NATL INST. OF STAND & TECH R.I.C

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NisrUnited States Department of Commerce

Technology Administration

National Institute of Standards and Technology

N/ST Technical Note 1395

NIST Technical Note 1395

Noise-Temperature Measurement

System for the WR-28 Band

J. Randa

L.A. Terrell

Electromagnetic Fields Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

August 1 997

Hf °'' Cr

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, Robert E Hebner, Acting Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1395, 36 pages (August 1997)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1997

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

Page

1. BACKGROUND 2

1.1 Introduction 2

1.2 Radiometer Equation 3

2. SYSTEM DESCRIPTION 5

3. MEASUREMENT PROCEDURES 12

4. SYSTEM CHARACTERIZATION AND CHECKOUT 16

5. UNCERTAINTIES 22

6. SUMMARY 29

7. REFERENCES 30

111

NOISE-TEMPERATURE MEASUREMENT SYSTEM

FOR THE WR-28 BAND

J. Randa and L. A. Terrell

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, CO 80303

The NIST Noise Project has constructed and tested a radiometer for the measurement of noise

sources in the WR-28 waveguide band (26.5 GHz to 40 GHz). It is a total -power radiometer

which incorporates a six-port reflectometer for the measurement of relevant reflection

coefficients. The radiometer is similar in design to existing NIST systems covering the WR62 (12.4 GHz to 18 GHz) and WR-42 (18 GHz to 26.5 GHz) bands. This paper reviews the

theory and describes the design, testing, and operation of the system. Because of the

similarities between the present system and the existing WR-62 and WR-42 systems, much of

this document also applies to those systems.

Keywords: noise; noise measurement; noise temperature; radiometer; thermal noise
1. BACKGROUND

1.1 Introduction

The NIST Noise Project has recently completed the construction and testing of a

system for the measurement of the noise temperatures of sources with WR-28 output flanges.

The system covers the entire frequency range of the WR-28 band, 26.5 GHz to 40.0 GHz. It

extends NIST waveguide noise capabilities, which already comprise systems for the WR-90

(8.2 GHz to 12.4 GHz), WR-62 (12.4 GHz to 18 GHz), and WR-42 (18 GHz to 26.5 GHz)

frequency bands. The WR-90 system uses a switching scheme originally proposed by Dicke

[1]. Its design and operation are described in reference [2]. The WR-62 and WR-42 systems

are total-power radiometers which incorporate six-port reflectometers to measure relevant

reflection coefficients. The general design and underlying theory for these systems and

similar coaxial systems are covered in reference [3]. Details of the design of the waveguide

systems, the tests used in the initial checkout of the systems, and actual measurement

procedures have not been published for the waveguide systems.

This paper reports the design, system checks, and operational procedures of the new

WR-28 system. Since descriptions and details of the other similar NIST systems have not

been published, the present account will also serve as a description of their design, checkout,

and operation. The remainder of the paper is organized as follows. The next subsection

reviews the theory underlying noise-temperature measurements with a total-power radiometer

and derives the radiometer equation. Section 2 gives a detailed description of the

measurement system. In Section 3 we review the steps used to make a noise-temperature

measurement with the system. Section 4 presents the checkout procedure, including a review

of the different tests which ensure that the system is functioning properly. The uncertainty

analysis for the WR-28 system is presented in Section 5, and the paper closes with a brief

summary in Section 6.
1.2 Radiometer Equation

Conceptually, derivation of the radiometer equation for the total-power radiometer is

quite simple. The radiometer is assumed to respond linearly to the power delivered to it.

Generally, the linear response varies as a function of the impedance of the source, but our

radiometers for 1 GHz and above all have sufficient input isolation that their response can be

taken to be independent of the impedance of the source. The radiometer therefore requires

two known delivered powers for its calibration. The standards used are noise-temperature

standards, which have a known available power rather than delivered power. We must

correct for loss and mismatch to relate the delivered powers to the known available powers.

Once the radiometer is calibrated, it is used to measure the delivered power from the device

under test (DUT). We then correct for mismatch and loss in the DUT measurement to obtain

its available power and consequently its noise temperature.

Before proceeding, we establish some notation and conventions. We use the term

noise temperature to mean the spectral density of available power from the source, divided by

Boltzmann's constant. Thus for a small bandwidth B, over which the available power density

is constant, the available power is given by P = k^BT^. Available powers will be denoted by

capital P, and delivered powers by lowercase p. The subscript on an available power

generally indicates the device, except in the case of P^, where it indicates the ambient,

Pg = k^BT^. The subscript a will denote ambient, s will denote the cryogenic standard, and x

will denote the DUT.

To derive the explicit expression for the radiometer equation, we refer to the

simplified block diagram of figure 1. The subscripts on the delivered powers and mismatch

factors will indicate the reference plane and the configuration. Thus Pq^ refers to the

delivered power at plane when the DUT (x) is connected. For an isolated radiometer, the

derivation follows the basic treatment by Daywitt [3], with a few notational changes. When

the switch is connected to the DUT at plane 2, the noise temperature at plane is related to

the DUT noise temperature T^ by
Figure 1. Basic setup for measurement of noise temperature.

Pq.x 0,X = ao2^x '*02*x + [l-ao2] Pa' (1)

where 0Lq2 = PJPi is the available-power ratio between planes 2 and 0. The delivered power

is then given by

Po,x = Mq,x<^Q2Px + ^0,x [1 -ao2] Pa + Pex> (2)

where p„ is the intrinsic effective input noise power of the radiometer for this configuration,

and A/q^ is the mismatch factor at plane when the switch is connected to the DUT x.

Similarly,

Po,s ='M'o,sa03^fl + M^,B [l-aoa] Pa ^ Pes'

Po.a = Mo,aPa ^ Pea

Due to the isolator to the left of plane 0, the intrinsic effective input noise power of the

radiometer is (approximately) independent of the source configuration, p,^ « /?,, « p^.

Combining eqs (2) and (3), and using the relation P = k^T, we obtain

(3)

T = T + (T - T ) °'^"°^ Jf + (AT). 'X 'a ^'B 'a' T^ ~ V _ 1

^ x' is ' (4)

where Y^ = pjp^, Y^ = pjp^, and (Arj;, is the error in T^ due to the (small) effect of an

imperfect isolator. Equation (4) can be put in Daywitt's form by noting that Mq^oLq^ = A/jTIoj

and A/o^(Xo2 = A^2^o2> where the efficiency r\^^ is defined as the ratio of the delivered powers at
planes i and 7, r|y = pJPy In addition, we neglect (Arj^ and include its effect in the

uncertainty. The radiometer equation then assumes the form

T-x = ^a -^ (^« - rJ 4?-^^ ^^^ . (5)

Equation (5) is the form of the radiometer equation which is used in measurements of noise

temperature on the NIST waveguide systems. The noise temperatures appearing on the right

side of the equation are those of the ambient and cryogenic standards and are therefore

known. The Ys are the ratios of measured powers. The mismatch factors Mj and M3 are

determined from

^ _ (1 - \T^^) (1 - ir^,^!^)

(o) ^ ^ _a - |r,|2) (1 - \T,j-)

|i-r,r3,,|2

where the reflection coefficients are measured with the six-port reflectometer built into the

system, and the subscript R indicates that the reflection coefficient is from the radiometer at

the plane indicated. We refer to the ratio of efficiencies, T|o3/'no2. ^ the asymmetry; it is

evaluated by the method described in reference [3] and Section 3 below.

2. SYSTEM DESCRIPTION

The radiometer system is similar in design to other NIST radiometers with internal sixport reflectometers [3]. Diagrams of the system, showing different degrees of detail, are

given in figures 2(a) and 2(b). Figure 2(a) presents a somewhat simplified diagram, in which

it is easier to follow the measurement flow and to distinguish between the six-port and the

noise-power subsystems. Figure 2(b) shows a more complete schematic, with various components labelled to facilitate discussion. In both figures, the switches are set for a six-port

measurement. The switch S3 between the low-pass filter LPFl and the mixer is switched to

the down position to make the noise-power measurements. Similarly, switch S2 switches the

local oscillator (LO) to the mixer and away from the six port for noise-power measurements.
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A manual switch (SI) is used on the front end to select among the three sources, the

ambient standard, the cryogenic standard, and the DUT. The noise measurement path

proceeds through two 27 dB isolators (II and 12) and a filter, to the mixer. The frequency of

the local oscillator signal to the mixer is set to the nominal measurement frequency. The

down converted signal from the mixer is amplified and then filtered to pass only frequencies

below 20 MHz. The power emerging from the filter is measured by a NIST type-FV power

meter [4]. The combined gain of the intermediate-frequency (IF) amplifiers is about 57 dB.

The power measured by the power meter is typically a few milliwatts. The noise power

spectral density available from the noise source ranges from about 1 fW/MHz for the

cryogenic standard to about 0.14 pW/MHz for a typical "hot" (10 000 K) source.

The six-port reflectometer built into the system is used to measure reflection

coefficients of the sources and of the ports at which the sources are connected. These

reflection coefficients are used to compute the mismatch factors at planes 2 and 3. The sixport is calibrated by attaching a series of impedance standards (flat short, sliding short, sliding

load) to the port of interest [5,6]. The source used as the local oscillator is a Gunn diode for

the WR-28 system. Three different diodes are used to span the WR-28 band. For the WR-62

and WR-42 systems a frequency synthesizer is used, but power and financial considerations

dictated use of the Gunn diode source for WR-28. The coupler and sensor in the LO arm are

used to measure the frequency in locking the diode. The variable attenuator Al is used to set

the LO power to a convenient level for the six-port measurements and for the noise power

measurements. The low-pass filter (LPFl) for the WR-28 system has a cutoff frequency of

about 45 GHz. It prevents harmonics of the measurement frequency from reaching the mixer.

The preamplifier immediately following the mixer is not present in the WR-62 and WR-42

systems. The IF box of figure 2(b) is housed in an electronics rack and is used with all the

waveguide systems. The input switch configuration of the IF box allows several systems to

be connected simultaneously. The variable attenuators A3 and A4 are used to check the

linearity of the IF unit, and the low-pass filter LPF2 cuts off at 20 MHz. The switch (S4) in

front of the power meter P5 allows periodic dc bias readings for the meter.
Two noise-temperature standards are used to calibrate the system for each

measurement of a DUT. One is a cryogenic standard, described in detail in references [7] and

[8]. It consists of a specially designed horn antenna, looking into a cavity containing silicon

carbide pyramids immersed in liquid nitrogen. The silicon carbide pyramids constitute a

blackbody radiator at a known physical temperature, the boiling temperature of liquid

nitrogen. The thermal radiation characteristics of such a surface are known and can be used

to calculate the available power at the output reference plane [8], which is taken to be at the

flange of the WR-28 waveguide emerging from the horn. The calculation includes the effects

of reflections from the cavity walls (which are not all at liquid nitrogen temperature), losses

in the horn, the antenna pattern of the horn, and the variation of the boiling point of liquid

nitrogen with the barometric pressure in the laboratory (which is measured). The noise

temperature at the output reference plane is typically about 80 K. The second noisetemperature standard used in the system is the ambient standard. This consists of a

commercial WR-28 termination with a small hole drilled in the side. A thermistor is inserted

through the hole and into the load inside the waveguide, to monitor its temperature. The

termination is then encased in a water jacket. Water from a constant-temperature bath is

circulated through the water jacket to keep the termination at a constant temperature. The

temperature of the ambient standard is kept within a few tenths of a kelvin of 296 K; the

value used in all computations is the thermistor reading.

The water from the constant-temperature bath is also used to control other parts of the

system whose temperature might otherwise differ significantly from the ambient temperature.

The temperature control is important because the correction for noise power added by lossy

components, eq (1), is dependent on the temperature. The derivation of our radiometer

equation, eq (5), assumed that all lossy components between planes 3 and and between 2

and were at ambient temperature, the same as the ambient standard. This is accomplished

by encasing all relevant components in water jackets. The water first flows to the ambient

standard, where a thermistor measures the temperature. It then circulates through the jackets on the other components of the system and back to the water bath. A parallel water circuit is

used to maintain the standard horn of the cryogenic standard at ambient temperature The
temperature of the water is measured as it emerges from the horn, and we require that it be

within 0.6 K of the ambient temperature. In addition, the temperature of the laboratory is

maintained at 23 ± 0.5 °C, and it is continuously monitored and recorded. In general, the

noise-temperature measurements are insensitive to small deviations from ambient in the

temperature of lossy components; these are small corrections to small corrections. The

measurements are, of course, sensitive to small variations in the temperature of the ambient

standard, which is why its temperature is monitored by the thermistor. The relative humidity

of the laboratory is also monitored and controlled; it is maintained at 40 percent ± 5 percent.

A photograph of the radiometer system, without the cryogenic standard or DUT

attached, is shown in figure 3. The input switch SI is at the far right side. The horizontal

section to the left of the switch is the directional coupler. The vertical arm emerging from

the coupler contains the isolator, 13 in figure 2(b). The horizontal arm from the coupler is the

noise measurement path, which proceeds through the two isolators II and 12, which are

encased in the tubular water jacket in the photograph. A short waveguide section containing

the low-pass filter LPFl leads from the isolators to the switch S3, which is located near the

middle of the photograph. Just above S3 is the mixer, with the IF emerging from the front,

out of the page. The IF output goes down and to the right into the variable attenuator A2 and

the IF amplifier, with the amplifier output concealed behind it, going into the page and to the

electronics rack. To the left of the switch S3 is a large rectangular water jacket containing

the "bare" six port and its power sensors. The local oscillator is at the far left end of the

radiometer, with power supplied through the dark cable and temperature-control water through

the two clear tubes. To the right of the oscillator are the isolator 14, the attenuator Al, and a

coupler, followed by the switch S2. The upper switch port feeds into the mixer, and the port on the right side feeds into the six port. The rectangular box in the left foreground is the

power supply for the local oscillator. A few noise sources and impedance standards also lie

on the bench top.

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3. MEASUREMENT PROCEDURES

A noise-temperature measurement on one of our waveguide radiometers begins with a

system calibration and check, comprising an IF linearity check, calibration of the system sixport, and measurement of the asymmetry between the measurement path beginning at the

DUT port and the path beginning at the cryogenic standard port. The IF linearity test consists

of a series of measurements of the detected power p^ of a hot noise source for a variety of

settings of the IF attenuators A3 and A4. The ratio of the power measured with a given

attenuator setting to the power measured with 3 dB more attenuation is plotted as a function

of detected power. The system is considered to be linear as long as the ratio of powers does

not deviate by more than 0.005 dB from its low-power value. In the actual measurement, all

detected powers are required to be in the linear range. Typically, the linear range extends

above 3 mW, and in most noise-temperature calibrations, the detected power is kept below 2

mW.

The system six port is calibrated by attaching a series of impedance or reflection

standards to the two measurement ports, the DUT port and the cryogenic-standard port, ports

2 and 3 in figure 1 . The standards used are a flat short, a sliding short, and a sliding load;

and the method is described in references [5] and [6]. The precise locations of the reference

planes at the two measurement ports are defined by the six-port calibration. The reflection

coefficient of each standard is modelled at the waveguide flange of the standard.

Consequently, the system six port is calibrated to the reference plane defined by the surface

of the waveguide flange at each of its measurement ports. This means that the noise

temperature of the standard must be known at this reference plane (it is) and that the noise

temperature measured for the DUT is at this reference plane. Once the six-port is calibrated,

the operator measures the reflection coefficients of the two measurement ports, the cryogenic

standard, the DUT, the check standard(s) to be used in the noise-temperature measurement,

and the two auxiliary standards to be used in the asymmetry measurement. The measured

reflection coefficients are compared to the historical data for the devices, to confirm that the

six-port has been properly calibrated, and the DUT reflection coefficient is checked to see that

12
it is below 0.2 in magnitude. A larger reflection coefficient would result in unacceptably

large uncertainties.

The final step of the system calibration is the measurement of the asymmetry, which is

the ratio of efficiencies 1103/1102 appearing in the radiometer equation, eq (5). In principle, we

can determine the asymmetry from measurements with the system six port, but in practice we

use a "manual" method [3], which is more accurate and robust. The basic idea is that to

measure the difference between the two measurement paths, we just attach the same source to

the two ports (planes 3 and 2 in figure 1), measure the two different delivered powers, and

make appropriate corrections for differences in ambient contributions and mismatch factors.

The detailed implementation of that basic idea is as follows. A noise source x is connected to

the two measurement ports and the delivered power is measured in each case, as is the

delivered power from the ambient standard at port 1 . We refer to the case with the source

attached to the cryogenic-standard port (reference plane 3) as x and the case with it attached

to the DUT port (plane 2) as x'. From eq (2) the equations for the three measured powers are

Px = Ar3,^Tlo3 (P^ - PJ + Mq^^P^ + p^^ ,

Px' = ^,x'Tl02 (^x - Pa) "- M^.x'Pa "^ Pex' > (7)

Pa = ^O.a^a + Pea '

where we have used P^- ~ ^x > ^o,x0^o3 ^ -^s^^os ^nd M^^o^^ ^ ^2.x'no2- Because of the

isolator, M^^ = M^^ = Mq^ and p^^ = /?„ ~ Pa . ^nd the equations of eq (7) can be combined

to yield

^03 ^ ^x'~^ ^2,x

1I02 " i'x-l ^3 ' (8)I02 -^ X -^ 2,x

where we have dropped the unnecessary prime on the mismatch subscript. Equation (8) can

be used to determine the asymmetry, but it is sensitive to errors in the measurement of the

mismatch factors at the two ports. We can improve the measurement significantly with

relatively little additional effort by measuring two noise sources, Xj and x^, simultaneously,

one at each port, and then interchanging them and remeasuring each [3]. We thus obtain two

versions of eq (8), one for each source. We use unprimed subscripts to denote the

13
configuration with Xj attached at plane 3 and x^ at plane 2, and we use the primed subscripts

to denote the configuration with the two sources interchanged. The two measurements of the

asymmetry can then be combined to yield

This is the form used for determination of the path asymmetry in the NIST waveguide

radiometers. It is relatively insensitive to errors in measurement of the mismatch factors. It

is also insensitive to instrument drift, which was an important concern in previous generations

of radiometers.

In using eq (9) to determine the path asymmetry, four independent Y-factors are measured to determine just one quantity. The additional information contained in these

redundant measurements can be used to check the consistency of the measurements and also

to provide an independent measurement of the noise temperatures of the auxiliary standards

used as noise sources. If we combine the measurements with a measurement of the cryogenic

standard, then for each noise source we have sufficient information to determine its noise

temperature and the path asymmetry. The measured noise temperatures are compared to the

historical values for the noise sources to check that the system is working properly. The two

independent determinations of the path asymmetry could be compared to check the

consistency of the measurements which go into eq (9). In practice, the software does not

compute the two determinations of the asymmetry. Instead it computes two noise

temperatures for each noise source. These are then compared to each other to check the

consistency of the measurements.

Once the system has been calibrated, the noise temperature of a noise source can be

measured. Determination of an unknown noise temperature from eq (5) requires that we

measure the mismatch factors at the DUT and cryogenic ports, the noise temperatures of the

ambient and cryogenic standards, and the delivered powers from the DUT and the two

standards. The measurement begins by connecting the source to be measured and the

14
cryogenic standard to their respective measurement ports and using the system's six port to

measure their reflection coefficients. The reflection coefficients of the measurement ports

themselves were determined in the course of the six-port calibration, and consequently the

two mismatch factors can be determined from eq (6).

The noise temperature of the cryogenic standard is derived in references [7] and [8].

The boiling temperature of the liquid nitrogen in the standard is corrected for the barometric

pressure in the laboratory, read from a mercury barometer. The noise temperature r„„^, of the

ambient standard is computed from the thermistor reading of its physical temperature Tp^^^

using

^B-^noiee . tif v

" (10)

This form includes quantum effects; for high temperature or low frequency it reduces to the

familiar T^^i,, « 7),;,^, for passive devices. For room temperature and a frequency of 40 GHz,

the difference between the two is about 0.3 percent, which is small but significant.

The delivered powers are then measured. The front-end switch is manually switched

to read the powers from the two standards and the DUT, in the sequence ambient standard,

cryogenic standard, ambient, DUT, ambient. The average of the two ambient readings

bracketing the cryogenic or DUT reading is used in computing the Y-factor. Each power

measurement consists of an average of five readings of the power meter, with each reading

representing an average over 1/6 second. The detected power is monitored to be sure that it

remains in the linear range of the IF subsystem. The entire sequence of five power

measurements is repeated twenty times for one measurement of the DUT noise temperature.

The average values are used in computing the noise temperature from eq (5), and the standard

deviation of the mean for each sample is computed. The sampling times and numbers of

repetitions were chosen so that the uncertainty introduced by the spread in the readings is

negligible.

15
The process just outlined constitutes a single noise-temperature measurement. In

measuring an unknown source, we first measure the noise temperature of a check standard

and check that its reflection coefficient and noise temperature agree with past measurements.

This ensures that the system has been properly calibrated and is functioning as it should.

Using the same system calibration, we then perform a measurement of the noise temperature

of the DUT. For a relatively new system, such as the WR-28 system, we repeat the noisetemperature measurement of the DUT three times, to verify repeatability. For a mature

system, such as WR-62 or WR-42, we measure the noise temperature of the DUT just once

for a given system calibration. This entire process is then repeated two more times, resulting

in three independent system calibrations, each with a measurement of the DUT's and check

standard's noise temperatures (three DUT measurements for each of the three calibrations in

the case of a new system). The standard deviation of the mean of the three independent noise

temperature measurements should be significantly less than the type-B uncertainties (Section

5). If it is not, additional measurements are made.

After the measurements have been completed, the uncertainty is evaluated, and the

results are checked a final time (by someone other than the person who made the

measurements) to see that they are reasonable, that the spread of measured values is small,

that the system parameters (gain, system noise temperature, reflection coefficients, etc.) are

consistent with past values, and that the check standard results agree with past measurements.

4. SYSTEM CHARACTERIZATION AND CHECKOUT

The NIST Noise Project has developed and formalized a series of steps to characterize

and validate a new noise-temperature calibration system. The procedure is detailed in an

internal document. This document defines three levels of certification for such systems. The

idea is that the system must be tested and characterized at the first level before it can be used

to perform special tests for customers. As the system is used in measurements over the

course of months or years, additional tests of the system are performed, refinements may be

made, and operators become familiar with any idiosyncracies peculiar to that system. This

16
process leads to certification at level 2, which corresponds to a mature, stable system with a

significant history. Level 3 tests comprise those additional tests necessary to qualify the

system for formal certification as a NIST Calibration Service, as opposed to a Special Test

Service [9]. The WR-28 system has been tested and characterized at level 1, as is appropriate

for a new system. In this section we review the checkout procedure and report the results of

the various tests.

In principle, verification of the radiometer performance is simple. There are just a few

critical features of the system required for its proper performance. The system must respond

linearly to delivered power, as assumed in the derivation of the radiometer equation; it must

respond only to the intended frequencies; it must correctly measure mismatch factors and

efficiencies, to relate delivered power to available power; it must have good isolation, to

justify our form for the radiometer equation; the software used to control the system and

compute the results must be correct; and the standards used to calibrate the system must be

valid. If we verify that the system meets these requirements, we can be confident that it

correctly measures the noise temperature of a noise source. The checkout procedure addresses

each of these critical elements individually. It also includes checks of the system as a whole.

Measurements are made at the band edges and compared to measurements on other systems

covering adjacent frequency bands. Measurements are also made on check standards, to

establish a baseline for their history and to demonstrate that the system can actually measure

practical noise sources. Besides the critical elements just mentioned, there are several

characteristics of the system which are useful to know for diagnostic, predictive, or general

documentation purposes. These properties include the intrinsic noise figure or effective noise

temperature of the system itself, the pre-detector bandwidth, the post-detector integration time,

the operating power of the LO, the dynamic range of the system, the calibration of the

thermistors used to measure the ambient-standard and water-bath temperatures, and a

schematic diagram (and photograph) of the system. The checkout procedure includes steps to

measure or estimate these properties, as well as to verify the critical elements.

17
We consider the characterization steps first. Once the construction of the system is

complete, a schematic diagram of the radiometer, in its final form, is required. This is similar

to figure 2(b), except that it includes model and serial numbers of the components, and more

detail is given of the IF section and power meter. The intrinsic noise figure, or effective

input temperature, of the system controls its sensitivity. The effective input temperature T^ of

the system was measured at three frequencies, at the bottom, middle, and top of the band.

This was done in conjunction with the measurement of check standards discussed below. The

values measured for the WR-28 system were 2396 K at 26.5 GHz, 2357 K at 33.0 GHz, and

2318 K at 40.0 GHz. The pre-detector bandwidth and the post-detector integration time are

estimated using the manufacturers' specifications for the relevant components. The predetector bandwidth was specified to be 10 MHz to 100 MHz, but measurements indicated that

it extends down to about 1 MHz. The post-detector integration time was 0.5 s. The output

powers of the Gunn diodes used as the LO ranged from 50 to 290 mW, but the attenuator Al

is adjusted so that the power reaching the mixer is 20 mW. Identification and calibration data

for the thermistors used in the system were entered into the system records.

The next step is to estimate the dynamic range. To avoid saturation in the

radiometer's operation, the maximum allowable input noise power is estimated. The

specification is that the power at every amplifier stage be 20 dB below the 1 dB compression

point for that amplifier. This ensures a linearity error for the amplifier of less than 0.

1

percent [10]. For this calculation, the manufacturers' specifications are used, and the power at

the detector is assumed to be 1 mW. The maximum allowable DUT noise temperatures were

calculated for three settings of the attenuators A3 and A4 in figure 2(b), corresponding to no

attenuation, the default attenuation (7 dB for each), and maximum attenuation (11 dB for

each). The resulting maximum temperatures were 43 050 K, 227 000 K, and 575 000 K.

Since typical commercial noise sources seldom exceed 12 000 K in noise temperature, this

represents more than adequate dynamic range.

Consideration of the critical elements begins with the software, since it is used in

virtually all the other tests. The same software is used for the WR-28 system as for the

18
existing WR-62 and WR-42 systems. It has already been thoroughly checked and has

performed successfully for several years. Nevertheless, an additional test is performed on the

six-port software. The reflection coefficient of a device is measured with the six port, and the

readings of the power meters are recorded. These values for the powers are read into an

independent six-port simulation program, written for this purpose by a person not involved in

writing the system software. The differences between the results of the two programs must

be less than 10'', and they were.

Derivation of the radiometer equation, eq (5), assumed an isolated radiometer, with

departures from perfect isolation treated as an uncertainty, eq (4). To keep this uncertainty at

an acceptable level, the isolation should be at least 40 dB, and preferably 50 dB. To check

this, the isolation provided by the two isolators II and 12 was measured on a vector network

analyzer. The isolation exceeded 50 dB across the entire WR-28 band. The uncertainty

associated with imperfect isolation is then negligible.

The harmonic response test addresses the question whether the system responds only

to the frequency of interest. Because noise sources are broadband sources, there will always

be higher frequencies present at the system input, and we must check that harmonics of the

measurement frequency are not down converted and combined with the signal of interest.

This test is usually performed by measuring the detected power from a broadband source and

then repeating the measurement with a low-pass filter between the source and the

measurement system. Since the WR-28 system includes a low-pass filter in its input section

(LPFl in figure 2(b)), this test was replaced by a measurement of that filter. Its insertion loss

was about 58 dB above 50 GHz, compared with about 0.2 dB across the WR-28 band.

Three tests are performed to verify the linear response of the system. The IF-linearity

test measures the detected power for which the IF unit becomes nonlinear. It also serves as a

check that the software and hardware of the IF unit are functioning properly. This test was

described above, in Section 3, since it is repeated in every calibration. The IF unit was found

to be linear up to a detected power of 7.0 mW. In actual noise-temperature calibrations, the

19
detected power is kept below 2 mW. The second linearity test is the radio-frequency (RF)

linearity test. The system is first calibrated and used to measure the noise temperature of a

typical noise source. A 3 dB attenuator is then attached to the DUT port, and the system is

recalibrated, treating the attenuator as part of the measurement system. The noise source is

then remeasured with the attenuator in place, and the two measured noise temperatures must

(and did) agree to within 0.5 percent. The third linearity test is the mixer linearity test, which

ensures that small changes in the LO power have no significant effect on the system

performance. This is done by first calibrating the system at the normal LO power and

measuring a noise source. The LO power is then reduced by 3 dB, and the noise temperature

of the source is remeasured. The results of the two measurements must agree to within twice

the standard deviation of the mean of the readings for the measurement done with normal

power. (As explained below, multiple readings are taken and averaged for each

measurement.)

The mismatch factors appearing in the radiometer equation are computed from

reflection coefficients measured with the system's six-port reflectometer. The verification of

the six port begins during the final construction of the system, when the phase of the six port

is checked. This is done before the water jacket is sealed, in case any modifications of the

wiring are required. The check consists of attaching a sliding short to the DUT port and

requiring that the measured phase increase as the short is pulled out, in accord with

convention. The overall performance of the system six port is checked by comparing

measurements made with it to results of the same measurements made with either a vector

network analyzer or the six port maintained by the Network Analysis and Measurements

Project of the NIST Microwave Metrology Group. The first measurements were made on the

radiometer itself, looking into the DUT port, plane 2 in figure 1 or 2(a). The real and

imaginary parts of the reflection coefficient were measured at 26.5 GHz, 33.0 GHz, and 40.0

GHz using both the system six port and the network analyzer. The two measurements were

required to agree within 0.014, which corresponds to the worst-case uncertainty

(approximately 3a) for the network analyzer measurements in the WR-28 band, and they did

so. We shall use ±0.007 as the standard uncertainty (la) in the measurements of real and

20
imaginary parts of reflection coefficients measured with the system six port. Additional

measurements were made on four different artifacts attached to the DUT port. The artifacts

comprised a 3 dB attenuator terminated with a flush short, a 3 dB attenuator terminated with

an offset short, a solid-state noise source (turned on), and a matched load. Again,

measurements were made at 26.5 GHz, 33.0 GHz, and 40.0 GHz on each artifact, and

agreement between the system six port and the network analyzer was within 0.014 for both

real and imaginary parts, for each device at each frequency.

In measuring the noise temperature of an unknown device, the system six port is used

to measure the reflection coefficients needed to determine the mismatch factors, using eq (6).

The six port could also be used to determine the asymmetry, which is the ratio of efficiencies

r[Q^/y\o2 appearing in the radiometer equation, eq (5). As discussed above, however, we can measure the asymmetry more reliably using the "manual" method described in Section 3 than

we can with the six port, and so we use the manual method in our measurements. The

manual asymmetry method contains a check which is applied each time the method is used.

In measuring the asymmetry, the delivered powers from the two auxiliary standards are measured both on the DUT port and on the cryogenic-standard port. The software

automatically records the powers, Y-factors, and reflection coefficients from these

measurements. Then, when the cryogenic standard is measured on its port, we have sufficient

information to compute the noise temperature of each auxiliary standard two different ways.

One way uses the Y-factor measured when the auxiliary standard was connected to the DUT

port, treating the auxiliary standard as a DUT and using eq (5) with the measured asymmetry.

The other way uses the Y-factor measured when the auxiliary standard was attached to the

cryogenic-standard port. In this second case the noise temperature can be computed without

using the asymmetry, since the noise source being measured is attached to the same port as

the cryogenic standard. For each auxiliary standard we then have two noise- temperature

measurements, one which used the asymmetry and one which did not. We require that the

two results agree with each other and also with past measurements on that auxiliary standard.

21
The final test of a new system is a measurement of one or more known noise sources,

or a comparison to existing systems in adjacent bands. This checks the proper performance

of the system as a whole. For this test we measured the noise temperature at 26.5 GHz of

our WR-42 primary standard, using a WR-42 to WR-28 taper. The effect of the taper was

accounted for by the method developed in references [11] and [12]. The measured value of

the noise temperature was 76.71 K, whereas the value calculated by the program for the

standard was 76.66 K. The difference is 0.05 K or 0.07 percent, which is far smaller than the

uncertainties in either the standard's temperature or the measurement procedure. Once all the

tests were completed, the noise temperatures of two solid state noise sources were measured

several times to begin their recorded histories. They will then be remeasured in conjunction

with all future calibrations to ensure that the system has not changed significantly.

5. UNCERTAINTIES

The uncertainty analysis for the current generation of MIST total-power noise

radiometers, both coaxial and waveguide, will be presented elsewhere [13]. Here we review

the results for the WR-28 system. The equation used to compute the noise temperature of the

DUT is eq (5), where a perfect isolator is assumed, as is a linear radiometer. Uncertainties

in T^ arise due to uncertainties in the determination of the quantities appearing on the right

side of eq (5) and due to departures from perfect isolation and linearity. In keeping with the

notation of references [14] and [15], we use Uxx to denote the standard uncertainty in the

measurement of T^. We deal first with type-B uncertainties; the type-A uncertainty and the

statistics of combining multiple measurements will be treated near the end of this subsection.

We use ^ to denote the fractional standard uncertainty in the parameter z. Thus, for example,

^Crj ~ %Cry' ^CryThe uncertainty in the noise temperature of the cryogenic standard contributes to the

uncertainty in T^ as

Uj, [Ciy)

T

1 - —

T

22

^5

Ta-'^s ^cry (11)
The fractional uncertainty in the WR-28 cryogenic primary standard is ^cry = 0.17 percent

[13]. This is the most accurate of the NIST waveguide primary standards, due to the fact that

the horn anterma and associated waveguide are fabricated of solid copper, and consequently

the standard does not suffer from uncertainties associated with characterization of the behavior

of a plated conductor. For a typical, high-temperature DUT, with noise temperature of 10,000

K, this results in an uncertainty in T^ of approximately 0.06 percent, or about 0.12 percent for

an expanded (2ct) uncertainty. This will prove to be a minor contribution to the combined

uncertainty. The other primary noise standard used is an ambient-temperature load. Its

temperature is measured directly by a calibrated thermistor. The uncertainty in the

temperature of the ambient standard is 0.1 K, corresponding to ^^ = 0.034 percent. This

results in a contribution to the uncertainty in the DUT noise temperature of

uTM iamb)

T

T - T

T -T

-^ X 0.034% . (12)

^x

For a typical high-temperature source this results in an uncertainty of about 0.05 percent in

T

The power ratios Y^ and Y^ are determined from measurements of the delivered

powers, using a NIST Type-IV power meter [4]. The uncertainty in the term involving the

power ratios has been analyzed in references [16] and [13]. If we let 7 = {Y^-\)l{\-Y^, the

result for the contribution to the fractional uncertainty in T^ is — ^ T^x

1 -—

T•^x xO.04%, (13)

which typically is negligible.

The ratio of mismatch factors in eq (5) is one of the principal sources of uncertainty.

The standard uncertainty in the ratio of mismatch factors will be denoted m^^/^j. It depends on

the correlation between variations in the measurements of different reflection coefficients,

which are measured with the system's six-port reflectometer. If such variations are all

perfectly correlated,

23
Uti/ti(cor.) = 4 u^ 17^ + 73^^ -7^-72,^1 , (14)

where x and y refer to real and imaginary parts of T, and where we have assumed that the

reflection coefficients are small. This is the corrected version of the form in reference [3]. If, on the other hand, the variations are all completely uncorrelated,

1

^^^^

where we have used Mr^p = Mj^r- I*^or WR-28 the uncertainty in our measurements of real or

imaginary parts of reflection coefficients is [13] Wr^j- = Mj^j- = 0.007. Since we do not know

the degree of correlation between uncertainties in the measurements of the different reflection

coefficients, we will use the greater of eqs (14) and (15),

^M/M = Max{UM/jf{cor) , Ui^^^iuncoi)) . (16)

The resulting uncertainty in the DUT noise temperature is then

Uj, (AT/Af)

T

1 -—

T•^ X

X Max^u„ftf { cor) , iz^/^^

(

uncor) } , (1 7)

where we have used the fact that the ratio of mismatch factors is very near 1, and therefore

%Aiu ~ Wma</(M/M) « Uy^^. Equation (17) leads to typical uncertainty contributions of about

0.3 percent to 0.5 percent for WR-28, for sources with reflection coefficients less than 0.1.

The measurement of the path asymmetry 'X\q^I'X\q2 was discussed in Section 3. The

asymmetry is given by eq (9),

103 _

102

K,/ - 1 Y^ -1 M^ ^ M^ .

\ i^x,-! ^xr^ ^3,x, ^,:

(18)

where the Y factors are the ratios of the delivered power from the designated source to the

delivered power from the ambient standard, 7^,' = PxiVPa . ^tc. The uncertainty in this

24
determination of the asymmetry is dominated by the uncertainty in the measurement of the

ratios of mismatch factors. Using typical values of reflection coefficients, the uncertainty in

the asymmetry is u^/^ « 0.4 x i/r^i- = 0.28 percent for WR-28. The resulting uncertainty in

the DUT noise temperature is

Uj. {r\/i\)

1 - —

xG.28% , (19)

which is one of the largest components of the uncertainty. There is also an uncertainty that

arises from the variability from one waveguide flange to another, even when both meet the

speciflcations. Such variations are already included in our estimates of u^^^, and they require

no further special treatment for their effects on mismatch factors. They do, however, affect

the measurement of the asymmetry, and this effect was not included in u-^^(r[/r[). When the

asymmetry is measured, diode noise sources are attached to the ports of interest, and the

delivered powers are measured. When this asymmetry is used in a calibration, we assume

that the connectors of the DUT and the primary standard are identical. The error in that

assumption can be written as

AT.X _ 1 -—

ISC -1

ixc

(20)

where the last term contains the ratio of the efficiencies of the cryogenic-standard connector

and the DUT connector. This last term was estimated in reference [3]. Subsequent revisions

resulted in an approximate value of ±0.003 dB x /"^(GHz) for the range of | r|/r|-l | , which

we will use as the standard uncertainty in that quantity. To convert from decibels to a natural

number we multiply by 0.23, thereby obtaining

Uj. {conn)

= 0.069% \- -J- yff. (21)

where /is in gigahertz. This is a sizable contribution to the uncertainty, roughly 0.4 percent

for a typical device at 36 GHz, and is probably an overestimate. An improved analysis could

reduce this uncertainty significantly.

25
The form for the worst-case error due to neglecting (ATJ^^ in eq (4) was derived in

reference [3] for 50 dB isolation. The isolation at the front end of the radiometer was

measured to be greater than 50 dB across the entire WR-28 frequency band. Converting that

worst-case error to a standard uncertainty and correcting a minor arithmetic error in reference

[3] results in [13]

Ut {isol)

I

0.24 ir^l 1 - —

5

+ 0.024 1

- + 54

|rj

% . (22)

For a typical DUT this uncertainty is about 0.05 percent, which is negligible.

The six-port reflectometer of the system measures reflection coefficients at what is, for

present purposes, a single frequency, the nominal calibration frequency. The noise power,

however, is measured over a finite IF bandwidth, and the range of RF frequencies

contributing to this measurement band could be offset from the nominal calibration frequency

by the IF frequency. The uncertainty introduced by the possible variation of the reflection

coefficients across the measurement band is called the broadband mismatch uncertainty, and

the uncertainty due to the offset between the frequency of the noise power measurement and

the calibration frequency is called the frequency offset uncertainty. Both effects were

calculated in references [3] and [17], with slightly different results. The form we use [13] is

based on [3],

UrjBBMM) ^ 200% COS ^t sm

30 {^

X (Ir5r3,,h|r.r3,j) 1 - _a

-1

(23)

with

le = 1

\

1

- 72

(24)

26
For the WR-28 system, the parameter values are/p = 0, I = 50, B = 0.04, and/, = 21.1 GHz.

Because /f = 0, the frequency offset error vanishes, and we are left only with the effect of the

broadband mismatch. This contribution to the total uncertainty is typically negligible.

The final contribution to the type-B uncertainty is due to the possibility of small

nonlinear behavior by the radiometer. The radiometer is tested for linearity in the initial

checkout procedure, and an additional routine linearity check is performed before each

measurement of a customer's device. This routine linearity check can be used to place a limit on the uncertainty due to nonlinear behavior. The test consists of switching a (nominally) 3

dB attenuator in and out of the circuit in front of the IF amplifier. The ratio of the two

output powers is measured and plotted as a function of input power. The "linear" result is

established by averaging the low-power points, and we then require that the measured ratio

not deviate from the "linear" result by more than 0.005 dB (0.12 percent). This allows us to

deduce [13]

Ur (lin)

TX

1 - —

2

T^ X

^ If

(25)

^x

= 0.06%

for the uncertainty in T^ due to departures from linearity.

The type-B standard uncertainty for a single noise temperature measurement is

obtained by forming the square root of the sum of the squares of the individual contributions

eqs (11, 12, 13, 17. 19. 21. 22, 23, 25),

u^ = [UrJCry) + ul{amb) + ulW + u}AM/l^ + u}jr]/r\)

(26) + u}jisol) + u}^{con) + UT^iBBMht) + u}^{lin)]'^ .

In measuring a customer's device, we make several measurements of the DUT noise

temperature. Because the uncertainty defined by eq (26) depends on the measured noise

temperature and on various measured reflection coefficients, it is in principle different for

each of the separate measurements of the DUT noise temperature. In practice, however, there

27
is little difference between the values, and we use the maximum.

To evaluate the type-A uncertainty, we consider those measurements which are

repeated several times and which thus present the opportunity for a statistical evaluation of

their uncertainty. As described in Section 3, we perform multiple measurements of each

delivered power (p^, /?„ pj for a single measurement of the noise temperature, and we

perform several independent measurements of the noise temperature to obtain the final result. For each quantity, we take the type-A uncertainty to be the standard deviation of the

arithmetic mean of the measurements. For the power measurements, the number of

measurements and the sampling time were chosen large enough that the type-A uncertainty is

negligible in each case. The sole significant type-A uncertainty arises from the repetition of

the entire noise-temperature measurement. For the mature systems (WR-62, WR-42), we

perform three or more independent measurements of T^, performing an independent system

calibration for each. The type-A uncertainty for these cases is the standard deviation of the

mean of the set of values measured for T^. The situation is somewhat more complicated for a new system, such as WR-28. For such systems, three or more independent system

calibrations are performed, but several noise temperature measurements are made for each

calibration. The spread among the measurements for each calibration is small compared to

the variations from calibration to calibration, however, and so again we just use the standard

deviation of the mean of the set of average noise temperatures. If we let <T^>i be the average

of the noise temperature measurements for a given system calibration (/"), then the final result

for the measured noise temperature is

and the type-A uncertainty is

"a

= —- y^ (28) (<T > - T

\ N{N-1)^ ^ ^^ ^

.)

For typical measurements with the waveguide radiometers, u^ is less than about 0.2 percent.

The expanded (k = 2) combined uncertainty is computed from eqs (26) and (28),

28
U-2fJT^s- (29)

The uncertainty was computed for the initial measurements of the check standards, to obtain

an indication of the uncertainties we can expect in calibrations of WR-28 noise sources. The

expanded combined uncertainty varied with source and frequency, but the values fell between

1.2 percent and 1.5 percent.

6. SUMMARY

The NIST Noise Project has recently completed constructing and testing a noisetemperature measurement system for noise sources with WR-28 waveguide flanges. This

paper presented the derivation of the radiometer equation for the system, a description of the

system, an outline of the procedures for a noise-temperature measurement, a detailed review

of the tests used to verify that the system is functioning properly, and the uncertainty analysis.

The derivation of the radiometer equation, the measurement procedures, the checkout

procedure, and the general system design also apply to the other NIST waveguide systems for

measuring noise temperature (WR-62 and WR-42 at present).

We are grateful to D.F. Wait, R. Billinger, and J. Rice for extensive help and suggestions

during this work. The system design, measurement procedures, and checkout procedures

reported in this paper were developed by the NIST Noise Project over a number of years.

Current and recent members of the Project who made significant contributions to this

development include D.F. Wait, J.W. Allen, W.C. Daywitt, S. Pucic, R. Billinger, and J.

Rice. Development of the checkout procedure was spearheaded by J.W. Allen, and the

internal memorandum documenting the procedure was coauthored by Allen, Wait, Pucic,

Billinger, Rice, and Terrell.

29
7. REFERENCES

[1] Dicke, R.H. The measurement of thermal radiation at microwave frequencies. Rev.

Sci. Instrum. 17(7): 268-275; 1946 July.

[2] Miller, C.K.S.; Daywitt, W.C. The NBS switching radiometers. Nat. Bur. Stand.

(U.S.) Internal Report 84-3004; 1984 May.

[3] Daywitt, W.C. Radiometer equation and analysis of systematic errors for the NIST

automated radiometers. Natl. Inst. Stand. Technol. Tech. Note 1327; 1989 March.

[4] Larsen, N.T. A new self-balancing DC-substitution RF power meter. IEEE Trans.

Instrum. Meas. IM-25(4): 343-347; 1976, December.

[5] Engen, G.F. Calibration of an arbitrary six-port junction for measurement of active

and passive circuit parameters. IEEE Trans. Instrum. Meas. IM-22(4): 295-299; 1973

December.

[6] Hoer, C.A. Using six-port and eight-port junctions to measure active and passive

circuit parameters. Nat. Bur. Stand. (U.S.) Tech. Note 673; 1975 September.

[7] Daywitt, W.C. Design and error analysis for the WRIO thermal noise standard. Nat.

Bur. Stand. (U.S.) Tech. Note 1071; 1983 December.

[8] Daywitt, W.C. The noise temperature of an arbitrarily shaped microwave cavity with

application to a set of millimeter wave primary standards. Metrologia 30: 471-478;

1993/1994.

[9] Simmons, J.D. NIST calibration services users guide 1991. Natl. Inst. Stand.

Technol. Special Publication 250, Ch. IC; 1991 October.

30
[10] Cohn, C.E. Errors in noise measurements due to finite amplitude range of the

measuring instrument. Rev. Sci. Instrum. 35: 701-703; 1964 June.

[11] Daywitt, W.C. Determining adapter efficiency by envelope averaging swept frequency

reflection data. IEEE Trans. Microwave Theory Tech. MTT-38(11): 1748-1752; 1990

November.

[12] Pucic, S.P.; Daywitt, W.C. Single-port technique for adapter efficiency evaluation.

45th ARFTG Conference Digest; Orlando, FL; 1995. 113-118.

[13] Randa, J. Uncertainties in NIST noise-temperature calibrations at and above 1 GHz.

Natl. Inst. Stand. Technol. Internal Report; in preparation; 1997.

[14] ISO Guide to the Expression of Uncertainty in Measurement. International

Organization for Standardization; Geneva, Switzerland; 1993.

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

NIST measurement results. Natl. Inst. Stand. Technol. Tech. Note 1297, 1994 edition;

1994 September.

[16] Pucic, S.P. The uncertainty in Y-factor measurements. URSI National Radio Science

Meeting Digest; Boulder, CO; 1995. 39.

[17] Perera, S. Broadband mismatch error in noise measurement systems. Conference on

Precision Electromagnetic Measurements Digest; Paris; 1992. 256-257.

31

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