NAT'L INST. OF STAND & TECH R.I.C.

A111DS IMITEM

M\ST

PUBUC/^ONS

United States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Technical Note 1390

1

Noise Temperature Measurements

on Wafer

J. Randa

1 1

r

NIST Technical Note 1390

Noise Temperature Measurements on Wafer

J. Randa

Electromagnetic Fields Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

March 1997

*^TES °*

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

TECHNOLOGY ADMINISTRATION, Mary L. Good, Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Arati Prabhakar, Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1390, 64 pages (March 1997)

CODENrNTNOEF

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

INTRODUCTION 2

2 THEORETICAL BACKGROUND 4

2 .

Normalization and Power 4

2.2 Generator Waves and Noise Temperature for Lossy Lines .. 8

2 .

Mismatch , Available Power , Etc 10

2.4 Radiometer Equation and Noise Temperature on Wafer 12

2 .

Use of "Pseudo-Waves" 14

3THE EXPERIMENT 15

3 .

Experimental Setup 15

3 .Noise Sources 20

3.3 Results 24

3.4 Uncertainty Analysis and Checks 26

4. SUMMARY AND DISCUSSION 31

5REFERENCES 33

APPENDIX A 36

APPENDIX B 39

B . 1 Some Pseudo-Wave Algebra 39

B.2 Power and Noise Equations 41

in

NOISE TEMPERATURE MEASUREMENTS ON WAFER

J . Randa

Electromagnetic Fields Division

National Institute of Standards and Technology

Boulder, CO 80303

The NIST Noise Project has developed the theoretical formalism and

experimental methods for performing accurate noise-temperature

measurements on wafer. This report presents the theoretical

formulation and describes the design, methods, and results of

tests performed to verify our ability to measure on-wafer noise

temperature. With known off-wafer noise sources, several

different configurations were used to obtain different, known, on- wafer noise temperatures. These were then measured, and the

results were compared to predictions. Good agreement was found,

with a worst-case disagreement of 2.6 percent. An uncertainty

analysis of the measurements resulted in an estimated standard

uncertainty (la) of 1.1 percent or less for most values of noise

temperature. The tests also confirm our ability to produce known

noise temperatures on wafer.

Keywords: noise; noise measurement; noise temperature; on—wafer

noise; thermal noise
1. INTRODUCTION

The move toward miniaturization and on-wafer integration in the

electronics industry has brought with it the need for accurate, reproducible

measurements of microwave properties of devices and structures on wafer. An

area of considerable importance and interest is the measurement of noise

parameters on wafer, in particular the noise figure of a two—port device, such

as some variety of low—noise transistor. The noise figure of a device is a measure of the noise added to the input signal by the device itself. It is

determined by measuring the output noise power from the device for different

known levels of input noise power. Because the noise figure of a device

depends on the impedance of the input source, it must be measured for several

different input impedances to characterize that dependence. Alternatively, if

there is a single input impedance of interest, for example, 50 ft, then the

noise figure can be measured at just that one impedance. A good deal of work

has been done over the past several years to develop and improve techniques

for measurement of noise figure on wafer [1—11]. Methods and even commercial

systems exist for such measurements. There is always room for improvement and

extension of such methods, of course, but a more pressing need at present

appears to be in the areas of accuracy assessment, traceability , and general

quality assurance.

To address this need, the Noise Metrology Project, in the Microwave

Metrology Group of the National Institute of Standards and Technology (NIST)

is developing the capability to measure noise figure (NF) on wafer. This work

builds on our long—established ability in noise—temperature measurements in

waveguide and coaxial structures [12,13] as well as on recent work [14] on coaxial noise-figure measurements. The first major step in the development of an on-wafer noise-figure capability is to establish our ability to measure

noise temperature on wafer and to determine the accuracy of those

measurements. This is a necessary first step because the measurement of the

noise figure consists of a series of measurements of noise power (or

equivalently noise temperature) at the output of the device under test (DUT)

for different known input noise sources. Thus, in order to measure noise

figure on wafer, it is necessary to be able both to produce known on-wafer

noise temperatures and to measure unknown noise temperatures (or their ratios).
Besides its necessity for noise—figure measurements, a NIST capability

in on—wafer noise—temperature measurement would be useful in its own right.

It could serve as the basis for a measurement service for on-wafer noisetemperature transfer standards, or for intercomparisons involving such

transfer standards. Such a service or series of comparisons would enable

private industry to verify their own on-wafer noise measurements. For these

reasons, we have developed the necessary analytical foundation and performed a series of measurements to test our ability to measure noise temperature on

wafer. In doing so, we have also verified our ability to produce known noise

temperatures on wafer.

On—wafer noise measurements present a number of difficulties or challenges not encountered in traditional noise measurements with waveguide or coaxial connections. One problem is that it is difficult to obtain a good

impedance match between the measurement system, the probe, and the on—wafer

system. Consequently, the assumption of a well—matched system is not

justified, and scalar quantities, such as the noise figure for a SO Q system,

cannot be measured directly. Furthermore, even when corrections are made for

the relevant mismatch factors, the uncertainties in those corrections are substantial, and they can lead to a significant increase in the uncertainty in

the noise temperature or noise figure. Several other problems can be

associated specifically with either the wafer environment or the probe. Onwafer transmission lines typically have significant losses, due mostly to

dielectric losses in the substrate but also to resistive losses in the thin

conductor strips. The presence of these losses changes the form of the

various power equations (and consequently of the mismatch factors, availablepower ratios, etc.) used in computing the noise temperature of a device under

test from the measured powers. Therefore, the entire formulation of the

radiometer equation must be reexamined and rederived. Another potential

problem associated with the wafer is that it is an open environment, which

raises the possibility of outside radiation entering the system and

contaminating the measurements. For its part, the probe, which serves as a transition from the transmission line on wafer to the coaxial line of the

measurement instrumentation, is unlike ordinary transitions in at least two

important respects. It has significant loss (of order 0.5 dB to 1.5 dB) , and

there are no standard noise sources which can be connected directly to the
wafer side of the probe. These two facts preclude the use of the methods

which NIST normally employs to evaluate and correct for the effects of

adapters and transitions. Thus we cannot treat the probe as just another

adapter. We must characterize it by direct measurement of its S—parameters

,

and that characterization will prove to be the principal source of uncertainty

in our measurements. These difficulties all occur before we even begin the

measurements. They will be considered in some detail below, as will several

additional theoretical concerns and practical problems which arise during the

course of the measurements.

The remainder of this paper is organized as follows. The next section

presents the theoretical background and foundations for on-wafer noisetemperature measurements. It establishes notation, reviews the expression for

power, gives the connection between travelling—wave amplitudes and noise

temperature in the case of lossy transmission lines, derives the relevant

radiometer equation and the expressions for mismatch factor and available

power ratio for lossy lines, and discusses the use of the "pseudo—waves" of

Marks and Williams [15]. Section 3 is devoted to the measurements. It

describes the experimental setup, presents the different configurations of

noise sources which were measured, provides an uncertainty analysis, and

reports the measurement results. Section 4 contains a discussion and summary

of the results and of some of the techniques used. There are two appendices,

which are devoted to algebraic details.

2. THEORETICAL BACKGROUND

2.1 Normalization and Power

In this section we establish notation and normalization conventions.

Considerable detail is presented, in part for future reference, but also

because there are some necessary departures from the "usual" [16, 17]

treatments. Losses in transmission lines on wafer can be significant,

resulting in modifications of some old familiar results, which rely on lossless or low-loss lines. Since the lossy case is still viewed as a bit of

a curiosity (not to say aberration) by some, it may be useful to be specific

about some of the basics and the form they take with our choice of notation.
Much of the development in this section parallels that of reference [15], but

we use a somewhat different notation, which we find more convenient for this

application.

For a single mode a of a uniform waveguide, the electromagnetic fields

of travelling waves propagating in the positive or negative z direction take

the form

2;{jtt ,z) = c*e*Y* z(eat ±Saj?),

(l)

H*(xt ,z) = ±cte^z(Rat ±Raz),

with an implicit time dependence eJut. In eq (1) , Ca is the amplitude of the

wave in the ±z direction, eat and hat are in the transverse plane, §az and

haz are longitudinal, and all four depend only on the transverse coordinates,

eat = eat {xt

) , eaz

= eaz {xt

) 2 , etc. For Ea and Ha to satisfy Maxwell's

equations, the modal functions must satisfy

ya Rat + Vhaz = juezxeat , R*z = l^X§at ' (2)

Note that eq (2) could be used to write all other components in terms of just

eat . Consequently, in the normalization considerations, we need (can) only

fix the normalization of eat , and the normalization of the other three

functions is then fixed by Maxwell's equations. When travelling waves in both

directions are present, the fields from mode a can be written as Ea = (aa + ba

) eat + (aa - ba

) eaz , (3)

Ha = (aa - ba

) Rat + (aa + ba

) Raz ,

where we have introduced
+ -Y.z aa = aAz) = ca e

ba = ba [z) = ca"eYaZ (4)

The (complex) power flowing in the positive z direction can be written as

0> = JEa xH;-zd2xt = [\aa \ 2 - \ba \ 2 -2jlm(aa b;)]la , (5)

with

Ia - feat xE;t -zd2 xt /»-"£ jcoefxeat -?^?xeat -i>)]| -f d

2 xt

(6)

The physical power is then given by

Pa = Re{<p) = [\aa \ 2 - \ba \ 2 ^ 2tdLnCa Im(aa b:)]Re(Ia

) ,

tanCa = Im(IJ (7)

i?e(Jj '

where f a has been defined as the phase of the integral Ia

. This expression

for the power differs from the familiar (lossless) form by the presence of the cross term proportional to tanf a , which is determined by Maxwell's equations

via eq (6). In the lossless case, 7a is purely imaginary, Ia is real, and

tan^ a vanishes. In general, however, the cross term is present [15,18], and

it necessitates modifications of the usual expressions for quantities

involving power or power ratios (mismatch factors, efficiencies, etc.).

We now turn to the question of normalization. Basically, there are two

choices to be made. One is whether we are more interested in the fields or in

power and S-parameter calculations. The second (rather trivial) consideration

is where we want to put the dimensions — in aa and b a or in ea and ha

. In

the present work we are interested in power and S—parameter calculations, and

we shall use a "power normalization." This consists in setting
Re{Ia ) == i?eUeat x|AJjco€fxeat -^-^^xeat -fjj| •£ d

2x = 1. (8)

Note that this is a condition on eat only; the normalizations of the other

components are determined from eq (2) . The expression for the power in mode a then becomes

P* = [\a a \ 2 - \ba \ 2 + 2tanCa Im(aa b;)]. (9)

The dimensions of the various quantities in this scheme are

3a [yfW] , ba [y[W] , Ct [yfW] , $a [yfU/m] , A

yfUm

(10)

As mentioned above, we could choose to shift units around so that, for

example, aa , ba , and c* were all dimensionless and ea had dimensions V/m, but

for present purposes we shall use eqs (9) and (10). The remaining practical

question is what is the physical significance or interpretation of f a , and how

does one determine or measure it? Comparison to reference [15] indicates that

the integral which we are calling Ia is their p . The phase of Ia is then the same as the phase of p and therefore of (their) Z . Thus f a is just the

phase of the characteristic impedance of the line (for that mode)

Measurement of £ a will be discussed below. For those not familiar with

reference [15] , the connection between Ia and the impedance is clearer in the

alternative normalization scheme discussed in the next paragraph.

An alternative normalization scheme (which will not be used in this

paper) is what could be called field normalization. If our interest were primarily in the fields, it would be most natural to choose a normalization

like /I e I 2 Gat\ d

2Xt = 1. With this normalization choice, the dimensions are

e[m x

] , 5[(Q\m) x

] , and aa [V] , ba [V] , ca*[V]. The integral Ia then has

dimension fl-1

, and so it is natural to identify it with an (inverse) impedance

characterizing the mode a. In general, there is no single wave impedance for
a general mode (cf. reference [19]), but for the simple case of hat 3at = ,

have Eat x2 = Z~x eat , and therefore Ia = (l/Z*) f\eat \ 2 d

2Xt we = l/Z*.

Thus the phase of Ia is the same as the phase of Za

. In this normalization,

the expression for power involves Re(\/Z*) , which is somewhat cumbersome to

carry through power calculations.

2.2 Generator Waves and Noise Temperature for Lossy Lines

To relate travelling—wave amplitudes to noise temperature, we need an expression for the available power which is valid for a lossy line. Consider

the general configuration of figure 1. In terms of the amplitude of the

generator wave (&G ) and the reflection coefficient Ta ba/aa , eq (9) for the

delivered power can be written as

PaaeI = |a a | 2 [1 - |I\J

2 - 2 tanCa ImTa] — [l-|ra |2-2tan£a J;nra]

(11)

|i-ra rG

The available power is obtained by replacing Ta by the expression for the

optimal reflection coefficient, which is no longer simply the complex

conjugate of the generator reflection coefficient, r

opt=rG

*, but rather

rft m JJ-jtanC.. _ (12)

l-jT;tanCa

To calculate the available power, we set Ta = raopt in eq (11). A little

algebra then yields

• avail . ftP

[1 - |rG | 2 -2 ZmrG tanC] cos2 C

' (13)

where we have suppressed the subscript a since we will be assuming a single

mode in the present work. For a thermal noise source at noise temperature T, we can then equate the available power to kBTB , thereby obtaining
<|£G | 2

> = kB BT[l - |rG | 2 -2 ZmrG tanC]cos2 C , (14)

where the brackets < > refer to the time average.

Similar expressions can be derived for the intrinsic noise sources in a passive, linear two-port, figure 2. The two—port can be characterized by

(15)

where 5 is the usual 2x2 matrix of scattering parameters, and S1

, B2 are the

emerging wave .amplitudes due to the internal thermal noise sources. To fix

j62 we assume that the entire circuit is in thermal equilibrium at temperature

T. (For those worried about quantum effects, what we really mean is at the

physical temperature which corresponds to a noise temperature of T.) To

obtain an expression for \

| ^2

1

2

' » we choose TG = in figure 2 and require that

the available power at plane 2 be given by kBTB. This leads to eq (14), but

with the reflection coefficient and generator wave amplitude being those

appropriate to plane 2, that is those of the generator-two-port system. If we refer to the generator plus the two-port as GS , then

<l4sl

2

> = ^B BT[l-\YGS Y-2 J;nrG5 tanC2]cos2 C2 , (16)

where {" 2

*- s tne phase of the characteristic impedance at plane 2, and where

£ = b la =0) = £ + <7 °

+ T

°Zl

1 l G^ll

(17)

p . q +

,^12'^21*g

1 GS °22 TTr~c ' X 1 G°11

We then set TG - in eq (17), substitute it into eq (16), use eq (14) for

(|j6g | 2), and solve for (^J2) . The result is

(\£2 \ 2

) = kB TB[(l - |522 | 2 -2tanC2 JinS22)cos2 C 2 - |S21 | 2 cos2 CJ , (18)

where {^ is the phase of the characteristic impedance at plane 1. A similar
exercise can be applied at plane 1, lumping together the two-port and the load

and considering the available power from them at plane 1. The result is

(\£x \ 2

) = kB TB[(l - \S1X \ 2 -2tanC1 ImS^) cos2 { x - |S12 | 2 cos2 C2] U9>

The expression for the correlation between the two amplitudes can be derived

by using a nonzero rG in figure 2. Again we require that the available power

at plane 2 (and at plane 1 when G and L are interchanged) satisfy eq (14),

using the appropriate TG and BG of course. After a bit of algebra, we obtain

(£x £;) = -kgTBls^S^ + jtanC^cos2 ^ + S12 (S2

*2 - j tanC2)cos2 C2]

. <2

It is reassuring to note that when f lf f 2 = 0» ecl s (18), (19), and (20) reduce

to Wait's results [20]. Note that this result does not assume any

relationship between the various scattering parameters, such as S 12 and S2 i.

2.3 Mismatch, Available Power, Etc.

The expressions for delivered and available power, eqs (11) and (13),

lead directly to equations for the mismatch factor and available power ratio

which are valid for lossy transmission lines or waveguides. For the mismatch

factor we use eq (11) for the delivered power and eq (13) for the available

power, resulting in

pdel M = p avail

(21)

[1 - |rL | 2 - 2 tanC ImTL] [l - |rG | 2 - 2 tanC ImTG] cos2 C

|i-rL rG | 2 "

For a passive two-port device, the available power ratio is defined as

a2i P2 avail/P1 avail

. Referring to figure 2, the available power at plane 1 is

given by eq (13), with f = fj. At plane 2, eq (13) again applies, with

f — f2 i Dut &g anc* ^g now refer to the combination of generator plus two-port,

These are given in eq (17) for the more general case allowing for internal

sources in the two-port. For evaluation of a21 we want to neglect any

10
internal sources. Thus we use eq (17) with £x = £2 = , and the available

powers take the form

r, avail \££

[1 - |rG | 2 - 2 tand ImTe] cos2 d

l^il'l^'3 (22)

D avail _ 1^21 1 \**Q

*2

|1 -rG5xl | 2 [l - \YGS \ 2 -2 J/nrG5 tanC2 ]cos2 C2

The available power ratio is then given by

l-g2 il

2 [1 - |rG | 2 -2 Zm^tand] cos'Ci

«2i " -: =—-:h~: r=

it— = —

;

—, r=- # (23)

|i -iyjj2 [1 - |rG5 | 2 - 2 J^rGS tanC2] cos2 C2

'

with rGS given by eq (17) . We could substitute the explicit expression for TGS into eq (23), but the result is not particularly enlightening. For the case

of lossless lines, $i — f 2 = 0, q21 reduces to

°" " n-r^Hi-irln ' (24>

which is the familiar form for an attenuator.

A lossy two-port, such as an attenuator, is not a perfectly passive

device: it contains noise sources. Consequently, the available power at plane

2 includes not just the contribution from the attenuated available power at

plane 1, but also a contribution from the sources between planes 1 and 2.

General considerations can be used to show that the available power at plane 2 is given by

P2avaU

= «ai pi Vail + [1 " « 2 J kBTA > <25>

where TA is the noise temperature of the attenuator. Equation (25) can also

be derived directly from travelling-wave amplitudes, S-parameters , reflection

coefficients, and some algebra. This is done in Appendix A.

11
2.4 Radiometer Equation and Noise Temperature On Wafer

We can now obtain the explicit expression for the radiometer equation,

relating the noise temperature on wafer to the noise temperatures of the

standards and the powers delivered to the radiometer. The general

configuration and relevant reference planes are shown in figure 3. The

radiometer itself also contained an isolator, so that there were isolators

immediately to the left and right of plane 0. 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 Pa , where it indicates the ambient, Pa — kBT&

. The subscripts on the delivered

powers and mismatch factors will indicate the reference plane and the

configuration. Thus p2x refers to the delivered power at plane 2 when the

DUT (x) is connected. For an isolated radiometer, the derivation follows the

basic treatment by Daywitt [13], with a few notational changes. The power

delivered to the radiometer, at plane 0, when the switch is connected to the

DUT at plane 7 , is given by

Pq.x = Mo,x*Q7 Px

+ M0,x [l-«o?] Pa + Pex' < 26 >

where Pex is the intrinsic effective input noise power of the radiometer for

this configuration. Similarly,

Po,8 " #0, S «03 Ps + M0,e [1 " "(J Pa + Pes » (27)

Po,a = M0,a Pa + 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, pex ~ pes ~ pea . Combining eqs (26) and (27), we obtain

Daywitt's form [13],

M a Y - 1

Tx =Ta+ (TB -Ta

) ^±^1^-^ + (ATx) lgl (28)

where Yx = px/pa , Ya ps /pa , and where (ATx ) is is the error in Tx due to the

(small) effect of an imperfect isolator. The general expression for the ratio

of Ma's is rather cumbersome. It simplifies somewhat if we use the identity

12
(in the notation of figure 2)

(i-s22 rL) (i-iy\/L ) = (i-slx rG) (i-r2/GrL ) , (29)

and furthermore note that f 3 ~ 0, since plane 3 is in a coaxial line with real

impedance, and that S22(7-0) » S22 (3-0), due to the isolators. As a matter of

notation, for reflection coefficients or mismatch factors with two subscripts,

the first subscript refers to the reference plane, and the second indicates

the direction of incidence. Thus r1L is the reflection coefficient from the

load at plane 1. The ratio of Ma's can then be written as

Mq, s *o3 m |s21 (3-o)| 2 |i-rxr7<r | 2

i (30)

^o,*«o7 |521 (?-o)| 2 |i-rs r3/r | 2

ft - Ir3 , J

2

) cos2 C7 [1 - \TX | 2 - 2 tanC7 ImTx]

We use S^CN-M) to refer to the S—parameters between planes N and M, where N

is considered the "first" plane; see eq (15).

Equations (28) and (30) can be used to determine the measured noise

temperature on wafer, at plane 7. In our on-wafer tests, we also need to

compute the noise temperature at plane 7 from a known noise temperature at

plane 9 for the configuration of figure 4. This is easily done by using eqs

(25) and (23) to write

T7 = a19 T9 + [1 - <X 79 ] Ta , (31)

with

«79

|S21 (9-7)| 2 (l-|rg | 2

) cos2 C7 |l-rfl 511 (9-7)|2 [l-|r7#fl | 2 -2tanC7 Xmr7/a]

'

In this equation, the subscript s represents whatever source is connected at

plane 9

.

13
2.5 Use of "Pseudo-Waves"

The significant losses in typical on—wafer transmission lines mean that

in general it is not a good approximation to take the characteristic impedance

to be real. Therefore, the phase f is nonzero, and we should use the full,

cumbersome, general forms for the mismatch factors, available power ratios,

etc., as derived in the preceding section. Simplification is possible,

however. Marks and Williams [15] have suggested and developed the use of what

they call "pseudo-waves," which are linear combinations of the travelling

waves, where the linear combination depends on the characteristic impedance

and on a reference impedance of the user's choice. This transformation then

induces a corresponding transformation of reflection coefficients and S—

parameters at the reference plane (s) affected. The advantage of pseudo-waves

is that if we choose a real reference impedance (typically 50 0) , use of

pseudo-waves and their associated reflection coefficients and S-parameters

results in the familiar, lossless-line form for power, |a| 2 (l-|r| 2 ).

Consequently, ratios of powers, such as mismatch factors and available power

ratios, also revert to their lossless-line forms. In fact, the travelling

waves can be considered as just a special case of pseudo-waves, with reference

impedance chosen to be the modal impedance of the travelling wave. Thus, the

equations derived above for travelling waves also hold for pseudo-waves,

provided that the £"

' s are taken to be the phases of the reference impedances,

and provided that all reflection coefficients and S-parameters are those

appropriate to the reference impedance (s) chosen. (This may not be entirely

obvious; it is proved in Appendix B.)

The price that one pays for the simplifications engendered by pseudowaves is that the reflection coefficients and S-parameters must also be

transformed to the reference impedance chosen. For reflection coefficients or S-parameters at reference planes in (nearly) lossless lines, this problem Is

absent since the characteristic impedance is real, to a good approximation.

At reference planes on wafer, however, the characteristic impedance is

complex, and J" * 0. If we use travelling waves, then we must use the phase of

the modal impedance for f in the equations above. The reflection coefficients

and S-parameters in that case are the "usual" ones defined for travelling

waves. If we use pseudo-waves with Zref — 50 0, then we set f - f ref - in

14
the equations, but we must use pseudo-wave reflection coefficients and Sparameters for the on—wafer reference planes. Which choice is more convenient

is determined to a large extent by the software used in making the on-wafer

measurements. We shall use the NIST-developed package MultiCal® [21], with a multiline TRL calibration [22] to characterize the probes. One of the

features of MultiCal is that it allows one to measure pseudo—wave quantities

,

and consequently we choose to use a reference impedance of 50 Q and use the

simplified (f = 0) version of the equations. (MultiCal also provides for

measurement of f, the phase of the characteristic impedance [23].) The form

of the radiometer equation, eq (28), is unchanged, but eq (30) for the ratio

of mismatch factors and available power ratios becomes

iy fl « 03 _ \s£0) (3-o)\ 2 li-r^rj^l2 (i - |it° }

I 2

) ^o,*«o7 \sil

0) (7-o) | 2 |i-ri50,

rifj

)

| 2 (i - |ri50)

I 2

)

' (33)

where the superscript "(50)" indicates that the reflection coefficient or Sparameter is with respect to a 50 Q reference impedance. In computing the on- wafer noise temperature due to an off—wafer source, eq (31) remains the same,

but eq (32), for the available power ratio, takes the form

|52

<150) (9-7)| 2 (l-|ri50,

| 2

) , , (v = ' Z1

:

' \ !_£ !_J . (34) 79

11 r.(50)M50) i-ri50,

5k

(1

50) (9-7)p[i-|r7

( ?!)

| a

]

If our on-wafer methods and software had measured only travelling-wave

quantities, then it could be more convenient to use eq (30) as derived, with

the measured travelling-wave reflection coefficients and S-parameters anc* the

measured $"

3. THE EXPERIMENT

3.1 Experimental Setup

Figure 5 contains a block diagram of the general experimental setup,

with relevant reference planes numbered. The radiometer is switched between

the ambient standard noise source (plane 1) , the nonambient standard noise

15
source (plane 3 or 6), and the on-wafer DUT (plane 7), measuring and recording

the delivered power from each. The nonambient standard is usually the NIST

cryogenic coaxial (GPC-7) primary standard [24] , which is connected at plane

3. For some of the measurements, a previously calibrated, high—temperature

check standard, connected at plane 6, is used as the nonambient standard.

This is done when the cryogenic standard is being used elsewhere in the

measurement or when we measure an on-wafer noise diode of very high noise

temperature

Detail of the detection system is shown in figure 6. It was originally

built as a prototype of the 8 to 12 GHz detection section for the new

radiometers discussed in the following paragraph. The design is similar to

that in other NIST radiometers. The incident broadband noise power is

amplified by the initial radio—frequency (rf) amplifier and then mixed with

the signal from the local oscillator (LO) . The output from the mixer is

amplified and then filtered to pass frequencies within 5 MHz of 0. Thus the

rf frequencies that contribute to the output power are in the range f — f(L0)

± 5 MHz. The output power is measured by a NIST type-IV power meter [25], and

corrections are made for the effects of the filter shape. For reasons

discussed below, the detection unit was designed and constructed to be very

stable. Tests indicate that its output is stable within ±0.001 dB/12 h. The

other critical feature of the detection unit is its linearity. The IF

subsystem is the potential problem since it must handle the greatest power.

The IF subsystem was tested and found to be linear within ±0.005 dB per 3 dB

up to a power of 17 mW. Our typical measurements were done at IF powers less

than 2 mW, and all measurements were kept well within the linear range. The

internal ambient source shown in figure 6 is used for certain checks of the

radiometer but not for noise measurements on a DUT.

The major difference between the radiometer of figures 5 and 6 and the

"traditional" [13] NIST radiometers is the lack of a six-port reflectometer in

the present system. All current NIST radiometers for 1 GHz and above include

six-port reflectometers, which measure all relevant reflection coefficients

for each measurement of a DUT. (Many separate measurements of the noise

temperature are made at each frequency in calibrating a noise source.) A new

generation of radiometers is being developed in conjunction with the

16
development of an amplifier noise-figure measurement capability [14]. These

new systems will not have their own internal six-ports. Instead they will

rely on an original set of measurements (plus periodic updates and checks) of

the system reflection coefficients and path losses. This simplifies the

radiometer and allows quicker calibrations, but it requires a high degree of

stability and repeatability in the system.

Photographs of the measurement apparatus are shown in figures 7 and 8

.

If we begin with the closeup view of figure 7, the chuck on which the wafer

rests during a measurement is located directly below the microscope. The

probe to the right is probe 2, connected by a short section of semirigid cable

to a bracket and GPC—7 connector. This connector corresponds to plane 9. In

several of the measurements which used off-wafer sources to produce on-wafer

noise, the noise source was connected at this plane. In the photograph, a cable is connected here. The other end of the cable, visible in figure 8,

corresponds to plane 10 and is where the noise source was connected in the

other tests using off-wafer sources. The cable is held securely, preventing

any flexing during the course of the experiment. In figure 8, the structure

to which the cable is secured is a jig, which was built to position the chuck

and hence the wafer. This allowed probe 1, the left probe in the photographs,

to remain fixed during the entire experiment, reducing the risk of changes in

reflection coefficients and S-parameters to the left of plane 7. Probe 1 is

connected by semirigid cable to the switch assembly, which is the light

colored cylinder visible in figure 7. The switch assembly also houses the

ambient standard, whose temperature is monitored by a thermistor. The

connector emerging from the top of the switch assembly is port 6. The

rectangular box connected to the axial (front) port of the switch is the

detector unit. The connector emerging from the front of the detection unit,

out of the page in figure 8, is the access port for plane 0, between the two

isolators. The box and its contents are held at ambient temperature by the

brass plate on top, with its water circulation. Ambient-temperature water is

also circulated through the switch assembly. In figure 8 the cryogenic

standard is the large, vertical, cylindrical canister below the switch,

between the probe station and the instrumentation rack. The rack contains

supporting electronics: the NIST type-IV power meter, a voltmeter to read the

thermistors, the synthesizer, switch drivers, power supplies, filters, etc.

17
We do not circulate water through the probes or through the platform

which supports the wafer. These elements could experience resistive heating,

but for the power levels of this experiment we do not expect much effect. The

most worrisome case was the on-wafer noise diode, which could heat up during

use. To check this, we divided the run into halves and into thirds and

checked for temperature change as a function of time. No significant

difference was found. If the physical temperature of the diode is rising, it

is not affecting the noise temperature. Another potential problem is that the

temperature of the room is not as well regulated as the temperature of the

circulating water. The two can differ by as much as about 2 K. We use

"ambient" temperature to refer to the temperature of the ambient standard.

The temperature of the circulating water is set for 296,0 K and is typically

within about 0.1 K of the ambient-standard temperature. Consequently the

switch assembly and the contents of the detector box are at ambient

temperature. The wafer, the probes, and what we call "ambient" loads (which

are not in water jackets) are at "room" temperature (in the absence of

additional heating) . This has little effect on the noise temperature

measurements, but it does mean that the ambient loads in our tests are really

"room temperature" loads, and consequently their noise temperatures may differ

somewhat from ambient temperature.

We use the radiometer equation, eq (28) , to compute the noise

temperature Tx of the DUT from the delivered powers measured by the

radiometer. Equation (33) is used for the ratio of mismatch factors and

available-power ratios, requiring the measurement of the various reflection

coefficients and S-parameters . The S-parameters and reflection coefficients

which must be measured include S2 i(3-0), S2 i(7-0), Tx , T7 r , Ts , T3 r , and r6r . The two subscripts on some of the reflection coefficients refer to the

reference plane and the direction, with r referring to the radiometer

direction. S-parameters [Sij (2-0), 5^(3-0), Sij (6-0)] from the switch ports

through the switch to plane 0, between the two isolators, are measured with a VNA. In cases for which the reference plane occurs at a connector (planes 2,

3, 6, 9, 10), the reference plane is taken at the center of the connector,

which is GPC-7 in all such cases. The radiometer has a port which allows

access to plane 0. The reflection coefficients (Ts ) of the cryogenic standard

and the high-temperature check standard are also measured with the VNA. For

18
T3 r we use r3r « Sn (3-0) , and similarly T6 r ~ Sn (6-0) . The accuracy of this

approximation can be inferred, from a comparison of T7 r , which was measured,

to Sn (7-0) , which can be constructed from the measured S(7-2) and S(2-0).

This comparison indicates that the approximation should be accurate within

0.07 in the real and imaginary parts of T3 r and T6 r (0.1 in the magnitudes).

On—wafer quantities were measured using MultiCal [21]. An on-wafer

multiline TRL calibration [22] was performed. The calibration kit consisted

of a through, a reflect, and three transmission lines of different lengths,

all of gold on a GaAs wafer. It was fabricated by the NIST High-Speed

Microelectronics Project. In the calibration, the probes were defined to

extend to the center of the through in the TRL calibration standards. The

through is 0.50 mm long, and thus plane 7 is 0.25 mm from the probe-1 end of

the through. Each probe thus includes a short (0.25 mm) section of coplanar

waveguide (CPW) , of which about 0.225 mm is between the probe tip and the

reference plane, and 0.025 mm is behind the probe tip. In principle this

length is chosen long enough to assure a single mode at planes 7 and 8. In

practice we did not check for higher modes. The on-wafer calibration provides

a measurement of Sij (7-2) and Si j(9—8). It also extends the VNA calibration to

the reference planes 7 and 8 on wafer. The VNA and MultiCal can then be used

to measure reflection coefficients at plane 7, both of the radiometer (r7r) and of the DUT (Tx ) . A number of different on-wafer DUT's were measured

(discussed below) , and for each the reflection coefficient was measured at

plane 7. The S—parameters Si j(7-0) between planes and 7 were not measured

directly but were obtained by cascading Sij (7-2) and 5^(2-0).

In the course of the VNA and MultiCal measurements , a good deal of

redundant information was obtained. We used this information to perform

checks on our methods and measurements. For example, T7 r , r2>r , and S(7-2)

were all measured separately, but T7 r must equal the result of cascading 5(7-

2) and r2(r . A number of such checks were performed, and agreement was typically within a few percent. The probes were calibrated before and after

the on-wafer measurements, and the largest difference in S21 for either probe

was found to be 0.17 percent. The averages of several VNA measurements for

the reflection coefficients of the primary standard and check standard were compared to results of independent measurements by personnel of the NIST Six19
Port Project at 8.0 GHz. The two agreed within ±0.001. It was also found

that the magnitudes of S21 for the three switch ports were equal within about

0.1 dB. They need not have been equal, since we correct for any difference,

but it is reassuring that they are. A number of other repeatability checks

were performed, with similar results. These checks give us confidence that we

are correctly measuring the reflection coefficients and S—parameters

3.2 Noise Sources

The principal purpose of the experiment was to test our ability to

measure noise temperature on wafer. In addition, we wanted to resolve two

specific questions which had arisen in preliminary measurements. One was whether any (nonambient) radiation was entering the system through the open,

on-wafer transmission line, thereby adding additional power to the lines and

corrupting the noise measurements. The other issue was whether flexible

cables could be used to connect off-wafer sources to one of the probes and

thus to a transmission line on wafer. The cables would have to be

disconnected and reconnected in order to measure their characteristics and

then to use them in the noise measurements. Earlier tests had suggested that

this process could introduce variations as large as about 12 percent in the

noise— temperature measurement, which was considerably larger than we were

willing to tolerate.

To address these questions, we measured a number of different noise

sources . We began by measuring a high—temperature check standard which had

previously been measured at 8 GHz on our coaxial noise-temperature calibration

system. This standard was measured at port 6, in figure 5, which is not on

wafer. Measurement of its noise temperature tells us nothing about our onwafer capabilities but does provide a check that the new radiometer and the

associated computations are functioning properly.

The simplest on-wafer noise source was just a resistor on a GaAs wafer.

The leads from the resistor are the same as the CPW line used in the on-wafer

calibration kit. Reference plane 7, at which we measure the noise

temperature, is therefore a distance 0.25 mm from the end of the CPW (about

0.225 mm from the tip of the probe), as discussed near the end of section 3.1.

20
Since the resistor is at the same (room) temperature as the line, the .exact

location of the reference plane is not especially important in this

measurement, but in other measurements it is critical. The resistor is in

equilibrium with its surroundings, at room temperature. As discussed above, room temperature may not be exactly "ambient" temperature, but it is close

(within about 2 K) . Measurement of the resistor's noise temperature

constitutes a (not very demanding) test of the measurement methods and system.

It also provides a test of whether outside radiation is entering the system.

If the resistor and transmission line are absorbing (nonambient) radiation

from the surrounding environment, then the measured noise temperature will

differ from the room or ambient temperature. Preliminary measurements

indicated that a nearby incandescent lamp could affect the measured noise

temperature. Such obvious local sources were removed, but there were still

the fluorescent room lights, emissions from equipment in the room, and various

external sources — the room is shielded, but not very well.

The second on—wafer source was a noise diode bonded to a short section

of CPW line on a GaAs wafer, with no attenuating circuit to control its

reflection coefficient. The on-wafer configuration is shown in figure 9.

Bias for the diode was supplied through probe 1 from a monitored current

source. The section of CPW to the left of plane 7 is the same as that used in

the calibration kit, and therefore the on-wafer calibration and

characterization of probe 1 is still applicable. Two problems render this

diode source less than ideal. The lack of an attenuator means that its

reflection coefficient will probably not be very well matched to the line or probe and that it may exhibit rather erratic behavior as a function of

frequency. In addition, the noise temperature of the diode is not known by

some independent means . We therefore have no way of checking that the answer

we obtain is correct. Nevertheless, the exercise should provide practice and

may uncover difficulties in handling a source with very high noise

temperature

Because the diode is not a linear device, its reflection coefficient may

depend on the incident power. In measuring its noise temperature, we are interested in its reflection coefficient (TD ) for very low power. We

measured rD for three different values of incident power, including the lowest

21
allowed by our VNA. The power levels from the synthesizer of the VNA were -9

dB, -10 dB, and -11 dB, all relative to 1 mW. The corresponding powers

incident on the diode were roughly 11 dB lower. We found that TD varied

little over the range measured, and was unchanged within measurement accuracy

between the two lowest powers. Consequently, the value at the lowest power

should be valid for the incident powers encountered in the noise temperature

measurement. The noise powers encountered are far smaller than the VNA test

levels. Noise is broadband, but even using a 1 GHz bandwidth the available

powers from sources with noise temperatures of 102 K, 10* K, and 106 K are -88.6 dB, -68.6 dB, and -48.6 dB, all relative to 1 mW.

In order to properly test our ability to measure noise temperature on

wafer, we need on—wafer, nonambient (preferably both high—temperature and lowtemperature) noise sources with known noise temperatures. These are not

available, and so we produced known noise temperatures on wafer by using known

off—wafer noise sources. The configuration is shown in figure 10(a). A check

standard with known noise temperature was connected to probe 2 at plane 9, and

probe 2 was then connected to an on-wafer transmission line at plane 8. The

transmission line was one of those in the calibration kit mentioned in Section

3.1; both the through and the longest line (6.565 mm between planes 7 and 8)

of the kit were used. Since the properties of probe 2 were determined by the

on-wafer calibration, and since the properties of the through and the line are known, we can use eqs (31) and (34) to calculate the noise temperature at

plane 7 on wafer in terms of the known noise temperature at plane 9. The

calculated value can then be compared to the measurement result. We also

connected an ambient source at plane 9, with both the line and the through on

wafer, and measured the resulting noise temperatures at plane 7. The

cryogenic primary standard must remain vertical, and therefore it cannot be

connected directly to plane 9. It was connected by a flexible cable, with the

connection between the cable and standard being labelled as plane 10, as in

figure 10(b). The check standard was also attached at plane 10. For both

cases both the through and the line were used on wafer, and the noise

temperature at plane 7 was calculated and measured in each case. In

measurements with the cable, great care was taken to minimize any movement or flexing of the cable between the time its properties were measured on the VNA

and the time of the measurement of the noise temperatures.

22
To facilitate discussion of the various measurement configurations, we introduce some additional notation. Each configuration will be labeled by the

plane at which the noise temperature was measured and what was connected at

that plane. We will use Cr to denote the cryogenic primary standard, Ck for

the check standard, A for an ambient load, R for the on-wafer resistor, D for

the on-^wafer noise diode, L for the on—wafer calibration—kit line, T for the

on-wafer calibration-kit through, and the respective number for each reference

plane. Thus the measurement of the check standard at port 6 in figure 5 is

referred to as 6Ck; the measurements of the on-wafer diode and resistor are 7D

and 7R respectively; the ambient load connected at plane 9 with the line on wafer is 7L9A; the cryogenic primary standard connected through the cable with

the through on wafer is 7TlOCr; etc.

To summarize, we measured a variety of noise sources, providing a range

of significant tests of our ability to measure noise temperature on wafer.

The direct measurement of the check standard (6Ck) tested the off—wafer

aspects of the system, including the radiometer, the switch assembly, and a portion of the data-analysis software. The on—wafer noise diode measurement

(7D) allowed us to measure an unknown noise source with very high noise

temperature (nearly 106 K) . It tested whether we could get an answer for such

a device , but we do not know what the correct answer is . The three

measurements of ambient loads (7R, 7T9A, and 7L9A) provided a test of our ability to measure a known noise temperature, albeit a rather easy one since

measurement of an ambient load is insensitive to some common errors. Since

the ambient measurements involve three different on-wafer configurations , they

do provide a very good test of whether any (nonambient) outside radiation is

getting into the system. The remaining six noise—temperature measurements are

a good test of our entire system and methods. The two using the cryogenic

primary standard (7T10Cr, 7L10Cr) test our ability to measure low noise

temperatures (about 160 K and 180 K) on wafer, and the four using the check

standard (7T9Ck, 7L9Ck, 7Tl0Ck, 7Ll0Ck) test our ability to measure high

temperatures (about 5000 K to 7600 K) . The fact that we measure the check

standard both when it is connected directly to probe 2 at plane 9 and when it

is connected to the cable at plane 10 enables us to isolate any problems

introduced by the flexible cable.

23
3.3 Results

Measurements were made from 7 . 8 GHz to 8.2 GHz in increments of . 1 GHz

.

These frequencies were chosen in order to compare to earlier, preliminary

measurements. We intend to expand the frequency range in future tests. The

first test performed was the direct measurement of the noise temperature of

the check standard (6Ck) . The results of these measurements were compared to

results of previous measurements of the same device using the present system

and to an earlier measurement using the traditional NIST radiometer which is

used for official calibrations. The agreement was excellent. The present

result at 8.0 GHz differs from the calibration-system result by 4 K, out of

9238 K (0.04 percent). The two sets of measurements on the present system

differed by at most 0.15 percent. We conclude that the radiometer is

functioning properly for off—wafer measurements and that its repeatability is

very good.

The results of the measurements on the ambient loads (7R, 7T9A, and

7L9A) are shown in figure 11. The agreement between the measured noise

temperature and the ambient temperature is very good in all three cases . The

fractional difference between measured and ambient temperatures,

^ _ 2 T(measured) - T(predicted) , 35) T {measured) + T {predicted)

is plotted in figure 12, where the predicted noise temperature is the ambient

temperature in this case. The measured noise temperature is consistently

about 0.5 percent (1.5 K) above the ambient temperature. As discussed in

section 3.1, even this small discrepancy can be attributed to the fact that

the sources being measured are at "room" rather than "ambient" temperature,

and the two can differ by as much as 2 K. We therefore conclude that our system and methods correctly measure on-wafer noise temperatures near ambient.

Because the three ambient loads measured correspond to three different

configurations on wafer (resistor, through, line), the fact that none of the

three exhibits signs of external radiation effects is a strong indication that

such effects are absent in our on—wafer noise measurements.

24
Figure 13 contains the results for the two sets of measurements for

which the high—temperature check standard was connected to probe 2 at plane 9.

For both the through (7T9Ck) and the line (7L9Ck) on wafer, the noise

temperature was measured at plane 7. The predicted results in figure 13 are

the noise temperatures at plane 7 calculated from the known noise temperature

of the check standard and the measured properties of probe 2 (or probe 2 plus

line) using eqs (31) and (34). The agreement between measured and predicted

noise temperatures is good in both cases, around 0.5 percent for 7T9Ck and

around 1 percent for 7L9Ck. The largest difference, at 8 . 2 GHz in 7L9Ck, is

110 K (1.75 percent). To put this in perspective, a typical expanded (2a)

uncertainty in our coaxial noise-temperature calibrations is 1.0 percent to

1.5 percent. (The uncertainty analysis for the present experiment is

presented in the next subsection.) Results for the measurements with the

check standard connected to probe 2 through a cable (7T10Ck and 7L10Ck) are presented in figure 14. The agreement between measurement and predicted noise

temperatures is good for 7L10Ck (around 1.5 percent) but somewhat worse for

7Tl0Ck (around 2.2 percent). The results for the cryogenic standard, attached

through a cable to probe 2 (7Tl0Cr and 7L10Cr) are presented in figure 15.

Agreement between measurement and prediction is again good, around 1 percent

for most frequencies, though it is about 2 percent and 2.5 percent at 8 . 2 GHz.

The comparison of measurement and prediction for nonambient, on-wafer noise

temperatures is summarized in figure 16, which plots the A of eq (35) for each

of the six known nonambient temperatures we measured. Most of the points lie

in the |A| < 2 percent range, with a few between 2.0 percent and 2.6 percent.

Finally, in figure 17, we show the noise temperature measured for the

on—wafer noise diode. As we discussed above, we do not know the diode's noise

temperature from other information. The measurement indicates that the noise

temperature of the diode is very high, approaching 106 K. In order not to

saturate the radiometer, an attenuator was introduced in front of it, between

plane 2 and the first isolator. This in turn lowered the power from the

cryogenic standard unacceptably , and so the previously measured hightemperature check standard was used as the nonambient standard in this

measurement

.

25
3.4 Uncertainty Analysis and Checks

To assess the significance of the differences between measurement and

prediction in the preceding section, we need to estimate the uncertainties in

both the measured and the predicted values. We must also consider the

correlation between possible errors in measurement and prediction. The

comparison we .performed magnifies some potential errors and is insensitive to

others. We will first present an uncertainty analysis for our measurements of

noise temperature on wafer. The analysis will hardly be definitive, but will

be sufficient to judge the significance of the observed differences between

experiment and theory. We will then consider uncertainties in the predictions

and in the A defined by eq (35).

The noise temperature of the DUT is calculated from eq (28) , with

(ATx ) is neglected,

Tx

= Ta + T - Ta ) °' s °

3 3 3 ^,*<*07

<30

This form assumes a perfect isolator as well as a linear radiometer.

Uncertainties in Tx arise due to uncertainties in the determination of the

quantities appearing on the right side of eq (36) and due to departures from

perfect isolation and linearity. For the present analysis, we will be

concerned with the uncertainties arising in a single measurement of Tx. In

keeping with the notation of the ISO [26,27], we will use uTx to denote the

standard uncertainty in the measurement of Tx. We shall deal primarily with

type-B uncertainties; type-A uncertainties arise in measurement of the powers,

but enough samples are taken that these uncertainties are negligible in the

present experiment. We use Wz to denote the fractional standard uncertainty

in the parameter z, for example, Wq^ = uTCry/^Cry

The uncertainty in the noise temperature of the cryogenic standard

contributes to the uncertainty in Tx as

UT (Cry)

1 - _£ r,Cry ' (37)

26
The fractional uncertainty in the GPC—7 cryogenic standard which was used in

all the measurements (except of the on—wafer diode) is about 1 percent at 8 GHz. This results in an uncertainty of roughly 0.35 percent in Tx for Tx much

larger than Ta.

The contribution of the uncertainty in the ambient standard temperature

to the uncertainty in the DUT noise temperature is given by

UT {Amb)

TX

TX X

- TJ 8

T - T

-? rr

. (38)

* X

The uncertainty in the ambient temperature is uTa = 0.1 K. Since the ambient

temperature is kept at 296 K, this results in £^a = 0.034 percent. The type-A

uncertainty in the ambient temperature measurement was evaluated in one of the

tests. It was found to be 0.015 K, or 0.005 percent, and was therefore

assumed negligible in all the measurements. The ambient-temperature

contribution to uTx is negligible for most values of Tx , but it survives near

Tx = Ta , where the other uncertainties vanish.

The uncertainty in the power ratio measurements (Ys and Yx ) was evaluated in reference [28], where it was found to be negligible. A similar

analysis in the present case results in ^ < 0.05 percent, which can be safely

neglected. The linearity of the detection unit of the radiometer was discussed in subsection 3.1. The powers involved in the present measurements

are less than 2.5 mW. Any error due to radiometer nonlinearity for these

powers is negligible. The uncertainty due to finite (40 dB) isolation can be

evaluated following the calculation in reference [13] , with appropriate

changes for 40 dB isolation rather than the 50 dB assumed there. This leads

to an uncertainty in Tx of about 0.1 percent for small values of Tx and much

less for large values of Tx

. We neglect this contribution to uTx .

The final contribution to uTx is due to uncertainties in the measurement

of the various S-parameters and reflection coefficients which appear in the

expression for (^o,s a 03) / ^o,x a 07^ > e(l (33). If we use K to denote this

ratio of Ma's, and compute the variation in S due to small variations in the

S-parameters and reflection coefficients, we obtain

27
= 2 5|521 (3-0)| 6|521 (7-0)

|521 (3-0)| " |521 (7-0)|

Dp (39)

Dr is a rather lengthy expression containing variations in the reflection

coefficients. Each of the terms in Dr is of the form gx\ri T^\x^., where g is

of order 1, Tt and Tj are reflection coefficients each of whose magnitudes is

of order 0.1, and ^ is the fractional uncertainty in measuring either the

magnitude or phase of a reflection coefficient. For typical values of ^, Dr is less than about 0.1 percent and can be neglected, so that

59i m

/ a|s21 (3-o)| a|g21 (7-o)h

*

'

I |521 (3-0)| |521 (7-0)| ' (40)

which in turn leads to

« 2 1- —1

\

"1*21 (3-0) | |S21 (3-0)| : Ul-g2 l(7-0)l

|S21 (7-0)| 2 (41)

The magnitude of S21 (3-0) is determined by a coaxial VNA measurement. From

the manufacturer's specifications, the fractional uncertainty in this

measurement is

, U'^ (3 -

0)

', « 0.19%

|521 (3-0)|

(42)

S(7-0) is formed by cascading 5(7-2) and S(2-0) . The uncertainty which

results is

U|*2l(7-0)|

|52 i (7-0) |

"|521 (7-2)| U|S21 (2-0)|

|521 (7-2)| 2 |521 (2-0)| : (43)

The fractional uncertainty in the magnitude of S2 i(2-0) is the same as that

for S21 (3-0) , 0.19 percent. The uncertainty in the magnitude of S2 i(7-2) is

somewhat more problematic. Repeatability of such measurements was checked

both with the Verify feature of the MultiCal program and by comparing results

of repeat measurements. This led to a type-A uncertainty of 0.2 percent in

28
the magnitude of S21 (7-2) . The type-B uncertainty has two components, one due

to the VNA measurements and the other due to the on—wafer calibration. Using

the manufacturer's specifications for the VNA uncertainty and typical values

for S21 (7-2) and S21 (9-8) , we obtain a fractional uncertainty in |S21 (7-2)| due

to the VNA measurements of 0.15 percent, The uncertainty due to the on-wafer

calibration (imperfect calibration standards, etc.) is difficult to assess. We estimate that it is double the uncertainty in the VNA measurements and use u(o-w cal) ~ 0.003, u(o-w cal)/|S21 (7-2) | =0.4 percent. Combining the

various (independent) components of the uncertainty, we obtain for the

fractional uncertainty in |521 (7-2)|,

I J

521 ' 7

"211

, * VO-OC^ + O.OOIS 2 + 0.00402 = 0.0047 . (44)

\S21 (7 2) |

Equation (43) then yields a fractional uncertainty in |S21 (7-0)| of 0.51

percent, and eq (41) for the fractional uncertainty in the ratio of mismatch

factors and q's becomes

« 0.011

x

TX

1 - _£

TM x (45)

Our estimate for the standard uncertainty in the measurement of Tx is

then

TX ~\

Utx

( Cry) Utx {Amb) u|x

( Bt)

Tx Tx Tx

(46)

with the individual components given by eqs (37), (38), and (45). This result

is plotted as a function of DUT noise temperature in figure 18, with the

fractional uncertainty given in figure 18(a) and the standard uncertainty

given in figure 18(b). For DUT noise temperatures down to about 150 K, the

uncertainty is below about 1.1 percent. For comparison, a typical standard

uncertainty for our calibrations of coaxial noise sources is about 0.6 percent

or 0.7 percent at this frequency. The dominant component of the uncertainty

is uTx (R) , which by itself accounts for an uncertainty of about 1 percent in

the DUT noise temperature (for large Tx ) . It is unfortunate that this dominant

component is also the one which is most approximate, due to our ignorance of

29
the uncertainty in the on-wafer calibration. Our uncertainty estimate is

therefore quite tentative at this time, although we do have evidence that it

is not too wrong, as discussed below.

In comparing measured to predicted on—wafer noise temperatures, we also

must take into account the uncertainty in the predictions. The predicted

noise temperature is calculated from eq (31) , where plane 9 is replaced by

plane 10 when the cable is used. The two principal sources of uncertainty are

in T9 , the noise temperature of the known source which is connected at plane 9

(or 10), and in a79 , the available power ratio between planes 7 and 9 (or 10).

Denoting uncertainties due to these two sources as uTx (T9 ) and uTx (a) , we have

UT (a) T 1--2 u|S21 (9-7)| m

|S21 (9 -7)

1 - _£ xO.9% , (47)

and

UT_(Tq ) 1- (l-a7 ,)-?

"i 7

Un i-(i-a79 )-i

"i 7 x0.6% (48)

Combining the two in quadrature leads to a fractional uncertainty in the

calculated value of T7 of about . 8 percent for the low values of T7 and about

1.1 percent for large T7

.

These numbers are not directly applicable to the difference between

measurement and prediction, however, because the uncertainties in measured and

predicted noise temperatures are highly correlated. In the case of uTx (Tg) , the correlation is due to the fact that the known noise temperature of the source which is attached at plane 9 was determined by comparing it to the same primary standard which is being used in the present measurement. In computing

A from eq (35) , any error in the measurement of the noise temperature of the source at plane 9 cancels insofar as it is repeatable. Only the nonrepeatable

part of the comparison of the two sources contributes to A, and that is small.

For the contribution of the uncertainty in a79 , there is the question of

correlation between uncertainties in a7g and in a27 , or between uncertainties

in |S21 (7-9)| and those in |S2 i(2-7)|. In the characterization of the probes, an error could be made in measuring the product of |S21 (7-9)| and |521 (2-7)| or

30
in separating the product into the two factors. An uncertainty in the product

leads to a positive correlation between the two uncertainties and a negative

correlation between the uncertainties in the measured and predicted values for

T-j. Such uncertainties would then add linearly in the uncertainty in A, which

measures the difference between measured and predicted values. Conversely,

any error in separating the product of |S21 (7-9)| and |S21 (2—7) | into the two

factors would cancel in forming A. Given our relative ignorance of the

uncertainties the on-wafer calibration, we cannot make an informed judgement

regarding the correlation.

To summarize the uncertainty results, the uncertainty in the measured

noise temperatures on wafer is about 0.9 percent for the two low noise

temperatures and about 1.1 percent for the high noise temperatures. The

relevant part of the uncertainty in the predictions is about 0.8 percent for

the two low noise temperatures and about 0.9 percent for high noise

temperature. The uncertainties in measurement and prediction may be highly

correlated, and therefore the uncertainty in A can be as large as about 1.7

percent for low noise temperature and about 2 percent for high noise

temperature. All these uncertainties correspond approximately to la. For a

95 percent confidence level (2a), we would double all the values. We return

then to the discrepancies between measurement and theory, the A plotted in

figure 16. For the high noise temperatures (7T9Ck, 7L9Ck, 7Tl0Ck, and

7L10Ck) , |A| < 2.5 percent. This is consistent with the estimated

uncertainties. For the low temperatures, |A| < 2.1 percent except for one

point, where |A| = 2.56 percent. This also is consistent with the estimated

uncertainties , provided that the uncertainties in measurement and prediction

are correlated. We conclude that our measurement results agree with the

predictions as well as should be expected. We also regard the agreement as an indication that our estimate of the uncertainty is not grossly wrong.

4. SUMMARY AND DISCUSSION

The core of this paper comprised theoretical and experimental sections.

The theoretical section presented the theoretical background and developed the

formalism necessary for the analysis of noise-temperature measurements on

wafer. The relevant equations were derived, including the radiometer equation

31
and expressions for the mismatch factors and available-power ratios. In

general these equations differ from the usual ones due to the presence of

significant loss in the on-wafer transmission lines. The equations can be

transformed into the traditional forms at the expense of using transformed

("pseudo-wave") reflection coefficients and S-parameters . The software we used for our on-wafer measurements [21] provided these transformed quantities,

and consequently we used the transformed versions of the equations. The

general versions of all equations were also presented, however.

The experimental portion of the paper reported a series of measurements

performed to test our ability to accurately measure noise temperature on

wafer. The experimental setup was presented, and the procedures were

outlined. Several different configurations were used to produce known onwafer noise temperatures, which were then measured and compared to the

predicted values. Different ambient sources on wafer allowed us to test for

the effect of outside radiation. Several measurements through a flexible

cable permitted us to test for its effects as well. An on-wafer noise diode

with very high noise temperature (nearly 106 K) was also measured. The

uncertainties in the noise-temperature measurements were estimated.

The tests confirm both that we can measure noise temperature on wafer

and that we can produce known on-wafer noise temperatures using off—wafer

sources. Measurements of ambient loads agreed with room temperature to within

about 0.5 percent, which is less than the uncertainty in the room temperature.

Any effect of outside radiation entering the system was negligible. Results

for nonambient noise temperatures agreed with predictions to within the

estimated expanded (k = 2) uncertainty. The estimate of the standard

uncertainty was 1.1 percent and below for noise temperatures above about 150

K. For lower noise temperatures, the fractional uncertainty increased, but

the standard uncertainty remained below 3.5 K. Performing measurements

through a flexible cable did not degrade the accuracy noticeably, provided

that great care was taken to minimize movement of the cable during the course

of the experiment. All measurements on wafer were performed using old probes

with appreciable loss (about 1.5 dB) . Future measurements will use newer,

less lossy probes, resulting in a slight decrease in the uncertainty.

32
While successful, the tests did have limitations. Only a narrow band of

frequencies was measured (7.8 GHz to 8.2 GHz). In addition, our comparison of

measured and predicted results was insensitive to certain errors in the

measurement of the S—parameters of the probes. The tests were sensitive to

the product of the available—power ratios of the two probes, but not to the

available-power ratio of either probe individually. These points constitute

significant shortcomings of the set of tests described in this paper,

shortcomings which will be remedied in future experiments.

I am very grateful to R. Billinger and J. Rice for performing the

measurements. I also thank D. F. Wait for valuable comments and assistance in

designing the experiment, D. Williams and D. Walker for extensive help in

using MultiCal for on-wafer measurements, and L. Dunleavy of the University of

South Florida for comments and suggestions on the manuscript. This work was supported in part by the NIST/Industrial MMIC Consortium.

5. REFERENCES

[1] Gupta, M.S.; Pitzalis, 0.; Rosenbaum, S.E.; Greiling, P.T. Microwave

noise characterization of GaAs MESFET's: Evaluation by on—wafer lowfrequency output of noise current measurement. IEEE Trans. Microwave

Theory Tech. MTT-35(12): 1208-1218; 1987 December.

[2] Davidson, A.C.; Leake, B.W. ; Strid, E. Accuracy improvements in

microwave noise parameter measurements. IEEE Trans. Microwave Theory

Tech. MTT-37(12): 1973-1978; 1989 December.

[3] Adamian,' V. 2-26.5 GHz on-wafer noise and S-parameter measurements

using a solid state tuner. 34th ARFTG Conference Digest; Ft. Lauderdale,

FL, 1989. 33-40.

[4] Dunleavy, L. A Ka-band on-wafer s-parameter and noise figure

measurement system. 34th ARFTG Conference Digest; Ft. Lauderdale, FL;

1989. 127-137.

33
[5] Hughes, B. ; Tasker, P. Improvements to on—wafer noise parameter

measurements. 36th ARFTG Conference Digest; Monterrey, CA; 1990. 16-25.

[6] Woodin, C; Wandrei, D. ; Adamian, V. Accuracy improvements to on-wafer

amplifier noise figure measurements. 38th ARFTG Conference Digest; San

Diego, CA; 1991, 129-138.

[7] Dambrine, G. ; Happy, H. ; Danneville, F. ; Gappy, A. A new method for on wafer noise measurement. IEEE Trans. Microwave Theory Tech. MTT-41(3):

375-381; 1993 March.

[8] Caddemi , A.; Sannino, M. Comparison between complete and simplified

methods for determining the microwave noise parameters of HEMTs . 43th

ARFTG Conference Digest; San Diego, CA; 1994. 121-126.

Fenton, J.R. Noise parameter data comparison while varying the on-wafer

S—parameter calibration technique. 44th ARFTG Conference Digest;

Boulder, CO; 1994. 89-97.

[10] Boudiaf , A. ; Dubon-Chevallier , C. ; Pasquet, D. Verification of on-wafer

noise parameter measurements. IEEE Trans. Instrum. Meas . IM-44(2) : 332-

335; 1995 April.

[11] Boudiaf, A.; Scavennec, A. Experimental investigation of on-wafer noise

parameter measurement accuracy. 1996 IEEE MTT-S International Microwave

Symposium Digest, Vol. 3; San Francisco, CA; 1996. 1277-1280.

[12] Miller, C.K.S.; Daywitt, W.C; Arthur, M.G. Noise standards,

measurements, and receiver noise definitions. Proc. IEEE, 55(6): 865-

877; 1967 June.

[13] Daywitt, W.C. Radiometer equation and analysis of systematic errors for

the NIST automated radiometers. Natl. Inst. Stand. Technol. Tech. Note

1327; 1989 March.

34
[14] Wait, D.F.; Randa, J. Amplifier noise measurements at NIST. IEEE

Trans. Instrum. Meas . , to be published; 1997 April.

[15] Marks, R. ; Williams, D. A general waveguide circuit theory. J. Res.

Natl. Inst. Stand. Technol. 97(5): 533-562; 1992 September-October.

[16] Collin, R.E. Foundations for Microwave Engineering. New York: McGrawHill; 1992. Ch. 3, 4.

[17] Ramo, S.; Whinnery, J.R.; Van Duzer, T. Fields and Waves in

Communications Electronics. New York: Wiley; 1984. Ch. 5, 8.

[18] Marcuvitz, N. Waveguide Handbook. New York: McGraw-Hill; 1951; and

London: Peter Peregrinus; 1986. Ch. 1.

[19] Jordan, E. ; Balmain, K. Electromagnetic Waves and Radiating Systems,

2nd ed. Englewood Cliffs, NJ: Prentice Hall; 1968. Ch. 7.08.

[20] Wait, D.F. Thermal noise from a passive linear multiport. IEEE Trans.

Microwave Theory Tech. MTT-16(9): 687-691; 1968 September.

[21] Marks, R. ; Williams, D. NIST/Industrial MMIC Consortium Software

Manuals. 1992 February.

[22] Marks, R. A multiline method of network analyzer calibration. IEEE

Trans. Microwave Theory Tech. MTT-39(7): 1205-1215; 1991 July.

[23] Marks, R. ; Williams, D. Characteristic impedance determination using

propagation constant measurement. IEEE Microwave & Guided Wave Lett.

1(6): 141-143; 1991 June.

[24] Daywitt, W.C. A coaxial noise standard for the 1 GHz to 12.4 GHz

frequency range. Nat. Bur. Stands. (U.S.) Tech. Note 1074; 1984 March.

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

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

35
[26] ISO. Guide to the Expression of Uncertainty in Measurement.

International Organization for Standardization; Geneva, Switzerland;

1993.

[27] 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.

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

Radio Science Meeting Digest; Boulder, CO; 1995. 39.

36
APPENDIX A

It is instructive, though tedious, to derive eq (25) explicitly from the

travelling wave amplitudes, S-parameters , and reflection coefficients. To do

so we use eq (13) for the available power at plane 2, using BGS from eq (17)

for the amplitude of the generator wave. We obtain

i avail >21 i-rasn

VfsV^-^A

1

-

'21 rG5 | 2 -2J/r?rG5 tanC2]cos2 C2

'

(Al)

where it is understood that we wish to average the entire expression over

time. When the expression involving the wave amplitudes is expanded and

averaged over time, it yields terms proportional to |jDg| 2

, |-Oi| 2/ 1^2 | 2

' an<* Re(B1 £2*) By using eqs (14), (22), and (23), we can rewrite the term

proportional to \BG \ 2 as

•^21 1-Wi

<I4|

2

> [1 - |rG5 | 2 - 2 lmT0S tanC2

] cos2 C; (A2)

= a

i avail

21^1 = a21 kB BTG

.

That accounts for the first term in eq (25). That's the easy part. The

remaining piece requires more work. First expand the remaining part of the

numerator of eq (Al) , and use eqs (18) , (19) , and (20) to eliminate the wave

amplitudes

,

37
r<A

i -raG-'ll s

s21

\ ro\

2

[ (1 " \Su I 2 " 2 tan d J/nS^) cos2 ^ - |S12 1 2 cos2 C 2] PA

+ ^ iJ^

1112

[ (1 " \ S"\ 2 - 2tanC2 Jin522 ) cos2 C 2 - |S21 | 2 cos2 ^] PA

- 2 Re

rG a-r s,,)*

[fl£ (5ii + J

. tanCi) cos2Ci

'21

+ 512 (52

*2 -jtanC2

) cos2 £2

] PA ,

(A3)

pa

s MrA

.

By regrouping terms proportional to cos2 ^ and cos 2 f 2 , w® get

'21 1-IVSu

/ rG4 + x

"J^

Sl1 4

2 \ = [x1 cos2 c1 +x2 cos2 c2

] pa , (A4)

where

*i = |52 i |rG | 2 [1 - \S1X \ 2 -2tanCi ImSlx ] li-r^j2 - 1

-2fle

rg (S1:L + jtanCx

)

(A5)

*2 =

I 1 1 G'^lll

-2i?e

521 512 rG (^.^t^^j l-^Sn

(A6)

With a little effort and patience, these can be put in the form

38
X, = - l^21 ! 2 [1 - |TJ 2 -2tanC, lmrG ] , (A7)

X2 = [1- |rGS | 2 -2tanC2 J/nrG5 ] , (A8)

with rGS still given by eq (17). Referring back to eq (Al) , we can use eqs

(A2) and (A4) to write

P2aVaU = ^iPr*11 + U2 CQS2 C2 ^1 COS2 C 1 ] [1 - |rGS | 2 - 2 J/nrG5 tan C2 ] cos2 C 2

Substituting eqs (A7) and (A8) into eq (A9) then leads to the desired result,

P

avail = a 21 praii + [l - o21 ] icB B rA

. (Aio)

The derivation of eq (AIO) or (25) is interesting for several reasons. For one thing, it constitutes a nice check that we know what we are doing and

that the expressions we have derived for attenuation, wave amplitudes, etc. are at least consistent. It also provides an explicit, rather general, proof

of eq (AIO) and eq (25), without any assumptions about impedance matching, S 12 — S2 i, etc. Finally, it verifies that the correlation term KD-^ jD2

*) is properly

included in the expression for P2 avail in terms of a, eq (AIO).

APPENDIX B

B.l Some Pseudo-Wave Algebra

Before tackling the pseudo—wave noise equations, it is useful to review

some of the basic algebra of pseudo-waves [15]. As a matter of notation,

primes will be used to indicate pseudo-wave quantities in this appendix. The

pseudo-wave amplitudes, a' and b', are obtained from the travelling-wave

amplitudes, a and b, by the transformation

(Bl)

39
with

Q= 4

1

2 Z

1 ReZ'

1 + — 1-.

z'

1 +

(B2)

and where Z is the modal impedance of the travelling waves and Z' is the

pseudo—wave reference impedance. Travelling waves at a given reference plane

are labelled by a or b according to their direction of motion, or whether they

are input or output. Pseudo-waves do not have a single direction of

propagation, and so when we need some way of referring to the two components

of the vector in eq (Bl) we shall refer to them as either type—1 or type—

2

pseudo-wave amplitudes (or pseudo-waves) , according to whether they transform

like the top or bottom component of the vector.

The pseudo-wave reflection coefficient is defined by

V = »-. (B3)

We can derive the relationship between V and the travelling-wave reflection

coefficient V by using b = Fa in eq (Bl) , and then forming T' from eq (B3)

.

The result is

1 + yr

' (B4)

with 7 = (Z -Z ' ) / (Z +Z ' ) . The travelling-wave relation a = TGb + £G generates

a corresponding pseudo-wave equation,

= T>b> + £' (B5)

where £'

G = N(l+Z'/Z ) £c and TG

' is related to TG by eq (B4) . This can be

seen by substituting a = TGb + BG in eq (Bl) and solving for a'. Combining

eqs (B3) and (B5) yields the expression for a' in terms of BG ,

40
= s' M + ^

& W &

a' = 4-7 . (B6)

where rL

' is the pseudo-wave reflection coefficient of whatever is to the

right of the reference plane

.

Type—1 and type—2 pseudo—waves of a two—port between reference planes 1

and 2 are related by the pseudo-wave scattering matrix,

(B7)

where Blt B2 are the generator pseudo-wave amplitudes of the two-port. The

pseudo—wave S—parameters and the generator pseudo—waves can be related to the

travelling—wave S-parameters , but we will not need to use those relationships.

B.2 Power and Noise Equations

We can now work on the power and noise equations for pseudo—waves

.

The problem is as follows. Given that the travelling-wave equations derived

in the text for measuring noise on wafer are valid, show that those same equations hold for pseudo—waves , provided that the pseudo-wave reflection

coefficients and S-parameters are used and that the phase of the reference

impedance is used in place of f . This amounts to proving the invariance of

the on—wafer noise—temperature equations under pseudo—wave transformations.

The equations of interest are virtually all the equations in subsections 2.2

through 2.4. Of these, the key equations are those for delivered power and

available power, since equations for mismatch factors, available power ratios,

and the radiometer equation all follow from the power expressions.

As in the travelling-wave case, we consider only reference planes at

which only a single mode (in each "direction") is present. The pseudo-wave

equation for delivered power at some reference plane [15] is given by

P

dei =

| a '|2[i- |r/|2-2 Xmlv tanC/

] , ( B8 )

41
where $*' is the phase of Z' . This is the same form as the first part of eq

(11) for the delivered power in terms of travelling-waves. To obtain the

pseudo-wave version of the second part of eq (11) , we simply use eq (B6) in eq

(B8) , which yields

\£'\ 2 pdei = ' gj [i - jr'l 2 - 2 tanC7 ImTn . (B9)

Thus eq (11) for delivered power is the general form for pseudo-waves,

provided that pseudo-wave amplitudes, reflection coefficients, and reference

impedance are used.

The expression for the available power is obtained from eq (B9) by using

the (allowable) value of T' which maximizes p

del

,

paVaU = 1 w

g|2

wi2 I 1 " |r^t|2 " 2 tanCx JiBl^J . (BIO)

This is the same form as the equation for travelling waves, but that fact is

not really significant since we have not yet given an expression for i pt •

To prove that the expression for available power is invariant under pseudowave transformations we must show that the expression for ^opt is invariant.

This is done by taking the travelling-wave equation for Topt ,

_ r*-jtanC

1 - jrG tanC

and transforming it according to eq (B4) to obtain i pt » ^-T^fe- (B12)

With some tedious algebra (too boring even for an appendix) , we can then show

that

I^ - ^iTi (B13)

1-jT^tanC7

42
This is the same form as eq (Bll) or eq (12) , and thus the equation for Topt

is invariant. As in the travelling-wave case, we can then use eq (B13) in eq

(BIO) to get

\£'\ 2 o avail = _J_ GJ (B14)

[l -

ll^l

2 - 2 Hut's tan {] cos2 C'

'

which is the same form as eq (13) for travelling waves. Thus the equations

for both delivered and available power, derived for travelling waves, are valid for pseudo-waves as well.

The equations for delivered and available power, plus the algebraic

relations of section 7.1 above, are all that is needed to derive the pseudowave versions of eqs (14) through (32) of the main text. The same steps are followed as for the travelling—wave development, and since the underlying

equations all have the same form, so do the derived equations. As an example,

if we set the available power, eq (B14) , equal to kB BT, we obtain the equation

for the generator wave amplitude,

<|££|

2

> = kB BT[l-\T/G \ 2 -2 ImY,G tan $] cos2 C', (B16)

which is the same form as the travelling-wave equation, eq (14) . All other

equations are obtained by following the same steps as the travelling-wave

development.

Therefore, the power and noise equations derived for travelling waves in

the main text are valid for pseudo-waves as well, provided that the pseudowave reflection coefficients and S-parameters are used and that the pseudowave reference impedance is used in place of the characteristic impedance of

the mode.

43
ba

: a

a

Figure 1. Lossy line connecting generator and load.

Subscripts refer to mode.

1

G —i S —;— L

b1

a1 > <:

a bFigure 2. Two-port between generator and load.

Subscripts refer to reference plane,

44
Figure 3. Basic setup for measurement of on-wafer noise source

1 O-h

19

Amb —I—

o

I 3 —° /

I 2 /

I Std -> I Rad

I

Known

Source Pr2 Pr1

\

\! !/

/

i LorT I

7

Figure 4. Basic setup for measurements of known on-wafer noise

temperatures from off-wafer standards.

45
Figure 5. Configuration for measurement of on-wafer noise temperature,

level control

Plane

output

oI 1 I 0.01-26 GHz^t

directional detector

40 dB /N

2

n.c. 20 dB

12.4 GHz LPF

55 dB rejection >out

Internal Ambient

30 dB Gain

1 .0 dB Noise Figure

Input

Figure 6. Detail of radiometer,

46
ex3

•uVw

•uc

CD

<D

>-i 3W

COd>eOa3

<uno

i—i u

<uu3

60

•H

47
48
< > 0.25 mm i

Figure 9. On-wafer noise diode (shaded circle) bonded

to coplanar waveguide

.

49
1

1

Amb —I—

I 3 —° /

I 2 /

I Std > I Rad

I

Chk or Amb Pr2 Pr1

1

9 \i !/

1

e

LorT I

7

Figure 10(a). Configuration for producing known noise temperature on wafer.

Figure 10(b) Alternate configuration for producing known noise

temperature on wafer. Pr2' consists of Pr2 plus a length of

flexible cable.

50
350 —i

300 —

*

250 —

I

200 —

150

7.5

(5 i) A (ft 9

+ Measured

O Ambient

i r

8.0

f (GHz)

1

1 1

1 8.5

Figure 11(a). On-wafer noise temperature for configuration using on-wafer

room-temperature resistor (7R)

.

350 —i

300 —

250

200 —

150

(5 A A & tib

+ Measured

O Ambient

1 1 1 1

1 r

1 1 1

1 7.5 8.0 8.5

f (GHz)

Figure 11(b). On-wafer noise temperature for configuration using ambient

source, on-wafer through (7T9A).

51
350 —

,

300

*

250 —

200 —

150

® 9 ® * *

+ Measured

O Ambient

T r

8.5

1 1 1 —

1

1

1 F—

7.5 8.0

f(GHz)

Figure 11(c). On-wafer noise temperature for configuration using ambient

source, line on wafer (7L9A)

.

0.03 —i

0.02 —

0.01 —

< 0.00

-0.01 — -

-0.02 —

-0.03

o

O 7R

7T9A

O 7L9A

i 1 r

7.5 8.5

1—ih—i—

r

8.0

f(GHz)

Figure 12. Fractional differences between measured and predicted on-wafer

noise temperatures for ambient sources.

52
euuu —

* * * + $

7000 —

+ Measured

O Predicted

6000 —

^nnn ouuu i i i 1

1

i i i i |

7.5 8.0 8.5

f(GHz)

Figure 13(a). On-wafer noise temperature for configuration using

high-temperature source, on—wafer through (7T9Ck).

fVVV —

* J

+

o * *o

6000 —

+ Measured

O Predicted

5000 —

Afinn

i i i i i

i i i i 1

7.5

Figure 13(b)

8.0 8.5

f(GHz)

On-wafer noise temperature for configuration using

high-temperature source, on-wafer line1

. (7L9Ck) .

53
7000

6000 —

5000

4000

+o

+o

+o

+o

+ Measured

O Predicted

7.5 8.0 f(GHz)

8.5

Figure 14(a). On-wafer noise temperature for configuration using hightemperature source, cable, on-wafer through (7T10Ck).

6000

5000 —

*

H

4000 —

3000

+

o +

o

+ Measured

O Predicted

7.5

I 8.0

f(GHz)

8.5

Figure 14(b) . On-wafer noise temperature for configuration using hightemperature source, cable, on—wafer line (7Ll0Ck)

.

54
250 —

i

200 —

150

100 —

50 —

7.5

*

+ Measured

O Predicted

t

1 1 r t r

8.5

1

' r

8.0

f (GHz)

Figure 15(a). On-wafer noise temperature for configuration using

cryogenic source, cable, on-wafer through (7Tl0Cr)

.

Z5V —

200 —

* # * * $

150 —

+ Measured

100 — O Predicted

50 —

i 1 1 1 |

i i i i |

7.5

Figure 15(b)

8.0 8.5

f (GHz)

On—wafer noise temperature for configuration using

cryogenic source, cable, line on wafer (7Ll0Cr)

.

55
0.03 —i

0.02 —

0.01 —

< 0.00

ft &

o

o___o.

o

ft 7T9Ck

A 9 O 7L9Ck

($;

o

° B

ft 7T10Ck

O 7L10Ck

a 7T10Cr

v 7L10Cr

U

-0.01 —

-0.02 —

V

A

-0.03

7.5

V

t 1 1 r —r~

8.0

f(GHz)

t 1 1 r

8.5

Figure 16

12 —

Fractional differences between measured and predicted

on—wafer noise temperatures for nonambient sources.

1.0 —

+ + + +

0.8 —

"b 0.6 H

0.4 —

0.2 —

0.0 t

1 1 r

7.5

Figure 17

1 1 1 T

8.0

f(GHz)

8.5

Measured noise temperature of on-wafer noise diode (7D)

56
0.20 —i

Figure 18(a)

10 —i

9 —

8 —

c

"c5 c

oo

c

D

7 —

6 —

4 —

£ 3

2 —

1 —

10000

T(K)

Fractional uncertainty (la) in on-wafer noise-temperature

measurements

.

1 I I I I I I I I l I I I I l I I I I l I I I I l I I I I I I I I I I I I I I I I I I I I I I I I

| 100 200 300 400 500 600 700 800 900 1000

T(K)

X Figure 18(b). Absolute uncertainty (la) in on-wafer noise-temperature

measurements

.

57

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