NATL INST, OF STAND & TECH R I

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A11105 SbMMS?

NfST

PUBLICATIONS

' NisrUnited States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 151

1

N/ST Technical Note 1511

NIST Microwave Power Standards

in Waveguide

J. \Nsiy6e Allen

Fred R. Clague

Neil T. Larsen

Manly P. Weidman

Radio-Frequency Technology Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

February 1999

tkf °^ c.

*^4rES o^

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION, Gary R. Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1511, 52 pages (February 1999)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1999

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
CONTENTS

ABSTRACT 1.1

1. INTRODUCTION 1.1

1.1 NIST Microwave Power Standards 1.1

1 .2 Bolometer Mount-Microcalorimeter Operation 1.2

2. TRANSFER STANDARD 2.1

2.1 Design 2.1

2.2 Performance 2.2

2.2.1 Effective Efficiency 2.2

2.2.2 Microwave Leakage 2.3

2.2.3 Reflection Coefficient 2.4

3. MICROCALORIMETER 3.1

3.1 Design 3.1

3.2 Thermal Isolation Section 3.1

3.3 Thermopile Assembly 3.3

3.4 Heat Pipe Rings 3.4

3.5 Electronic Control 3.5

3.6 Other Design Features 3.7

4. AUTOMATED CALIBRATION SYSTEM 4.1

4.1 Hardware 4.1

4.2 Software 4.2

5. MEASUREMENT CORRECTION 5.1

5.1 Microcalorimeter Operation Theory 5.1

5.2 Determination of Calorimetric Equivalence Correction Factor g 5.3

6. UNCERTAINTY ANALYSIS 6.1

6.1 Uncertainty in the Correction Factor g 6.1

6.2 Uncertainty Due to Voltage Ratios 6.3

6.2.1 Power Meter Voltage Ratio 6.3

6.2.2 Thermopile Voltage Ratio 6.4

6.2.3 Thermopile and Nanovoltmeter Nonlinearity 6.5

6.3 Other Contributing Factors 6.5

6.4 Random Effects 6.5

6.5 Combined Standard Uncertainty 6.6

6.6 Measurement Assurance 6.6

7. REFERENCES 7.1

APPENDIX 1. Determination of g Using Waveguide Loss Estimates A 1.1

APPENDIX 2. Determination of Incident Power Using a Directional Coupler A2.1

iii

NIST MICROWAVE POWER STANDARDS IN WAVEGUIDE

J. Wayde Allen, Fred R. Clague, Neil T. Larsen, and Manly P. Weidman

National Institute of Standards and Technology

Boulder, Colorado 80303

The National Institute of Standards and Technology (NIST) microwave power

standards in waveguide consist of automated microcalorimeters and associated

transfer standards. Each transfer standard is a bolometric dc substitution power

detector (a thermistor mount) of special design whose effective efficiency is measured by the microcalorimeter. The general design and operation of the

microcalorimeter and transfer standard are described. The theoretical basis for the

procedure used to determine the microcalorimeter correction factor, called the

calorimetric equivalence, is also described. A detailed uncertainty analysis is included.

Key words: microcalorimeter; microwave; power; standard; waveguide

1. INTRODUCTION

1.1 NIST Microwave Power Standards

The information in this document applies to a series of four power standards built in the same

physical configuration except for the waveguide dimensions. The four standards are in the

following waveguide bands: WR-42 (18 to 26.5 GHz), WR-22 (33 to 50 GHz), WR-15 (50 to 75

GHz), and WR-10 (75 to 1 10 GHz). The specific details for the design of each standard plus the

results of the uncertainty analysis will be reported in separate documents.

The microwave power standards in use at the National Institute of Standards and Technology

(NIST) consist of microcalorimeters and associated transfer standards [1-4]. The microcalorimeter

is used to measure a correction for the transfer standard called the effective efficiency. The transfer

standard is used to calibrate units submitted by customers. Transfer standards are highly modified

commercial bolometric power detectors of the "dc substitution" type, generally called bolometer

mounts. Figure 1.1 shows the WR-15 version of the microcalorimeter with the transfer standard

attached and figure 1 .2 shows it with the transfer standard and heat pipes removed.

1.1
Figure 1.1 Microcalorimeter with the Figure 1.2

transfer standard attached.

Microcalorimeter with the

transfer standard and heat pipes

removed.

1.2 Bolometer Mount-Microcalorimeter Operation

The bolometric power detector uses a heat sensitive resistor (bolometer) which terminates the

transmission line and absorbs the microwave energy. Two types of bolometers are used: (1) a platinum wire with a positive temperature coefficient called a "barretter," and (2) a thermistor bead

with a negative temperature coefficient. An external power meter supplies a dc current which biases

the bolometer to an operating resistance that produces a match with the characteristic impedance

of the transmission line. For waveguide mounts, the operating resistance is typically 200 Q. When

microwave energy is applied to the mount, the dc bias supplied by the power meter is automatically

reduced to maintain the operating resistance constant [5]. If the microwave energy applied to the

mount were totally absorbed by the bolometer element and if the element were heated identically

by equal amounts of dc and rf power, then the microwave power would be equal to the dc power

reduction. This is called a "substitution type" power meter, because the rf power replaces a portion

of the dc bias power. The substituted dc power (also called the bolometric power) is calculated

using the equation

1.2
P,c-—^^^ (1-1)

where Vj is the power meter's output voltage (the dc vohage across the bolometer elements) with no rf, V2 is the power meter's output voltage with rf, and Rq is the dc operating resistance of the

bolometer element.

The microwave energy incident on a mount is not all absorbed by the bolometer elements. The

dielectric and conductor losses in the input connector, the input transmission line, and the bolometer

mounting structure, plus any leakage from the mount result in a measurement error characterized

by a correction factor called the mount efficiency. This efficiency is always less than 1 . In addition,

the bolometer elements are not heated identically by equal rf and dc powers. This is known as the

rf-dc substitution error. The combination of these two effects, which is measured by the

microcalorimeter, is the correction factor defined as the effective efficiency tj^. The rf power

absorbed at the input of the mount is calculated by dividing the substituted dc power by the effective

efficiency. The mount's effective efficiency is independent of mismatch corrections, which are treated separately at the time of calibration transfer to an unknown mount.

The bolometer elements usually used in the transfer standards are thermistors. Thermistors are rugged and resist burnout in the event of an rf overload. Disadvantages in using thermistors include a continuous drift in the bias current, even in a constant temperature environment. Also, thermistors

are not usable in an alternative efficiency measurement technique known as the impedance method

[6].

A thermopile is used to determine the steady-state temperature rise of the bolometer mount

connected to the microcalorimeter. During the measurement, the microcalorimeter is immersed in a temperature-controlled water bath to minimize the effect of external temperature changes [7, 8].

The measurement procedure determines four parameters at each frequency of interest: the power

meter and thermopile output voltages with only dc applied to the mount (V, and ej, and then the

same voltages with both rf and dc applied ( Vj and e^. The effective efficiency \\^ is calculated at each test frequency using the equation

1

^ V.'9

2

^2

^1 ^1;

The g term in eq (1.2) is a frequency-dependent correction factor for the microcalorimeterbolometer mount combination. It is also known as the "calorimetric equivalence correction." The

uncertainty of the r|^ measurement is controlled primarily by the uncertainty in g. The derivation

of eq (1.2) and the method of determining g are described in section 5 of this document.

1.3
Figure 1.3 shows a typical thermopile

output that results when rf is applied to the microcalorimeter and bolometer

mount at a single frequency. The change

in output from the dc value is about 3 %.

A unique software algorithm determines

when thermal equilibrium has been

attained and the rf can be turned on or off

[9].

A typical waveguide transfer standard is calibrated at 1 GHz intervals over the

band. Most of the measurement

procedure is automated using the system

described in section 4. As figure 1.3

shows, even with the automated system

the measurement can be very time

consuming because of the slow thermal processes involved. In addition, the WR-15 and WR-10

microwave sources at present are manually tuned Gunn diode oscillators rather than a computercontrolled source such as synthesized sweeper. This slows measurements in those bands to about

3 frequencies per day versus 10 or more with a computer-controlled source.

iJ«»U 1 1 1 1 1 1 1 1 1 1 1 1 1

I

1 1 1 I—1—

1

•

535 ^-^"^ '

>^ 530

D

O 525

:/ 1

-

V

520

- 1 . . i . . 1

. 15 30 45 60 75

ELAPSED TIME, min

90 105

Figure 1.3. Thermopile output of WR-15

microcalorimeter at 75 GHz.

1.4
2. TRANSFER STANDARD

2.1 Design

Since the function of the microcalorimeter is to accurately measure the microwave energy dissipated

in the mount, there should be minimal thermal resistance between the areas of dissipation and the

sensing thermopile. Thus the mount is made primarily of brass and copper and, during the

measurement, the thermopile is located very close to the mount. The mount is also gold-plated to prevent deterioration of surface characteristics such as thermal emissivity and electrical

conductivity.

The mount will function best as a transfer standard if it has a high effective efficiency. This means

that the input transmission line should be made of high electrical conductivity material and have

low surface roughness (=0.5 |jm) so that it will have low rf loss. This is accomplished by using

gold-plated electroformed copper for a significant portion of the input transmission line.

Valid measurements of the thermopile output and the power meter voltage cannot be made until the

microcalorimeter and mount are in thermal equilibrium with the water bath, a condition indicated

by a stable thermopile output. The time to reach stability may be long if the mount has a long

thermal time constant because of its mass or internal thermal isolation. An effective way to reduce

measurement time is to minimize the thermal mass (heat capacity) of the bolometer mount by

reducing its size and eliminating any internal thermal isolation. Unfortunately, the mount design

described here did not originally have any thermal isolation, nor has it been possible to reduce its size.

Any rf leakage from the bolometer mount is a first-order source of error in the measurement. The

leakage energy, because it is not dissipated in the mount, is not detected by the bolometer element

or by the microcalorimeter thermopile. Leakage may radiate or conduct through mechanical joints

in the mount body, the dc bias leads, or the rf input connector. The effort to minimize leakage has

focused on rf containment by the mount body and rf by-pass of the dc bias circuit.

Also leakage or nonrepeatability at the waveguide flange joint to the microcalorimeter can be a problem. This is addressed by using a flange that eliminates any cocking of the mount when it is attached to the calorimeter [10].

As described earlier, the "substitution type" power meter measures the microwave power in terms

of a change in the dc bias power. Any uncertainty in the bolometer's dc resistance will be reflected

as an error in the power calculation. Lead-wire and connector contact resistance in the dc bias

circuit will generate such an error. The effect of this resistance is eliminated by using a four-wire

connection from the bolometer element to a power meter which has external sense leads such as the

NIST Type IV power meter (also made commercially). Thus the mount dc bias connector has four

conductors, and a four-wire connection is made as close as possible to the thermistor bead.

2.1
The physical design features are indicated in figure 2.1, which shows a

cross-sectional view of the WR-15

mount with the major parts identified.

The thermistor bead assembly is part of

a commercial mount. The thermistor

interface block with the electroformed

copper waveguide section and the cover are custom fabrications. The

four-conductor connector is a commercial component.

2.2 Performance

4-CONDUCTOR DC

BIAS CONNECTOR

COVER

THERMISTOR BEAD ASSEMBLY

INSULATING FILM THERMISTOR

INTERFACE

BLOCK

ELECTROFORMED COPPER

INPUT WAVEGUIDE

Figure 2. 1 . Cross section of reference standard.

Material presented in this section reports examples of the measured performance of several mounts.

Specific results for each standard are reported in the documentation for each waveguide size.

2.2.1 Effective Efficiency

A desirable feature for the mount is that the

effective efficiency be a smooth function of

frequency. Unfortunately, many thermistor

mounts display one or more significant

dips in ri^. An example of a very

pronounced dip is shown in figure 2.2,

which is the calorimeter-measured

effective efficiency of a WR-15 mount

(WR1503 is a WR-15 mount, serial no. 3). In the dip, r\^ changes very rapidly with

frequency so the random uncertainty is greater and also interpolation between

measured points at or near the dip

minimum is not possible.

96

UJ> fl4

1-O

LU 82

IL

III BO

92 -I

O 90

Z

LUO 88

u.m 86

50 55 60 65

FREQUENCY. GHz

70 75

Figure 2.2. Effective efficiency of WR1503.

2.2
Not all waveguide mounts exhibit the

effect to the degree seen in WR1503.

Figure 2.3 shows an example of the more

desirable behavior of a WR-10 mount.

As described in the next section, these dips

are primarily the result of microwave

energy leaking from the mount. A cure

that sometimes reduces the leakage and

thus minimizes the dip is also described.

74 77 80 83 86 89 92 95 98 101 104 107 110 FREQUENCY. GHz

Figure 2.3. Effective efficiency of WRIOOI.

2.2.2 Microwave Leakage

Detection of microwave leakage from a mount is relatively easy; accurate measurement of its magnitude is not. Development of special techniques and facilities such as the reverberation

chamber and the TEM cell make such measurements potentially feasible [11]. Unfortunately, the

facilities are not presently available in these waveguide bands, so direct measurement of the leakage

has not been possible.

The design objective is to keep the total leakage from the mount at more than 40 dB below the input

(less than 0.01 % of the input). Indirect measurements giving approximate values of leakage from

mounts in the WR-22 band have been made using a vector network analyzer (VNA). The mount is connected to one port of the VNA, and the leakage is sampled with a waveguide horn connected to the second port. These measurements have shown that the leakage in some portion of the frequency

band may be as high as -20 dB, or 1 %, below the input. This leakage could result in a 1 % error

in the effective efficiency measurement because it escapes without affecting the thermistor bead or heating the mount (and thus sensed by the microcalorimeter thermopile). The leakage is primarily

from the joint in the thermistor bead assembly that contains the insulating film which allows dc bias

to be applied to the thermistor bead. See figure 2.1. At frequencies where the leakage is high, the

measured effective efficiency shows a pronounced dip as indicated in section 2.2.1.

The dip is caused indirectly by the power-leveling circuit (see section 4.1) which adjusts the

microwave source output to maintain an approximate 10 mW of dc-substituted power in the mount.

When the leakage increases, the leveler must increase the incident power to the mount to maintain

the constant dc-substituted power. This increases the heating from the losses in the mount and

results in increased thermopile output and thus an apparent drop in efficiency.

In coaxial mounts the effect has been reduced or eliminated by filling the cavity behind the

thermistor bead assembly with a ferromagnetic material (iron powder mixed with two-part RTV;

2.3
see [12]). This same material has been applied to the back of a waveguide thermistor assembly

(actually, by completely potting the back side) with similar results. At these frequencies (above 18

GHz) the material is probably acting more as a reflector of the leakage than an absorber.

An example of the improvement obtained

when this material is used on a WR-22 mount

is seen in figure 2.4. In this case the

measured leakage with the absorber material

dropped to about 40 dB or 0.01 % of the

input, which means the leakage error is also

less than 0.01 %. Unfortunately, applying the

material to the back of a WR-15 mount did

not result in the same level of improvement.

Thus the material is not the best solution and

ultimately the mounts may have to be

redesigned.

o

FREQUENCY, GHz

Figure 2.4. Effective efficiency of WR2202.

2.2.3 Reflection Coefficient

An important performance parameter for the

transfer standard is the input reflection

coefficient. A low reflection coefficient (less

than 0.1) is not necessary for the

microcalorimeter measurement, but it is desirable for reducing the uncertainty in the

calibration transfer and for reducing the

minimum output power requirement on the

microwave source.

The measurements shown in figure 2.5 were made on a VNA. The values are not less than

0. 1, but they agree with typical values for the

commercial mount on which the standard is based.

0.3 I

I I I I I

I

60 65

FREQUENCY. GHz

Figure 2.5. Reflection coefficient of WR1503.

2.4
3. MICROCALORIMETER

3.1 Design

The microcalorimeter is nonstandard in the sense that it is designed to measure power rather than

energy. In other words, this is not a bomb type calorimeter. It does not integrate the total energy

input, but rather is designed to measure the rate of energy transfer across a thermal barrier. When

power is input, the temperature of the bolometer section rises in proportion to the applied power.

This causes heat to flow across the thermal barrier in proportion to the temperature rise. When the

heat lost equals the power input, the temperature of the bolometer section stabilizes, and the

resulting thermal gradient across the thermopile assembly can be measured. This is similar in

concept to the measurement of a dc current by measuring the voltage appearing across a known

resistance.

Measurement of the resulting thermal drop does of course require a stable thermal environment.

This is achieved by immersing the microcalorimeter in a water bath whose temperature is controlled

to nominally ±50 \iK [7,8]. This effectively isolates the microcalorimeter from temperature

fluctuations in the room. However, factors such as water turbulence in the bath itself can cause

short-term temperature fluctuations in the microcalorimeter baseplate. These fluctuations are caused by the conversion of the kinetic energy of the moving water to heat upon striking the bottom

of the microcalorimeter, and can amount to a few tens of microkelvins. To mitigate this problem,

the microcalorimeter is designed so that the actual thermal measurement is not made directly

between the bolometer and the microcalorimeter baseplate, but rather between the bolometer mount

and an intermediate thermal reference point. This reference point is the outer heat pipe ring mounted

on top of the thermal isolation section. Figure 3.1 is a cross sectional view of the base of the

microcalorimeter with the reference standard attached. The major parts are labeled to show the

relationship between components.

3.2 Thermal Isolation Section

The thermal isolation section is a plastic disk (acrylo-butadiene-styrene, or ABS) that physically

separates the bolometer and heat pump ring assemblies from the calorimeter base plate. Details are shown in figure 3.2. The walls of the rf transmission line needed to deliver the rf power to the

bolometer mount are formed directly in the plastic base, and the disk is plated with a thin layer of

copper and gold. The metallization provides the necessary electrical conductivity while keeping the

thermal conductivity as low as possible.

The thermal isolation section is designed to ensure that the thermal paths to the base plate are nearly

identical for the bolometer and the outer heat pipe ring. It also increases the thermal resistance

which helps slow the response time of the calorimeter to small short-term temperature fluctuations.

These balanced thermal paths force any temperature variation in the base plate assembly to affect

the bolometer and the reference temperature of the outer heat pump ring identically. Since the

temperature rise of the mount is referenced to the outer heat pipe ring, these temperature

fluctuations cancel out. This is the well-known "twin Joule" calorimeter design principle described

in references [1] and [2].

3.1
THERMISTOR MOUNT

HOLD DOWN CLAMP

THERMOPILE ASSEMBLY

THERMAL ISOLATION

SECTION

INPUT WAVEGUIDE BASE PLATE

Figure 3.1. Cross section of WR-15 microcalorimeter with an attached mount.

DC LEAD

FEED-THROUGH

ALIGNMENT

SLOT

HOLD DOWN

CLAMP SCREW

HOLE

MOUNTING

SCREW

WAVEGUIDE

OPENING

ABS PLASTIC DISK

(GOLD PLATED)

FLANGE

ALIGNMENT

PIN

Figure 3.2. Thermal Isolation Section

3.2
3.3 Thermopile Assembly

COPPER HEAT

TRANSFER BLOCKS

PLATINUM RESISTANCE

THERMOMETERS

PELTIER HEAT PUMP

The previous section pointed out that the

calorimeter is designed to measure the

Steady state temperature difference between

the bolometric power sensor being tested

and the outer heat pipe ring. The thermopile

assembly is the structure that provides the

primary thermal path between the bolometer

and the outer heat pipe ring (thermal

reference) and is designed to convert the

resulting temperature gradient into a measurable electrical signal. In the older

coaxial microcalorimeters the thermopile

consisted of a series arrangement of

thermocouples made of copper/constantan

wire wound around a plastic annulus. In the newer microcalorimeter design this structure has been replaced with a series string of Peltier crystals sandwiched between two platinum

resistance thermometers (see figure 3.3) and is about an order of magnitude more sensitive than the

old copper/constantan thermopile.

EPOXY-GLASS

LAMINATE

SIDE PLATES

Figure 3.3. Thermopile assembly.

The new thermopile design gives the microcalorimeter two possible modes of operation. First, by

measuring the voltage generated by the temperature difference across the Peltier crystal assembly,

the microcalorimeter can be used with the same sense-electronics as the qlder thermocouple-based

microcalorimeters, usually nothing more than a sensitive digital voltmeter. For this reason it is not

surprising that this has remained the primary operating mode used so far.

In the second, isothermal mode of operation, the platinum resistance thermometers are connected

as half of a self-balancing ac bridge circuit. The other half of the bridge circuit consists of an

inductive voltage divider. A high gain bandpass amplifier circuit is connected across the center of

the bridge and is used to provide current to the Peltier crystals. This circuit will be discussed in more detail in section 3.5. The output signal from the microcalorimeter is provided by monitoring

the heat pump bias current.

In this arrangement, the operator initially adjusts the inductive voltage divider to set the starting

balance point for the circuit. The bias current to the heat pump assembly is then switched on, so

that the heat pump generates a counterflow of heat in direct proportion to the change in the

bolometer's heat generation rate. This forces the calorimeter to operate with a constant temperature

difference between the bolometer and the outer heat pipe ring. The internal heat generation rate is balanced by the rate of heat transferred to the external water bath. This maintains the thermal

energy balance (heat input to heat output) without a corresponding change in the storage of energy

in the thermal mass of the calorimeter/bolometer assembly. It also means that the time lag

associated with a redistribution of stored energy is ideally eliminated. This should significantly

improve the response time of the calorimeter. However, in tests we have made so far, the loss of

3.3
precision due to noise in the heat pump feedback control loop has overshadowed the gain in

measurement speed. An overall lack of funding and time has prevented us from further pursuing

this design option.

3.4 Heat Pipe Rings

As already discussed, the microcalorimeter is designed to measure the temperature difference

between the bolometer power sensor being tested, and some reference temperature. The challenge

is to design the structure so that the heat generated in the bolometer mount can be easily sampled.

Ideally, heat generated at any point in the bolometer should be directed across the thermopile sensor

so it can be measured. To this end we designed the calorimeter as a collection of concentric

cylinders with the bolometer structure located at the center. This maximizes the contact area with

the bolometer. It also minimizes the length of the thermal path from any point on the circumference

of the bolometer to the thermopile assembly. Figure 3.4 shows the layout of the structure. Additionally, the thermal masses of the inner bolometer/ring structure and the outer reference ring

are designed to be equal so that both structures see the same temperature rise if given the same

increase in thermal energy.

In the assembled microcalorimeter, the

thermopile assembly serves as a physical

spacer and thermal path between the inner

ring and the outer thermal reference ring.

The thermal isolation section discussed in

section 3.2 provides the physical support for

the rings themselves. While this means that

some heat flows between the rings and the

thermal isolation section, as long as the

conduction paths from each ring to the

thermal isolation section are equal, the

relative temperature difference between the

two rings remains unaffected.

BOLOMETER MOUNT

THERMOPILE ASSEMBLY

Figure 3.4. Heat pipe rings.

Ideally we would like the thermal conductivity of these rings to have as little effect on the

measurement as possible. The purpose of the rings is simply to collect the thermal energy and

conduct it to or from the thermopile assembly where the resulting temperature gradient can be

measured. Any thermal resistance that these rings offer to the heat flow forms a temperature

gradient outside of the thermopile assembly that will not be detected. For this reason, heat pipes

which are capable of much higher thermal transfer rates than any known solid materials were chosen

for the design.

The heat pipe is basically a closed tube whose walls are lined with a porous copper wick saturated

with methanol. The vapor phase fills the remaining open space inside of the structure. Heating any

point on this structure vaporizes some of the local methanol resulting in a vapor pressure difference

between this region and the coldest section of the tube. This pressure difference drives the vapor

3.4
down the tube where it condenses, giving up its latent heat of vaporization to the tube walls. The

resulting increase in the liquid phase at the condensation point creates a capillary pressure difference

directed towards the heated region. In effect this pumps the liquid back to the vaporization point

by capillary action. Figure 3.5 shows a cross sectional view of the heat pipe ring structure. Details

concerning the construction of the heat pipe rings are located in the engineering drawings for each

individual calorimeter. However a brief overview of the process is presented here.

COPPER LID

WELD

SEAAAS

HEAT PUMP

ASSEMBLY

Construction begins by machining a ring

with a U-shaped channel. A stainless steel core is also constructed to fit inside this

channel. This stainless steel core is machined to leave space between the walls

of the channel in the regions where we

wish to place the wick material. This

space is filled with copper powder, and the

entire assembly is sintered to fuse the

powder and adhere it to the walls of the

channel. The stainless steel core is then

removed, leaving a layer of porous copper

wicking material needed for heat pipe

action. A lid with a fill tube is then

soldered over the top of the channel.

Finally, the methanol required to saturate the wicking layer is metered through the

fill tube into the heat pipe assembly. The entire assembly is then cooled in liquid nitrogen to lower

the vapor pressure of the alcohol and a vacuum pump attached to the fill tube. Once a sufficiently

low pressure has been achieved, the fill tube is crimped off, and the structure is allowed to return

to room temperature.

Tests done on these heat pipe rings shortly after their construction showed that the thermal

conductivity of the structure exceeded that which could be obtained by making them out of solid

copper. However, subsequent testing has given thermal conductivities roughly equal to what one would expect if the rings were simply made of copper. It appears that either the solder seam around

the top plate of the structure or the fill tube crimp may have failed allowing air to enter the structure. This may have lowered the overall sensitivity of the calorimeter somewhat, but doesn't affect the

measurement accuracy.

Figure 3.5. Cross sectional view of heat pipe rings

(not to scale).

3.5 Electronic Control

The instrument requirements needed to run the calorimeter in its traditional thermopile mode are actually quite modest (see figure 4.1). All that is really needed is a voltmeter to read the output

from the thermopile assembly. However, the isothermal mode discussed earlier is a bit more

complicated.

3.5
As was discussed in section 3.3, the thermopile is constructed using two platinum resistance

thermometers between which a Peltier heat pump assembly has been sandwiched. These platinum

thermometers allow the temperature drop across the thermopile assembly to be directly measured.

For the calorimeter to operate in the isothermal mode, the control circuitry monitors the temperature

difference between the two platinum thermometers, and forces it to remain constant by adjusting

the bias current supplied to the Peltier heat pump crystals. Since we do not really need to know the

actual temperature at either of the thermometer points, and since the resistance of the platinum

thermometer varies proportionally to its physical temperature, the circuit only needs to establish and

maintain a fixed resistance ratio between these two thermometers.

Our prototype sensing circuit is an ac impedance bridge. The platinum resistance thermometers

make up half of the bridge circuit with an inductive voltage divider completing the other half (see

figure 3.6). Quadrature balance is provided by a differential capacitor connected across the bridge.

The bridge design was chosen due to the insensitivity of the inductive voltage divider to temperature

BRIDGE EXCITATION (COSINE)

—QiscT^

INDUCTIVE VOLTAGE

DIVIDER ^

X

AMPLITUDE STABILIZER

-/

/-

> I 1I

/'

./

PtSENSOR ON MOUNT UNDER

TEST (HOT) — HEAT FLOW 1

i HEAT PUMP h

: AT PI nw —

PtSENSOR ON REFERENCE

MASS (COLD)

DC AMP

AC AMP AC AMP

r[^]>—{IE>—P>

H^^-OZE]—j^::^ ^

QUADRATURE EXCITATION (SINE) ^[I>

DVM

SHUNT

QUADRATURE ERROR

SIGNAL

MEASUREMENT SEQUENCE

1. INDUCTIVE VOLTAGE DIVIDER IS ADJUSTED TO APPROXIMATE

NULL WITH NO DC OR RF POWER IN MOUNT UNDER TEST,

2. DC BIAS POWER IS APPLIED AND CHANGE IN HEAT PUMP CURRENT

IS RECORDED AFTER EQUILIBRIUM IS REACHED AGAIN

3. RF POWER (ABOUT 10 mW)IS ADDED. NEW EQUILIBRIUM CURRENT

AND CHANGE IN DC BIAS POWER ARE RECORDED,

4. EFFECTIVE EFFICIENCY OF MOUNT UNDER TEST IS COMPUTED FROM

THE CHANGE IN THE DC BIAS POWER AND THE TOTAL CHANGE IN THE HEAT INPUT TO THE MOUNT UNDER TEST.

Figure 3.6. Block diagram of the control electronics for isothermal operation.

3.6
variation and allows the voltage divider half of the bridge to be physically separated from the

calorimeter assembly without introducing balance errors caused by fluctuations of the laboratory

room temperature. It also makes the controls for setting the initial bridge balance point accessible

outside of the water bath. The balance condition of the bridge circuit is sensed using a low noise

lock-in amplifier circuit. The resulting error signal is used to drive the Peltier heat pump crystals

in the thermopile assembly to close the loop.

In this mode the calorimeter is placed in the water bath and allowed to stabilize to simplify setting

the bridge balance point. With the heat pump current loop open, the bridge circuit is then balanced

to establish the reference or set point temperature gradient across the heat pump assembly. The

temperature difference between the two thermometers is small; the exact value is unimportant.

Once the rough balance has been achieved, the heat pump current loop is closed, actively locking

the temperature gradient at this point. When the power dissipated in the thermistor mount changes,

due to the introduction of dc or microwave power, the current supplied by the lock-in amplifier

changes in such a sense as to maintain the original set point. The current through the heat pump is nearly a linear function of the thermal power passing through it, and it can be measured to provide

the data on which the mount efficiency calculation is based. Any small deviations from linearity are easily removed by an empirical fitting function.

As was noted in section 3.3, the reason for considering the isothermal mode is to lower the response

time of the calorimeter. If the thermal masses are not allowed to change temperature, due to the

feedback of the lock-in control amplifier, then it is not necessary to move energy into or out of the masses (except for an infinitesimal amount). This was expected to provide a significant reduction

in the response time of the microcalorimeter. While our initial experiments did show that this

technique shortened the measurement time, we ran into problems with noise in the feedback

circuitry limiting the precision of the measurement. This problem could ultimately be overcome,

but due to lack of project resources, little work is currently being done to refine the technique.

3.6 Other Design Features

The rf input leads, the mount's dc bias leads, and the thermopile's output leads are brought in

through the bottom of the microcalorimeter. This provides a more convenient arrangement for

removing the top cover and also keeps the leads in the water bath for a greater distance to provide

better thermal tempering.

The entire assembly, including the cover, is gold plated for corrosion protection. The gold-plated

interior of the cover is polished to provide a high infrared reflectivity. When in use, the unit is suspended in the temperature-controlled water bath by a rod extending from the top of the cover.

3.7

4. AUTOMATED CALIBRATION SYSTEM

The automated system allows a completely unattended measurement of the effective efficiency

provided the source can be computer controlled. As noted earlier, that is true at present for only

WR-42 and WR-22 waveguide bands. The automation is accomplished using mostly off-the-shelf

computer-controlled GPIB instrumentation and custom software. The power leveling circuit is an

in-house design using the NIST Type n power meter.

4.1 HARDWARE

The system block diagram is shown below in figure 4.1. The actual instrumentation, measurement

system console layout and schematic diagram are not shown here because they are essentially

identical to the system described in reference [9].

CONTROLLER

DIGITAL

VOLTMETER

POWER

LEVELER _

SWITCH

CONTROL

UNIT

REFERENCE

VOLTAGE

^ SOURCE

NANOVOLTMETER

TYPE IV POWER

METER

MOUNT

MODULATOR

OR

J_

MANUAL

SOURCE

LOCKING

COUNTER

-\iTHERMCPILE

L_._U _..

CALORIMETER

WATER BATH

Figure 4. 1 . Automated calibration system block diagram.

4.1
4.2 SOFTWARE

The measurement program is a modification of the software described in reference [9]. That

program was written for the Type N coaxial system, but the major features are the same, except that

the waveguide version has been written as two programs. The first program controls the

measurement and the second provides the post-measurement processing to compute the effective

efficiency. In the coaxial version, these two functions are contained in the same program. (A postmeasurement computation is required because of the need to correct for the effect of drift in the

reference standard bias voltage during the measurement.) Additionally, the waveguide measurement

begins without first measuring and comparing data at five test frequencies as is done with the

coaxial system.

One of the critical points in the measurement is the determination of when the thermopile output

has reached equilibrium or stability. This is especially difficult because the bias voltage for the

reference standard essentially never stops changing; in other words, there is continual aging. This

means that there is always a drift in the thermopile output, aside from the effect of the microwave

loss. In addition, the nanovoltmeter reading of the thermopile output is subject to random

fluctuations and noise produced by both the meter and the thermopile itself. The NIST Statistical

Engineering Division has developed an algorithm to determine when stability has been reached

under these conditions of operation. The algorithm is described in detail in Appendix C of

reference [9].

4.2
5. MEASUREMENT CORRECTION

The factors listed below all potentially contribute to measurement uncertainty and are included or mentioned in the analysis, hi this chapter, a correction is determined for the first three (largest)

factors; the remaining are evaluated as uncertainties in section 6.

1. Microcalorimeter microwave transmission line loss.

2. Microcalorimeter/bolometer mount microwave connector loss.

3. Bolometer mount microwave transmission line loss and thermal conductivity effect.

4. Instrumentation errors (voltmeters and dc-substitution power meter).

5. Nonlinearity of thermopile and nanovoltmeter.

6. Bolometer mount microwave leakage.

7. Bolometer mount internal dc lead resistance.

8. Microwave connector repeatability.

9. External temperature stability.

5.1 Microcalorimeter Operation Theory

This section begins with a detailed theoretical development based in part on formulations by both

Engen [2] and Weidman [4]. Figure 3.1 is a cross section of the reference standard connected to the calorimeter isolation section and the thermopile. Referring to the figure may be helpful in

understanding the following derivation and equations.

The thermopile measures the temperature rise of the attached bolometer mount when the mount is biased with dc alone, or with dc plus rf. The expression for the thermopile output voltage with only

dc bias applied to the mount may be written as

^1 =^i^.ci = -V-' (5-1)

where ki is a proportionality factor characteristic of the thermal transfer path from the mount to the

thermopile and is a constant unless the thermopile output is nonlinear. The other terms were

originally defined in section 1 .2. P^^, is the dc bias power dissipated in the mount, V, is the power

meter output voltage (equal to the voltage across the bolometer elements) when P^^i is applied, and

Rq is the bolometer element dc operating resistance maintained by the power meter.

With both dc and rf applied to the mount, the new thermopile output voltage is given by

^2 =^2(^.c2 ^«n ^^^vv ^^^,)' (5-2)

where ^2 will equal ki if the thermopile output is linear, Pj^2 is the dc bias power dissipated in the

mount. Pi, is the rf dissipation in and near the bolometer element, P,^, is the rf loss in the walls of the

mount input section transmission line, P, is the loss in the isolation section transmission line, and

a, b, and c are constants that account for thermal paths that are different than the one described by

k,.

5.1
Equation (5-2) may also be written as

^2 ^2 P,c2 - Prf

^ P, P P^

p P p

rf ' rf) where P^ is the total rf power delivered to the mount. Letting

r = PJPrf,

s = P./P^,

we can write eq (5-3) as

^2 = K ^Pdc2 ^ Prf^^q + ^^ + ^'^)]

Then eq (5-7) can be written as

where g is the correction factor given by

g = aq + b r + c s

.

(5-3)

(5-4)

(5-5)

(5-6)

(5-7)

(5-8)

(5-9)

g is also called the calorimetric equivalence correction factor because it corrects for the difference

in the heating effect of the dc bias versus the rf loss.

Referring back to eqs (5-4) and (5-5), note that

q + r = \ because each term represents a fraction of the total rf power absorbed in the mount.(5-10)

Writing eq (5-8) in terms of Vj gives

Cj k.^ gPrf

^2 ^2

rf kK Ro;

(5-11)

(5-12)

(5-13)

^2 " ^1

(5-14)

which is a good assumption because usually e^ and 62 differ by less than 10 %, and tests indicate that

at the typical level of e,, the thermopile is very linear for these small changes. After substituting

eqs (5-13) and (5-14) in (5-12), we have

Solving for P^ we find that

From eq (5-1), k^ is given by

We also let

^1^0

V,'

5.2
or

P^ =

1 ^]-

2 v/l

M . ^1

, ''^O ^0

/ _.,x [ / \ / .. \ 2 Prf--

v^r ^^2

"" g ^n ^1 y,

V / V 1 ) ^ 1 / .

(5-15)

(5-16)

The definition of effective efficiency (for a bolometric detector) is P.

\

=

rf where P^ is the bolometric substituted power given by

^0 ^0

1

/ \ 2

(5-17)

(5-18)

and P^is the total rf power delivered to the mount. After substituting eqs (5-16) and (5-18) in (5-

17), we finally have

^. = S

/ \ 2 (5-19)

5.2 Determination of Calorimetric Equivalence Correction Factor g

This section develops a procedure to determine the correction factor. The process is based on the

results of a finite element thermal analysis of the calorimeter and mount plus measurements made

with a specially constructed flat short circuit. The short is identical to the transfer standard in

physical size and mass and thus identical in thermal characteristics.

Recall that

g = aq + br + c s

.

where a, b, and c are thermal constants.

(5-9)

We look first at the value of the thermal constants. Since a is essentially the thermal path also

described by k^, we can say by definition that a = \. (5-20)

5.3
An approximate value for the thermal constant b has traditionally been obtained by measuring the

effect of small heat sources placed in the calorimeter. This process was difficult, not very accurate,

and potentially damaging to the calorimeter. A better way to obtain the information is to do a thermal model of the calorimeter using finite element methods. An example, with results of that

process for the specific case of the WR-15 calorimeter, is shown in appendix 1. Since all of the

calorimeters are identical except for the waveguide size, we assume that the WR-15 results may be

applied to all.

Results from the thermal model analysis show that to within 1 %,

^ - 1 . (5-21)

By eq (5-10)

q = \ - r, (5-22)

and then substituting eqs (5-20, 21, and 22) in (5-9) gives

g ^ 1 + C5. (5-23)

Thus the only contribution to g comes from the loss in the isolation section.

To determine c we use a flat short. In the same way as eqs (5-1) and (5-2) were developed, the

thermopile output with the flat short attached is

^Fs = K^^ Pps ^ cP.^J, (5_24)

where Pp^ is the loss in the shorting plate and P,^^ is the power dissipated in the calorimeter thermal

isolation section. This assumes that the loss in the flat short is not negligible compared to the loss

in the isolation section. The constant k^ continues to be valid because during the flat short

measurement it is biased (heated using an external resistor) to produce a level for the e^^

measurement that is in the range of e^ and gjThe loss in the short is just the power dissipated, which is given by

"fs ~ "iFS " "rfs ' (5-25)

where P,ps is the power incident on the short and Pj^p^ is the power reflected by the short.

Since by definition the reflection coefficient of the short is

r^ I FS\

P' RFS

P' IFS (5-26)

eq (5-25) can be written as

Pfs -P,Fsi^ - \^Fs\^)- (5-27)

The loss in the thermal isolation section is proportional to the sum of the incident and reflected

power passing through it. Since the isolation section is very short, the loss is small. When the flat

5.4
short is connected, the isolation section loss is given by

^iFs ~ ^i ^~ ~ ^ ^/?F?)»

1 - K

RFS (5-28)

where /T, is the proportionality factor and, because the loss is small, K^ « 1. Since K^ is small, eq

(5-28) may be written as

"iFs ~ ^i ^ "iFs "^ "rfs ^ ' (5-29)

or in terms of the short's reflection coefficient

p. r- c ~ K- P.r-C ( i^ "•" -trc )• iFS I IFS ^ ' FS ' ''

Then, substituting eqs (5-21, 27 and 30) in (5-24), we have

^FS-KP,FS[^ - \^FS\' -CK^{\ ^ |r^,p)]

Solving for c gives

e. c ~ FS 1 - ir p

Next, to determine s recall that

rr

(5-30)

(5-31)

(5-32)

(5-6)

where P, is the power loss in the isolation section with the mount attached and P^ is the net power

delivered to the mount.

As with eq (5-30), let p^ K p,^(\ + ir^l^), (5-33)

where K^ has been defined, Pj^ is the power incident on the mount, and T^ is the mount reflection

coefficient. And as with eq (5-27), the net power delivered to the mount is given by

p^ ^ p c 1 - ir I ^)

rf ^ IM ^

^ \^ M\ ^

Substituting eqs (5-33 and 34) into (5-6) gives

s = K

Finally then, by eqs (5-32) and (5-35)

2 /

1 + ir

c s M

1 r p

1 * \^m\'

1 - ir I- I M I

FS 1 - ir

-» \

FS

V KPiFs^^ ^ ir.sl') 1 ^ \'^FS\' )

(5-34)

(5-35)

(5-36)

5.5
and, finally, by eq (5-23)

g = 1 +

1 + irM

A/

2 \

FS FS

V KPjFsi^ -^ \^FS\') 1 - |r..l^

(5-37)

The incident power P;^^ is determined using a directional coupler, where in general terms (see

appendix 2),

^/ =

3L 1

/«:, 1 - r r P

(5-38)

P; is the incident power for a load with reflection coefficient of F^, Pj^ is the side arm power with

the load attached, and Fq^ is the equivalent generator reflection of the coupler. ^^ is a calibration

factor for the coupler (including the waveguide to the calorimeter) given by (also derived in

appendix 2)

Kc =

35 n.d r |2 ^51

1 - r r 1^ ^ ^ GE ^ S\

(5-39)

where P35 is the coupler side arm power when a standard power meter is attached to the output (arm

2), P5 is the reading of the power standard, ri^ is the effective efficiency and T^ is the reflection

coefficient of the standard. We can then combine eqs (5-38) and (5-39) to give

3L

1.(1 - irj^) P35

1^ - r^ GE r^ S P\

1 - r r |2 ^ ^ GE ^ L I

(5-40)

For Pjps^ eq (5-40) becomes

IFS Ti5(i - ir,l')

3F5

35

F F 1^ ^ GE ^ S \

1^ - F F 1^ ^ GE ^ FS \

(5-41)

If it is not possible to measure the phase of F^^^, the values of K^ and the incident power can only

be bracketed based on worst case phase combinations. Then eq (5-41) becomes,

3F5 (1 GE\ F I y

IFS Ti,(l - |FJ2) P35 (1 ± IF,

(5-42)

G£ FS\

which means that g, calculated using eq (5-37), will also lie between bracketed values.

It is also possible to calculate a value for the correction factor based on theoretical estimates of the

waveguide loss. The calculation, which is described in appendix 1, offers a way to independently

5.6
check the measured result.

In the derivation of eq (5-37) for g, the effect of the location of the standing wave that is heating the

isolation section is not addressed. With the flat short attached, the points of maximum heating are generally not at the same locations as when the mount is connected. If the isolation section were

long compared to the guide wavelength the effect of the difference in heating locations would be

reduced, but for the microcalorimeters described here the length of the isolation section is comparable to the guide wavelength. To address this situation the measurement with the short is made at the frequency in each band where the loss in the narrow walls is out of phase 180° with

the loss in the broad walls [13,14]. Since the heating effect should be fairly well integrated by the

calorimeter structure, the effect of the total power loss in the standing wave from the short is uniform with distance along the guide at that frequency. Evidence based on results of the

calculation described in appendix 1 and on past evaluations of older waveguide calorimeters

indicate that g is not a strong function of frequency. Thus the value determined at the this single

frequency is used for the whole band.

5.7

6. UNCERTAINTY ANALYSIS

From section 5.1, the expression for ri^ is

Tl, = ^

Equation (5-19) can be simplified by letting

Yi

v, and

so eq (5-19) becomes

1 -^;

^. = S r

(5-19)

(6-1)

(6-2)

(6-3)

With the assumption that the variables g, Fy, and/^ are independent and their uncertainties can be

expressed as a standard error, differentiating eq (6-3) and using a sum of squares combination gives

ATI.

1 -F 2 \2

,fe-Fv

Ag^ + g

( 2FAL - 1)

/

(/. -^v)' ,

AF^ - g'

1 - F,

\2

,(fe - Fy)'

A/; , (6-4)

or in terms of the relative uncertainties

Ari,

^ A^

\ >e /

2Fy'(f-\) V-(

[i^-Fy)(frFv)j

AF, /.

\2

Je Fy ^

(6-5)

In the following sections we obtain uncertainty expressions for each of the variables.

6.1 Uncertainty in tiie Correction Factor g

This analysis is based on the last equation for g (eq 5-37) in section 5.2. We assume that the

6.1
thermal models of all the calorimeters will exhibit similar behavior so that the value of the thermal

constants will continue to be given by eqs (5-20) and (5-21).

From the preceding chapter, substituting (5-1) and (5-40) in (5-37), we find

= 1 +

1 + irM

M

^FS "dc 1 "35 ^s ^'^ - \^ GeW^ FS )'(1

e,1*5' p,p,,A\T |r^j|rj)2 (1 3FS GE\ FS )

1 - ir p ^

^ \^ FS\

1 + ir 1^

^ \^ FS\

(6-6)

Again, assuming that the variables are independent and that their uncertainties can be expressed as a standard error, differentiation and sum-of-squares combination of eq (6-6) give the expression

Ar = dg \2

airA/l

/ lArMl

dg

\ del ^dcl - dg AP35- (6-7)

for the uncertainty in g due to uncertainties in each contributing factor (total of 12 variables).

Before deriving the expressions for the partial derivatives, we can simplify eq (6-6) by letting

M =

and

Then

1 + r„ 2

1 -

1 -

2

2

1 + ir„ 2

g ^ \ + M

( ^Fs Pdci P3S ^s (^ ± ir^^iir^.D^d - |r,|^)

- F

(6-8)

(6-9)

(6-10)

For the quantities e^^, P^^j, P35, and tj^, a general expression for the partial derivatives is

dx X

where each quantity can be substituted for x. G is given by

(6-11)

G = g-\+MF (6-12)

For the quantities e,, P5, and P3;r5, a general expression for the partial derivatives is

dy y

(6-13)

where each quantity can be substituted for y.

6.2
The other partial derivatives aredg

air

= 4(g - 1)

M\

A/l 1 - ir 1^ (6-14)

dg ±2G (|rFS\ rj)

airGE\ (i±|r^j|r„|)(iTir^j|rj) (6-15)

dg ±2G(|rjT|r^j)

air. (1 r_iirj)(i GE\ r.l^:

(6-16)

dg 2G (|rF5 I "^ \^ Ge\ 4 M I rFS\

airF5l (i±|r ,ir )(1 F5 ) (1

2 n2 F5l

(6-17)

In each of these equations, g also has a double value as indicated and calculated by (6-6).

In the expression for g, as given by eq (6-6 ), the quantities e^s and e, appear as a ratio. In their

measurement a correction for the zero offset is made. In terms of the measured quantities these are given by

and

^FS ^^FS ^ 1 (^F5 ^

^1 = (^i)i - (^i)o'

(6-18)

(6-19)

where the external subscript q denotes the zero correction value and the external subscript , denotes

the measured value. These terms appear in eq (6-6) as a ratio. As will be explained in the next

section, under these circumstances, at least to first order, only the random part of the nanovoltmeter

error contributes to the uncertainty.

6.2 Uncertainty Due to Voltage Ratios

6.2.1 Power Meter Voltage Ratio

Differentiating eq (6-1), we obtain the relative uncertainty in Fy

(6-20)

Because of mount drift, V, does not remain constant during the measurement, so V, is actually an

/ \ 2 / \

I ^1

J

2 +

i ^2 j

6.3
interpolated value between two end point measurements. V^ is given by

(6-21)

where Vj, and Viy^are the initial and final values of the V^ measurements and y is a fraction between

and 1 . The worst case uncertainty in V^ is

lAVjl = (1-Y) lAVjJ + Y \^y1/ (6-22)

Since both the initial and final values differ by only a small amount and are measured on the same

range, a good approximation is lAVj,! = l^Vif \- Then by eq (6-22), lAVj = lAVi,], so the

uncertainty in Vj will be no worse (and could be less) than for a single measurement.

A numerical calculation of the uncertainty in r|^ due to AFy, which is a function of r|^ and P^, can be made using eqs (6-5) and (6-20).

6.2.2 Thermopile Voltage Ratio

The expression for/^ is given by eq (6-2). In measuring/^, a correction for the zero offset must be

made. This involves measuring Cq before measuring the dc bias term e^ or the dc-plus-rf term ej.

When we take Cq into consideration, eq (6-2) becomes

/.

The uncertainty in/^ is given by

/ _ \2

A/; = ——

4

or in terms of the relative uncertainties

A^o -

. ^2 -- ^0

^1 -- ^o'

^2 - ^0

\2

(e, - e^)\

Aef + \2

\^l ^0 J

Ae',

'Af^ ^ e^ie^-e^)

f (e, - e^){e^ - e„)

\2

) i 'o J

2 +

/ \ ^1

2

/ \ 2 +

^2

2

[ '2 \ J

\ J i ^2-^0

J

(6-23)

(6-24)

(6-25)

Like V,, e, is obtained by linear interpolation, so the uncertainty Ae, is also approximately that of

a single measurement.

The error in a voltmeter reading is generally specified as a percent of reading factor (a) plus a percent of full scale (P). The factor a comes from the error of the internal reference, while the

factor Pis due to random and zero correction errors and nonlinearity. In a ratio measurement, if the

two voltages are measured on the same scale and close in value, the alpha factor can be neglected.

In addition, if the zero drift is explicitly corrected (as in the/^ case), the only contribution to the

uncertainty is from the random part of p.

6.4
The numerical calculation of the uncertainty in r|^ due to A/^ is based on the applicable parts of eqs

(6-5) and (6-25).

An additional factor that may add to A/^ is the uncertainty in knowing when the thermopile has

reached equilibrium. This is a critical element in the measurement. A software algorithm

determines when equilibrium has been reached at each measurement frequency. The algorithm is described in appendix C of [9]. It has been tested by letting the measurement continue for several

minutes beyond the point the algorithm indicates stability has been reached and noting that the result

essentially does not change. While it has not been possible to detect any systematic uncertainty in the process, there is a random component that is included in the uncertainty.

6.2.3 Thermopile and Nanovoltmeter Nonlinearity

The linearity of the thermopile and nanovoltmeter affects the validity of eq (5-14) and thus the ratio

f^. Linearity can be tested by performing a series of measurements on the calorimeter using a mount

with a resistor in place of the thermistor bead. A dc bias is applied to the resistor, and the output

as measured by the nanovoltmeter is noted as a function of the dc bias power. In other words we

look for the expression

^ = -^ ' (6-26)

to remain constant as P^^ is varied between values that give nanovoltmeter outputs e that are approximately equal to e^ and Cj. As noted in section 5. 1

, tests have shown any change to be very

small. So rather than develop a correction, we will add any measured deviation to A/^.

6.3 Other Contributing Factors

Other factors contributing to the uncertainty are microwave leakage from the mount, resistance in

the dc bolometer leads not corrected by the four-wire connection, and Type FV power meter errors. The expressions for these effects, which are developed in sections 6.5 through 6.7 of reference [9], are also applicable to this case and will not be repeated here.

6.4 Random Effects

Uncertainty factors that primarily affect the result randomly are the water bath stability and

waveguide flange (the waveguide connector) repeatability. The effect of these will be included in the Type A evaluation of the standard uncertainty for the measurement process.

The Type A evaluation is generally based on repeated measurements of a single reference standard

which will continue to be used as a check standard. Ideally, the standard uncertainty for the

bolometer mounts should be determined through repeat measurements for each individual mount.

6.5
This is impractical due to the time required for a complete set of measurements. Therefore, we

assume that the standard uncertainty inherent in all mounts behaves in basically the same fashion, so the standard uncertainty we derive for the check standard mount will apply to the population of

mounts as well. Since the observed standard deviations may be different for each frequency, a

single value of standard uncertainty which is valid for all frequencies will be based on a "worst

case" standard deviation.

6.5 Combined Standard Uncertainty

Table 6.1 is a summary of the how the different uncertainty components will be evaluated. The

distribution used to obtain the standard uncertainty and the basis for the analysis is also given. The

section in this chapter or in reference [9] that describes the uncertainty is also listed in the table.

Definitions of the terms "evaluation type," "distribution," and "standard uncertainty" are found in

reference [15].

The largest contributor to the uncertainty is AlF/r^l. In fact the combined effect of all the other

factors is an order of magnitude smaller.

6.6 Measurement Assurance

One of the most important aspects of maintaining a microcalorimeter system is measurement

assurance. Since individual mounts cannot be measured repeatedly, it becomes even more

important to ensure that the system is behaving as it should. Several techniques are employed to monitor the system and assure measurement quality. These are described in detail for the coaxial

microcalorimeter in reference [9], but they are also used for the waveguide systems. They are

basically a set of charts that monitor system behavior through regular measurements made on check

standards.

6.6
Table 6.1. Uncertainty components.

Uncertainty factor Section Evaluation Distribution

reference type

Based on:

Aeo5 6.1 B Rectangular

^Pdc\ 6.1 B Rectangular

AP35 6.1 B' Rectangular

A% 6.1 B Rectangular

^e, 6.1 B Rectangular

^s 6.1 B Rectangular

^ws 6.1 B Rectangular

Airj 6.1 B Rectangular

Air^^i 6.1 B Rectangular

Air,i 6.1 B Rectangular

Air,,i 6.1 B Rectangular

AFy 6.2.1 B Rectangular

A/. 6.2.2 A

Normal

Linearity 6.2.3 B Rectangular

Mount leakage 2.2.2 B Rectangular

Lead resistance Ref [9] B Rectangular

Type IV power meter Ref [9] B Rectangular

Random effects 6.4 A Normal

Nanovoltmeter measurement

Voltmeter and Type IV power meter

Voltmeter and Type IV power meter

Uncorrected calorimeter measurement

Random error in nanovoltmeter meas.

Voltmeter and Type FV power meter

Voltmeter and Type IV power meter

Network analyzer measurement

Network analyzer measurement

Network analyzer measurement

Network analyzer measurement

Voltmeter and Type IV power meter

Random part of nanovoltmeter meas.

plus end-point determination

Voltmeters

Indirect measurement

Not a factor in tj^ measurement

Op amp offset, reference resistor

Repeated transfer standard meas.

6.7

7. REFERENCES

[I] MacPherson, A.C.; Kems, D.M. A microwave microcalorimeter. Rev. Sci. Instrum. 26(1): 27-33;

1955 January.

[2] Engen, G.F. A refined x-band microwave microcalorimeter. J. Res. Nat. Bur. Stand. (U.S.) 63C(1):

77-82; 1959 July-September.

[3] Harvey, M.E. WR 1 5 microwave calorimeter and bolometer unit. Nat. Bur. Stand. (U.S.) Tech. Note

618; 1972 May. 33 p.

[4] Weidman, M.P.; Hudson, P.A. WR 10 millimeter wave microcalorimeter. Nat. Bur. Stand. (U.S.)

Tech. Note 1044; 1981 June. 11 p.

[5] Larsen, N.T. A new self-balancing dc-substitution rf power meter. IEEE Trans. Instrum. Meas. IM25: 343-347; 1976 December.

[6] Engen, G.F. A bolometer mount efficiency measurement technique. J. Res. Nat. Bur. Stand. (U.S.)

65C(2): 113-124; 1961 April-June.

[7] Larsen, N.T. 50 microdegree temperature controller. Rev. Sci. Instrum. 39(1): 1-12; 1968 January.

[8] Harvey, M.E. Precision temperature-controlled water bath. Rev. Sci. Instrum. 39(1): 13-18; 1968

January.

[9] Clague, F.R. A calibration service for coaxial reference standards for microwave power. Natl. Inst. Stand. Technol. Tech. Note 1374; 1995 May. 109 p.

[10] Maury, M.A.; Simpson, G.R. Improved millimeter waveguide flanges improve components and

measurements. Microwave J. 29(5): 337-346; 1986 May.

[II] Crawford, M.L.; Koepke, G.H. Design, evaluation, and use of a reverberation chamber for

performing electromagnetic susceptibility/vulnerability measurements. Nat. Bur. Stand. (U.S.) Tech.

Note 1092; 1986 April. 146 p.

[12] Clague, F.R.; Voris, P.G. Coaxial reference standards for microwave power. Natl. Inst. Stand.

Technol. Tech. Note 1357; 1993 April. 46 p.

[13] Brady, M.M. In-Une waveguide calorimeter for high-power measurement. IRE Trans. Microwave

Theory Tech. MTT-10: 359-356; 1962 September.

[14] Brady, M.M. Correction to "In-line waveguide calorimeter for high-power measurement" - accounting for transverse waveguide wall currents. IEEE Trans. Microwave Theory Tech. MTT-1 1

152; 1963 March.

[15] Taylor, B.N.; Kuyatt, C.E. GuideHnes for evaluating and expressing the uncertainty of NIST

measurement results. Natl. Inst. Stand. Technol. Tech. Note 1297 (1994 edition); 1994 September.

20 p.

[16] Ramo, Simon; Whinnery, John R., Fields and Waves in Modem Radio, Second Edition, John Wiley

and Sons, New York, NY, 1962.

[17] Beatty, R.W. Application of waveguide and circuit theory to the development of accurate microwave

measurements and stamdards. Nat. Bur. Stand. (U.S.) Monograph 137; 1973 August.

[18] Yates, B.C.; Counas, G.J. Summary of WR15 Flange Evaluation at 60 GHz. Nat. Bur. Stand. (U.S.)

Tech. Note 642; 1973 October.

[19] Fantom, A. Radio Frequency and Microwave Power Measurement, BEE Electrical Measurement

Series 7, Peter Peregrinus Ltd., 1990.

7.1

APPENDIX 1. Determination of g Using Waveguide Loss Estimates

The correction factor g can also be calculated by using the methods in [4]. This includes an estimate

of the loss in the microcalorimeter isolation section, the waveguide flange joint, the mount walls,

and the shorting plate at the back of the mount.

Again, the basic equation is

g = aq + br + cs + dt, (Al-1)

where terms a, b, c, and d represent the relative heating effectiveness at the thermistor bead, the

mount walls, the mount waveguide flange and the thermal isolation section, respectively. The

quantities q, r, s, and t are power dissipations at the corresponding locations relative to the net

power in the mount. Equation (Al-1) explicitly includes the waveguide flange loss as s and the

isolation section loss as t, but in eq (5-9) of section 5, both losses are lumped together as s. The

heating effectiveness a is the reference for the other three terms, and by definition is unity. The next

equation is q = I - r - s, (Al-2)

which describes the fractional power dissipated in the mount away from the thermistor bead (the

walls, the back plate, and the flange). The mount wall and back plate dissipation is combined in r. The isolation section loss t is missing from eq (Al-2) because the effect of the loss there is measured by the microcalorimeter temperature sensor as if it were part of the rj^ although it is not. The loss t is corrected for directly rather than proportional to its fractional difference from 1 . The

loss calculations are used to determine the quantities r, s, and t, which are the fractional part of the

power in the incident wave dissipated in different parts of the microcalorimeter and the thermistor

mount whose rj^ is being measured by the microcalorimeter.

We begin by calculating the waveguide conductor loss a using an equation,

a = ^ ^ (Al-3)

from Ramo and Whinnery [16], where w and h are the waveguide width and height, rj is the

characteristic impedance of the dielectric (approximately 377 Q for air), R^ is the surface resistivity

of the waveguide conductor, / is the frequency of interest, and /^ is the cutoff frequency of the

waveguide. The/^ is v/2w where the length units in v (the velocity of light in air) and vv are the same. The conductivity for the gold plated waveguide is used for these calculations with a 20 % increase

in loss for surface finish and conductor uncertainty. The conductor uncertainty exists because of the

uncertainty in the plating process and was determined experimentally. For all the rectangular

waveguides 2h/w is 1 . The R^ used for the calculations is R=3x 10"^

v/?' (Al-4)

Al.l
where R^ is in ohms and /is the frequency in hertz. The value of 3 in eq (A 1-4) is a compromise

among the resistivity values published in various references for gold.

The loss per unit length (dB/cm) for the different waveguides at the desired frequency can be

calculated using the previous assumptions. With this information we can then determine the

contribution to r that is due to loss in the mount walls. The length of the side walls is determined,

and after converting from decibels to power ratio, the fractional values for the wall loss can also be

calculated.

The loss in the back plate of the mount is calculated using eq (A 1-5) which comes from Beatty [17]

(eq 5.33, p. 133 should be 4/[a6ZJ ). ^sp 4

~r ^ ~^T' (Al-5)

where Pj is the incident power, a is the conductivity of the back plate metal, 6 is the skin depth and

Zf, is the wave impedance of the waveguide, given by „ X

^h - "^ T-- (Al-6)

The guide wavelength X is K

^~ "

2

' (Al-7)

/^'1 - (fjf)

where X is the air wavelength. The power reaching the end plate will be less than the power

incident at the mount input since much of it will be absorbed by the thermistor bead. But since this

factor is such a small part of the overall g calculation, we will assume that half of the incident power

reaches the end plate. There is the additional higher order effect that wall losses reduce the power

available for dissipation in the end plate, but this effect is negligible. The actual values for r would

be slightly less. The values for r are the total of wall and end plate losses.

The calculation of the flange loss s is based on separate measurements of the loss. For instance,

Yates [18] measured flange loss in WR-15 for various types of flanges and this can be extrapolated

to other bands by assuming that the loss is proportional to /J. The thermal isolation section loss

t can be calculated using the loss per unit length values for the different waveguides by simply

multiplying a by the length of the section.

The parameters a, b, c, and J in eq (Al-1) are the heating effectiveness from various regions within

the microcalorimeter and thermistor mount being measured. The effectiveness is calculated with

respect to the heating at the thermistor bead as measured by the microcalorimeter temperature

sensor. The temperature sensor is typically a thermopile or in this case a heat pump used as a sensor. The microcalorimeter is "calibrated" by applying an accurately known dc power to the bead and

noting the sensor indication. When microwave power is applied, heating occurs in other regions

than the bead itself. This is the reason a correction factor is needed. The value of a is 1 since the

heating is caused by power in the thermistor bead, although the dc power dissipation in the bead

occurs in a slightly different region than the millimeter-wave power. The bead is very small (< 0.

1

mm diameter) so the difference in heating within the bead is insignificant.

A1.2
The relative heating is determined using a two- (or three-) dimensional finite element thermal

analysis of the specific microcalorimeter and mount. All of the millimeter wave microcalorimeters

and mounts have very similar dimensions and the same geometry. Consequendy, the effectiveness

values will all be approximately the same.

The relative heating effectiveness through the isolation section d changes linearly from a value of

approximately one at the mount flange to almost zero at the far end. As a result, one half of the

heating in the isolation section is measured by the microcalorimeter sensor giving an approximate

value for d of 0.5 which is representative of all the microcalorimeters.

The calculation of ^ using eqs (Al-1) and (Al-2) implies that all millimeter-wave losses not already

discussed occur around the bead and have a relative heating effectiveness very close to one.

An example using the WR-15 microcalorimeter follows. The three frequencies shown for these

calculations correspond to the ones where measurements were taken.

The loss per unit length values for WR-15 waveguide using the assumptions mentioned with eqs

(Al-3)and(Al-4)are

a = 0.0267 dB/cm @ 50 GHz, (A 1-8) = 0.0189 dB/cm@ 69 GHz, = 0.0183 dB/cm @ 75 GHz.

With this information we can determine the contribution to r that is due to loss in the mount walls.

The side walls are 1.25 cm long, and converting from decibels to power ratio, the fractional values

for the wall loss based on the previous calculations are

0.0077 @ 50 GHz (0.77 % of incident power), (Al-9)

0.0055 @ 69 GHz,

0.0053 @ 75 GHz.

The loss in the back plate of the mount is calculated using eq (Al-5) along with eqs (Al-6) and (Al7). The fractional loss values in the end plate are

0.0002 @ 50 GHz (0.02 % of incident power), (A 1 - 1 0)

0.0003 @ 69 GHz,

0.0004 @ 75 GHz.

The values for r are the total of wall losses and end plate loss:

r = 0.0079 @ 50 GHz, (Al-11) = 0.0058 @ 69 GHz, = 0.0058 @ 75 GHz.

A1.3
The calculation of the flange loss s is again based on Yates [18], who measured flange loss in WR15 for various types of flanges. The average of a flange similar to the thermistor mount flange used

in the microcalorimeter was 0. 16 % (0.007 dB) of the incident power at 60 GHz. If we assume a v//

dependence, which is appropriate for resistive skin effect losses, then the following values for s occur:

5 = 0.0015@50 GHz (0. 1 5 % of incident power), (A 1 - 1 2) = 0.0017® 69 GHz,

= 0.0020 @ 75 GHz.

The thermal isolation section loss t is also calculated using the loss per unit length values for WR-15

waveguide. The isolation section is 0.559 cm in length so the losses are

t = 0.0034 @ 50 GHz (0.34 % of incident power), (Al-13) = 0.0024 @ 69 GHz,

= 0.0023 @ 75 GHz.

The values for the relative heating effectiveness, a, b, c, and d, were determined using a twodimensional analysis of the WR-10 microcalorimeter and mount. All of the millimeter-wave

microcalorimeters and mounts have very similar dimensions and the same geometry so the

effectiveness values are approximately equal. The two-dimensional model and three-dimensional

models also agreed.

The average relative heating effectiveness in the mount walls was approximately 0.4 % less

effective than heat at the bead, giving

^7 = 0.996. (Al-14)

The average relative heating effectiveness at the mount flange was about 1 % less effective than heat

at the bead, giving c = 0.990. (Al-15)

The heating effectiveness through the isolation section d changes linearly from approximately 1 at the mount flange to almost at the far end. One half of the heating in the isolation section is measured by the microcalorimeter sensor giving

d = 0.5. (Al-16)

The calculation of g using eqs (Al-1) and (Al-2) implies that all millimeter-wave losses not already

discussed occur around the bead and have a relative heating effectiveness very close to 1 . Using eq

(Al-2), we have

^ = 0.9906 @ 50 GHz, (Al-17) = 0.9925 @ 69 GHz,

= 0.9922 @ 75 GHz.

A1.4
Then finally, by eq(Al-l)

g= 1.0017 @ 50 GHz, (Al-18) = 1.0012 @ 69 GHz, = 1.0011 @ 75 GHz.

These values agree very well with that obtained using a flat short, the method described in section

5. At 69 GHz, the flat short measurement gives g = 1.0014.

The uncertainty in the above calculations is now discussed. The total differential of ^ in (Al-1)

gives the incremental uncertainty in g. ^ in (Al-1) is a function of r and s. Rather than taking the

partial derivatives, we will only increment each of the variables b, r, c, s, d, and t by an estimated

uncertainty and note its effect on g. When the values of r or 5 are incremented, q must be

recalculated.

The uncertainty in the loss calculations for r, s, and t is assumed to be ±20 % in power ratio. The

±20 % estimate is considered a conservative value. This uncertainty is due primarily to the

uncertainty in the waveguide conductivity. The contribution to loss from conductivity has been

experimentally verified in the WR-15 band to better than 20 % of the loss for small losses (< 0.

1

dB). For example, the largest loss in this analysis is 0.79 % of the incident power or 0.034 dB. A

20 % uncertainty in this loss would make it 0.95 %, which corresponds to a loss of 0.041 dB. The

0.007 dB change is within the experimental uncertainty of a careful loss measurement.

The values of b, c, and d come from the finite element thermal analysis and are also estimated to be within ±20 %. The value for c is then 0.99 ± 0.198 which is a 2 % change in relative heating

effectiveness. There were seldom differences in heating effectiveness greater than 2 % for different

locations within the thermistor mount. Changing from two-dimensional to three-dimensional

analyses or changing meshes had similar results.

The individual uncertainties in g are a weak function of frequency and are as follows:

uncertainty from r = 0.000 1 , or 0.0 1 % (A 1 - 1 9)

" 5 < 0.0001

"

f = 0.0003

"

Z? = 0.0015

" c = 0.0011

" J = 0.0003

These uncertainties are Type B, and the plus or minus limits shown above can be considered as upper and lower limits. We assume a rectangular distribution, so the limits can be divided by /T

before combining. The combined uncertainty is the root sum of squares of the standard

uncertainties and for this example is is 0.001 1 or 0.1 1 %. This value agrees well with the value of

0.12 % obtained for the flat short measurement.

A1.5

APPENDIX 2. Determination of Incident Power Using a Directional Coupler

This appendix shows the derivation of eqs (5-38) and (5-39) from the basic scattering parameter

equations for a directional coupler. The coupler ports and associated wave amplitudes are shown

in Figure A2. 1

.

1 'WV

h

X

t

9

b3

bi a, ^ fcb

Figure A2. 1 Wave amplitudes for a three-port coupler.

The scattering equations for the coupler are (see appendix 4 in [19]):

^2 ~ "^21 ^\ ^ "^22 ^2 ^ "^23 ^3 '

(A2-1)

(A2-2)

^3 = -^Sl^l " "^32^2 ^ -^33^3 (A2-3)

Since the incident wave amplitude on a load attached to arm 2 is bj, we wish to develop an

expression giving Z^j in terms of b^, the side arm output. Solving eq (A2-3) for a, and substituting

into eq (A2-2) gives, after combining terms,

^31

'22

"^21 "^32

'31 ;

«2 ^ "^23

•^21 "^33

'31 J

*3- (A2-4)

The factor multiplying ^2 is the equivalent generator reflection coefficient F^f for the coupler

(appendix 4 in [18]). With a load having a reflection coefficient F^ attached to port 2,

«2 = r^^2' (A2-5)

A2.1
and with a detector having a reflection coefficient of F^ on port 3,

«3 = ^D^3-

Making these substitutions in eq (A2-4), combining terms and solving for b2 gives

(A2-6)

1

1 -r r

^2\

"^23

'^21 '^33

'31 ;

(A2-7)

The incident power P, on the load connected to port 2 is given by (assuming the wave amplitudes

are normalized by the characteristic impedance, see appendix 1 in [19])

P, = \b,\'

Squaring the amplitude of both sides of eq (A2-7) and substituting eq (A2-8)

P,-

1 ii-rc^r.P

^21

V

'^31

"^23 ^21 ^33

'31

\b^\'

(A2-8)

(A2-9)

IZ73P is the power incident on the port 3 detector. For this application that detector is a power

sensor. In general, the power incident on a power sensor is given by the meter reading divided by

the sensor calibration factor Kf, (see p. 74 in [19]). Thus

\b/ = K

(A2-10)

b?, where P3 is the power read by the sensor on port 3 and K^^, is the calibration factor for the sensor. So with eq (A2-10), plus combining all the terms that are constant for a given coupler and sensor

into a single constant, eq (A2-9) can be written

P,- 1 Kr \\ -T F |2 (A2-11)

where

K.

K,

b3

^21

V

"^31

'23

"^21 "^33

'31 ;

(A2-12)

Equation (A2-1 1) is essentially eq (5-38) except that in eq (5-38) Pj is replaced with ^3^ to indicate

that the power on port 3 is read with a particular load on port 2.

To determine K(^ we connect a standard (calibrated) power sensor to port 2 and note the port 3

reading. Again the incident power is given by dividing the sensor reading by the sensor calibration

A2.2
factor, so we have for the standard on port 2

^/ = —

•

(A2-13)

In terms of measured quantities, ^^^5 is given by (also p. 74 in [19])

^w = ^5(1 -ir^l'. (A2-14)

where ri^ is the effective efficiency of the standard and T^ the reflection coefficient. With eqs (A2-

11), (A2-13) and (A2-14) we have then

and solving for K<^

which is eq (5-39).

"s "35 1 Ti,(i-ir,P) K, ii-r^,r,P

A2.3

(A2-15)

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