
The discussion of noise power output and error calculations for the standard are contained in section 2. The discussion of important design specifications resulting from these

calculations is found there also. Section 3 contains a description of, and the design and construction details for

the standard. Measurement results and observations taken

during the course of construction and final testing of the

standard are found in section 4, as are the performance tests

supporting the output and error calculations.

In many cases detail drawings of an item under discussion

are not presented and the reader is hereby referred to the main

assembly drawing (drawing #1). However, detail drawings are available upon request.

Most of the fabrication was done in the Shops Division

(282) and measurements in the Electromagnetics Division (272)

of the Institute for Basic Standards of the National Bureau

of Standards , Boulder Laboratories

.

Throughout the text SS stands for subsection, ap for

appendix, and ( ) for an equation. For example, the equation

for AT is to be found both in SS 2.1 as (2.2), and in ap A

as (A. 2).

A proposed standard must undergo rigorous NBS internal

review before acceptance as a national standard. This review

requires complete documentation of all work associated with

theory, design, construction, and evaluation of the proposed
standard. Therefore, since this note was drafted for such

documentation, and since it is intended for metrologists with

interests similar to the authors', a number of items are contained herein which ordinarily would be" omitted from a document intended for more general distribution.

2. ANALYSIS

The average thermal noise power output of a standard is

described by the noise temperature T [1] which is the thermal

noise power P per unit bandwidth available at its output

connector divided by Boltzmann's Constant k. That is

T _= P.k

In the standard, T is a calculated quantity [2] against which

the noise temperature of another noise source can be compared,

This calculated noise temperature depends upon a number of

parameters of the physical source, and the corresponding

error, 6T, in T is the result of uncertainties in these

parameters

.

This section deals with the calculation of T and 6T and

the resulting design specifications. In particular, SS 2.1 covers the details of calculating T, and SS 2.2 with those

of 6T. Subsection 2.3 discusses the design specifications.

2.1. Noise Temperature Output

A schematic drawing of a heated thermal noise source is
shown in figure 2.1. The impedance Z terminates a transmission line used to convey the noise power from the impedance

to an accessible output port. The impedance and part of the

line is maintained at an elevated temperature by an appropriately designed oven. The available output power P is the sum of two effects; the noise power generated by Z and

attenuated by the line, and the noise power generated by the

line itself. The calculation of P or T requires the line to

be uniform and reflectionless , and is the subject of this

subsection.

An equivalent circuit model of figure 2.1 is shown in

figure 2.2. T represents the measured temperature of the

impedance Z terminating the end of the line at x = . T

is the measured temperature distribution along the line

from x = to the output connector at x = I. a is the

available power ratio [1] for the length of line from x to

x = £, and a is the attenuation per unit length (dB/length)

of the line at x. T is the output noise temperature and is

the result of the attenuated noise a T of the impedance

o m

r and the noise contributed by the line. T can be written as

the sum of the impedance temperature T and a correction

temperature AT which accounts for the total effect of the

line

.

T = T + AT m ^^ m (2.1)
A convenient expression for the correction is given by

(ap A)

£ , AT = (Tv -T )(l-a ) + / T (1-a ) dx

o nr *• o

J

' x

v x^ ro . o (2.2)

where T is T „ , a is a n , and T is the temperature

o x=0 ' o x=0 ' x

F gradient along the waveguide. In terms of the decibel

attenuation A of the line from x to x = I (ap A)

-A /10 2| r | 2 a = 10 X

- Sinh(A /10 log e) X i|2 X

l - |r | 2 A

(2.3)

I where

I A = / a dz

.

ro /i-i x £ z (2.4)

The last term in (2.3) K J is both a function of the line loss A

x and the standard's reflection coefficient T

g

. A and r. are usually small, making the last term small and resulting in

a noise temperature T that is independent of the reflection coefficient. A rough estimate of the size of the uncer- tainty in AT when this last term is neglected is given by

2(T-T )| T | 2 (0.23A) (2.5) m a* where T is the average temperature of that portion of the

T curve from the high temperature fall off to x = I, and A

is the attenuation in dB of that same region.
The attenuation per unit length is given by

a x

= cp^ (2.6)

where c is a constant that is a function of the frequency and

the geometry of the line, and p is the resistivity of the line

material. The variation of this resistivity with temperature

for an alloy of 901 platinum - 10% rhodium (Pt - 10 Rh) is

shown in figure 2.3.

The attenuation per unit length can be treated in either

of two ways; it can in general be measured as a function of

temperature, or calculated from (2.6) in certain instances.

Measurement data for a as a function of temperature is

difficult to obtain and generally unavailable. Therefore a

is calculated from (2.6). Justification for this decision

is to be found in SS 4.1.4.

The WR15 noise standard employs a Pt — 10 Rh waveguide

(SS 3.1.2) of inner dimensions 0.148" x 0.074", with a terminating element whose reflection coefficient is not greater

than 0.006 (SS 3.1.1). A computer program (ap D) has been

written for the calculation of AT (fig. 1.1) and its associated

error (fig. D.I.), neglecting the second term in (2.3) (ap A).

In order to perform this calculation, the computer requires

the waveguide temperature distribution x versus T (fig. 2.5),

the resistivity dependence upon the temperature
(p

2 = A + A, t + A? t2 + A,t 3 ), the operating frequency F in GHz,

the transverse waveguide dimensions A and B, and the termination temperature T . For the sample temperature distribution (SS 4.4.2) shown in figure 2.5, where the termination

temperature is 962. 0°C (1235.2 K) , the computed correction

temperature AT and its error are

AT = -26.3 K

and

6AT = ± 1.5 ± 0.9 = ± 2.4 K,

0.9 K being added due to uncertainties in the temperature

distribution (SS 4.4.2). The variation of 6AT with frequency

for the sample data in figure 2.5 is shown in figure 2.4.

AT as a function of frequency is found in figure 1.1.

2.2. Error Analysis

The total maximum uncertainty, or error , 6T in the output noise temperature can be written as (ap C)

6T = (6T)

T

+ (6T)

T

+ (6T)

£

+ (6T)

q

+ (6T) m o

+ (6T)

c

+ (6T)

g

+ (6T)

1 + (5T) w

+ (6T) A (2?)

where

(6T) T

= the uncertainty in T caused by the uncertainty

m

ST in T (SS 4.4.1)

.

m m

v J

(6T) T= the uncertainty in T caused by the uncertainty

o in T .
(6T) . = the uncertainty in T caused by the uncertainty

in the position of the output connector at

x = I. Since the reference position is taken

at the output connector, (ST)

? = 0.

(6T) = the uncertainty in T caused by the uncertainty

in the position (x=o) of the termination.

(ST) = the uncertainty in T caused by the uncertainty

in p

.

(6T) = the uncertainty in T caused by the uncertainty

in c

.

(6T) = the uncertainty in T caused by the uncertainty

I in the temperature gradient T along the

(ST)

waveguide

.

5 the uncertainty in T caused by neglecting the

second term in (2.3).

= the uncertainty in T (ap C) caused by different

wall gradients (SS 4.4.4).

= the uncertainty in T (ap I) caused by air

attenuation in the waveguide.

(ST) can be estimated in either of two ways as pointed

out in ap C. The second method is employed here as explained

in SS 4.4.2.

(6T)

(ST)

w

A
Using the sample temperature distribution in figure 2.5,

the results of the error calculation for the WR15 standard

(figure D.l.) are tabulated below along with their computer

output designations where applicable.

Parameter Uncertainty Corresponding Percent of

(With Computer Designation) Uncertainty in T Total Uncertainty

6T (DTM) = 0.4 K

6T

T (DTO) = 0.5 K

6T

£

(DDB) =

6T (DDO) = 1/4"

0.342 14.2

0.0724 3.0

0.0234 1.0

0.637 26.3

0.92 38.1

0.36 14.9

0.05 2.1

0.01 0.4

6T (DR) = 10%

P 6T (DC) = 2.46%

(6T) (See SS 4.4.2)

g (6T) w

(See ap C)

(6T) A(See ap I)

C6T)

1 (See ap A)

Error (Total Uncertainty) 2.41 K

The value for (6T) was obtained from the three computer

correction calculations AT shown in figure 2.6 f as the difference between the first and second or second and third AT

s

The curve in figure 2.5 is the curve C in figure 4.7, from

which the correction temperature AT (Delta T in the computer

10
output) for the standard's output noise temperature is calculated. Thus the noise temperature output is

T = T + AT ± 6T m

= 1235.2 - 26.3 ± 2.4

= 1208.9 ± 2.4. (2.8)

The calculations leading to (2.8) were carried out for

the operating frequency of 55 GHz. Figure 2.4 shows this

error as a function of frequency for the band from 55 GHz

to 65 GHz.

2.3. Critical Design Specif ications

Before a final design for the WR1 5 standard was chosen,

a number of error calculations similar to the calculation

in SS 2.2 were performed on different assumed temperature

distributions. One important characteristic of the

temperature distribution can be seen in figure 4.7. With

the separate parameter uncertainties being held constant,

the three distributions shown in the figure each produce

an error 6AT as shown. It is obvious from the figure the

farthest right produces the least error. Thus the temperature

transition region, that region where the temperature distribution falls from a value near the termination temperature

T to a value near the output connector temperature T , m r r o

11
should be kept as near the output connector as possible if

the output error is to be reduced, to a minimum. This

consideration is given considerable weight in the present

design (SS 3.1).

Another uncertainty, (6T) , which is negligible at lower

frequencies (e.g., WR62, 90, and 284), contributes a large

portion of the error in WR15. Most of this uncertainty

(ap C) comes from dimensional tolerances (SS 3.1.2) and

shows that the transverse dimensions of the waveguide must

be held to as tight a tolerance as possible.

The next largest uncertainty in T comes from the meas- urement of the termination temperature T . The uncertainty,

6T in T (SS 4.4.1) comes from the uncertainty in the m m

v J } temperature gradient across the termination, and the calibration uncertainty of the thermocouple used in the measurement.

The other sources of uncertainty are seen to be insignificant when compared to these first three discussed. The

details of their origin may be found in ap C.

3. DESCRIPTION AND DESIGN

A block diagram for the operation of the WR15 noise

standard is shown in figure 3.1. The termination and waveguide are placed in an oven that feeds information in the form

of thermocouple EMF ' s to a potentiometer for temperature

measurement, and to the heating control circuits. The EMF '

s

12
fed to the control circuits can, at will, be measured by

the potentiometer. This measurement allows the heating coil

temperatures to be adjusted to insure that a predetermined

temperature distribution can be repeated (SS 4.4.3). The

outputs from the circuit control transformers that supply

currents to three heating coils in the oven, allowing the

temperature gradient within the oven to be held constant. A

separate temperature controlled (22°C ± 0.05°C) water

cooling system keeps the output connector of the standard

at room temperature and cools the oven casing.

These components can be located in figures 1.2 and 1.3.

The cylindrical object that has been placed on the table is

the oven with the output connector at its left end as shown in

figure 1.2, and with the thermocouples and ice baths evident in

figure 1.3. The clear plastic tubing conducts water to the

water cooled output flange, through coils inside the cylindrical

casing to the rear oven cooling plate, then back to the recirculating cooler at the bottom right of the photographs. The oven sits on an oven carriage that can ride in the same rail

on which the comparison radiometer is mounted. The carriage

has four adjustments that allow the output connector of the

standard to be precisely mated to the radiometer input

connector. The thermocouples which monitor the coil temperatures and those used to measure the termination temperature

are inserted through the rear cooling plate (fig. 1.3).

13
They are connected in the ice baths to thermocouple grade,

Teflon* coated copper wire leads. The ice baths are contained in the silvered vacuum bottles and ride on a platform that is connected to the oven carriage. The copper

leads conduct the thermocouple EMF ' s to the measurement

and control rack at the left in the figures. These leads are contained in a small plastic tube that enters the rack just

under and to the left of the rack desk. The short looped

piece of larger plastic tubing attached to the rack allows

the thermocouple leads to be held without kinking. These leads

then enter a terminal strip contained in the aluminum shell

just under the rack desk. The EMF ' s from three of the leads,

from the thermocouples monitoring the coil temperatures,

are balanced against three internally generated EMF's and

are then amplified by the three amplifiers located in the

lower half of the rack. The amplified outputs are then con- ducted to the three control circuits at the bottom interior of

the rack. The three dials at the bottom of the rack adjust the

three internally generated EMF's. The resulting coil currents

are conducted through three fused ammeters and out through the

cord at the bottom of the rack into the rear of the oven (fig.

1.3) to the oven heating coils. The precision potentiometer

^Certain commercial materials are identified in this paper in

order to adequately specify the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Bureau of Standards, nor does it imply that

the material identified is necessarily the best available for

the purpose.

14
used to measure the EMF's is located at the top of the rack.

The current source for the potentiometer is located inside

the rack. The null detector used with the potentiometer, and

the switch used to connect the individual leads to the

potentiometer, are located just above the rack desk.

The details of the design and construction of these

components are contained in the following subsections.

SS 3.1 contains the details of the internal oven components,

including the waveguide termination, the waveguide, the heat

distributor, heating coils, sleeve, and the thermocouples.

A description of the thermocouple ice baths is also given

in this subsection. SS 3.2 contains the details of the

external oven components, including the oven casing, the

support spider from which the internal components are suspended, the cooling coils, and the carriage. SS 3.3

contains the details of the auxiliary components consisting

of the temperature measurement system, the heating control

system, and the water cooling system.

3.1. Internal Oven Components

Drawing #1 shows the oven assembly and carriage. The oven assembly itself (items 25 through 41) shows the internal

oven components (items 26, 32, 33, 34, 40, and 41) suspended

in the center of the oven casing (items 24, 31, 35) by

the supporting spiders (item 36) which are bolted to

15
the oven end plates (items 29 and 35) . The internal com- ponents shown include the resistive termination (item 41)

,

the high temperature waveguide (item 26) , the inconel heat

distributor (item 32) with three sets of bifilar wound heating

coils, and the locking rings (item 42) which hold the heat

distributor together and support it in the heat distributor

sleeve (item 33). Not shown in the drawing is the insulation

packed between the coils and the sleeve, at both ends of the

heat distributor, and just inside the cooling coils (item

30) leaving an air gap between this insulation and the insulation around the sleeve. Two of the thermocouple grooves in

the heat distributor are shown.

When in operation, the front coil (left in the drawing)

is used to keep the front end of the heat distributor as near as possible to the termination temperature (SS 2.3);

the center coil is used to set the termination temperature;

and the back coil is used to compensate for heat loss from

the rear of the oven.

3.1.1. High Temperature Resistive Generator

The high temperature termination (resistive generator)

from which most of the standard's noise power output originates

is designed for high RF loss, high thermal conductivity, and a

low reflection coefficient. To insure that the termination

material had sufficient loss from 55 to 65 GHz, the losses of

16
a number of materials were measured (SS 4.1.2) in this band.

From this data the length of termination needed could be

estimated to be great enough to completely terminate the waveguide, and to provide a low reflection coefficient.

A low reflection coefficient (SS 4.1.3) was achieved

by cutting the termination material at an angle to its length

resulting in a face length (ap F) of 0.75". The length of

material needed turned out to be 0.28" (ap G) resulting in a minimum termination length of approximately 1". It is over

this 1" length that the termination temperature T is

determined (SS 4.4.1). The final overall length chosen was

2.3" (drawing #2)

.

To achieve a high thermal conductivity at high temperatures , the material chosen was a homogeneous mixture of

beryllium oxide and 40% silicon, the beryllium oxide providing

the high thermal conductivity and the silicon the high RF

loss. Figure 3.2 shows a table of thermal conductivities for

a number of materials.

The final design, shown in drawing #2, has a cutting angle

of 23.4° corresponding to vertical and horizontal face angles

of 10° and 24° respectively. The cutting angle is used by

the manufacture in fabricating the termination, which could

not be done "in-house" because of the toxic nature of

beryllium [3]. The edges of the termination have a 0.006"

17
chamfer to allow good thermal contact with the waveguide

walls. A 0.5" groove is provided at the end of the termination

to allow a hollow ceramic (Al-^0-) rod to be attached (A1~0,

cement) . The rod is used to position the termination

longitudinally in the waveguide and to provide a means for

inserting a thermocouple into the back of the termination.

After cementing, the load and rod are cured at 1100°C in a laboratory furnace.

3.1.2. High Temperature Waveguide

The high temperature (962°C) waveguide provides a low loss transmission path from the high temperature termination to the output connector of the noise source. To allow

the use of (2.6) (SS 2.1) in calculating the noise output,

the inside waveguide dimensions must be precisely known (to

calculate c accurately) , and the waveguide resistivity as a function of temperature known to calculate p

2

. The dimensions of the waveguide are 8 3/8" x 0.228"

(± .001) x 0.154" (± .001) with corner bend radii less than

0.031" outside; by 0.148" x 0.074" (± .001) with corner bend

radii less than 0.006" inside. The dimensional tolerances

can produce a reflection as large as 0.01 (ap H and SS 4.1.3)

from the waveguide when compared to a perfect waveguide.
The length of the waveguide, although not critical, was chosen

long enough to protrude out of the heat distributor and into

the cooler region of the insulating felt at the rear end of

the oven. This was done to avoid contamination of the inside

of the waveguide by heat distributor.

An alloy of 901 platinum and 10% rhodium was chosen for

the waveguide material because it has proven to follow (2.6)

quite well (SS 4.1.4) in the past. Other important reasons

for choosing this material were [2]: 1) its nonmagnetic

character avoids uncertainties associated with the Curie

Point suffered by magnetic materials; 2) it has a high

resistance to oxidation and corrosion; 3) it has a high

melting point (fig. 3.3); 4) it is not too soft for repeated

high temperature use; 5) it is fairly workable; and 6) there

is a large amount of resistivity data available for platinum

101 rhodium [4]. Some care must be taken to reduce the free

silicon content around the waveguide in the high temperature

region of the oven. This silicon can combine with the

platinum in the waveguide and the standard thermocouples to

form a eutectic that melts around 800°C [5].

For the length of line from the termination to the output connector, atmospheric attenuation (fig. 3.4) in the waveguide produces a completely negligible effect on the output

noise temperature (ap I).

19
3.1.3. Heat Distributor Assembly

The heat distributor assembly consists of the heat

distributor (item 32 in drawing #1) . the heating coils,

the heat distributor sleeve (item 33), the locking rings

(item 34) , and the insulation surrounding the sleeve and

both ends of the heat distributor, and between the coils

and the inside of the sleeve.

The heat distributor is approximately 2 1/4" in diameter

and is constructed in two halves (fig. 3.5) with four flanges

to separate and contain the heating coils. By studying the

photograph, six thermocouple grooves and the main waveguide

groove can be discerned. A radial bifilar coil is wound

into the front end section (right end in the photograph) . The

distributor is fabricated from inconel "601," a high temperature

alloy compound of approximately 76.0% Ni, 0.04% C, 0.20% Mn

7.20% Fe, 0.007% S, 0.20% Si, 0.10% Cu, and 15.8% Cr [6].

The thermal properties of this material for comparison with

other materials can be found in figure 3.2.

Boron nitride [7] is another material that was considered

for the heat distributor. This material has a very high

thermal conductivity at 1000°C (fig. 3.2) and is very

machinable. Figures 3.6 and 3.7 show a finished boron nitrade

distributor. The center and back coils are wound directly on

the distributor (fig. 3.7). In tests with this material it was found that when heated to 1000°C a sticky substance,

ZO
possibly boric oxide [7], was formed that became a "glass" at room temperature. This flaw prevented its use in the noise

standard. Some work with the material was done in a nitrogen

atmosphere with the same results, but was not conclusive.

Experimentation with the material was discontinued as soon as

the high stability of the inconel "601" distributor at

elevated temperatures was varified.

Drawing #3 shows the dimensions of the heat distributor

and the placement of the thermocouple grooves. By referring

to the bottom profile the three separate heating coils,

which are all bifilar wound, may be located. The back (left

hand) coil is wound from left to right and back. The center

coil is wound from right to left and back, and the front

coil is wound from inside to outside along the radial groove

provided. The coils are an #18 gauge (0.040" diameter) resistance wire on which are strung alumina (Al-O.,) fish spine

beads (0.11" O.D. x 0.056" I.D. x 0.110" length) to prevent

shorting. The wire is an alloy of 5.5% Al , 221 Cr, 0.5% Co,

and 72% Fe with a resistance to oxidation considerably

greater than the nichrome wire used in previous NBS noise

standards

.

The inconel sleeve which contains the distributor

and coils is shown in figure 3.8 on the left of the photograph. Also shown are the inconel locking rings which

hold the two halves of the distributor together and support

21
them in the sleeve. The assembled heat distributor with

the waveguide and eight thermocouple grooves are shown at

the right. Figure 3.9 shows the whole assembly, including

the sleeve, locking rings, and heating distributor from

the front. The front and center heating coil leads are brought through two of the front slots while the rear heating coil lead is brought through a slot in the rear of

the assembly.

Three forms of zirconium oxide insulation [7] were used

in the standard, a 0.15" felt, a cloth, and a yarn. The

insulating characteristics of this material are indicated

in figure 3.10 and in SS 4.2.1.

3.1.4. Thermocouples

The detailed locations of the thermocouple grooves

are given in drawing #3. Figure 3.11 shows a schematic

diagram of the location of the tips of the thermocouples.

The dots represent the points at which the temperature of

the heat distributor is sampled by the thermocouple junction

The three control thermocouples B, C, and F are located in

close contact to the back, center, and front heating coils

respectively, and are connected to three separate servo- control circuits that maintain the coils at given temperatures. S~ and S, are calibrated standard thermocouples

22
in contact with the waveguide and can be positioned anywhere along the dotted line to be just above and below the

termination. The thermocouples are used, in conjunction

with a third (S, ) inserted in the rear of the termination,

to determine the average termination temperature (SS 3.1.1).

The other thermocouple grooves shown in drawing #3 turned

out to be unnecessary and are not used.

The thermocouples are constructed by fusing two dissimilar metal leads together and running the two leads

through a double bore ceramic tube. The junction resulting

from fusing generates the EMF which indicates the temperature.

The ends of the leads are soldered to thermocouple grade

copper wire leads and are immersed in a non-conducting liquid

which is cooled in an ice bath to 0°C. The copper leads

then convey the resultant EMF to a suitable measuring

instrument

.

The standard thermocouples S, , S~, and S, employ a reference grade, 0.010" diameter platinum wire and a platinum —

10% rhodium wire for the two leads. The ceramic tube is a high purity (99.81) alumina (A1

2

) tube with 0.047" ± 0.003 O.D., and 0.014" bores. The table in figure 3.2 shows some of the properties of the alumina and figure 3.12 shows a graph for the EMF output versus temperature for the platinum 101

rhodium thermocouple. The leads are cut to 36" lengths and

sent to NBS-Gaithersburg where they are fused together at

23
one end, annealed, and calibrated (fig. 3.13) according to

Schedule 221.112Z found in the NBS Special Publication 250.

After the thermocouple has been calibrated, it is returned

with a calibration report (fig. 3.13), inserted into a double

bore ceramic rod, and soldered to the copper leads. Extreme

care must be exercised in handling the thermocouple [5] after

it has been calibrated.

The control thermocouples B, C, and F are constructed

from 0.005" diameter Platinel #7674 and #5330 wire leads in

a similar fashion to the standard thermocouples. The rod has

a 0.031" ± 0.003 O.D. with 0.007" bores. This thermocouple

has a high output as a function of temperature (fig. 3.13)

and a longer life, making it more suitable for control purposes.

3.2. External Oven Components

The oven casing (drawing #1) is constructed from a welded

aluminum cylinder of 5.75" diameter onto which two brass

end plates are bolted. The rear plate supports the rear support

spider, the rear guide plate, and waterjacket. The output (front)

end plate supports a support spider, and contains a concentric

2.5" diameter hole into which is bolted the water cooled flange

of the high temperature waveguide.

The support spiders are constructed so that (ap J) as

the heat distributor sleeve expands on heating, the ends of

the sleeve in contact with the tapered spiders remain in

24
contact, keeping the sleeve and heat distributor concentric

with the oven casing, thus preventing damage to the waveguide . A 3/16" helical copper cooling coil is inserted just

inside and in contact with the cylindrical oven casing. This

coil protrudes through slots at both ends of the casing where

it is connected to the lower adaptors of the end plates.

When in operation, coolant flows in the front top adaptor,

through the coil, and out the back top adaptor of the rear

end plate to maintain the oven casing at room temperature.

The platinum-rhodium waveguide is soft soldered into the

front water cooling flange, protruding enough to allow a WR15 flange to be attached. The composition of the solder

used is 95% Tin - 51 Silver. A cylindrical jacket of

insulation is located inside the I.D. of the cooling coil with

an air gap between this insulation and the insulation surrounding

the heat distributor sleeve.

The oven carriage is designed for single-handed adjustment

of the oven position while mating the output waveguide flange

to the flange of a radiometer. The plastic wheels of the

carriage are designed to run in the same rail to which the

radiometer is attached.

25
3.3. Auxiliary Components

Figure 3.1 shows the three auxiliary systems used in the

standard; the temperature measurement system (fig. 3.14),

the heating control system (fig. 3.15), and the water cooling

system. These systems are described in this section.

3.3.1. Temperature Measurement System

The ice bath, used as a 0°C reference junction where

the thermocouple leads are soldered to copper leads, con- sists of a 440 cc . vacuum insulated bottle filled with distilled water and ice (made from distilled water) in

equilibrium at 0°C. Glass test tubes prepared from 1/4" tubing

contain the soldered junctions and are immersed in the ice

baths. Before the junctions are inserted into the test tubes,

each tube is partially filled with a f luorochemical liquid

to reduce temperature gradients along the leads and junctions.

The thermocouple grade, teflon coated copper leads

conduct the EMF ' s from the bath to the terminal board. Approximately 13' of this wire is used for each lead (ap L)

The terminal board is housed in a metal shell to encourage

a uniform temperature distribution along the junction terminals, thus minimizing the effects of thermal EMF ' s (SS 4.3.1)

generated at the contacts of the copper leads and brass terminals of the terminal board.

26
The switch is a commercially available, low thermal-EMF

switch that connects one switch output lead to any of the

thermocouple input leads

.

The potentiometer used to measure the EMF ' s is a com- mercially available high precision laboratory potentiometer,

with a limit of error on the 9.1 mV range equal to 0.1°C

when used with a constant current standardizing supply.

The brass lugs used on the leads between the switch and

potentiometer, and between the potentiometer and the null

detector were gold flashed to resist oxidation and minimize

contact EMF ' s

.

3.3.2. Heating Control System

A diagram of the heating control system is shown in

figure 3.15. Both the oven and rack are gounded to the line

ground. The current in the three heating coils are servo controlled to maintain known and small temperature gradients

in the oven. The heating control is obtained by sampling the

coil temperatures and maintaining them at a desired temperature

via control circuits that are mechanically coupled to the current

control transformers through drive motors. The maximum current

settings of these control transformers are limited by the current limiting transformers to obtain maximum control sensitivity

and to prevent the oven from overheating during warmup . The

control transformers are commercially available 7.5 amp units,

27
three of whose shafts have been modified for coupling to servo control drive motors.

A diagram showing how the servo drive voltage is obtained, and how the coil temperatures are measured, is given

in figure 3.16. The thermocouple EMF on the upper terminal

of the board can be measured by the potentiometer to obtain

the coil temperature. For control purposes, this EMF is

opposed by an offset voltage set to a value corresponding

to the desired coil temperature. The resulting correction

voltage is amplified and fed to the control circuits.

A diagram showing the operation of the control circuits

(ap M) is given in figure 3.17. A non-zero correction voltage

changes the width of a square wave which is then compared to

the width of a reference square wave by an "AND" gate. The

resulting output signal actuates the transformer drive motors

which adjust the transformers to control the coil currents.

The oven is brought up to temperature by the following

procedure: 1) the limiting transformers are set to a value

that will limit the maximum current available to the control

transformers to a value that will not operate the coil fuses

or burn out the coils; and 2) as the correction voltage approaches zero, as evidenced by the needle indicators on the

amplifiers coming on scale, the limiting transformers are separately adjusted upwards in current to provide just enough

28
current to maintain the heating coils at temperature with zero correction voltage, or when the needle indicators read zero. Once up to temperature the heating controls need no further

adj ustment

.

3.3.3. Cooling System

The oven casing is cooled by circulating distilled

water through the end plates and the cooling coil. The

coolant is supplied from a constant temperature (± 0.05°C)

bath and recirculated to the bath.

A manifold was constructed that allows the water pressure drop across the oven to be adjusted (fig. 1.2). A

thermometer is provided in the manifold to monitor the water

temperature entering the front cooling plate of the oven, and

two pressure gauges allow the pressure drop across the manifold

to be checked.

4. MEASUREMENTS AND OBSERVATIONS

This section contains measurement reports and observations made during the course of the design, construction,

and testing of the noise standard. In addition, a few brief

descriptions of measurement procedures and critical comments

are given. For ease in locating specific data the section

is subdivided into six subsections. Subsection 4.1 covers

the measurements made on the internal oven components.

29
SS 4.2 and SS 4.3 cover the rest of the oven and auxiliary

components

Subsection 4.4, entitled "System Performance," contains

the main measurement documentation supporting the conclusions

drawn in previous subsections (SS 2.1 and 2.2) concerning

the standard's output and accuracy.

Subsection 4.5 contains a potpourri of measurement data,

some more important than others, that was accumulated during

work on the standard. Much of the data is only tangentially

related to the noise standard, but could be of use for future

work and is therefore recorded here for later convenience.

Subsection 4.6 contains critical comments on the standard's construction, which although not incorporated in the

present standard, could be put to profitable use later.

The various data appear under brief descriptive headings

in a roughly descending order of importance.

30
4.1. Internal Oven Components

4.1.1. Thermocouple Accuracy

The thermocouples used to determine the termination

temperature T were constructed (SS 3.1.4.) from 0.010"

diameter thermocouple wire that was calibrated at NBSGaithersburg to an accuracy of ± 3 microvolts at the fixed

points (fig. 3.13), and to an accuracy of ± 5 microvolts

elsewhere in the range from 0°C to 1100°C. The termination

temperature is held close to the silver point (961.93°C) to

take advantage of the smaller ± 3 microvolt uncertainty in

the calibration data. This amounts to a 0.27°C uncertainty

at that temperature

.

In measuring the thermocouple EMF with the laboratory

potentiometer the measurement uncertainty is estimated to be

(SS 3.3.1) 0.1°C. Thus, the total uncertainty in the

measurement of a temperature around the silver point with

a calibrated thermocouple is 0.37°C.

4.1.2. Lo ssy Termination Materials

The approximate attenuation per unit length of three

materials was measured at 55.8 GHz. These measurements

were performed to assure that the load material chosen

(60% BeO-40% Si) for the high temperature termination

31
(SS 3.1.1.) would have adequate loss prior to its being

fabricated, and to obtain some feeling for the loss characteristics of other load materials. The results were:

Silicon Carbide: 96 dB/inch

Polyiron: 69 dB/inch

High Loss Plastic: 126 dB/inch

The BeO-Si termination should therefore have a loss of

approximately 40% of a similar Silicon Carbide load, or approximately 92 dB/inch.

4.1.3. Reflection Coefficient

of the Termination and Waveguide

Three reflection coefficient measurements of the BeO-Si

terminations (SS 3.1.1.) were performed; two swept and one fixed frequency measurement of the termination by itself,

and a swept frequency measurement of the termination-hightemperature waveguide combination. The output traces of

the three swept measurements are shown in figures 4.1, 4.2,

and 4.3. The first figure shows a conventional swept meas- urement [8] where the labels for the return loss calibration

lines appear at the left. The top set of lines contains a calibration line and two lines made by commercial terminations. The second set shows a calibration line and a line made by another commercial termination. The bottom

set contains four calibration lines and a line made by the

BeO-Si termination.

32
Figure 4.2 shows a Holloway-Somlo (H-S) swept reflectometer measurement [8] of the BeO-Si terminations using two calibrating reflections whose coefficients are 0.024 and 0.001

(at most) respectively. The top trace is a frequency calibration trace. The next set of traces consists of the

0.024 reflection and the BeO-Si termination which is seen, by

comparing the vertical magnitude of the lines, to have a reflection coefficient of 0.006 or less. The third set

shows the BeO-Si termination compared to the 0.001 termination

Comparison of these magnitudes shows the BeO-Si reflection

coefficient to be about 0.008. The bottom trace is from

the BeO-Si termination again, shifted slightly in the H-S

reflectometer input waveguide lead.

The two sets of traces in figure 4.3 show the BeO-Si

termination-high temperature waveguide combination compared

to a 0.024 reflection, and to a 0.048 reflection in the H-S

reflectometer. These traces indicate that the combination

has a reflection coefficient of approximately 0.012 (c.f.

aps G and H)

.

The reflection coefficient of three BeO-Si terminations

were measured in a tuned reflectometer [8] at 59.4 GHz. The

results, including measurement uncertainties, show that the

reflection coefficients of all three terminations fall in

the range from 0.002 to 0.006.

33
4.1.4. High-Temperature Waveguide Loss

The attenuation per unit length of the high-temperature

waveguide (SS 3.1.2) was measured [9] at 59.4 GHz and 22°C.

The average result of five measurements shows this loss to be

0.023 dB/inch with an uncertainty no greater than 20%.

4.1.5. Thermocouple Insertion Distance

The thermocouple used in the temperature distribution

measurement of the high- temperature waveguide is inserted by

holding the thermocouple stationary and moving the oven along

the support rail by rotating the plastic wheels of the oven

carriage. If need be, the oven can be positioned to within

a few tenths of 0.001" by this technique. A typical measurement setup is shown in figure 4.4. The thermocouple is being

inserted into the waveguide from the left. Once the zero distance setting is established by positioning the point of

contact between the thermocouple bead and the waveguide at

the flange reference plane, the apparent insertion distance

of the thermocouple into the waveguide can be measured by the

steel scale on the rail or the dial indicator secured

to the rail at the right in the picture. By setting the

pointer attached to the oven carriage to a given mark on the

scale, the apparent insertion distance can be measured to an accuracy approximately 0.005". By using the dial indicator

at the right, this distance accuracy is approximately 0.002".

34
The actual insertion distance is obtained from the

apparent distance by adding to the apparent distance a correction accounting for the expansion of the thermocouple

rod upon heating as it is inserted into the waveguide. This

correction is calculated (ap E) from knowledge of the distribution curve (fig. 2.5) and the expansion characteristics

[10] of the Al-0, rod (fig. 4.5). The accuracy of this

calculation is estimated to be 0.0005".

4.1.6. Inconel Heating Test

Before deciding to use inconel 601 for the heat distributor, a piece with nominal dimensions 4 x 1 x 3/16 inches

was maintained at 1100°C for 34 hours. Before heating, one end of the piece was measured to be 0.197" and the other end

to be 0.204" in thickness. After heating, the piece was re- measured and found to have the same dimensions to within the

measurement accuracy (0.0005"), and was found to have no measurable warp caused by the heating.

Observation of the final heat distributor after many

hours of use shows it not to have oxidized further than the

initial oxidation acquired upon first heating.

35
4.1.7. Heating Coil Resistances

The heating coil resistances were measured at 22°C

[room temperature) and 1000°C. At room temperature the

coil resistances, front to back, are 3.3, 22, and 10 ohms

respectively. When heated to 1000°C, these same coil

resistances increased to 3.8, 24, and 11 ohms respectively.

These resistances appear not to have changed over

3 months intermittent usage (SS 4.1.7).

4.2. External Oven Components

4.2.1. Zirconium Oxide Insulation

A 3/4" cylinder of boron nitride was heated to 1000°C

by a heating coil wrapped tightly around it. The combination

was insulated by a 0.15" thick zirconium oxide felt wrapping,

and suspended in air during heating. The temperature drop

from the inside to the outside of the insulation was measured

to be 700°C.

4.3. Auxiliary Components

4.3.1. Residual Thermal EMF

The residual EMF generated in the contacts of the terminal board, the thermocouple switch, and the potentiometer

36
(fig. 3.14) reduce the accuracy of the temperature measurements. This EMF was measured by tying together a pair of the

copper leads in the ice bath and measuring the EMF appearing

at the potentiometer. This EMF was less than 0.1 microvolt,

corresponding to an error of 0.009°C at the Silver Point

Temperature (961.93°C) where the high-temperature termination is maintained.

4.3.2. Copper Lead Resistance and Resulting Measurement Error

The resistance of the copper leads between the thermocouple leads in the ice junction and the measuring apparatus

(fig. 3.14) was measured to be 1.5 ohms, or approximately

0.1 ohms per foot for the total length of 13'. The error

in a temperature measurement caused by this resistance and

a slight unbalance at the null detector is estimated (ap L)

to be no greater than 0.002°C.

4.3.3. Water Temperature Control and Measurement

The temperature of the water coolant entering the oven casing at the waveguide flange is held at approximately

22°C to ± 0.05°C. The estimated error in the measurement of

this temperature by the manifold thermometer (SS 3.3.3,

fig. 1.2) is ± 2°C.

37
4.4. System Performance

4.4.1. The Termination Temperature

The temperature of the high- temperature termination is

determined by measuring the EMF of thermocouple S-. (SS 3.3.1).

The error in this measurement is no greater than 3 microvolts

or 0.27°C (SS 4.1.1) when operating near the Silver Point

(fig. 3.13). A measurement of the temperature in the waveguide just in front of the termination, and under the waveguide

just below the termination, revealed these temperatures to be

the same as the termination temperature to within at most

0.1°C. Therefore the determination of the termination temperature by thermocouple S-. is uncertain to no greater than

0.4°C (0.27°C + 0.1°C) .

4.4.2. Determination of the Waveguide Temperature Distribution

The presence of the thermocouple rod inside the waveguide

disturbs the waveguide temperature distribution at both ends

and in the temperature transition region. Therefore, the

normal (unperturbed) distribution cannot be measured directly

in these regions. Instead, an area is located between two

perturbed distributions in which the normal distribution must

lie.

38
This area is established in the following way. If the

high- temperature termination is removed from inside the waveguide, two perturbed temperature distributions can be meas- ured (fig. 4.6); one by inserting the thermocouple into the

waveguide from the back end of the oven, and one by inserting

the thermocouple from the front. In the first measurement,

heat is conducted by the thermocouple rod from the heat

distributor region of the waveguide into the temperature

transition region as the thermocouple enters this region,

giving a higher than normal temperature indication. In the

second measurement, as the thermocouple enters the transition

region from the front, heat is conducted via the rod away

from the transition region giving a lower indication than

is normal. It is clear that the normal distribution must

lie in an area somewhere between the two perturbed distributions . Since the predominant heat transfer in the

transition region is along the waveguide, the distribution

in this region should be nearly linear. This is seen to be

the case from curves A and B in figure 4.7.

The area in which the normal distribution must lie can

be reduced further, as shown by the following argument. The

two perturbed distributions from figure 4.6 are expanded in

39
figure 4 . 7 in the transition region as curves A and B.

In the water cooled region the normal curve is closer to

curve B since the distribution is less perturbed in this

region when measured from the front than when measured from

the back of the oven. Similarly, the normal distribution is

closer to curve A in the heat distributor region. Thus the

normal distribution lies between the unlabeled curve (which

is halfway between curves A and B in the water cooled and

heat distributor regions) and curve B in the water cooled

region, and between the unlabeled curve and curve A in the

heat distributor region. Then if the partial curves in the

water cooled and heat distributor regions are joined linearly

as shown in figure 4.7, it is clear that the normal curve will lie in the shaded area bordered by the resulting two curves

The solid curve C which is vertically halfway between

the bordering curves is then taken to be the normal

distribution, and the correction temperature AT (SS 2.1) is

calculated from it. This correction temperature is -26.34°C

in the figure. The uncertainty in this correction (SS 2.2),

(<5T) , is taken to be one-half of the difference between the

correction temperatures as calculated from the bordering

curves, since the normal curve cannot lie outside these

curves. From the figure, this uncertainty is 0.92°C.

40
The foregoing procedure is valid provided that the curves A and B remain substantially unchanged when the

termination is reinserted into the waveguide . This is seen

to be the case in figure 4.8 which shows two distribution

measurements from the front just before and after the

termination was inserted.

The difference between curves A and B is plotted in

figure 4.9 for the average coil temperature needed to maintain

the termination at 962°C. This curve can be used to predict

curve A around the transition region from curve B, obviating

the need to remove the termination from the waveguide if it can be shown that the differential curve is relatively independent of the average coil temperature. That this is the case is seen in figure 4.10 which shows the three differential

curves for three different average coil temperatures to be

closely the same. The dates on which the differential curves were taken indicate the stability and repeatability of the oven characteristics.

4.4.3. Temperature Measurement Repeatability

The ability to repeat a temperature measurement at a specified point in the waveguide is very important if one is

to have confidence in the temperature distribution measurements . In order to do this in the temperature transition

41
region, one must be able to reposition the thermocouple in

the waveguide (SS 4.1.5) quite accurately. For example, a 0.001" error in repositioning the thermocouple in the transition region causes a 1°C change in the temperature measurement.

In order to check the repeatability, a set of temperature

measurements were performed at three points (0", 0.8", 1.3")

in the waveguide. The table in figure 4.11 shows the results

of these tests. The time in hours measured from the beginning

of the first measurement along with the temperature-distance

sensitivity around the various points are also given in the

table. The results indicate that the measurement of a temperature at a given point in the waveguide, even in the

highest gradient region of the temperature distribution, should

be repeatable to 2°C. This result is consistent with the

fact that the thermocouple can be repositioned to within

0.002" anywhere along the waveguide interior.

4.4.4. Wall Temperature Distributions

The temperature distributions along the four walls inside

the waveguide differ from each other in the temperature

transition region. Figure 4.12 shows this effect, where

the difference between the temperature of each wall and

the average temperature of the four walls is plotted as a function of distance into the waveguide from the output

42
flange. These differences are accurate to 2°C, showing

that the wall temperatures are closely the same outside the

0.3" to 1.6" length of waveguide. The error caused by these

different temperature distributions is discussed in SS 2.2

and ap C

4.5. Additional Measurements

4.5.1. Oven Power Consumption

The power consumed by the oven when operating at 962°C

was measured to be

Front Coil 7.2 A x 30.7 V = 221 Watts

Center Coil 2.1 A x 51.3 V = 108 Watts

Back Coil 3.85 A x 44.8 V = 172 Watts

Total 501 Watts

By measuring the temperature rise (22°C -> 30°C) and flowrate (811 m£/min) of the oven casing coolant, the heat removed

from the oven is calculated to be 453 Watts.

4.5.2. Laboratory Environment

The temperature and relative humidity of the laboratory

in which most of the measurements described in this report

were carried out were 69°F and 401, respectively. A recording

of the variation of these quantities over a seven-day period

appears in figure 4.13.

43
4.6. Possible Improvements

The following comments are recorded here for future use. They involve both suggestions for improvement of the present

WR15 noise standard, and comments that may prove useful in

later work

4.6.1. Thermocouple Grooves

The thermocouple grooves in the inconel heat distributor

were machined with a milling cutter, leaving a circular

runout of the cutter radius at the end of the groove. This

circular runout prevents the thermocouple from making

repeatable contact when the thermocouple is removed and

reinserted. The design of the groove for the front coil

thermocouple also prevents this thermocouple from making

repeatable contact with the front coil. This non- repeatability prevents changing the control thermocouples

without remeasuring the gradient to be sure it hasn't

changed. This problem can be remedied by milling off the

radius in grooves B and C (fig. 3.11 and drawing #3), and

plugging the hole in groove F leaving a thin wall between

the thermocouple bead and the front coil.

44
4.6.2. Isolation Between Heating Coils

The ability to shape the temperature distribution down

the waveguide depends on the amount of thermal isolation

between the regions heated by the front, center, and back

heating coils. In the present design of the heat distributor

this isolation is not great enough to allow much control over

the position of the high temperature fall off between the

water cooled and heat distributor regions (fig. 2.5). For

accuracy reasons (SS 2.3) it is beneficial to push this

high-temperature fall-off to as close to the output flange

as possible.

One possible means of effecting greater thermal isolation is to cut annular spaces between the front, center, and

back coil regions

.

4.6.3. Diameter of the Heat Distributor

The diameter of the heat distributor was chosen

intuitively, the smoothing of heating irregularities along

the central heating coil being the main factor in the choice.

Time permitting, some experimentation may show that a smaller

diameter is quite feasible.

45
4.6.4. Different Wall Temperature Distributions

By examining the wall temperature differential curves

in figure 4.12, one is led to the conclusion that the different distributions are caused by varying contact between

the waveguide and insulation in the transition region (fig.

2.5), and between the waveguide and heat distributor at the

end of the heat distributor. At present this effect is not

important, amounting to only 2.9% of the total error in

the calculated output temperature (SS 2.2).

46
5 . ACKNOWLEDGMENTS

The success of this project is due in part to the

efforts of the following people: R. D. Hunter, M. Kanda

,

A. C. Newell, M. P. Weidman, and B. C. Yates of the

Electromagnetics Division for many V-band measurements

and consultations; P. F. Biddle, W. F. Decker, R. J. Fischer,

H. H. Garing, P. G. Karas , V. Lecinski, W. E. McNaney, K. C. Nuss,

A. Padilla, and to D. L. Smith of the Shops Division;

Sharon C. Foote of the Electromagnetics Division for the

excellent job of typing; and to D. B. Miner of Audio Visual

Aids . Thanks are also due to Dave Sawyer for making up the

conductivity tables.

47
6 . REFERENCES

[1] Miller, C. K. S., W. C. Daywitt, and M. G. Arthur,

"Noise Standards, Measurements, and Receiver Noise

Definitions," Proc. IEEE, 55_, pp. 865-877, June 1967.

[2] Wells, J. S., W. C. Daywitt and C. K. S. Miller,

"Measurement of Effective Temperature of Microwave

Noise Sources," IEEE Trans, on I § M, IM-13 , pp. 17-28,

March 1964.

[3] Ferreira, L. E., "Recommended Practices for Safe

Handling of Beryllium Oxide Ceramics," Symposium on Materials and Electron Device Processing, Special

Technical Publication No. 300, American Society for

Testing and Materials, 1961.

[4] Vines, R. F. and E. M. Wise, "The Platinum Metals

and Their Alloys," The International Nickel Company,

Inc. , New York 5, N. Y.

[5] Zysk, E. D., "Platinum Metal Thermocouples," Temperature, Its Measurement and Control in Science and

Industry, 3_, Part 2, Reinhold Publishing Corp., 1962.

[6] "Nickel and Nickel-Base Alloys -- Their Use in the

Design of Corrosion-Resistant Machinery and Equipment,"

Technical Bulletin T-13, The International Nickel

Company, Inc. "Properties of Some Metals and Alloys,"

The International Nickel Company, Inc.

48
[7] Kohl, W. H., Handbook of Material and Techniques for

Vacuum Devices , Reinhold Publishing Corporation,

New York, 1967.

[8] Newell, A. C, Private Communication, National Bureau

of Standards, Boulder Laboratories. Hollway, D. L.

and P. I. Somlo, "A High Resolution Swept-Frequency

Reflectometer," IEEE Trans. MTT , MTT-17 , No. 4, April

1969. Anson, W. J., "A Guide to the Use of the

Modified Reflectometer Technique of VSWR Measurement,"

NBS Report 6095, April 1960.

[9] Weidman, M. P., Private Communication, National

Bureau of Standards, Boulder Laboratories.

[10] Alumina and Beryllia Properties Handbook , Bulletin

952, Coors Porcelain Company, July 1969.

[11] Kerns, D. M. and R. W. Beatty, Basic Theory of Wave -

guide Junctions and Introductory Microwave Network

Analys is , Pergamon Press, Long Island City, New York, 1967

[12] Yates, B. C, Private Communication, National Bureau

of Standards, Boulder Laboratories.

[13] Kerns, D. M. and W. T. Grandy, Jr., "Perturbation Theorems

for Waveguide Junctions, with Applications," Program and

Digest of the 1962 PGMTT National Symposium, Boulder,

Colorado 80302.

49
[14] Haus , H. A. and R. B. Adler, Circuit Theory of Linear

Noisy Networks , The Technology Press of the Massachusetts

Institute of Technology and John Wiley and Sons,

New York, 1959.

[15] Wait, D. F., "Thermal Noise from a Passive Linear

Multiport," IEEE Trans. MTT , MTT-16 , No. 9, p. 687,

September 1968.

[16] Sees, J. E., "Fundamentals in Noise Source Calibration

at Microwave Frequencies," U.S. Naval Research Lab.,

Report 5051, January 1958.

[17] Stelzreid, C. T., "Temperature Calibration of Microwave

Thermal Noise Sources," IEEE Trans. MTT (Correspondence),

MTT-13 , p. 128, January 1965.

[18] Kerns, D. M. and R. W. Hedberg, "Propagation Constant

in Rectangular Waveguide of Finite Conductivity,"

Journal of Applied Physics, 25, p. 1550, 1954.

50
7. FIGURES

1.1. Output Noise Temperature Versus Operating Frequency.

1.2. Photograph of the WR15 Noise Standard Showing the

Output Flange.

1.3. Photograph of the WR15 Noise Standard Showing Thermocouples and Ice Junctions.

2.1 Schematic for a Thermal Noise Source.

2.2. Equivalent Circuit of a Thermal Noise Source.

2.3. Line Resistivity Versus Temperature.

2.4. Output Error Versus Operating Frequency.

2.5. Sample Temperature Distribution for Calculations.

2.6. The Effect of the Temperature Transition Region

on the Output Error.

3.1. Block Diagram of the Standard's Operation.

3.2. A Table of Thermal Conductivities and Thermal

Expansion Coefficients

3.3. Table of Some Properties of Some of the Noble

Metals

.

3.4. Atmospheric Attenuation Versus Frequency (Courtesy

Microwave Journal).

3.5. Photograph of the Inconel "601" Heat Distributor

3.6. Exploded View of the Boron Nitride Heat Distributor

3.7. Photograph of the Assembled Boron Nitride Heat

Distributor

.

3.8. Exploded View of the Inconel Heat Distributor,

Sleeve, and Locking Rings

3.9. Photograph of the Heat Distributor Assembly.

3.10. Thermal Conductivity Versus Temperature for

Zirconium Oxide.

51
3.11. Thermocouple Junction Locations.

3.12. Thermal EMF Versus Temperature for Pt-Rh and Platinel

Thermocouples

3.13. Sample Page from a Thermocouple Calibration Report.

3.14. The Temperature Measurement System.

3.15. The Heating Control System.

3.16. The Control Thermocouple Hookup.

3.17. Operation of the Control Circuits.

4.1. Conventional Swept Frequency Measurement of the BeO-Si

Termination Reflection Coefficient.

4.2. H-S Swept Frequency Measurement of the BeO-Si Termination

Reflection Coefficient.

4.3. H-S Swept Frequency Measurement of the BeO-Si Termination

and High-Temperature Waveguide Reflection Coefficient.

4.4. A Typical Temperature Distribution Measurement Set-up.

4.5. Expansion Coefficient of the A1~0_, Rod Versus Temperature.

4.6. Temperature Distribution from Front and Back.

4.7. Temperature Distribution, Expanded scale.

4.8. Distribution Just Before and After Termination is

Inserted.

4.9. Temperature Differential Between Perturbed Distributions.

4.10. Temperature Differential at Different Coil Temperatures.

4.11. Table of Temperature Measurement Repeatability Tests.

4.12. Temperature Differential Curves Along the Four Inside

Waveguide Walls.

4.13 The Laboratory Environment

D.l Sample Printout of the Output § Error Calculations.

E.l. Sample Output from Program "TEX 998."

52
F.l. The Waveguide Termination Geometry.

J.l The Support Spider.

L.l. Schematic for Lead Error Calculation.

M.l. Block Diagram of the Temperature Control System,

M.2. Circuit Waveforms.

M.3. Circuit Diagram for Block IV.

M.4. Circuit Diagram for Block VI.

N.l. Generator attached to a Two-Port Transducer.

N.2. Scattering Parameter Description.

N.3. A Noisy Two-Port.

N.4. Illustration for (N.l).

N.5. A Thermal Noise Source.

N.6. A Uniform, Ref lectionless Line.

53
T = Tm + AT

Tm = 1235. 2K

FREQUENCY (GIGAHERTZ)

Figure 1.1. Output Noise Temperature Versus Operating

Frequency.

54
Figure 1.2. Photograph of the WR15 Noise Standard Showing the

Output Flange.

55
Figure 1. 3, Photograph of the WR15 Noise Standard Showing

Thermocouples and Ice Junctions.

56
COI—

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Figure 2. 2. Equivalent Circuit of a Thermal Noise Source,

58
o

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100 200 300 400 500 600 700 800 900 1000

DEGREES CENTIGRADE

Figure Z„ 3. Line Resistivity Versus Temperature,

59
FREQUENCY (GIGAHERTZ)

Figure 2.4. Output Error Versus Operating Frequency.

60
INCHES

Figure Z„ 5. Sample Temperature Distribution for Calculations.

61
1 000,—

962°C

INCHES

Figure 2, 6 The Effect of the Temperature Transition Region

on the Output Error.

62
TEMPERATURE

MEASURING

POTENTIOMETER

HEATING

CONTROL

CIRCUITS

HEATING

CURRENT

TRANSFORMERS

OVEN WITH

TERMINATION

AND WAVEGUIDE

TEMPERATURE

REGULATED

WATER COOLANT

RF

OUTPUT

Figure 3. 1. Block Diagram of the Standard's Operation.

63
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Melting Temperature Electrical Resistivity (20 C)

Material in C in y> d. - cm

Gold 1063 2.4

Iridium 2454 7 Osmium 2700 60

Palladium 1549 11 Platinum 1773 10

Rhodium 1966 5 Silver 961 1.6

Figure 3. 3. Table of Some Properties of Some of the Noble

Metals.

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71
3.0,-

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2.0

1 .5 -

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0.5 I i l_l I 1 ' 500

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100 200 300 400 500 600 700 800 900 1000

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74
FORM NBS-U3

(REV. 4-1 1-63)

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON 25, D.C.

NATIONAL BUREAU OF STANDARDS

REPORT OF CALIBRATION

PLATINUM vs. PLATINUM-RHODIUM THERMOCOUPLE

Submitted by

National Bureau of Standards

Division 272, Section 60

The emf of the thermocouple was determined at 1064.43 °C (gold point),

961.93 °C (silver point), 630.74 °C, and 419-58 °C (zinc point) with

the reference junctions at °C. The values of emf found are given in

Table 1. The uncertainties in these values are estimated not to exceed

3 microvolts.

Table 2 gives the values of the coefficients A, B, and C in the equation

E = A + Bt + Ct

2

,

where E is the emf of the thermocouple in absolute microvolts and t is

the temperature in degrees Celsius (IPTS-68). The equation may be used

for interpolation in the range 630. 74-° to 1064.4-3 °C.

Table 3 gives values of emf from 0° to 1450 °C. The uncertainties in

the values given are estimated not to exceed 5 microvolts in the range

0° to 1100 °C and then increase to not more than 30 microvolts at 1450 °C. These uncertainties are discussed in National Bureau of Standards Circular

590, Methods of Testing Thermocouples and Thermocouple Materials.

All temperatures in this report are given in degrees Celsius (IPTS-68).

The International Practical Temperature Scale of 1968, IPTS-68, was

adopted by the International Committee of Weights and Measures at its

meeting in October, 1968, and is described in "The International Practical

Temperature Scale of 1968," Metrologia, Vol. 5, No. 2, 35 (April 1969).

The calibration of a thermocouple is subject to change during use. The

mangitude of the change depends upon such factors as the temperature

,

the length of time, and the conditions under which it is used. Factors

Work Order No. Test No. Completed272-0242

3.1d/8432D

June 3, 1971 Page 1 of 2 pages

Figure 3. 13. Sample Page from a Thermocouple Calibration

Report.

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85
26.34°±0.92'

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Figure 4.7. Temperature Distribution, Expanded Scale,

86
BEFORE TERMINATION

IS INSERTED

INCHES

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88
220,-

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INCHES

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.

89
Distance in From Output Flange

0.8" 1. 3"

22°C/1:29 397°C/1:34 828°C/1:41

21°C/1:50 395°C/1:57 828°C/2:03

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21°C/2:25 396°C/2:36 828°C/2:45

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Figure 4. 11. Table of Temperature Measurement

Repeatability Tests.

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91
TEMPERATURE (°F)

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4 BASE (FIGURE M.3)

Figure M„2„ Circuit Waveforms,

99
+15VDC

o rn 1 OK

WAVEFORM A "bFL

o+15VDC Zj?35yf

2K

IH-W 1 QsrT

10V$

ZENER ^ /l/W

DC LEVEL AT

Q

g EMITTER

DC ERROR

SAWTOOTH

+

i

*—*- •*—>- •*—*- WAVEFORM A

Figure M„ 3, Circuit Diagram for Block IV.

100
4.7K

2.5K

1 .5K

o +24VDC

10W

+12VDC

o OV

Figure M.4. Circuit Diagram for Block VI.

101
i

r*-

i M

a ri

Figure N. 1. Generator attached to a Two-Port

Transducer.

fsj a n S -H

-»r- h

^r,

Figure N. 2. Scattering Parameter Description.

102
wvH a n T pvw

p^+p

Figure N. 3. A Noisy Two-Port.

A/W-j a T

'g—-* p a+p

Figure N. 4. Illustration for (N. 1).

103
Figure N. 5. A Thermal Noise Source,

104
1

rA A

X X

-<=N>

-0--

CD —iao

+->o

<u

I—

I

<u Hi

6

IIo

aD

u

105
8. DRAWINGS

1Oven Assembly

2. High Temperature Resistive Termination

3. Oven Details (Iconel Heat Distributor)

106
- * . - V - « - - - - - • ?

1:

jf

isJA

is!«

it

is

s

ij

1?

si

a'

3

II

3

3-. . SI \i

V

If

I!

! *

8'

1 j

3

i

3

IS

j

It

b «

5' !n>^:",r ;(.«^ s, •--: a V"

>: s ,* ,- s f

>O

o

bfl

PI

Q

107
8:

| 3

I i u ;!u|i

'I!

1 >!!!! i§*

108
3o.—I aouQa>oo

S-H Q

109
Appendix A -- The Output Equation

The output equation for the noise temperature of a noise

power standard is (ap N)

T = T + AT (A.l)

where T is the termination temperature,

m

r '

% , AT = (T -T )(l-a ) + J v T (1-a ) dx , . -. o nr

v oJ J xK xJ (A. 2)

o

v J

-A /10 2 1 r | 2 a = 10 X - Sinh(A /10 log e) X

1 - |T

£

| 2 X

(A. 3)

and

I A

x

= I

a

z dz - (A. 4)

Referring to figure 2.2,

T = the temperature at point x on the transmission

line (e.g. v 6 T = T n ) o x=Cr

T = the derivative of T with respect to x at point x

a = the available power ratio from point x on the line

to the end of the line at x = £

A = the attenuation in decibels of the line from x to

x = I

a = the decibel attenuation per unit length at point

x on the line

r . = the reflection coefficient of the termination and

transmission line.

110
The scattering matrix for the length of line from x to

x = £ is

' ° S 12~

S 21 ,

giving an attenuation [11] for this length of line equal to

(ap N)

J> A = -10 log IS.,, I 2 = J a dz.

x

s ' 21 ' J z

For a uniform transmission line with little loss, a r can be approximated by

(A. 5)

a = cp 2 z z (A. 6)

where c is a constant dependent upon the frequency, f, and the

transmission line geometry. p is the line resistivity. For

a rectangular waveguide [2]

c

x (f 2 + c

2

)

(A. 7) a

= —

r

where

C

f2 (f 2 - c,y

_ 20 • it 2 log e bCy'

r - k£2

z 2a 3

4a :

111
C = 2.99792 x 10 8 meter/sec,

_ 7 y = 4tt x 10 henry/meter,

and

log e = 0.434294.

With the frequency expressed in gigahertz, p in microhm

centimeters, a and b in inches, and a in decibel per inch,

r 1.44865 x 1Q' 4

i ;

p 69.6533 b

L

2 " ~T~

r 34.8266

3 2 a The second term in (A. 3) shows that the noise temperature of the standard is dependent upon the standard's reflection coefficient. The error in AT caused by dropping this

term can be estimated from

6AT oi 2(T-T ) I r I 2

v 0.23 A (A. 8) nr ' £v J

where T is the average temperature of the transition region

of the waveguide temperature gradient, and A is the average

decibel attenuation over this same region. Using the

resistivity curve given in figure 2.3 and temperature curve

C in figure 4.7 to calculate A results in

6AT < 0.01 K.

112
A maximum value of 0.01 (SS 4.1.3) has been chosen for the

reflection coefficient of the line and termination. Therefore for the WR15 standard, the second term in (A. 3) can be

dropped with negligible error.

113
Appendix B -- Quantum Correction

As the ratio hf/kT becomes significant, (A.l) should be

replaced by

kT = W(Tv ,£) + [W(T ,f) - W(T ,£)](l-a ) m' J LV o' m' J o

I

+ / W (T ,£) (1-a )dx rB .. ; v x' J K x

J (B. 1)

o

J

where

h£ W(T,f)

and

2u i e - 1

hf

u = 2kT

Here, h is Planck's Constant, k is Boltzmann's Constant, £ is

the frequency, and T is the absolute temperature. The significance of this correction can be determined by expanding (B.l)

to second order in u and comparing the result to (A.l).

T = T (1-u +u

2 /3) m

v m mJ

+ (Tv -T ) (l- a ) (1-u u /3)

o nr

v o o mJ

+

! T^(l- U2/3)(l-a )dx. (B.2)

o For T equal to 1200 K in the 55 to 65 GHz frequency

m

n n J range, the second order terms in (B.2) are found to be quite

negligible. 66 The linear term T u is found to be 1.6 K at mm

114
65 GHz and is independent of the absolute temperature of the

thermal noise source. The manner in which this linear term

is treated depends on the application to which the standard

is put. For example, in the comparison of noise sources this

term drops out, but the correction must be considered when

making a highly accurate noise factor measurement.

115
Appendix C - - Error Calculation

The maximum error 6T in the calculated output (SS 2.1)

T of the noise standard can be obtained from (A.l) and

expressed as

6T = 6T + 6AT m

= (6T)

T

+ (6T)

T

+ (6T)

o

+ (6T)

£ m o

+ (6T) + (6T) + (6T) + (ST)., + (6T) + (6T) (CI) v p ^^c g 1 ^ ^w v a

where the terms correspond to uncertainties in T caused by

uncertainties in T , T , the location of x = , the

m' o

' location of x = SI, p, c, T , neglecting second term in (A. 3)

(SS . 2 . 2) , differing wall distributions (SS 4.4.4), and air

attenuation (SS 2.2) respectively. These terms are calculated

from (see ap A for definitions)

(6T)

T

= (l-a

o )6Tm (c<2) m

(6T)

T

= (l-a

o )6T

o (c>3)

o

(6T) = 10.23 ca (T -T ) p h + (1-a )t'| 6(x=0) (C.4)

o ' o

v omo v o o ' v

(6T)

5 = 0.23 cpj |T

£ -Tm

-AT| 6 (x=£) (c . 5)

I . h

(6T) = 0.23 la (T -T )A + / a A dx I ±$— rr * J 61 n ' o

* o nr o opJ x x ' h 0-°J

(6T) v J = 0.23 I (T -T )A a + 7 t'a a dx I — rr 71 c ' * o nr o o

J x x x ' 1>«'J

o c

116
6c

c

3C.

f

2 + C. f

2

- C. f

2 + C.

and

2f 2

£

2 + C.

£ (ST) = / (l-a

x )(6T

x )dx

B o

§1

f

(C.8)

(C.9)

In the WR15 standard the output flange is taken as the

reference position, making 6(x=£) and (ST), vanish.

The last term, (C.9), can be treated by one of two

t methods . The gradient uncertainty ST can be broken down

into its two separate components At and Ax with each handled

separately; or it can be estimated by calculating the output

T for each of the possible gradients allowed by the temperature

measurement uncertainties and taking one-half the resulting

range in T as the uncertainty. The first method is the more convenient but places a much larger upper bound on ST

than the second method. The second method is used in the

present case

.

(ST) is obtained from the four temperature distributions used to generate figure 4.12 (SS 4.4.4). One-half

the range in the four resulting T's calculated from these

four distributions is 0.29 K. The distribution giving

117
T closest (0.07 K off) to the center of this range was the

right-wall distribution (fig. 4.12). Therefore, with the

right-wall distribution being used as the waveguide temperature distribution, the uncertainty incurred is no greater

than 0.36 K (0.29 + 0.07 K)

118
Appendix D -- Computer Calculation of AT and 6AT

The computef program written to calculate AT and SAT

(SS 2.1 and 2.2) is called "Delta T," a printout of which

is shown in figure D.l. The input data fed into the computer

consists of:

1. The coefficients (AO , ..., A3) of the least squares

fit to the curve of p

2 as a function of centigrade

temperature

;

2. the frequency F in gigahertz;

3. the broad and narrow waveguide dimensions A and B,

and their corresponding uncertainties DA and DB;

4. the termination temperature T in centigrade;

5. the coefficients (AR1 , ..., AR3) for the waveguide

expansion as a function of centigrade temperature

according to the law [4]

I = I (1 + AR1 * t + AR2 * t

2 )/AR3;

6. the temperature distribution (x,T) along the right

wall of the waveguide with x = at the termination;

7. the input uncertainties DTM, DTO, DDX , DR, DDT,

DDO, DDB, and DC, corresponding to the uncertainties

in the termination temperature, the temperature of

the waveguide at the termination, the length difference measurements, the square root of the resistivity, the temperature difference measurements,

the position of x = and x = £, and the c constant.

119
The computer processes this data to an accuracy of 0.1%

in the calculation of T.

The output results consist of:

1. the c constant;

2. the value of L shoxving how many times the computer

must subdivide the temperature distribution data

(x,T) to achieve the 0.1% calculational accuracy;

3. an approximate value (^ 10%) for the total decibel

attenuation of the waveguide;

4. AT in kelvins;

5. the separate uncertainties in AT caused by

DTM, . .

. , DC; and

6. the error in AT which is the sum of the separate

uncertainties appearing in 5. The data under the DDX and DDT headings are zero since the

uncertainty given by (C.9) is calculated by the second

method discussed in ap C.

120
Appendix E -- The Thermocouple Rod Expansion Program

As a thermocouple is inserted into the heated waveguide,

the apparent distance the thermocouple bead enters the waveguide should be corrected for the expansion of the

thermocouple rod. For any given temperature distribution,

this correction can be calculated by program "TEX998'' for

the 99.8% alumina rods used in the thermocouples. Figure

E.l shows a sample output of the program using the distribution shown in figure 2.5. The lengths shown are measured

in inches assuming the thermocouple to be inserted into the

waveguide from the front of the oven.

121
Appendix F -- Termination Formula

Figure F.l shows a portion of the termination, where

a and b are the broad and narrow dimensions. Given a, b,

and the angles a and g, the face angle y , the cutting angle

6, and the longitudinal face length £ are given by:

Y

= cos (cos a cos 6)

tan -1 tan H

sin a and

£

and

tan a tan 3 For the WR15 termination with a = 24° and g = 10°,

Y

= 25.9°

6 = 23.4°

£ = 0.75".

122
Appendix G -- The Minimum Termination Length

The minimum length of the termination is determined by

two factors : 1) the amount of taper needed to produce a low VSWR; and 2) the amount of material needed to completely

terminate the waveguide. Experience has shown that an effective taper geometry that produces a low VSWR and good

thermal contact between the termination and the waveguide

is achieved by the model shown in figure F.l for small

values of a and 3. The length required to effect the first

factor was determined in ap F. The length required for

the second factor and the radiation length (the length of

material behind the taper from which most of the thermal

radiation leaving the termination originates) are determined

in this appendix.

Terminating Length

An estimate of the length of material behind the taper

that is required to completely terminate the waveguide can

be made in the following way. Consider a length I of material

hich is characterized by a scattering matrix S, and which

is heated to a uniform temperature r

T . The reflection coef- m

ficient of the material is given by

w

r

, . S 12

S 2i r L

1 - J> 11

1 " S 22r L

123
where I\ is the reflection coefficient behind the material.

If the length is great enough, the power delivered (in units

of kB) P, into a matched load by the material is

p, = T (l - Irl 2

)

. d m^ \ \ j

If r

T changes to I\ , then r changes by an amount

.*

S 12 S 21 (;r L

' T ol -

(i - s 22 r L )(i - s 22 r L

)

and P, by an amount

6P, = T 6 Irl 2 < T |6r| 2. d m * ' — m '

'

i •; g The largest change in r is obtained from r

y = and I\ = e , giving

IS S I 2

I 1 2 71 I 6

I 2 = —iz^i

max , . o | 2

and

6T E (6P.) = —

h±-±±

max "• d^max n

. Q, 2 i - |b 22 |

In the present case

n -a£/10 |s 12 |' - |s 21 M = io

where a is the decibel attenuation per unit length of the

material. Then

T 1Q -2a£/10

6T = — . (G.l) max i i c i

1 " l b 22l

124
Or to achieve a change6 of 6T or less max

I > - loi — a ' m Id - Is 22 ' 7 max

(G.2)

For a = 92 dB/inch (SS 3.1.1),J |S 00 | = 0.5, T = 1200 K, ' ' 22 ' ' m

' and 6T = 0.01 K: I > 0.28". That is, if the termination

max ' — ' (minus taper) is greater than 0.28" in length, then a maximum VSWR change behind the termination can cause no greater than 0.01 K change in the noise power delivered by

the termination to the waveguide.

Radiation Length

A termination of infinite length with a temperature

distribution T has a noise temperature T given by

-A /10

T = / T (0.23 a dx)10 x (G.3)

where a is the decibel attenuation per unit length of the

termination material, and A is the decibel attenuation of ' x the material from x = to x

.

A

x

/ a dz . X ' z

Suppose that only the taper and the first I inches of

the termination could be maintained at a uniform temperature

T . Then

m

T = 0.23 T / a 10 m ' x

o

-A /10 » -A /10

+ 0.23 / T a 10

x dx.

I x x (G.4)

125
The length % can be increased to the point where the second

term in (G.4) is negligible. Taking T - T , and a - a,

A. U J\. the ratio R of the second to first term in (G.4) becomes

ail/10

R = T 10

o ^___

T (1 - lO"^710

)

(G.5)

This ratio is insignificant if % is greater than some radiation length £ D given by

_ 10

1 1

£ R log

'1 + T R/T m ' o T R/T m o

(G.6)

For a = 92 dB/inch, T - 1200 K, T = 300 K, and ' m ' o R = 0.01/1200; £ R

= 0.2".

126
Appendix H -- Waveguide Reflections

Broad and Narrow Dimensions

A rectangular waveguide whose broad and narrow dimensions

are in error by 6a and 6b respectively will produce a reflection coefficient (with respect to a perfect waveguide of

dimensions a and b) whose magnitude is given by [12]

AT =

X 6a

2a

2a 6b

(1 + a) 2 b

(H.l)

where A is the waveguide wavelength, X is the cutoff wavelength, and a is the VSWR corresponding to r. For WR15

(Xv = 0.296") at 55

c

J reflection (a - 1) ,

(Xv = 0.296") at 55 GHz (X = 0.3115") and a small

c

J V

AT = 3.7 6a + 6.8 6b

For 6a = 6b = 0.001", Ar = 0.010.

(H.2)

Corner Bend Radii

Non- vanishing corner bend radii inside an otherwise

perfect rectangular waveguide will cause a reflection whose

magnitude is given by [13]

AT =

'a r' g

. a J

2 4 - TT 8ab

(H.3)

where R is the radius of the corner bend.

For WR15 waveguide at 55 GHz with R = 0.006", AT = 0.002

127
Appendix I -- Atmospheric Attenuation

The maximum change in the output noise temperature of

the standard 6T due to the attenuation by the column of air

in the waveguide between the termination and the output

flange can be approximated by

6T = (T*

- T ) (1 - a) (1.1)

a nr v J K J

where T is the average temperature of the air column, T

is the termination temperature , and a is the average

attenuation of the column. With T = 300 K, T = 1200 K,

a ' m ' and a = 0.00025 dB/inch (60 GHz in figure 3.4); AT = 0.05 K.

1Z8
Appendix J -- Support Spider

The inconel sleeve (drawings 1 and 3) is suspended inside

the oven by a support spider (which is kept near room temperature by the end plate) on each end plate. The spider is so designed that as the sleeve expands on heating its center

line remains fixed. This is accomplished by choosing the

angle for the support spider shown in figure J.l so that as

the sleeve length £ and diameter D increase, the sleeve ends

climb smoothly up the support spider. It is apparent from

the figure that the proper angle 6 is given by

tan = £D/I. (J.l)

61/2

Since D and £ expand on heating by the same factor, (J.l)

reduces to

tan 6 = -. (J. 2)

£

For £ = 7.75" and D = 3.25"; = 22.75°.

129
Appendix K -- Thermocouple Rod Expansion

The expansion of the thermocouple rod upon heating can

be described in terms of a linear coefficient of expansion

e;

d£ = dx + e • At • dx (K.l)

where dx and dl are elemental lengths of the rod before and

after heating respectively, and At is the corresponding

temperature change. The length of the entire rod is the

sum of these elemental lengths . Thus

I I

I = / ° dl = £ + / ° e • At • dx (K.2)

o o where I is the length of the unheated rod.

o

& The following table [10] gives e in 10 /degree C for a 99.8% A1

2 3 rod:

Temperature Change e in 10 /degree C

-200 to 25°C 3.4

25 to 200°C 6.7

25 to 500°C 7.3

25 to 800°C 7.8

25 to 1000°C 8.0

25 to 1200°C 8.3

The coefficients of a least-square curve fitting the

product e • At over the to 1000°C temperature range are given in the next table:

130
where now

and

1.58 x 10

6.28 x 10

1.72 x 10

9.27 x 10

-13

-9.72 x 10 16

I 1=1 +/°adx o

; x

o (K.3)

a = aft ) = E a t x

y x

J n n x n=0

(K.4)

131
Appendix L -- Lead Resistance Error

The copper leads from the thermocouples (fig. L.l) to

the terminal board have a resistance r. In reading the

thermocouple emf an error E will be caused by this resistance

if an imperfect null (e + 1 uV) is obtained on the

potentiometer. Neglecting the small resistance of the

thermocouple itself, the current caused by this imperfect

null is

i=J^L CL . 1D

2r + R

where R is the balancing resistance of the potentiometer.

The corresponding error is

E = 2ri = —^^—

(L.2)

1 + 2r/R

When balancing at the silver point temperature with a platinum-rhodium thermocouple (9.127 mV) , R turns out to be

170 9,. The lead resistance is (SS 4.3.2) 1.5 ohms. Therefore E is 0.017 uV which corresponds to an error of 0.002°C

at the silver point temperature.

132
Appendix M -- Oven Temperature Control

General Description

The operation of the control system can be understood

from figure M.l and the block summaries given below.

I. The output of the reference voltage source is a variable DC voltage adjustable from zero to 50 mV.

II. The block II output is the algebraic sum of the

reference source and the thermocouple voltage.

This sum is zero under normal operating conditions.

III. The DC amplifier amplifies any deviation from zero

of the block II output (a calibrated meter indicates magnitude and polarity)

.

IV. The DC to duty cycle converter changes the

fluctuating DC (error signal) to a square wave

of fluctuating duty cycle. The converter output

is waveform A of figure M.2.

V. Waveform A (fig. M. 2) together with waveform B,

a waveform of fixed duty cycle, is presented to

an "and" gate to produce waveform AB (fig. M.2).

The width of the positive-going portion of AB

determines the position of the current transformer,

which in turn, determines the amount of current

133
delivered to the heating coil. The temperature control servo loop is closed through the heat conduction

path from the heater coil to the thermocouple.

DC to Duty Cycle Converter

The output of emitter follower Q4 (fig- M.3) is the

amplified sum of the DC input of Ql from the DC amplifier,

and the sawtooth input of Q3. This Q4 output is a sawtooth

waveform that translates vertically with changes in temperature

(changes in the DC amplifier output) . Q8 and Q9 form a bistable circuit with the Q8 emitter voltage fixed by zener diode Z. When the output of Q4 is greater than the emitter

voltage of Q8, Q8 and Q9 switch off. Q8 and Q9 switch on again when the Q4 emitter voltage drops sufficiently below

the Q8 emitter reference. As seen in figure M.3 the negativegoing transition of the Q9 collector always coincides with

the negative-going transition of the free-running sawtooth

waveform. The positive-going transition of the Q9 collector

occurs when the Q4 output becomes greater than the Q8 fixed

emitter voltage. This circuit configuration results in an output square wave which has a duty cycle determined by the

DC level from the DC amplifier. This variable-duty-cycle

square wave is waveform A of figure M.2. The frequency of

this square wave is determined by the free-running sawtooth

generator and is not critical.

134
Current Transformer Servo

Ql of figure M.4 receives a variable-duty- cycle square wave signal from the "and" gate. This signal is inverted

at the collector of Ql which is connected via Dl to a "oneshot" formed by Q2 and Q3. The incoming signal triggers the

"one-shot," and the collector of Q2 goes positive for a time

determined by the RC time constant of R3 CI, together with

the position of pot R4 . R4 is mechanically connected to

the transformer shaft. Therefore the rotational position of

the transformer shaft determines the width of the "one-shot"

output pulse. This pulse is compared to the width of the incoming signal, and any difference in width results in an error

signal at the base of Q4 . The signal at the base of Q4 is

a narrow positive or negative-going pulse depending on whether the Ql input is narrower or wider than the "one-shot"

output. If the error signal is positive-going, it will

cause Q5 to conduct, which in turn energizes the pulse

stretcher Q6 together with C2 and R5 . The pulse stretcher

output signal is sufficient to drive the servomotor in one direction through Q7 , Q8 , Q9 , and Q15. The same thing

happens for an error of the opposite sense via Q10 through

Q14 driving the motor in the opposite direction. The

servomotor will continue to drive until R4 adjusts the

135
"one-shot" pulse width to equal that of the incoming signal.

Q8 and Q13 are "nand" gates (inverting "and" gates) that are coupled so that both drive circuits (clockwise and counterclockwise) cannot be energized simultaneously.

136
Appendix N -- Derivation of the Output Equation

N. 1 . Introduction

A thermal noise source consists of a termination and a transmission line to convey the noise generated in the

termination to an output port. The transmission line is

lossy, so it both attenuates the termination noise and adds

noise of its own to the output, and the line must be chosen

in such a way that the output power can be accurately

calculated.

The derivation begins in SS N.2 with a review of some two-port power relationships which are used in SS N.3 to

find an expression for the noise output power of a lossy

two-port. Finally, this output power equation is applied

in SS N.4 to incremental segments of a transmission line

to obtain the output noise power equation for the noise

standard.

N.2. Some Basic Two-Port Equations

The work to follow requires the use of some two-port

power equations. These equations will be presented in this

section in a form that is most useful to SS N.3 and SS N.4.

Throughout this appendix a capital ' P' will stand for net

or delivered average power and a small 'p' for available

average power. It is to be understood that where the

137
parameters are frequency dependent, the bandwidth is narrow

enough to insure that these parameters are essentially constant

across it.

A passive, linear, two-port transducer is shown in

figure N.l with a generator attached to its input (first)

port, and a load attached to its output (second) port. M

and N are the mismatch factors of port one and port two

respectively, and are defined in the following equations:

M e P

1 /p 1

, N E P

2 /p 2

,

where p, is the average power available from the generator,

and p ? is that portion of p available at port two of the

junction. P.. is the net average power into port one from

the generator and P

? is the net average power from port two.

The ratio a of available powers is defined by

a e p 2 /p 1-

The corresponding transducer efficiency r\ is

n

~= P

2 /Pr

The definitions for M, N, a, and n can be combined to obtain

the following relationship between these four quantities:

Mn e Na

Furthermore, by considering the definitions of a and r\ , it

can be seen that if the transducer is lossless, then both

a and n are unity.

138
These definitions are general because they apply to a transducer with any number of propagating modes. However,

to have a workable expression for the noise power output

calculation, one is restricted to a single propagating mode,

in which case the transducer has an equivalent circuit like

figure N.l. This circuit is shown in figure N.2 where

scattering parameters [11] are used and where, in terms of

these parameters, M, N, a, and n take the following form

[11,1]:

[i--ir K l*}(i-|r 1

| a

J M =

N =

a =

l-r r 7

1 2

U-|r T

| 2 )(i-|r 7 | 2

) i-r T r. I 2 L L

'

(i-lr J

2 )|s

21

(i-

(i

! )|i-sui

(i-lr.l^U-s^r.r

The two-port scattering matrix is given by

S =

S

ll

S 12

'21 22,

The reflection coefficients of the generator, the input and

output ports of the two-port, and the reflection coefficient

of the load are denoted by r , l , T , and T L respectively.

139
The input and output port reflection coefficients are related

to the scattering matrix parameters and the terminal reflection coefficients through the equations [11]

r q S 12

S 2ir L

1 ~ 11 ' i - s r

S 12 S 2i r g

2 22

i - Sll r

"

It can be seen from the equations for a, n , r, , and T~,

that a is independent of the load reflection coefficient,

and that n is independent of the generator reflection

coefficient

N. 3 . Two-Port Noise

An expression for the average thermal noise power of

a lossy two-port transducer is derived in this section.

The expression to be obtained can be found in at least

two other sources [14,15], so the short derivation given

here is not intended to be new or unique. It is presented

because it is an important logical step between SS N.2 and

SS N.4 and because it will help familiarize the reader with

the parameters just described.

A linear, passive, two-port transducer is shown in

figure N.3, terminated at both ends. Both of these terminations and the two-port are thermally isolated from their

140
surroundings , and have come to a uniform absolute temperature

T. P, represents the average net power from the first termination, and P y that from the second. The portion of P,

that emerges from port two is P,q, P represents the noise

power added to P,ri by the two-port itself, and is the quantity

to be found. M and N are mismatch factors, and again a capital 'P' refers to delivered or net power while small 'p'

refers to the available power. For example, if p, and p~

denote the available powers from port one and port two terminations respectively, then the definitions in SS N,2 lead

to

P, = Mp

1 and P

2 = Np

2

.

Since the entire circuit is thermally isolated from its

surroundings, the temperature of the two-port and the terminations must remain equal even though there is a continual

exchange of electromagnetic energy between them. This fact

leads to the important conclusion that the average net powers

leaving and entering port two must be equal,

PjT, + P - P

2

.

In terms of the available powers p, and p~,

P = Np 2

- Mp , n .

141
Since both terminations are at the temperature T,

Pi = P2'

where both p.. and p~ are equal to kTB in the low frequency

approximation

Therefore

P = NkTB(l-a)

where the relationship

Mn = Na

has been used to eliminate n . Representing the available

power generated in the two-port by p,

p = P/N = kTB(l-a)

(N.l)

This equation is still general in the sense of the fourth paragraph of SS N.2, and is assumed to hold for all passive

input and output terminations

To illustrate the use of (N.l), consider figure N.4

and the total noise power available from port two that is

generated in the two-port at temperature T, and the termination at temperature T . This total power consists of the

g

attenuated power p a available from the termination and the

available two-port power p. By using (N.l) in place of p,

the total available power is given by

p a + p = kT Ba + kTB(l-a)

142
The net amount of this power actually delivered to the right

from port two is' equal to N times the total available power,

or N(p a+p) = NkT Ba + NkTB(l-a).

N.4 . The Thermal Noise Source and Standard

In 1958, Sees [16] derived an expression for the average

noise power output of a thermal source along the lines

presented here, but without the benefit of the expressions

found in SS N.3. Therefore, in this section those expressions will be applied to a lossy transmission line to find

the contribution of the line to the total noise output of

the source. Figure N.5 shows a thermal noise source consisting of

a termination at a temperature r T that terminates a transmis- m

sion line of length I . T is the temperature of the transmission line at point x along its length, and a is the

available power ratio of the section of line from x to £

.

Plots of T XXand a as a function of position f along& the line

are also shown in the figure

.

For analysis the line is divided into many small segments,

each of length Ax, where the particular segment at position

x is shown in the figure, and (N.l) of the previous section

is applied to each segment. Thus, the available power Ap

143
from the segment at x is equal to the average temperature

T of the segment times one minus the available power ratio

.A. Aa for the segment,

.X. Apr

= kT B(l-Aa ) x x *• x^

Using

leads to

x-Ax/2 x x+Ax/2

Apr = kT B x x

a x+Ax/2 " ax-Ax/2

x+Ax/2 J

For small segments

da a . # - a . ,

x . x^-Ax/2 x- Ax/2

dx Ax

and a . ,,, can be replaced by a . Therefore x+Ax/2 v ' x

Ap x

- kT Ba Ax

x x

The portion of this power that reaches the output port at

x = I is

a Ap = kT Ba Ax.

X

r X XX

To get the total effect of the line, the effects due to

each segment are added together:

a

l a Ap = I kT Ba Ax = kB / T a dx.

X

F X XX XX o

144
The amount of termination noise available at the output

is

kT Ba . m o Therefore the total available noise power output, kT B, of

tot

the thermal source is given by the sum of these last two

expressions and leads to a noise temperature T given by

I T.. = T a + / T a dx. (N.21 tot mo J xx «."«*j o Another form for this equation can be obtained from an integration by parts

:

T

tot

= Tm

+ AT ' ( N - 3 )

where the correction temperature AT is

£ , AT E (T -Tm

)(l-a

o

) + / T (1-a )dx. (N.4)

o The net power delivered across the output port corresponds

to

MT = M(T +AT)

.

tot * m

J

Equations (N.3) and (N.4) are valid for any number of

simultaneously propagating modes. However, to have a workable

expression for a to be used in calculating the output of

a noise standard it is necessary to select the transmission

line and operating frequency so that only one mode is present.

This means using a uniform, reflectionless line at a frequency below cutoff for all but the dominant mode. Figure N.6

145
illustrates such a condition, where now any portion of the

line, for example the section from x to I, can be represented

electrically by a two-port. The termination reflection coefficient is represented by r , the reflection coefficient

looking from point x towards the termination by r , and the

entire reflection coefficient of the thermal standard by r

a is the available power ratio from x to L and S is the

x

^ ' x

I

corresponding scattering matrix.

From Kerns and Beatty [11, p. 77], S for a uniform, reflec

tionless line is

/J X dy

x y

!

S = x /J X dy x j

where X is the propagation constant

A = e + ig

y y

and e is real positive and determines the wave attenuation.

y

F For example, the attenuation in decibels of the line is

8.68 / e dy. This attenuation constant depends on the

resistivity (which in turn is a function of the line temperature) of the material making up the line. It can be measured

[17] or, with care, calculated from a perturbation expansion

[18,2]. Using these scattering parameters in the expression

146
for a of SS N.2 leads to

CHrJ').-

2

^

where |r |, |r |, and |r | are related by the equation [11, x' ' ' I p. 42, eq. (2.12)]

r e 2/x

\ dy -2/ x

J e dy

o y

;

I

i „ i J o y

7

V l\e 2/

£

e dy J x y

}

The a ratio can be rewritten in the following form

x

6

ax

= e -l\ l

e dy 2|rJ 2

J x y

J ' I

'

i - |r,l 2 sinh 2/ e dy (N.5)

where the dependence on the reflection coefficient r of the

noise generator is more evident. In calculating T this

last term can usually be neglected.

N.5. Summary and Conclusions

The results of SS N.2 and SS N.3 have been applied in

SS N.4 to find the noise temperature r T of a thermal

tot

noise standard:

in which

T^ . = T + AT tot m(N.3)

AT E (T -T )(l-a ) + / T (1-a )dx * o m-* ^ o

J J x *• x^

o (N.4)

147
and

2 J* yy 2 l r

t

l 2

i - |r

t

|«

sinh 2

J £ v

dy

X y

(N.5)

Most output calculations neglect the second term in (N.5).

Little error results, however, since most thermal standards

are constructed from low-loss lines (small e ) and low

y

reflection coefficient terminations (small |r |), making

-2j £

e dy

i i i i J O V

r = r e

y

1 £! I g

1

small and the last term in (N.5) small also.

The net power delivered to a load at the output of the

standard source is MT , where M is the output mismatch factor,

If I\ is the load reflection coefficient, then

(i-|r

L

l 2 Hi-|r,| 2

) M = i-r r I 2

M and r . can also be written in terms of the standard and

load impedances, Z„ and Z

T

M =

4 ReZ

£

ReZ

L IVZ J

2

and

Z„ + Z

£ o where Z is the characteristic line impedance [11]

148
form NBS-114A (l-7i) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. 2. Gov'c Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE WR15 Thermal Noise Standard

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

W.C. Daywitt, W. J. Foote, andE. Campbell

8. Performing Organization

10. Project/Task/Work Unit No. Project #2726203

9. PERFORMING ORGANIZATION NAME AND ADDRESS NATIONAL BUREAU OF STANDARDS, Boulder Labs.

DEPARTMENT OF COMMERCE Boulder, Colorado 80302

11. Contract/Grant No.

12. Sponsoring Organization Name and Address Same as 9.

13. Type of Report & Period Covered Final

1-71 1-72

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 note describes the design and construction of a WR15 thermal

noise power standard. The standard is designed to operate around the Silver

Point Temperature (963. 19 C) with a noise temperature output accurate to approximately ± 2 K. Complete details of the theory, design, construction, and performance

tests are given.

17. KEY WORDS (Alphabetical order, separated by semicolons) Error analysis; millimeter wave; Noise; Nyquist's theorem; Thermal noise standard

18. AVAILABILITY STATEMENT

[XI UNLIMITED.

Zl FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

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21. NO. OF PAGES

154

22. Price

;i.25

JSCOMM-DC 66244-P71

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