NBS

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°'' STAND & TECH "^tiOHS

AlllDS TflSflSi

NBS TECHNICAL NOTE 1044

*^'?fAU OT ''

U.S. DEPARTMENT OF COMMERCE /National Bureau of Standards

WR 10 Millimeter Wave

IVIicrocalorimeter

lUO

.U5753

1981
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act ot Congress on March 3, 1901

.

The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

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TIOMAL BUaBAX' or STAKDABU8

LIBRAHT

AUG 1 1981

WR 10 Millimeter Wave Microcalorimeter ^ oo

no. jo'^c(

Manly P. Weidman

Paul A. Hudson

Electromagnetic Technology Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

7

""^aWJ^..

^lfeS 4tckAuc(Ll AtoH^

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued June 1981
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 1044

Nat. Bur. Stand. (U.S.), Tech. Note 1044, 16 pages (June 1981)

CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1981

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

Price $2.00 (Add 25 percent for other than U.S. mailing)
WR 10 MILLIMETER WAVE MICROCALORIMETER

by

Manly P. Weidman

and

Paul A. Hudson

A microcalorimeter has been built in WR 10 waveguide,

75-110 GHz, to serve as a power standard at the National

Bureau of Standards (NBS) . Included here is an evaluation

of the errors in using the microcalorimeter for the measurement of effective efficiency of bolometer mounts.

The error analysis shows a systematic uncertainty of

± .83 percent and a random uncertainty of .37 percent.

Key Words: calorimeter; millimeter wave; power; standard.

1. INTRODUCTION

The standards for waveguide power measurement at the National

Bureau of Standards (NBS) in the microwave and millimeter wave region

are a series of microcalorimeters which evolved from the work of

MacPherson and Kerns [1], Engen [2], and Harvey [3]. This paper describes the latest addition to the series, the WR 10 waveguide unit

which is identical in design and construction to the WR 15 microcalorimeter developed by Harvey [3]. The only difference between the WR 10

and WR 15 models is the waveguide size and the thermistor mounts used as working standards.

Details of construction (and operation) of the microcalorimeter are not included in this paper since they are described in reference [3].

The main purpose of this paper is to document the evaluation of

uncertainties in the WR 10 microcalorimeter. All of the work was done

in a two percent band centered at 95 GHz.

2. PRINCIPLE OF OPERATION

A complete derivation of the operating principle of the microcalorimeter is given in reference [2]. However, for the sake of com- pleteness, a brief summary is given below.

While the NBS microcalorimeter is not a true calorimeter (i.e., it

measures rate rather than total quantity of heat) , the calorimetric

principle is nevertheless used to determine the effective efficiency of

bolometric detectors such as waveguide thermistor mounts. The latter

consist of a thermistor (temperature sensitive resistor) mounted in a shorted section of waveguide, the combination forming a terminating load

to the incident microwave or millimeter wave energy. Connections to the

sensing thermistor are made via a low pass filter so that it becomes,

for example, one arm of a Wheatstone bridge. When dc power is applied

to the bridge (and thus to the thermistor) the power absorbed by the
thermistor causes Its temperature to increase and its resistance de- creases (negative temperature coefficient). Thus, by adjusting the dc

power, the bridge may be brought to a balanced condition and the thermistor resistance (typically 200S7) is determined by the bridge parameters. In recent years, self-balancing circuits have been developed

which automatically keep the bridge balanced. With negligible error, it can be assumed that all of the dc power input to the mount is absorbed

by the thermistor bead.

When mm wave power is supplied to the thermistor, the self-balancing

circuit automatically withdraws a portion of the dc bias power to maintain

the bridge in balance. However, some of the input mm wave energy does

not reach the thermistor bead, instead it is absorbed in the mount

structure. Thus, the dc power withdrawn from the thermistor bead is

smaller than the rf input power to the mount since only that energy

which actually reaches the thermistor contributes to its heating. This

leads to the concept of mount efficiency, t], which is less than unity.

A second problem is the so-called rf-dc substitution error which is due

to differences in the heating effect on the thermistor for equal amounts

of RF versus dc power. This is equivalent to a further change in mount

efficiency but may be either positive or negative. The microcalorimeter

measures the combination of the two effects which is defined as effective efficiency, r| .

The heat generated in the thermistor bead is conducted, convected,

and radiated to the mount structure so that the mount temperature, T,

rises above the ambient, T . With dc power only in the thermistor, this

o

2 temperature will be T, . When mm wave power is applied to the mount, I R

and dielectric losses in the mount structure generate additional heat

and the temperature of the structure rises above T to T„. The difference between T„ and T, is related to the difference between r| and

•*. 2 1 e unxty.

It is the above effects that the microcalorimeter is designed to

detect and measure. The principle components of the calorimeter are a waveguide flange which mates with the thermistor mount to be measured, a metal reference ring which surrounds this flange but is thermally

isolated from it and a 47 junction copper-constantan thermopile con- nected between the two. The thermopile generates voltages e, and e^

which are proportional to T^-T„ and T^-T„, respectively.

The bolometer units used as working standards in the WR 10 system

are commercially available thermistor mounts. No modification was required of the commercial design in contrast with the WR 15 mounts,

which were also commercial units but NBS modified to reduce mm wave

leakage on the dc leads. Instead, the WR 10 mounts have been improved

by the manufacturer to reduce millimeter wave leakage by an order of

magnitude (0.1 to 0.2%) and the resultant design is actually an improvement over the WR 15 mounts. The WR 10 working standard thermistor

mounts have a shorter input waveguide lead and better thermal coupling

to the calorimeter flange; they also have a lower reflection coefficient

than the WR 15 mounts.
3. ERROR ANALYSIS

The equation used to calculate the effective efficiency (n ) of

the working standard thermistor mount using the microcalorimeter is [2]

g[l - (V„/V )^]

\ =

2

' (1>

where V is the bridge voltage used for biasing the thermistor to its

operating resistance and e is the thermopile output voltage. Subscripts

1 and 2 in equation (1) denote mm-wave (millimeter wave) power OFF and

ON respectively. The term g is an algebraic correction for systematic

effects and was defined in reference [2].

In order to obtain a value for the systematic correction g, equation (3) in reference [2]

^2 = ^(^2dc ^ g^rf) ^2)

can be expanded to

e„ = k(P_, + aP ^, + bP ^ + cP ^^ + dP ^.) (3) 2 2dc rfb rfw rff rfi

In equation (3), the coefficients a...d are the relative effectiveness of heating from sources, other than the thermistor bead, on the

thermopile response as compared to heating from the thermistor bead and

power dissipation in its immediate vicinity. Here, P„ is the dc power

in the bead with mm wave power applied, P ^, the mm wave power dissipated

in the bead and its immediate vicinity, P ^ the mm wave power dissipated

in the bolometer unit walls, P the mm wave power dissipated at the

calorimeter-bolometer flange interface, and P ^. the mm wave power dissipated in the thermal isolation and flange waveguide sections.

It is assumed that mm wave heating in the vicinity of the thermistor

bead has the same effect on e„ as P„, so that a=l.

2 2dc

The mm wave powers, P ^, , P ^ , P ^^ , P j- . can be expressed as rfb rfw rff rfx

percentages of P _ (the total mm wave power dissipated in the bolometer

unit) . Comparing equations (2) and (3)

gP ^ = aP ^, + bP ^ + cP ^^ + dP ^. (4) ^ rf rfb rfw rff rfi
(5)

and

P = rP

rfw rf

P ^^

= sP ^ rff rf

P ^. = tP ^ rfi rf

where q...t represent that fraction of the total mm wave power dissipated in the bolometer mount which is dissipated in the various places

as outlined in the above definitions of P ^, ...P ^. In this case

rfb rf

q + r + s = 1 (6)

assuming P ^, , P ^ , and P ^j: account for all power dissipated within

the bolometer mount. (Note that P is dissipated outside the bolometer mount) . Using equations (4) and (5)

g = aq + br + cs + dt (7)

The factors b...d and q...t are evaluated in the following sections.

3.1 Bolometer Unit Walls and Flange

A given quantity of millimeter wave energy absorbed (i.e., con- verted into heat) in the thermistor mount between the input flange and

the thermistor bead will have a greater effect on the thermopile output

than the same quantity of energy absorbed in the thermistor bead. The

systematic correction which compensates for this effect is contained in

the terms cs and br in equation (7).

In order to evaluate this correction, measurements were made with a heat source (small dc heater with input power, P, ) at the microcalorimeterthermistor mount flange interface. This showed that the heat source at

the flange (worst case condition) had an approximately one percent

greater effect on the thermopile output than the same amount of power,

P, in the thermistor bead. The difference in thermopile response between

the two locations for the heat source is small owing to the large thermal

conductivity of the thermistor mount. The short input waveguide lead

(9 mm long) and the thermal coupling through the mount via an equivalent

metal, thick-walled (25mm diam.) cylinder accounts for the small difference between heat source locations.

Using flange loss measurements in the microwave and millimeter wave

region up to 60 GHz, an extrapolated value of 0.3 percent of the input mm wave power (P ) was obtained for flange loss at 95 GHz. These ts

lead to the values c = 1.01 and s = 0.003 in equation (7).
A combination of theory and extrapolation from WR 15 waveguide loss

measurements at 60 GHz was used to arrive at a figure of 0.0039 dB/mm

for waveguide loss at 95 GHz. In the 9 mm distance between flange and

thermistor bead this would lead to the estimate that 0.035 dB or 0.8 percent of the input power is dissipated in the input guide, or r = 0.008

in equation (7). Assuming uniform distribution of the loss, an estimate

of 1/2 times the increased effect of heating at the flange would be

appropriate. This implies that b = 1.005 in equation (7) for input

guide wall losses.

3.2 Thermal Isolation Section

The thin-wall thermal isolation waveguide section which terminates

in a flange forms a 9 mm long input waveguide ahead of the bolometermicrocalorimeter flange interface. The loss in this thin-wall section

which includes the distance through the flange "thickness" contributes

to the systematic uncertainty. Based on the microcalorimeter geometry,

an estimated 75% of the associated heat is conducted and convected to

the flange causing an increase in e„. Since this source of heat is

outside the bolometer mount, a correction must be applied. A value for

this correction is arrived at using the same arguments as for the bolometer unit wall losses in the previous section.

The power dissipation in a 9 mm length waveguide section, already

calculated in section 3.1, is 0.8 percent and 75 percent of this yields

0.006 for the value of t in equation (7). For d in equation (7) the

value of 0.5 percent is used for the increased heating effect in this

region (one-half the effect at the flange) . This means that d in equation (7) is 1.005.

3.3 Calculation and Uncertainty for g

From the preceding sections, r = 0.008 and s = 0.003, and from

equation (6) this implies q = 0.989 or 98.9 percent of the mm-wave power

dissipated in the bolometer unit is dissipated in the vicinity of the

thermistor bead.

Using the preceding values for a...d and q...t and equation (7)

yields g = 1.0061. If it is assumed that the contributions to g are in error by ±100 percent (i.e., 1 - g - 1.0122) the uncertainty in g is ±0.61

percent. The ±100 percent uncertainty is probably conservative, but

waveguide and flange losses and heating effects are difficult to measure

in the mm-wave frequency range, and a cautious approach is warranted.

A summary of these results is listed in Table I.

3.4 Millimeter Wave Leakage Effects

Millimeter wave leakage from the bolometer mount via the dc bias

leads causes a systematic error in the measurement of ri in the microe calorimeter. Since n is defined as P, /P ^ where P, is the substie dc rf dc

tuted dc power and P ^ is the total mm-wave power dissipated in the

bolometer unit, the leakage power as a percentage of P _ should be a
correction to ri as measured in the microcalorimeter . When the boloe meter is used outside of the microcalorimeter, it is assumed to measure

all of the mm-wave power at its input flange. The correction can be

seen by relating two values for ri as follows

:

n = P , /P . (8)

e dc rf

not accounting for leakage and

'e^ P ^ + P.

rf £

""^^ (9)

where P„ is the leakage power.

Then if

where u is the fraction of leakage power and using equations (8) -(10)

The leakage measurement was made by changing the orientation of the

dc biasing leads to the thermistor with millimeter wave power applied at

the waveguide input and noting the percentage change in substituted dc

power. This measurement showed an effect of approximately ±0.02 percent

which suggests that at least 0.02 percent of the input power was leaking

out via the dc leads. Since this measurement gives only an indication

of actual leakage, this result is multiplied by a factor of 10 for

estimating leakage with an uncertainty of ±100%. In equation (11)

(1 + u) = 1.002 ±0.002.

The leakage correction is listed in Table I.

3 . 5 Ins trumentation

Since the bridge voltages and thermopile voltages occur in ratios

in equation (1) there is no significant contribution to systematic

error. Instrumentation effects will appear in the overall random error.

3.6 Thermopile Nonproportionality

Calculation of T] from equation (1) assumes that the ratio, e„/e^ , is linear with power ratio, P^/P-, , where P- is the power absorbed in the

thermistor mount with mm wave power plus dc and P, is the absorbed power

with dc only. Linearity of e^/e , is assured if it can be shown that e, and e^ are individually linear with the temperature difference between

the thermopile hot and cold junctions, T, and that T varies linearly

with P.
Thermocouple output, e, is, in fact, somewhat nonlinear (increasing)

with respect to T. Also, nonlinear cooling due to radiation causes T to

be smaller than would be the case for linear cooling (i.e., conduction).

It is shown in the appendix, however, that these nonlinear effects on

e„/e^ are negligible.

3.7 Thermistor Radiation and Convection

As described in [3], this is a small contribution to the systematic

error (0.001 percent). The WR 10 mounts have a white, low-loss dielectric thermal barrier in the waveguide so that radiation and convection

of heat out of the bolometer mount are reduced and have even less effect.

3.8 Imprecision

Effects such as instrumentation error, temperature instability, and

flange non-repeatability are all included in the estimated value for

random error.

The combined long-term and short-term random uncertainty was estimated from repeat measurements on the two working standard bolometers at

94.0, 94.5, and 95.0 GHz, each on three occasions. The pooled value for

the standard deviation of the mean for either working standard bolometer

at any of the above frequencies was calculated to be 0.10%.

The estimate for random error has approximately 6 degrees of freedom

leading to a t value of 3.707 at the 99% confidence level. Therefore,

the random error at the 99% level is ±0.37%.

4. SUMMARY

The systematic corrections and their uncertainties are listed in

Table 1. The total estimated systematic correction, ^j

, —, is 1.0041.

1 + u The sum of systematic and random uncertainties is ±1.2 percent for

effective efficiency as compared to 0.25 to 0.30 percent for the microcalorimeters in the larger waveguide sizes WR 15, WR 28 and WR 42.

Table 1

Systematic Corrections and Limits of Uncertainty

^ =_A_ [ 1 - ('2--1)-]

"^e 1 + u e2/e^ - (V^/V^)^
Correction

Systematic

Uncertainty

Thermopile Nonproportionality

g = ag + br + cs + dt

= 1 (.0.989) + 1.005 (0.008) +

1.010 (0.003) + 1.005 (0.006)

Millimeter Wave Leakage (1 + u)

Thermal Leakage

Totals

0.0000

1.0061

1.0020

0.000

1.0041

± 0.02%

± 0.61%

± 0.20%

± .001%

± 0.83%

5 . REFERENCES

[1] MacPherson, A.C., and Kerns, D.M., "A Microwave Microcalorimeter",

Rev. Sci. Instrum., Vol. 26, No. 1, pp. 27-33 (January 1955).

[2] Engen, G.F., "A Refined X-Band Microwave Microcalorimeter",

J. Res., NBS, (U.S.), 63C, No. 1, pp. 77-82 (1959).

[3] Harvey, M.E., "WR 15 Microwave Calorimeter and Bolometer Unit",

NBS Tech. Note, No. 618, (May 1972).

[4] Souders, Mott; The Engineers Companion , John Wiley and Sons,

New York, 1966, p. 197.

[5] Meyler, D.S. and Sutton, CO., A Compendium of Mathematics and

Physics , D. Van Nor strand Company, New York, 1957, p. 325.
Appendix

Analysis of Thermopile Nonproportionallty

Nonlinear cooling effects on the flange In the microcalorlmeter are

due mainly to thermal radiation. As mentioned previously, when dc

power, P , is applied to the thermistor mount being measured, the equilibrium temperature of the flange rises from T„, the bath temperature,

to T- . This temperature difference gives rise to a thermopile output,

e^ . When mm wave power is substituted for a portion of the dc power,

the total power absorbed in the thermistor bead and mount increases to

P„, the flange temperature rises to T„ and the thermopile output in- creases to e„

.

Since it is required that e be a linear function of the dc and

mm wave powers, the analysis will be carried out in two steps. First

will be calculation of the nonlinearity of e with respect to T and

second the relationship between T and P.

A. Nonlinearity of e with respect to T.

For this analysis, only a single thermocouple will be considered

because of the linear relationship between the output voltage of thermocouples and thermopiles.

The response, e, of a copper-cons tantan thermocouple as a function

of At, the temperature difference between the hot and cold junctions, is

shown below (NBS Circular 508)

.

AT (°C) e(yV) e/AT (yV/°C)

1 38 38.0

10 389 38.9

20 787 39.35

30 1194 39.80

As can easily be seen, the response is nonlinear. The model for the

response is closely approximated by the empirical equation

e = 37.91(AT) + 0.09(AT)^ - 0.009(AT)-^

The temperature rise, AT, of the flange (hot junctions) relative to the

reference ring (cold junctions) is approximately 0.05K. Substituting

this value into the above equation

e = 37.91 (0.05) + (0.09 (0.05)^ (0.009) (0.05)^

= 1.895 + 0.00023 - 0.000001
The nonlinear fraction of e in percent is given by

1 • ^ 0.00023 T„^ „ „,„ nonlxnear percent = ——„ x 100 = 0.012

J- . by _) Thus, in assuming that the thermopile output, e, is linear for a temperature difference of approximately 0.05K, an error of 0.012 percent results,

B. Analysis of Nonlinear Cooling Effects

At thermal equilibrium, the rate of heat loss from the flange is

equal to the rate of heat input which, in turn, is proportional to

power, P. If the heat loss were due entirely to conduction, then linearity between flange temperature, T, and P would be assured. However,

5/4 other heat loss mechanisms exist, namely convective, K, AT , and radia4 4 tive, K„(T, - T„ ) where T, and T„ are absolute temperatures.

Calculating the convective heat loss [4]

2

q = h A AT watt/m K

For air in laminar flow around a vertical cylinder

h = 0.29(AT/L)-'-'''^

,1/4

1/4

= 0.29 (2.5)^

= 0.365

and

q — 36b L^T- 4

-1 .025

= 9 .12 X 10'-3 X 3 .14 X

10"-4

2 .87 X

10"-6

^ 3yW

The total power absorbed by the thermistor bead and mount structure

is approximately 25 mW (25,000 yW) and thus convective cooling is of the

order of 0.012 percent of the total.

Turning now to calculation of cooling by radiation, we use the

Stefan-Boltzmann law for net radiated power loss, E, [5].

E^ = ^-^(T^ - V)

10
where T = 5.67 x 10 watts/cm - K , and e is the emissivity of the

surfaces relative to a black body. The value of £ for bright metal

surfaces is in the range 0.030 to 0.047.

The value of T„ for our microcalorimeter is approximately 300 K

while T assumes the values 300.05 K (dc power only) and 300.055 K (dc plus

mm wave power) . We will calculate the rate of total radiative heat loss

and show that it is less than 0.01 percent of conductive heat loss and

thus nonlinearity of radiative heat loss is negligible.

The rate of maximum radiative heat loss is given by

'b E^ = 0.047 a 5.67 x 10 ^^ (300.055)^ - (300)^

= 2.67 x lO"-*--^ X 10^ (81.059 - 81.0)

= 1.58 X 10"^ W

= 1.58 yW

Since the total heat loss rate is 25 mW (25,000 yW) , the fraction of

radiative heat loss is 1.58/2.5x10 , or 0.0063 percent.

11
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS TN-1044

2. Performing Organ. Report No 3. Publication Date June 1981

4. TITLE AND SUBTITLE

WR 10 Millimeter Wave Microcalorimeter

5. AUTHOR(S)

Manly P. Weidman and Paul A. Hudson

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, Stote. ZIP)

10. SUPPLEMENTARY NOTES

\^^ Document describes a computer program; SF-185, FIPS Software Summary, is attached.

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

bi bliography or literature survey, mention it here) A microcalorimeter has been built in WR 10 waveguide, 75-110 GHz,

to serve as a power standard at the National Bureau of Standards (NBS)

.

Included here is an evaluation of the errors in using the microcalorimeter for the measurement of effective efficiency of bolometer mounts.

The error analysis shows a systematic uncertainty of ± .83 percent

and a random uncertainty of .37 percent.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Calorimeter; millimeter wave; power; standard

13. AVAILABILITY

[^ Unlimited

I I For Official Distribution. Do Not Release to NTIS

[^ Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

Q3] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

16

15. Price $2.00

^ U.S. GOVERNMENT PRINTING OFFICE: 1981 — 777-002/1258 Region No. 8


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Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures

published by the Department of Commerce in Part 10, Title 15, of

the Code of Federal Regulations. The standards establish nationally recognized requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NBS administers this program as a supplement to the activities of the private sector standardizing

organizations. Consumer Information Series—Practical information, based on NBS research and experience, covering areas of interest to the con- sumer. Easily understandable language and illustrations provide

useful background knowledge for shopping in today's technological marketplace. Order the above NBS puhlicaiions from: Superintendent of Documents, Government Printing Office, Washington, DC 20402. Order the following NBS publications—FIPS and NBSlR's—from

the National Technical Information Services, Springfield, VA 22 1 61

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Federal Information Processing Standards Publications (FIPS

PUB)—Publications in this series collectively constitute the Federal information Processing Standards Register. The Register

serves as the official source of information in the Federal Govern- ment regarding standards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended.

Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717(38 FR 12315, dated May 11, 1973) and Part 6 of Title 15 CFR (Code of Federal Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or

final reports on work performed by NBS for outside sponsors

(both government and non-government). In general, initial dis- tribution is handled by the sponsor; public distribution is by the National Technical information Services, Springfield, VA 22161,

in paper copy or microfiche form.
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