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NIST Technical Note 1525

The NIST 30/60 MHz Tuned

Radiometer for Noise

Temperature Measurements

Chriss A. Grosvenor

Robert L. Billinger

. r—iC'D I Institute of Standards and Technology

ULb » O 3 3y Administration, U.S. Department of Commerce

NIST Technical Note 1525

The NIST 30/60 MHz Tuned

Radiometer for Noise

Temperature Measurements

Chriss A. Grosvenor

Robert L. Billinger

Radio-Frequency Technology Division

Electronics and Electrical Engineering Laboratory

May 2002

o

^fATES 'TES 'O*

""

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Phillip J. Bond. Under Secretary ofCommercefor Technology

National Institute of Standards and Technology

Arden L. Bement, Jr. , Director
Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Technical Note 1525

Natl. Inst. Stand. Technol. Tech. Note 1525, 33 pages (May 2002)

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CONTENTS

1. INTRODUCTION 1

2. THEORETICAL BACKGROUND 2

3. DESIGN, CONSTRUCTION, AND OPERATION 4

3.1 Description of Measurement System 4

3.2 Measurement Sequence 6

4. TESTING 6

4.1 Primary Standards 6

4.2 Stability 7

4.3 Linearity 8 4.4 Measurement and Comparison 8

5. UNCERTAINTY ANALYSIS 9

5.1 Background 9

5.2 Primary Standards 9

5.3 Mismatch Factors 10

5.4 Asymmetry 11

5.5 Other Type-B Uncertainties 13

5.6 Type-A Uncertainty 14

5.7 Combined Uncertainty 17

6. SUMMARY 18

7. REFERENCES 18

APPENDIX A. TROUBLESHOOTING 20

A.l Placement of Components 20

A.2 Preamplifier Placement and Operation 20

A.3 Wiring fi-om Bolometer Mount to DVM 21

A.4.Repair of Ambient Standard 22

A.5 Nonlinearity of 3 dB Attenuator Measurements 22

111

The NIST 30/60 MHz Tuned Radiometer

for Noise Temperature Measurements

Chriss A. Grosvenor

Robert L. Billinger

Radio-Frequency Technology Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Boulder, CO 80305-3328

The NIST Noise project has completed reconstruction of its 30/60 MHz tuned,

coaxial (Type N) radiometer system. This system is used at low frequencies, where

isolators are impractical to incorporate. Without isolators, the ambient and

cryogenic standards are tuned to the impedance of the device under test to minimize mismatches. Although this system had existed prior to publication of

this technical note, enough modifications and improvements have been made to warrant a new report. This note will briefly review the original system, and

discuss the theory as well as the design, testing, and capabilities of the present

system. A more detailed uncertainty analysis, as well as details of system

troubleshooting, are also included.

Key Words: noise; noise measurement; noise temperature; radiometer; thermal

noise

1. INTRODUCTION

The new tuned radiometer system is an improvement on the original radiometer first

described in an National Bureau of Standards (NBS) internal report written in 1981 [1]. Most of

the original control hardware has been replaced and newer software has been incorporated. The

system has also been mounted in a measurement rack (see Figure 1 ) so that the system

temperature can be more tightly controlled and its mechanical stability improved.

Most of the radiometers in use by the National Institute of Standards and Technology

(NIST) [2, 3] are isolated radiometers with 40 to 60 dB of impedance isolation, thus minimizing

the effect of any change in source impedance. Below about 1 GHz, however, the isolators
become impractically large to incorporate and another approach is required. Without an isolator

in the measurement path, the radiometer is sensitive to a change in source impedance from one

standard or device to the next. However, in the 30/60 MHz system design, isolation is

unnecessary because the cryogenic and ambient standards are tuned to the impedance of the

device under test (DUT), thus creating a reflectionless load.

One difference between a tuned system and other measurement systems is that the

reflection coefficient i^of the system, the devices, and the standards does not need to be known.

Because everything is matched to the impedance of the DUT, mismatch and asymmetry ratios are

taken to be unity. A disadvantage of this system is that the impedance of the standards, although

tuned to the DUT and measured, can still lead to small mismatch and asymmetry errors, which

become the largest source of uncertainty. However, due to the simplicity of the system, we have

found that measurements are easily accomplished and tend to be very stable and repeatable from

year to year.

Section 2 explains the theory behind this system. Section 3 discusses the design, and

Section 4 presents the testing, measurements, and comparisons. Section 5 covers the uncertainty

analysis for this system, and Section 6 is reserved for a brief summary. Appendix A is describes

how to troubleshoot the present system.

2. THEORETICAL BACKGROUND

This section explains the basic theoretical equations used to derive the noise temperature

of the DUT. The theory is described in more detail in reference [3].

We assume that our radiometer systems are linear; therefore, we can determine the noise

temperature of an unknown device by measuring the output power of the DUT and two known

standards. We then fit these data to a straight line. The two known standards have wellcharacterized temperatures. The two standards are: (1) an ambient standard that is maintained at

room temperature, and (2) the cryogenic standard with a physical temperature of about 77 K (the

boiling point of liquid nitrogen). The temperatures and powers can be used to calculate the noise

temperature of the DUT by use of the following radiometer equation [4, 5],
The subscript x refers to the unknown device, subscript s refers to the cryogenic standard, and

subscript a refers to the ambient standard, symbol T denotes temperature, Mthe mismatch, JJ the

efficiency, and Fthe power ratio, where Y^ is the power ratio of the unknown DUT relative to the

ambient standard and F, is the power ratio of the cryogenic standard relative to the ambient

standard.

Figure 2 shows a typical measurement setup. The box with an arrow denotes the isolator

in a typical radiometer. However, there is no isolator in the 30/60 MHz system so the first

component before the radiometer is a preamplifier. The effects of this will be discussed in

Section 3.

In any power-measurement system, the power available to a load is not the same as the

power delivered to the load because of reflective interfaces and path losses. The two

mechanisms limiting the power are the ratio of mismatch factors and path asymmetries. The first

M = (i-r/)(i-|rj') -^, (2)

'-^Jl

mechanism is the mismatch factor,

where /^ and T[ are the reflection coefficients to the left and right of the discontinuity, as shown

in Figure 3. The mismatch between any two ports does not equal unity, but since all devices are

tuned to the same impedance and the switches are measured and found to be nearly identical, the

ratio of mismatches becomes very nearly unity. The uncertainty comes into play when we

actually measure the reflection coefficients with a vector impedance meter.

The mechanism is the ratio of path efficiencies (asymmetry) between measurement paths

and also limits the amount of power delivered to the radiometer. The efficiency depends on the
path loss $2, from the source at planes 1, 2, or 3, to the load (or radiometer) at plane 0, (see Figure

2):

n-^^. (3)

li-^^ii

|2

•

Equation (3) assumes a reflectionless load. For our system, the only path differences would be

due to the switch that connects between the DUT, cryogenic standard, and ambient standard,

since the cable to the first amplifier is the same in all three cases. Since the switches are

electrically identical in either direction, the ratio of efficiencies is nearly unity. For our system,

the measured efficiencies were found to be equal to within 0.000237, which is less than the

measurement uncertainty and will be discussed in section 5.

Because the ambient standard, cryogenic standard, and DUT all have the same impedance,

r, = r, + (7;-7;)^. (4)

s

the ratios of mismatches and efficiencies in eq (1) are set equal to one and the radiometer

equation reduces to

3. DESIGN, CONSTRUCTION, AND OPERATION

3.1 Description of Measurement System

Figure 4 is a schematic diagram for the present measurement system. A radiometer is

basically a receiver and is designed to amplify a noise signal to a level that can be measured by a NIST Type-IV power meter [6].

The DUT and/or standards are connected to the Type-N ports of two coaxial switches.

These two switches are then connected to a third switch that is followed by a preamplifier having

approximately 35 dB of gain. The signal is then fed into either a 30 MHz or a 60 MHz filter

having respective bandwidths of 0.77 MHz or 1.38 MHz. A variable attenuator, used to test the
linearity of the intermediate frequency (IF) section, has been included at this point. The

attenuator can be switched from to 1 2 dB depending on the frequency and noise temperature of

the DUT. The 5 dB attenuator that follows provides isolation into the next amplifier having 30

dB of gain. There is a level-set attenuator that allows the overall system signal level to be set

depending on the approximate noise temperature of the DUT. Since we measure devices with

noise temperatures ranging from 9000 K to 10,000 K we do not need to adjust the level-set

attenuator once it has been set. The next 5 dB attenuator again provides isolation into another 30

dB-gain amplifier. A 6 dB attenuator follows, that provides impedance matching into the last 30

dB-gain amplifier. At this point, the signal is either switched into a 50 Q load for power-off

measurements, or into a 200 Q bolometer for measurement with a digital voltmeter (DVM) and a

Type-IV power meter [6]. All of the components that follow the filters are mounted on a watercooled brass plate used to maintain the overall system temperature. The preamplifier and

switches prior to the filters sit on a separate water-cooled plate at the base of the cabinet (see

Figure 1). The noise source is either a DUT, a cryogenic standard, or an ambient standard. The

DUT is typically a noise diode generating an output noise temperature between 9500 K and

1 1 ,000 K. The ambient standard is a load submersed in an oil bath at room temperature. The oil

bath and the design of the Dewar ensure minimal temperature changes, giving a stable noise

power output [ 1 ] . The load temperature is measured with a thermometer immersed in the oil bath.

The cryogenic standard is similar to the ambient standard except that the load is now immersed in

a bath of liquid nitrogen. To determine the boiling point of liquid nitrogen, the atmospheric

pressure is measured and substituted into the vapor-pressure equation. The physical temperature

of the load is assumed to be at the same temperature as the liquid nitrogen, and a small

temperature correction is made to account for the losses along the coaxial lines and adapters. A

final noise temperature is obtained at the output port of the standard. Both standards have tunable

GR900 output ports that are connected to the Type-N ports of the switches through 14 mm

coaxial airlines and adapters. The noise power of each device is measured using a low-band

thermistor mount in combination with a NIST Type-IV power meter card and a DVM.
3.2 Measurement Sequence

A test of the customer's device consists of the following sequence:

(1) An impedance meter is calibrated using a one-port calibration measurement [7].

(2) The impedance of the DUT is measured, stored, and later converted to a reflection

coefficient r by means of the following equation:

p ^ ^meas ^0 (5)

meas u

where Zq = 50 Q and Z^^ may be complex.

(3) The ambient and cryogenic standards are tuned until their impedances are the same as

the DUT.

(4) The DUT is then connected to port 3, the cryogenic standard to port 2, and the

ambient standard to port 4.

(5) The program controls switches to various RF paths used to supply power to the preamplifier, and the measurement sequence begins.

(6) The output power is measured for the DUT, the ambient standard and the cryogenic

standard [6]. From these powers, a noise temperature is computed for the DUT. This

sequence is repeated for a total of 25 measurements.

(7) After the first 25 measurements, the operator reduces the attenuation by 3 dB,

doubling the output power.

(8) At the end of 50 measurements, the raw powers, temperatures, and uncertainties are

stored in a measurement file.

For this test, a reference or check standard is measured once according to the above sequence,

and the customer's device is measured a total of three times.

4. TESTING

4.1 Primary Standards

Figure 5 is a photograph of the ambient (right) and cryogenic (left) noise standards. The

ambient standard is a load enclosed in a metal housing that is in turn encased in an outer housing.

6
The inner housing contains the capacitor-plate tuning structure; all of this is immersed in mineral

oil. The temperature of the ambient standard is read directly by a thermometer inserted into the

inner housing. This standard was originally designed to be used as a hot standard. Power can be

supplied to eight power resistors located at the bottom of the inner housing. The resistors are

used to heat the oil to a known, controlled temperature. The ambient standard is able to maintain

its temperature to within 0.05 K over an 8 h period.

The cryogenic standard also uses a load, but the housing is now immersed in liquid

nitrogen. The capacitor-plate tuning structure for this standard is the same. The output

temperature of the cryogenic standard, which is calculated by the program, depends on the

barometric pressure in the laboratory. Both standards use GR900 precision airlines, connectors,

and adapters for the transition from the standard to the measurement ports.

4.2 Stability

One of the most important features of any radiometric system is its ability to remain stable

over a measurement period. This includes temperature stability, the stability of the power

measurement, and the stability of the other measurement equipment used by the system. Stability

in this sense is defined as small variations during the measurement period.

As mentioned previously, the ambient standard is able to maintain temperature to within

0.05 K over an 8 h period. Because of its stable thermal properties, the cryogenic standard's

design requires only one refill per day of liquid nitrogen. Both standards are stable over the

course of a complete measurement.

We need to determine the power stability of this system because the measured power is a

direct measurement of the noise temperature of a DUT. In our system, there are two components

that "measure" the noise temperature of a DUT. The first is the digital multimeter, and the second

is a Type-IV power meter that includes a bolometer. When we looked at the power stability of

our system, we first looked at the variations in readings coming from the digital multimeter. We

found that these measurements were accurate to within 3 parts in 2000. Because NIST is heavily

involved in power measurements, the accuracies of the bolometers are well known.

In this system, the impedance of the standards must be matched to that of the DUT

accurately. The precision of the measurement is useful when we want to know the DUT's

7
available noise temperature and standard deviation. The vector impedance meter used for this

particular system is not as precise as newer models, and therefore it is calibrated to improve

precision. The uncertainty analysis, covered in the next section, explains the measurements we

used to determine both the accuracy and precision of our measurements.

4.3 Linearity

All radiometers use amplifiers to amplify a signal, which is typically in the nanowatt

range, into the milliwatt range so that a detector can accurately measure the signal. However,

amplifiers can become nonlinear if overdriven by the input signal. Our use of the radiometer

equation to calculate a DUT's noise temperature is justified by the fact that we have a linear

system.

We check the linearity of the system by measuring 25 sets of noise powers. A set consists

of Type-IV power-meter card measurements with no power supplied to it (power off); these

provide the baseline reading [6]. Power is then supplied to the card, and we measure the

cryogenic standard, the ambient standard, and the check standard or DUT. Then, 3 dB of

attenuation is removed from the path (see Figure 4) and another set of 25 measurements is taken.

The two resulting noise temperatures are compared and, if they agree to within 0.2 %, we may

conclude that the system is linear.

4.4 Measurement and Comparison

The final tests on the system were to measure various check standards with known

histories and compare current measurements with those taken approximately two years ago.

Typically the criterion for satisfactory comparison is that the measured noise temperatures be

within 50 K of previous results and have standard deviations of around 20 K. Figures 6 and 7

compare measurement results at 30 MHz and 60 MHz to past measurements. Figure 6 shows a

measurement of the Type-N check standard X 1 3BHZ.61 7. The historical measurement results at

30 MHz have an average temperature of 10136 K and a spread of 36 K. The most recent results

at 30 MHz have an average temperature of 101 16 K, and a spread of 19 K. The historical

average at 60 MHz is 10180 K, compared to the recent average of 10185 K. The difference in

noise temperatures between the historical and current average is 20 K. Data on another Type-N

8
check standard X 1 3BHZ.8 1 7 are shown in figure 7. Historical data for this device exist only at

60 MHz. At that frequency the historical average is 9587 K and the recent average is 9570 K.

This is a difference of 1 7 K.

We have made measurements using other connectors as well, and based on the criterion

given above we have determined that the system is operating correctly.

5. UNCERTAINTY ANALYSIS

5.1 Background

The uncertainty analysis will follow the analysis as outlined in previous technical notes

for total-power radiometers. The notation is consistent with that found in references [3], [8], and

[9]. The standard uncertainty in the measurement of r, is denoted by Uj^. The combined standard

uncertainty is composed of Type-A and Type-B uncertainties. The Type-A uncertainty is

calculated as the standard deviation of the mean of several independent measurements of the

quantity of interest. The first part of this section will deal with type-B uncertainties; type-A

uncertainties are treated at the end of this section. We use #to denote the fractional standard

uncertainty in a parameter; for example, S^^^, - Uj^JT^^.. The contribution of the uncertainty in a

particular parameter (e.g., ^cr^.) to the uncertainty in T^ will be denoted ^^^(Cry).

The noise temperature of a measured device is determined by the radiometer equation (1).

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

the right side of eq (1). For quantities appearing in eq (1), the propagation of uncertainties is

treated in the manner outlined in reference [10]. We will treat the following contributions to the

uncertainty in T^ : the cryogenic standard, the ambient standard, lack of isolation, broadband

mismatch effects, nonlinearity effects, the power ratio measurements, connector repeatability, and

the errors introduced due to imperfect matching between ports and the asymmetry in the switches.

5.2 Primary Standards

The cryogenic standard contributes to the uncertainty in T^ as
UriCry)

a s rCry' (5)

The uncertainty attributed to the cryogenic standard is 0.22 K at 30 MHz and 0.28 K at 60 MHz

so that its fractional uncertainty is 0.29 % and 0.37 %, respectively [1]. These numbers are based

on a typical 10,000 K source. The contribution of the uncertainty in the ambient standard temperature to that in the DUT

noise temperature is given by

My, (amb) T,-T.

a s -^, (6)

The ambient standard's physical temperature is measured with a calibrated thermometer. A

conservative estimate of the uncertainty in the temperature measurement is Uj^ = 0.1 K or ^jg0.034 %.

5.3 Mismatch Factors

Mismatch factors and efficiencies are not currently used in the radiometer equation

because their ratios are close to unity; nonetheless, we still calculate their uncertainty. There will

always be some mismatch between the DUT and the standards due to imperfections in the

measurement software and the switching between ports, which cannot give repeatable results. The sections below describe how these values are obtained.

The ratio of mismatch factors contributes to the uncertainty in the DUT noise temperature

according to

uJMIM) T. T,

1- a 1- a u'MM' (7)

The mismatch uncertainty depends strongly on the impedance measured by our vector impedance

10
meter. This means that the uncertainty analysis of the mismatch factor determined in the

Technical Note for NFRad [3] is invalid, since a vector impedance meter is not used in the

NFRad system. Deriving the uncertainty from an analytical point of view is complicated, so we

used a Monte Carlo simulation to determine the uncertainty in the mismatch factor for the 30/60

MHz system.

The impedance of a device was measured on port 1 , then moved to port 3 and measured,

and then to port 4. This sequence was repeated for a total of five measurements. This was

completed at both frequencies. The mean and standard deviation of these measurements were

calculated and used as the random Type-A source of uncertainty for the mismatch. To determine

the systematic Type-B uncertainty for this specific impedance meter, several NIST impedance

standards were measured on the same vector impedance meter. The largest deviation was used

for the systematic error in the Monte Carlo simulation. The random and systematic uncertainties

were combined using root sum of squares to determine the overall uncertainties for the real and

imaginary parts at 30 and 60 MHz. To find the total mismatch factor uncertainty [eq (2)], a

generator of normally distributed random numbers was then used to simulate possible impedances

around the average obtained earlier. This was done for 100 samples and with several iterations.

We then calculated the reflection coefficients from the generated impedances and input these into

the mismatch equation, an example of which is given by eq (2). The standard deviations from

two different ports were then combined using root sum of squares to obtain the final value used in

computing the uncertainty in the mismatch factor. After running several simulations, the largest

value in the uncertainty was used as the final value, which is

^^^^^^ = 0.443%. (9)

5.4 Asymmetry

The asymmetry is defined as the ratio of efficiencies V\jT\„ appearing in the radiometer

equation (1). Its contribution to the uncertainty in the measured noise temperature is

11
Wr(Tl/Tl)

^,

1- -^ V.' (10)

where we have used ^„,„ « m„/„.

T|/ti rj/rf The asymmetry for the NFRad system was measured with a vector network analyzer and

utilized the reflective termination (RT) method developed by Daywitt [11-13]. The waveguide

systems use a manual asymmetry measurement [2] to determine the actual asymmetries, and then

the ratio is calculated. In this approach, one check standard is measured on one port and another

check standard is measured on a second port. The check standards are then switched and both are

again measured. The product of the ratios from these two measurements is the asymmetry and

should equal unity. The asymmetry measurement for the 30/60 MHz system was to be measured

using a vector network analyzer, but no analyzers operating at these frequencies were available.

Then, we considered using a manual asymmetry method using two hot standards and the ambient,

but the measured devices need to be tuned to the DUT's impedance. Since we cannot tune a

noise source/diode, there will be a mismatch for one of the DUTs in the measurement. In order to

determine the absolute uncertainty, we measured the two standards without matching the ambient

standard to either of them. The ambient standard was then tuned to one of the standards, the

DUTs were measured, the ambient standard was then tuned to the other DUT and measurements

were again taken. The two final measurements involved tuning the ambient standard to one DUT

during the first half of the measurement and tuning the ambient standard to the other DUT during

the second half of the measurement. This process was repeated but the roles were reversed. The

mean and standard deviation were computed for each measurement and a final mean and standard

deviation were computed for all the sets. This standard deviation was used as the uncertainty in

the asymmetry uncertainty. The random uncertainty for several asymmetry measurements was

0.000237, so the total uncertainty in asymmetry is

= 0.023%. (11)

12
5.5 Other Type-B Uncertainties

The measured powers enter the radiometer equation through the ratios Y = p Ip and

Y^ = pjpg in the factor 7 = {Y^ - 1)/{Y^ - 1). The powers are measured in the same way as

with all other NIST radiometers so the uncertainty analysis is the same, where

Uj,(Y)

-^—

1- -^ X 0.04 %. (12)

This is negligible unless T^^ 3T^ .

Although there is no isolator in this system, we must still consider the noise contribution

from the preamplifier. This involves calculating the uncertainty in the effective temperature T^, of

the source [4, 5]. This equation is given by

NT^= T,^T,\r^-^\\ (13)

where Tj and T^ are related to the uncorrelated and correlated parts of the noise from the amplifier

and y^ is a complex constant, experimentally determined for each amplifier. The reflection

coefficient r2 is the reflection coefficient looking back into the system from the amplifier,

r^,. = ^22-^ ^12^21 r,- (14)

The S-parameters are for the transmission line, connecting the DUT or test standard, /, to the

preamplifier, and the subscript / denotes the reflection coefficient of device /. By looking at the change in the effective temperature from source / to source y we obtain

A NT^y = 2 T^Re S,^S^, (S^^ - p )(r . - Tp

,

(15)

so that the corresponding DUT error becomes

AT, = 2T,[{(T^ -TJ/(T^ - TJ) ReS,,S,,(S;, - p)(r^ - T^)

(16)

13
Because the standards have been tuned to the impedance of the DUT, the reflection coefficients

of source / and sourcey are the same. In eq ( 1 6), AT^ is equivalent to zero, but even for small

differences in reflection coefficients between devices, AT^ is small. These small contributions

are accounted for in the mismatch and asymmetry uncertainties.

The uncertainty due to frequency offset and broadband mismatch is the same as that in

reference [8],

Ur^iBBMM)

_ 200%

^

cos

i Wnrl]

30

sine

( TlBf

15

-1 x(|rr hirr I) (17)

wherey;^ is for NFRad, B = 0.000773 at 30 MHz, and B = 0.00138 at 60 MHz are the

bandwidths in GHz, and /= 1 1 .43 is the physical length in centimeters from the input port to the

beginning of the first amplifier in the radiometer. The broadband mismatch uncertainty is

negligible.

The linearity of the IF section is tested as in previous systems. For each noise temperature

measurement, 25 readings are taken with a 3 dB attenuator switched in the IF section of the

system, and 25 readings are taken without the attenuator. The two resulting noise temperatures

must agree to within 0.2 %. This is taken to be the maximum or expanded (k = 2) uncertainty,

leading to a standard uncertainty of

Uj, (lin) = 0.10 %. (18)

5.6 Type-A Uncertainty

In noise-temperature calibrations using the present system, we repeat measurements on

two different levels. Typically, we make one measurement of the check standard's noise

temperature on the DUT port and three separate readings of the DUT on the DUT port. For each

of these measurements we take 50 readings (25 each with and without the 3 dB attenuator in the

14
IF section) of the delivered powers from the two standards and from the check standard or DUT.

A noise temperature of the device is computed for each power reading. Thus, in a typical

calibration of a customer's DUT, we have three separate groups of 50 measurements, for a total

of 150 values of the noise temperature, which are combined to obtain the final value for the

measured DUT noise temperature. The question of how to evaluate the type-A uncertainty in

obtaining the average value from the multiple measurements was addressed in Section 3.10 of

reference [8] for a more complicated measurement scheme. We follow that treatment here,

simplifying as appropriate.

We use Ty for the value of a single reading of the noise temperature. The index / denotes

the number of the measurements and runs from 1 to yV^ (typically 3); the indexy denotes the

reading number and runs from 1 to A^^^ (typically 50). We assume that the number of readings N,^

is the same for each measurement. We use T, to denote the mean of the Nf^ readings for each

measurement and use 5, for the associated standard deviation:

1 X^ r = — > T

(19)

where Tand s are the mean and standard deviation of the A^^ measurements:

(20)

s^= ! £ iT.-T)\

To develop the general expression for u^ we model [ 1 4] the variable T^j as

T^.= T^M.^Ry, (21)

15
where ris the true value for the noise temperature of the device being measured, M^ is a random

variable representing variations from measurement to measurement (/), and R^j is a random

variable that varies with the readingy and the measurement /. Our estimate of the true value is the

mean of all readings:

'^''T^ ——Z^ 52 ^7» (22)

which is also equal to the mean of the A^^ separate measurements. The means of the two random

variables are both zero, and their variances will be denoted by

(23)

where the averages are over all indices. The variances can be estimated from the measured values

Tyby

(24)

The equalities are only approximate because we are dealing with a limited sample. We can solve

eq (24) for v^j and v^, and use eqs (19) and (20) to write

, Vj, (25) ^

N

'

where the averages are over all free indices and where it is understood that if a negative value

16
results for v^ it is taken to be 0. The Type-A uncertainty in the determination of T ~ Tis then the

square root of the variance in T,

«^^

^ -^ + ^— . (26)

Comparison to eq (25) reveals that eq (26) is equivalent tow^ = s I Nj^, provided that eq (25)

does not result in a negative value for v^ . This is as it should be: if we did enough independent

measurements to determine s' well, that would be sufficient, since it includes the variations from

one reading to another. Since we make three separate measurements, we supplement that

information with the measured s}

.

5.7 Combined Uncertainty

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 (5), (7),

(9), (11), (12), (17), and (18),

Ug = [Uj {Cry) + u}{amb) + u}(Y) + u}{M/M) + u^(r\/r\)

I

In calibrating a customer's device, we make several measurements of its noise temperature.

Because the uncertainty defined by eq (27) 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 device's noise temperature. In practice, however, there is little difference

between the values, and so we use the maximum.

The expanded (k = 2) combined uncertainty is computed from eqs (26) and (27),

(27)

17
Uj,^ = 2ff^. (28)

The expanded uncertainty varies with the device being tested, the frequency, and the method of

measuring the asymmetry. A typical value for a Type-N source with high noise temperature

(above a few thousand kelvins) would be about 1 %. Sources with other coaxial connectors

would be measured through adapters and the uncertainty would be somewhat larger.

6. SUMMARY

In this technical note, we have described a tuned radiometer system used to measure noise

devices at 30 MHz and 60 MHz. We reviewed the previous system and the improvements and

modifications to that system. We also discussed the theory and the testing of the present system.

Included were measurement graphs and an uncertainty analysis used to verify the correct

operation of the present tuned radiometer.

We thank Andy Terrell for system measurements and Jim Randa for theoretical support.

7. REFERENCES

[1] Counas, G.J.; Bremer, T.H. NBS 30/60 megahertz noise measurement system operation

and service manual. Nat. Bur. Stand. (U.S.) IR 81-1656; 1981 December.

[2] Randa, J.R.; Terrell, L.A. Noise temperature measurement system for the WR-28 band.

Natl. Inst. Stand. Technol. Tech. Note 1395; 1997 August.

[3] Grosvenor, C.A.; Randa, J.R.; Billinger, R.L. Design and testing of NFRad-A new noise

measurement system. Natl. Inst. Stand. Technol. Tech. Note 1518; 2000 March.

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

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

18
[5] Wait, D.F. Radiometer equation for noise comparison radiometers. IEEE Trans. IM44(2): 336-339; 1995 April.

[6] Larsen, N.T. A new self-balancing DC-substitution RF power meter. IEEE Trans. IM25(4): 343-347; 1976 December.

[7] Kerns, D.M.; Beatty, R.W. Basic Theory of Waveguide Junctions and Introductory

Microwave Network Analysis. Pergamon Press: 89; 1967.

[8] Randa, J. Uncertainties in NIST noise-temperature measurements. Natl. Inst. Stand.

Technol. Tech. Note 1502; 1998 March.

[9] 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.

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

for Standardization; Geneva, Switzerland; 1993.

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

reflection data. IEEE Trans. MTT-38(1 1): 1748-1752; 1990 November.

[12] Pucic, S.P., Daywitt, W.C. Single-port technique for adapter efficiency evaluation. 45"" ARFTG Conference Digest, Orlando, FL, pp. 1 13-1 18; 1995 May.

[13] Randa, J.; Wiatr, W., and Billinger, R.L. Comparison of adapter characterization

methods. IEEE Trans. MTT-47( 12): 2613-2620; 1 999 December.

[14] Graybill, F.A. Theory and Application of the Linear Model. Duxbury Press; Belmont,

CA; 1976.

19
Appendix A. TROUBLESHOOTING

Details of the system design are important for troubleshooting purposes and therefore will be

covered in this section. We have already covered some basics such as the water-cooled plate and

the layout of the equipment, but we discuss the system in depth in this section.

A.l Placement of Components

The 30/60 MHz system was modified to improve system reliability and performance. In

the old setup, most system components, prior to the last amplifier, were not secured to a solid

surface and some were almost floating in air due to space limitations. Although the close

proximity of components minimized cable loss, we decided, based on prior experience, that the

components should be secured for mechanical stability. Also, in the previous system the

bolometer mount and the final amplifier were the only components that were water-cooled. We

knew from previous systems that this practice was not adequate to ensure temperature stability,

especially for the other amplifiers. In the new system, all components were mounted on a watercooled brass plate to control the temperature and ensure temperature stability. The brass plate is enclosed in a box and placed into a measurement rack along with the impedance meter, the DVM,

and a Type IV power meter manifold (described in Section 4). The front-end switches were mounted in a separate box at the bottom of the rack.

A.2 Preamplifier Placement and Operation

After the rebuild, our first measurements showed standard deviations of approximately

500 K. Knowing that the previous system was capable of measurements with standard deviations

of only 20 K, we concluded the system was not working properly. A power meter was used to trace measured powers through the system before and after every device to determine which

component was not working properly. These values are given in Table A. 1 and can be referenced

for future problems should they arise.

Table A.l. Initial power measurements through the 30/60 MHz system.

Measurement Position Power Power (dBm)

Check standard 2.9 nW -55.4

At input to pre-amplifier 1.2 nW -59.4

At output of pre-amplifier 4.0 |IW -24.0

After 30 MHz filter 1.3 nW -59.0

After IF attenuator 1.2 nW -59.2

After 5 dB attenuator 490.0 pW -63.0

After first 30 dB amplifier 370.0 nW -34.3

After level-set attenuator 27.0 nW -45.6

20
Measurement Position Power Power (dBm)

After 5 dB attenuator 8.9 nW -50.5

After second 30 dB amplifler 8.0 |iW -21.0

After 6 dB attenuator 1.9 |IW -27.2

After last 30 dB amplifier 1.5 mW 1.8

Into bolometer 1.5 mW 1.8

Table A.2. Power measurements after moving the pre-amplifier.

Measurement position Power Power (dBm)

At input to pre-amplifier 2.6 nW -56.0

At input to IF box 10.8 |iW -19.7

Into 30 MHz filter 10.4 |iW -19.9

Earlier we stated that all components in the original system were in close proximity to each other. In the present system, the preamplifier was separated fi^om the switches by a cable approximately

0.7 m in length. A co-worker suggested that the cable length between the switches and preamplifier might be too long, resulting in large skin-depth losses. The preamplifier was moved to within 5 cm of the switches. The powers were remeasured at the input to the preamplifier, just

afl:er the pre-amplifier and into the 30 MHz filter, and these new values are given in Table A.2.

There is a difference of almost 5 dBm at the input to the preamplifier. The small position

adjustment of the first amplifier reduced the standard deviations to approximately 20 K.

The pre-amplifier is a high-gain device and therefore if any of the measurement ports are open, one or more stages can be destroyed. Therefore, the program warns the user that power is about to be supplied to the preamplifier and that the user must check to make sure no measurement port is open.

A.3 Wiring from Bolometer Mount to DVM

While trying to rewire this section, we had to combine several old pieces of

documentation scattered in different locations. This section was written to avoid the problem in

the future. Figure A.l shows a simplified wiring diagram for the 30/60 MHz system starting from

the bolometer output. Pins 1, 2, and 4 are tied together at the output of the bolometer. These

connect to pins 6, 7, 19, and 20 on a male 25-pin connector that is wired to a 14-pin socket on a Type-lV power meter card. There are two circuits on this card, which is one of eight cards

located in the power meter manifold. Our card is in slot 5. From the card, three wires run to an

output 25-pin connector. Pin 6 is run to the negative side of the DVM, pin 18 to the positive side

of the DVM, and pin 19 is a common ground. We have labeled the diagram using six-port

diagram notation to avoid confusion.

21
A.4 Repair of Ambient Standard

The tuning assembly on the ambient standard became unstable, and during certain

movements of the dial, the phase would jump drastically from one reading to another. A decision was made to repair the standard but no complete documentation was available. A brief overview

of the repair of the standard is given in this section.

A photograph showing the interior of the ambient standard is shown in Figure A.2. In the

photograph one can see both the capacitor-plate structure (the upper photo) and the container that

holds the oil and the power resistors that can heat the oil to various temperatures.

The standard was refurbished on May 1 1, 2001. Upon opening the standard, we found

that a gasket had crumbled, allowing oil to seep into the chamber containing the capacitor-plate

tuning structure. The old oil from the chamber was replaced with mineral oil and a new gasket was inserted.

A.5 Non linearity of 3 dB Attenuator Measurements

While testing the system, we found consistent readings within the first set of 25

measurements, but there was a noticeable change after removing 3 dB from the path. We

concluded that one of the amplifiers was responding nonlinearly to the input signal. The first two

amplifiers have low input-power levels on the order of nW (see Table 1 ), and the last amplifier

has an input-power level on the order of a microwatt. We decided that the last amplifier was

being saturated, so we tested it and found that it was nonlinear. After replacing this amplifier, the

system responded linearly.

22
Figure 1 . Photograph of complete 30/60 MHz measurement system.

23
(1)

Ambient

1

1

Standard

i 2

DUT

3

(2)

Figure 2. Typical measurement setup.

i ^

'•«— ^''

Figure 3. Reflections at any junction giving rise to a mismatch.

24
Cryogenic SOQ

Ambient f o h

DUT

Switches DC-18GHZ

Preamp

+15Vdc

u 12 dB variable attenuator

30 MHz filter

60 MHz filter y

To Type IV

power meter &

DVM/

30 dB

24Vdc

amplifier

30 dB

20Vdc

0.5-100 MHz

amplifier

Level-Set Attenuator

5dB

attenuator

30 dB

20Vdc

0.5-100 MHz

amplifier

6dB

attenuator

Water Plate

Figure 4. Schematic diagram for 30/60 MHz system.

25
Figure 5. Photograph of cryogenic and ambient noise standards for the

30/60 MHz system.

10200-1

10180-

L_ZJCD

Q.

E

t-

<D

V) "o

B 10160

10140

10120-

10100

20

+

+

o

o

o

O May/June 2001 + History (Old system)

180 —I

I

I ^

40 60

Frequency (MHz)

Figure 6. Measurement results for Type-N check standard X13BHZ.617.

26
i-3

(D

i_<DQ.

E

t0)o

youu —

9580-

+

o

9560-

o

9540-

9520-

o

o

o

+

May/June 2001

History (Old system) 9500-

Q/ior> y4ou 1 1 1

1

1 1 20 40 60 80

Frequency (MHz)

Figure?. Measurement results for Type-N check standard X 1 3BHZ.8 1 7.

Plug from

Bolometer

1 2 3 4 5 6 7 8 9 10 11 12 13

125 24 23 22 2120 19 18 17 16 IS 14

Formerly

Front Panel

Six Port-2

1 14 2 13

3 12 4 11

5 10 6 9

7 8 PM#5

A 1 B 2 C 3 -DVM

D 4 E 5 F 6 H 7

J 8 K 9 L 10

J23

To Type IV ^.

Power Meter ^*^

1 2 3 4 5 6 7 8 9 10 11 12 13

25 24 23 22 2120 19 18 17 16 15 14 Cards ^ k 1 rr•— +DVM

M 11 N 12 P 13 COM

R 14 S 15 AnxH

PM1,2

Figure A.l. Wiring diagram for the 30/60 MHz system.
Mineral oil contained in this part

Capacitor

plates

Power

resistors

Figure A.2. Photograph of disassembled ambient standard.

28
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