** coA%

•"•EAU 0« */ NBS TECHNICAL NOTE 663

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

-
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

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1 11975

lOfi Characterization of a High Frequency

Probe Assembly for Integrated

^

Circuit Measurements

R. L. Jesch

C. A. Hoer

Electromagnetics Division

Institute for Basic Standards

|>| t $» National Bureau of Standards

Boulder, Colorado 80302

*Te&Vuu*eaP A#te ao, (?(*S

/

, °*tm

^o* j

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS. Richard W Roberts Director

Issued April 1975
National Bureau of Standards Technical Note 663

Nat. Bur. Stand. (U.S.), Tech Note 663, 55 pages (April 1975).

CODEN: NBTNAE

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

(Order by SD Catalog No. 013.46:663) $1.10
CONTENTS

Page

1. INTRODUCTION 1

2. ELECTRICAL CHARACTERIZATION OF THE

PROBE ASSEMBLY

4

2 . 1 Background 4

2.2 Probe Assembly Evaluation 5

3. MATRIX SOLUTION FOR CHARACTERIZING

AND EXTRACTING EFFECTS OF THE PROBE

ASSEMBLY

9

3.1 Probe Assembly Characterization 9

3.2 Extraction of the Probe Effects 14

4. RESULTS OF TEST DEVICE MEASUREMENTS 17

5. DATA ANALYSIS 19

5.1 Background 19

5 . 2 General Comments 32

6. CONCLUSIONS 38

7. ACKNOWLEDGMENTS 39

8. REFERENCES 40

APPENDIX I LISTING OF COMPUTER PROGRAM WRITTEN

IN BASIC

iii

41
ILLUSTRATIONS

Figure Page

1 High frequency probe assembly 3

2 Probe assembly for integrated circuit 4

measurements

3 Probe assembly with parasitic element 5

4 Measurement system for probe assembly 6

measurements

5 Method for achieving short circuit 7

6 Circuit representation of probe assembly 9

7 Matrix representation of the probe assembly, 9

where S indicates scattering parameters, T

represents v and i cascading parameters, and

Z represents impedance parameters

8 Defining the voltages and currents used with 10

Ti, T 2 , and T 3 9 Combined cascading matrix T 16

10 Shorted configuration 17

11 Thru-line configuration 18

12 All probe tips shorted Sii magnitude and 24

phase with 95 percent confidence intervals

for four SMA occasions

13 All probe tips shorted S 2 2 magnitude and 25

phase with 95 percent confidence intervals

for four SMA occasions

14 Thru-line Si 2 magnitude and phase with 95 26

percent confidence intervals for four SMA

occasions

15 Thru-line S 2 i magnitude and phase with 95 27

percent confidence intervals for four

SMA occasions

16 All probe tips shorted Sn magnitude and 28

phase standard deviation for four SMA

occasions

17 All probe tips shorted S22 magnitude and 29

phase standard deviation for four SMA

occasions

IV
ILLUSTRATIONS (contd.)

Figure Page

18 Thru-line S12 magnitude and phase standard 30

deviation for four SMA occasions

19 Thru-line S 2 i magnitude and phase standard 31

deviation for four SMA occasions

20 All probe tips shorted measurements 38

21 Thru-line measurements 38

TABLES

Table Page

I Representative S-parameter and parasitic 15

element values obtained from arms A and

B of the probe assembly

II Experimental S-parameters obtained from 20

measurements made on two test devices,

"all probe tips shorted" and "thru-line"

III Experimental S-parameters obtained from 21

measurements made on two test devices,

"all probe tips shorted" and "thru-line"

CHARACTERIZATION OF A HIGH FREQUENCY PROBE

ASSEMBLY FOR INTEGRATED CIRCUIT MEASUREMENTS

A detailed, applications-oriented description of

a measurement technique that characterizes a highfrequency probe assembly for integrated circuit

measurements is given along with the procedure that

extracts the parasitic effects of the probe assembly

from measurements made at the input connectors of

the probe assembly. The scattering parameters of

an integrated-circuit device or transistor can now

be extracted and accurately determined up to 2 GHz

at the wafer stage of assembly. This represents a

significant advance over conventional techniques

that enable only dc parameters to be measured. Measurement results using this technique are given along

with the precision of values obtained as well as the

nature of the measurement bias introduced by the

probe assembly.

KEY WORDS: High frequency probe assembly; integrated

circuit transistors; parasitic element;

S-parameters

1. INTRODUCTION

In response to a request from the Air Force Weapons

Laboratory (AFWL) , the National Bureau of Standards, in 1971,

undertook a project to assist in improving instrumentation

and procedures utilized in measurements associated with the

prediction of the effects of nuclear radiation on semiconductor devices. The work performed during the period January 1971

to August 1972 was reported in AFWL Report AFWL-TR-73-54

"Measurement of Transit Time and Related Transistor Characteristics" [1] .
That report discussed some of the causes of discrepancies in the measurement of transistor transit time. In

addition, a test plan for an interlaboratory comparison of

transistor S-parameter measurements was outlined, special

high-frequency probe assemblies (see fig. 1) for measuring

the characteristics of transistors in integrated-circuit

wafers were described, and techniques were developed for

determining the equivalent circuit representation of these

probe assemblies in the 0.2 to 2 GHz frequency range.

The work performed during the period September 19 7 2 to

July 1973 was reported in NBS Special Publication 400-5,

Semiconductor Measurement Technology: "Measurement of Transistor Scattering Parameters" [2]. This special publication

describes the results of the interlaboratory comparison of

transistor S-parameter measurements and shows how the equivalent circuit of the HF probe assemblies can be characterized

by means of S-parameters using previously-described techniques

The present report covers the work performed from

January 1974 to July 1974. It describes a refined measurement technique that more accurately characterizes the probe

assembly. The mathematical model used in the previous probe

assembly work was not general enough to correctly describe

the probe assembly, particularly at 1 GHz and above. Measurement results, and the technique for extracting the effects

of the probe assembly from measurements made at the input

connectors of the probe assembly, are given. The precision

of the values obtained and the nature of the measurement bias

introduced by the probe assembly are also shown.

-2-
>1

Xi6

CDww

rd

CD .QO

CL

>iOG

CDP

tr

CDu

•H

CD

•H

-3-
2. ELECTRICAL CHARACTERIZATION OF THE PROBE ASSEMBLY

2 . 1 Background

The probe assembly used for making measurements on

integrated circuit devices and transistors is illustrated

in figure 2. To determine the intrinsic characteristics

MINIATURE COAXIAL CONNECTORS

uuni'iun |.i" i ninuiuiiniuiuuiiimimuinmmmnn n)ni)nnuniiil3

Figure 2. Probe assembly for integrated

circuit measurements

of a device or transistor, the parameters of the probe

assembly must be separated from the S-parameters measured at

the miniature coaxial connectors. The parameters of the probe

assembly can be determined by making measurements at the ports

(miniature coaxial connectors) of the probe assembly, having

the probe tips in contact with elements of known impedance

values. Since each arm of the probe assembly network is represented by four (initially unknown) elements, four different

probe tip terminations are required. In effect, the sequence

of measurements yields four equations in the four probeimpedance unknowns, and so the unknowns may be determined

simultaneously. Three of the electrical terminations chosen

-4-
are an open-circuit, a short-circuit, and a resistor of known

value, all of which are small contact pads that are 0.002 inch

(0.05 mm) wide and 0.006 inch (0.15 mm) long deposited on an

alumina substrate. The material used for the resistor is a

layer of tantalum nitride that is chemically etched to achieve

different resistance values which are measured by dc potentiometric (Kelvin) methods. These resistors can be shown to have

values which are, to all practical purposes, independent of

frequency to beyond 2 GHz. The fourth electrical termination

is a large copper short circuit 1.375 inch (3.49 cm) long and

0.875 inch (2.22 cm) wide.

A work station equipped with a microscope is used that

enables the probe assembly and terminations to be moved

relative to each other so that a known termination such

as a short, open or resistance can be placed across the

appropriate probe tips

2.2 Probe Assembly Evaluation

The probe assembly can be represented as two sections

of transmission line with an additional element, y , that

has been added to account for the finite impedance of the

ground probe lead (fig. 3) . This parasitic element and its

measurement effects were summarized in an article in the

GOMAC Digest [3] . The previous work also forms the basis

for the procedures we used in this report to 1) characterize

the probe assembly, and 2) extract the effects of the probe

assembly and determine the S-parameters of the test device

from measurements made at the probe assembly's input

connectors.

port a zy , <y, >y„ <y,, ' <y a P0RT b

Figure 3. Probe assembly with parasitic element

-5-
Figure 4. Measurement system for probe assembly measurements

-6-
To characterize the probe assembly, measurements are

made at ports A and B with known terminations connected at

probe tips, 1, 2 and 3. The probe assembly is connected to

the NBS Automatic Network Analyzer as shown in figure 4.

The inter-connecting cable and adapter are attached to the

SMA connector on the probe assembly, which is the point designated as port A. Port B is left open. Measurements are

made in terms of the magnitude of reflection coefficient and

the phase angle, and are taken at 100 MHz increments starting

with 0.2 and ending at 2 GHz, or at every discrete frequency

of interest for each of the terminations. In order to

achieve a short circuit between probe tip 2 and ground, a large copper plate is used as shown in figure 5. The copper

plate short-circuits all the probe tips to the probe ground

plane. This technique introduces a low impedance between

the copper plate and the bottom of the probe ground plane,

which is small enough to effectively short out the small,

but finite impedance in the ground probe lead.

Probe

Ground Plane

Probes

^~~~ Copper Short Circuit

Figure 5. Method for achieving short circuit

With input at port A and electrical terminations between probe tips 1 and 2, the left side of the probe assembly (fig. 3) is characterized by measuring the admittance at

port A under the following conditions:

-7-
Y > = ya

+ yb

v +

a Yk + Y.

Large Copper

Short Circuit

_Tips 1, 2, & 3]'

(1

[Open Circuit

Tips 1 and 2 ' (2)

Y 3 = yb

( yc V + + Vc— J a y,J + y + y

h

J cJ p

Y.yL P v + £- y c YT +y

Y* = y + y,

Y^+Y + YT yI/p

b

T c YT +y L ^p

I Short Circuit j , [Tips 1 and 2

[Conductance Y

Tips 1 and 2 ]

(3)

(4)

These values can be used to solve for the components

of the equivalent network, y , y, and y . Hence:

y a = V yb • (5)

,W:y (Yi - Y 2 ) (Yi - Y 3 ) '^

yT^^ (6)

(Yi - Y 3 )y

p

Yc Y 3 - Y 2 Yb ' (7)

Yy Y

L

(Y : - Y 2 ) (Y 3 - Yf)

(Yi - Y 3 ) (Y 4 - Y 2 ) (8)

From these admittances, the S-parameters of the probe

assembly can be determined. Similarly, with input at port B

and terminations at probe tips 2 and 3, solutions in terms of

y ol y and y are found.

-8-
3. MATRIX SOLUTION FOR CHARACTERIZING AND EXTRACTING

EFFECTS OF THE PROBE ASSEMBLY

3.1 Probe Assembly Characterization

The mathematics of characterizing the probe assembly

and solving for the S-parameters of test devices or transistors can be simplified by using impedance and cascading

parameters [4] instead of admittance and Pi-network parameters. Figure 6 shows the circuit representation of the

PORT A PORT B

Figure 6. Circuit representation of probe assembly

probe assembly as two cascading matrices with the parasitic

element z = 1/y . Figure 7 is the matrix representation

SorT

T3

or Z3

Ti \

,0

Zr°

3

2 n Port A Po

Z

P o

Figure 7. Matrix representation of the probe assembly, where

S indicates scattering parameters, T represents v

and i cascading parameters, and Z represents

impedance parameters.

-9-
of the probe assembly where each section is represented

by the v and i cascading matrix T,

T = A B

= D

C D

a b

c 1

(9)

_ A

a = D

' b

= B

D

C

C = D

(10)

Let the voltages and currents be defined as indicated in

figure 8. For arm A, the equations are

Vi = Av 7 + Bi' (11)

ii = Cv 2 + Di- (12)

'1 '2 '3 »4 '5 '6

T

t T3 T2

"1 V 2 V 3 ^4 V 5 ^6

ARM A ARM B

Figure 8. Defining the voltages and currents

used with Ti, T 2 , and T 3

If arm A is reciprocal, the complex constants are

related by

AD - BC = 1 (13)

The cascade parameters of each arm can be obtained by

using the same four load conditions in a manner similar to

that used in section 2 to obtain the Pi-network parameters.

-10-
Define

Zi E Ji ; Z 2 = p- . (14)

ll 12

Then (11) and (12) give

. AZ 2 + B n , Zl " CZ 2 + D

(15a)

= aZ 2 + b /tct^n

cZ 2 + 1 * (15b)

For the different load conditions, let Zi be:

Z, - for a short circuit between probe tip #1 and ground,

Z, - for an open circuit between probe tips #1 and #2.

Z, - for a short circuit between probe tips # 1 and #2.

Z, - for a resistive load, Z , between probe tips # 1

and 2

For these four conditions, (15b) gives

Z, = b (16)

c Z, = a (17) lo

cZ, Z + Z, =aZ +b (18) lp p lp p

c Z 1T (Z T + Z J + Z 1T = a (Z T + Z ) + b . (19) 1L L p 1L L p

Using (16) and (17) in (18) gives

c Z, Z + Z, = c Z, Z + Z, , (20) lp p lp lo p Is '

or

c =

J-p ls

Z (Z n - Z, ) p lo lp

(21)

-11-
Using (16) and (17) in (19) gives

c Z, T (Z T + Z ) + Z, T = c Z, (Z T + Z ) + Z, , (22) 1L L p 1L lo L p Is

or

Z 1T " z i 1L Is

(23)

(Z L

+ Z p

} (Z lo" Z 1L>

Equating (21) and (23) to eliminate c,

Z T + Z (Z 1T - Z, ) (Z, - Z, ) L p 1L Is lo lp_ Z (Z n - Z, T ) (Z n - Z, ) p lo 1L lp Is

Z T (Z, T - Z, ) (Z, - Z, ) - (Z, - Z 1T )(Z, - Z, L _ 1L Is lo lp lo 1L lp Is

z (z, - Z, T ) (Z 1 - Z, ) p lo 1L lp Is

which gives

z =z

< z io - z il" 2 1p - Z ls>

P L (Z 1L- Z lp' (Z lo- Z ls> ' ' '

the parasitic element.

With Z known, c is obtained from (21) or (23) . The

p

program in Appendix I uses equation (21) . Then a is obtained from (17) , and b from (16) . Knowing a, b, and c, D can

be obtained from (13) which can be written

D =

x x (25)

VA B C \l a - be

D

' D D

and A, B, and C are obtained from (10) . The cascading

matrix Ti for arm A is now known.

The same process is repeated for arm B to obtain a cascading matrix Q 2 which is not quite the same as T 2 , shown

-12-
in figures 7 and 8, because of the different direction in

which T 2 is determined. Referring to figure 8,

v 5

Li 5 J |_l6j

(26)

whereas if arm B is evaluated from port B, one obtains

Let

Then

i;:H[:;]

N = [' °1

Lo -l J

(27)

(28.

[.::]-»[;:] -a [;:]. (29)

Using (29) in (27) gives

~v 6 " ~v 5 " N = Q 2 N

.^-e. .15 _ (30)

or

N

l Q 2 *N

v 6

is J

v 5 _is^

(31)

Comparing (31) and (26) shows that

T 2 = N

l Q 2

J N (32)

or

T 2 = N

X Q 2 N (33)

-13-
- 1 Since N = N, (33) can be written

T 2 _1 = NQ 2 N (34)

If

Q 2 =

qi l qi

2

q2 1 q2 2 (35)

then

NQ 2 N = T2 -'=[ qi1

"qi2

l

|_-q2 i q2 2 J

(36)

The probe assembly is now completely characterized.

Table I shows representative S-parameter and parasitic

element values that were obtained from the measured data

from arms A and B of Air Force probe assembly S/N 104. This

information is especially useful in analyzing design properties of the probe assembly, by pointing out non-symmetrical

variations between arms and showing resonant frequency points

3.2 Extraction of the Probe Effects

When a test device or transistor is measured with the

probe assembly, this measurement includes Ti, T 2 plus T 3

. This is shown in figure 9 as the combined cascading matrix T:

T = TiT 3 T 2 (37)

which gives

T

-l - i Ti TT 2 (38)

14-
Table I

Representative S-parameter and parasitic element

values obtained from arms A and B

of the probe assembly.

S-Parameters for Arm A

Sll S12 S21 ' S22 FREQ. MAG. ANG MAG. ANG. MAG. ANG. MAG. ANG. 200.000 0.009 -172 .2 0.998 -12.7 0.998 -12.7 025 21 9 300.000 0. 008 174 .8 0.993 -18.9 0.993 -18.9 023 15 6 400. 000 0.003 155 .2 0.994 -24.8 0.994 -24.8 022 ' 17 500.000 0.001 -25 . 0.999 -31.1 0.999 -31.1 022 19 1 600.000 0.007 -41 .9 1.000 -37.8 1.000 -37.8 023 37 2 700. 000 0.014 -49 . 2 0.990 -44.0 0.990 -44.0 027 23 4 800. 000 0.021 -61 . 4 0.991 -49.7 0.991 -49.7 027 2 3 9 900.000 0.026 -67 . 8 0.998 -56.0 0.998 -56.0 027 -1 2 1000.000 0.032 -76 . 7 0.997 -62.8 0.997 -62.8 017 1 2 1100.000 0.039 -83 . 3 0.991 -69.0 0.991 -69.0 011 4 1200. 000 0.047 -87 . 5 0.991 -75.1 0.991 -75.1 004 53 9 1300.000 0.057 -96 .3 0.994 -81.4 0.994 -81.4 012 86 7 1400.000 0.055 -104 . 7 0.993 -87.4 0.993 -87.4 005 135 1 1500.000 0.063 -93 . 6 0.991 -94.2 0.991 -94.2 004 36 7 1600.000 0.087 -124 . 6 0.993 -99. 8 0. 993 -99.8 044 148 5 1700.000 0.092 -130 . 5 0.990 -106.5 0.990 -106.5 057 133 9 1800.000 0.091 -137 .9 0.988 -112.4 0.988 -112.4 0. 065 121 6 1900.000 0.097 -143 .6 0.991 -118.6 0.991 -118.6 070 118 7 2000.000 0. 101 -151 .1 0.994 -125.2 0.994 -125.2 081 115 6

S-Parameters for Arm B

Sll

8

S12 S21 S22 FREQ. MAG. ANG MAG. ANG. MAG. ANG. MAG. ANG.

200. 000 0.009 163. 0.999 -12.7 0.999 -12.7 025 17 7 300.000 0./007 156. 3 0.993 -19.0 0.993 -19.0 022 18 400. 000 0.004 103. 0.995 -24.9 0.995 -24.9 021 16 9 500.000 0.005 16. 2 1.000 -31.3 1.000 -31.3 021 21 7 600.000 0.009 -14. 1 1.000 -38.0 1.000 -38.0 024 39 6 700. 000 0.017 -35. 1 0.991 -44.2 0.991 -44.2 028 25 3 800.000 0.025 -49. 4 0.992 -50.0 0.992 -50.0 027 25 8 900.000 0.029 -55. 7 0.998 -56.3 0.998 -56.3 029 1000.000 0.035 -67. 9 0.998 -63.0 0.998 -63.0 019 5 1100. 00Q 0.044 -75. 2 0.993 -69.3 0.993 -69.3 012 6 3 1200.000 0.052 -81. 0.993 -75.4 0.993 -75.4 007 38 7 1300.000 0.063 -89. 8 0.995 -81.8 0.995 -81.8 012 75 1400. 000 0. 062 -98. 8 0.992 -87.7 0.992 -87.7 002 -27 8 1500.000 0.071 -91. 0.991 -94.8 0.991 -94.8 005 -23 3 1600. 000 0.095 - 121. 4 0.993 -100.3 0.993 -100.3 041 147 9 1700.000 0.100 - 128. 5 0.990 -107.0 0.990 -107.0 055 133 2 1800.000 0.100 - 136. 7 0.988 -113.1 0. 988 -113.1 062 120 6 1900.000 0.106 - 140. 5 0.991 -119.2 0.991 -119.2 067 114 8 2000. 000 0.113 - 148. 4 0.994 -126.0 0. 994 -126.0 077 Hi 1

Averaqe Z P from Arms A & B

FREQ. REAL IM?iGINARY MAGNITUDE PHASE

200.000 0.1489 1 6686 1. 6752 84. 90 300.000 0.2233 2 5174 2. 5273 84. 93 400.000 0.2450 3 1555 3 1650 85. 56 500.000 0.2413 3 8789 3 8864 86. 44 600.000 0.1836 4 6648 4 6648 87. 75 700. 000 0.1570 5 5210 5 5233 88. 37 800.000 0. 2240 6 3835 6 3874 87. 99 900.000 0. 3442 7 0214 7 0299 87. 19 1000.000 0. 3042 7 7741 7 7800 87. 76 1100.000 0.2019 8 5858 8 5881 88. 65 1200.000 0.2982 9 4594 9 4641 88. 19 1300.000 0. 2704 10 1261 10 1297 88. 47 1400.000 0. 2653 11 7516 11 7546 88. 71 1500.000 0.5721 12 8007 12 8135 87. 44 1600.000 0. 2682 12 .1024 12 1054 88. 73 1700.000 0.2271 13 3697 13 3716 89. 03 1800. 000 0. 3076 14 .5672 14 5704 88. 79 1900.000 0.5706 15 1212 15 .1320 87. 84 2000.000 0.4274 15 .8854 15 .8911 88. 46

-15-
PORT A PORT B

Figure 9. Combined cascading matrix T

As shown in figure 7, T3 includes the parameters of the

test device and also the parasitic impedance Z . To extract

the transistor parameters from T 3 , it is best to express

these parameters in terms of impedances;

z t

-

" Zi 1 Zi 2 "|

_ Z 2 1 Z 2 2

J

(39)

The parasitic impedance can be expressed as an impedance matrix whose elements are all z ; P

z z P P

z z p p

(40)

Then

z. = z 3 - z t p

(41)

where Z 3 is the center matrix, T3 , converted to Z parameters,

Z, = A3

1

A3D3- B3C3

D 3 ]

(42)

-16-
and where A 3/ B 3/ C 3 , and D 3 are elements of T 3 . One can then

obtain the S-parameters directly from the impedance matrix

representing the test device or transistor,

Z t _^St

. (43)

A listing of the computer program is given in Appendix I for

calibrating the probe assembly and also for calculating the

S-parameters of a test device or transistor measured with

the calibrated probe assembly.

4. RESULTS OF TEST DEVICE MEASUREMENTS

To determine the soundness and accuracy of this measurement technique, a series of measurements of the probe assembly

were made with two test devices having known calculable

S-parameters. This measurement treats the probe assembly as

a two-port device and enables the S-parameters of the two

test devices to be determined experimentally by the method

described in section 3. The first test device was a small

pad that shorted probe tips 1, 2, and 3 together as shown

in figure 10.

Port A L Port B

Figure 10. Shorted configuration

The residual inductance of this pad was calculated to be

approximately two pico-henries or 0.01 ohms reactance at

1 GHz.

-17-
This particular load configuration, with all probe tips

shorted provides an exacting test for this measurement technique. The parasitic element of the ground probe lead becomes

an integral part of the load configuration and, therefore,

has the greatest effect on the measurement.

The S-parameters for all probe tips shorted for any

frequency are

Sn = S 22 = 1 / 180° ,

|Si2 I = |S 2 i | =

By using these known values as the basis for a standard, one

can readily establish how accurately the S-parameter values,

determined experimentally, compare with the above standard.

The second test device is a thru-line configuration as

shown in figure 11, where probe tips 1 and 3 are shorted, but

2 is open.

1 3

Q o o o

2

Port A I Port B

Z P

o

Figure 11. Thru-line configuration

The S-parameters of the thru-line for any frequency are

11 - P22 =

S 12 = S 21 = 1 / 0°

-18-
Again, this forms the basis for another standard that can be

used for comparison purposes.

Tables II and III show the S-parameters obtained experimentally for both test devices by utilizing the measurement

technique described in the preceding sections. Observing

the values listed in tables II and III, the S-parameters of

major interest for test device No. 1 are Sn and S 2 2/" for

test device No. 2, S12 and S 2 i- While the other S-parameters

should not be overlooked, it is felt that these are the ones

most likely to reflect measurement error in characterizing

the probe assembly.

The values shown in tables II and III are representative

of measurement data taken over a two-month interval . The

accuracy of the measurements is discussed in section 5.

5. DATA ANALYSIS

5.1 Background

Measurements were made at nineteen frequencies in

100 MHz increments between 200 and 2000 MHz on an automatic

network analyzer (ANA) having an accuracy +0.003 in magnitude and ± 0.5 degree in phase angle. These measurements

were made to experimentally establish the S-parameters for

the two electrical configurations using the probe assembly.

This was done on five different "occasions". The first

three occasions were close in time--within a two day period.

Each set of measurements made on an occasion was preceded

by a calibration of the ANA. These first measurements were

made using SMA connectors. Some weeks following, two additional replications of the measurements were made, one using

SMA connectors, and one using 7 mm precision connectors.

-19-
Table II

Experimental S-parameters obtained from measurements

made on two test devices, "all probe tips

shorted" and "thru-line".

S-Parameters for Test Device No. (All Probe Tips Shorted

:q. SllI S12 S21 S22

FRI MAG. ANG 4AG. ANG. MAG. ANG. MAG. ANG.

200 000 1 002 -179 9 002 -124 6 002 -125 6 998 180

300 000 1 002 -179 9 004 -157 3 004 -158 7 1 .001 179 9 400 000 1 003 -179 8 001 -91 6 001 -135 4 1 003 -179 7 500 000 1 004 -180 002 -146 2 003 -166 3 1 005 -179 4 600 000 1 000 -179 8 004 -105 4 004 -113 3 997 -179 2 700 000 1 005 -179 6 003 -146 3 005 -135 7 993 -179

800 000 1 002 -179 6 008 -134 010 -117 7 995 -179 2 900 000 1 006 -179 5 003 170 1 003 -116 8 999 -179 3 1000 000 1 004 -179 6 002 -35 7 004 -53 7 1 003 -179 4 1100 000 1 000 -179 4 011 -46 3 011 -38 1 998 -178 8 1200 000 1 002 -179. 3 007 -55 9 006 -38 4 999 -178 6 1300 000 1 001 -178 8 007 52 7 011 61 3 994 -178 8 1400 000 990 -178 8 050 -70 8 045 -70 5 985 -179 4 1500 000 928 -177 4 129 -71 8 128 -73 5 1 145 -177 5 1600 000 982 -178 8 052 -84 9 050 -91 5 995 -178 5 1700 000 988 -178 7 050 -94 6 051 -100 989 -177 6 1800 000 988 -178 9 061 -99 1 061 -99 2 976 -177 6 1900 000 984 -178. 7 051 -103 5 053 -97 975 -178 4 1999 990 986 -178. 4 057 -111 7 055 -103 983 -178 8

S-Parameters for Test Device No. (Thru- Line)

:q. Sll

3

S12 S21 S22

FRI MAG. ANG MAG. ANG. MAG. ANG. MAG. ANG.

200 000 006 -172 1.002 0.4 1.001 0.4 0.007 175.6

300 000 008 -175. 2 0. 999 0.0 0. 999 0. 0. 007 176. 3 400 000 005 144 7 0.999 0. 1 0. 996 0. 2 0.011 162.2

500 000 007 141 9 1.000 0. 1 1.000 0. 1 0.008 -177.5

600 000 003 -71 4 0.992 0.2 0. 994 0. 3 0. 009 -75.1

700 000 012 -144 4 0.991 0. 7 0. 991 0. 7 0. 009 -93.6

800 000 021 -152 3 0. 993 0.9 0.991 0.8 0.008 -143.2

900 000 029 178 6 0. 995 1.2 0. 992 1.2 0. 023 147.0

1000 000 026 156 3 1.006 1.0 1. 007 1.2 0.029 139.7

1100 000 027 138 5 1.002 0.6 1.001 0.6 0. 031 139.1

1200 000 021 121 1 1.000 0. 5 0.999 0.4 0.017 138.1

1300 000 010 159 4 0. 998 1.1 1.000 1.0 0.006 -115.7

1400 000 034 96 7 0. 998 -0.8 1.000 -0.8 0.029 85.3

1500 000 011 -20 4 1.062 -1.8 1.061 -1.8 0. 136 92.2

1600 000 061 78 1 0. 980 1.7 0. 982 1.7 0.061 81.6

1700 000 060 54 5 0.998 1.9 1.002 2.0 0.050 49.8

1800 000 055 36 8 1.002 1.0 1.004 1.1 0.052 35.9

1900 000 054 28 6 1.001 0.8 0.998 0.8 0.060 35.2

1999 990 055 20 1 1.001 0.8 1.005 0. 5 0. 054 39.9

-20-
Table III

Experimental S-parameters obtained from measurements

made on two test devices, "all probe tips

shorted" and "thru-line".

S-Parameters for Test Device No. 1 (All Probe Ti ps Shorted

3Q.

Sll S12

I S21 S22

FRI MAG. ANG. MAG. ANG. 4AG. ANC MAG. ANG.

200 000 1 000 178. 6 002 139 9 002 156 9 1 000 178 8 300 000 998 177. 9 001 -161 3 002 -152 5 1 000 178 4 400 000 989 176.7 004 72 4 003 87 1 996 177 7 500 000 984 175. 8 002 38 4 001 82 7 1 000 177 3 600 000 989 176. 2 003 -65 2 002 -120 3 1 002 177 6 700 000 1 001 177.0 005 -52 1 004 -78 1 1 006 177 8 800 000 996 176.9 010 -48 008 -48 7 1 003 177 4 900 000 982 176.4 012 -23 9 012 -17 6 1 000 176 9 1000 000 977 176.6 019 -52 7 019 -53 3 1 001 177 4 1100 000 991 178.0 033 -58 2 030 -58 7 997 178 9 1200 000 1 001 179.5 038 -60 3 033 -60 1 997 179 6 1300 000 991 179.9 038 -54 4 034 -47 7 989 179 4 1400 000 970 179. 6 071 -63 1 073 -61 7 978 177 5 1500 000 973 -178.9 079 -76 9 083 -73 5 979 179 4 1600 000 983 -178.6 077 -69 8 078 -69 6 982 -177 7 1700 000 1 001 -177.0 071 -72 2 069 -71 1 963 -174 7 1800- 000 0. 990 -177.9 063 -71 4 066 -67 3 950 -177 9 1900 000 0. 968 -179.

049 -75 8 055 -71 5 975 178 2 1999 990 0. 969 -179.0 063 -75 4 071 -81 4 988 -179

S-Parameters for Test Device No. 2 (Thru-Li ne)

Sll

2

S12 S21 S22

FREQ. MAG. ANG MAG. ANG. MAG. ANG. MAG. ANG.

200. 000 023 120 998 -0.4 998 -0.4 0.012 137.7

300.000 024 101 4 988 -1.2 995 -1.1 0. 025 115.7

400.000 035 91 7 993 -1.3 992 -1.2 0.036 106.2

500.000 049 96 6 993 -1.5 994 -1.5 0.041 104.1

600.000 051 106 5 990 -1. 5 990 -1.5 0.029 110.2

700.000 054 122. 8 994 -1.5 993 -1.5 0.036 137.2

800. 000 052 126 988 -1.8 990 -1.8 0.048 131.9

900.000 070 112 9 990 -1.6 991 -1.6 0.073 113.4

1000.000 081 104 2 998 -2.1 996 -2.1 0.074 105.6

1100.000 082 104 9 998 -2.8 995 -2.6 0.056 110.3

1200.000 061 109. 9 986 -3.1 987 -3.1 0.037 110. 8 1300.000 042 112 8 986 -2.5 986 -2.6 0.033 108.6

1400.000 070 93 7 990 -4. 3 987 -4.3 0.065 79.5

1500.000 071 78 5 .987 -3.8 988 -3.8 0.061 65.7

1600.000 081 78 9 979 -1.3 979 -1.2 0.056 76.6

1700.000 030 11 5 999 -2.1 998 -2.0 0.023 -38.7

1800.000 029 -24 4 990 -3.9 990 -3.8 0.027 -22.6

1900.000 038 -2 3 989 -4.4 988 -4.3 0.036 12.4

1999. 990 049 6 997 -4.0 995 -4.3 0.046 -15.0

-21-
These measurements shed some light on the precision of

values obtained using the probe assembly, as well as on the

nature of the bias introduced by the measurement system.

The eight components of each of the S-parameter matrices

were determined separately, frequency by frequency. The

reduced data consist of averages for the S-parameter values

obtained at each of the 19 frequencies, using the SMA connectors and estimates of the standard deviations of the values

going into these averages. Two types of typewriter plots

were prepared for the more important S-parameters (magnitude

and phase) of each of the two configurations. These parameters are Sn and S22 for all probe tips shorted, and Si 2 and S21 for thru-line. The first type of plot consists of a point plot of the average values versus frequency, as shown

in figures 12 thru 15. A "95 percent confidence" interval

is also shown with each of the average values. These intervals are calculated on the assumption that the distributions

of the components at each frequency are Gaussian; this is an

untested assumption. An additional caveat is that the

estimated deviations are based equally on all four SMA

occasions, even though the first three are very close in

time relative to the fourth. There is no basis at present

for weighting the individual occasions, however. The second

type plot is that of the estimated standard deviations of

individual determinations of a particular component versus

frequency, as shown in figures 16 thru 19.

On the plots of the mean values as shown in figures 12

thru 15, the symbol "*" represents the mean value as defined

for the tables; the symbol ($) represents the upper limit of

the "95 percent confidence" interval for the mean, and the

symbol "0" represents the lower limit. When plotting posi-

-22-
tions are so close as not to be distinguishable for plotting

purposes, the number of points "coincident" are printed

rather than any of the above-mentioned symbols . The confidence intervals are symmetric about the mean value, plus or

minus the resolution of the printer. Comments and conclusions about these plots are stated in section 5.2.

-23-
l.ltU'lll

i.til3-ao«

«.i;tr-iai

t.tlM-tll

9.1fc51-001»

».»CH»«OI

2.I3M»000

l.J71»>»0l

-Z.«".»»-0«1

-J.W7r.«oi

Figure 12. All probe tips shorted Sn magnitude and

phase with 95 percent confidence intervals

for four SMA occasions

-24-
i.mr>»tf

i.iitt»)i>

».0«.«>I00>

!.(?«.. Ilh

«.r«j«-iii>

t.Itll-ggi*

H-+ t++i-1-T-l

».«?91-IOt.

2.r3M-l02»

L-I.I40Z-tl3>

-3.»53l-OOi»

-».»WZ-0«Z»

-*.b<>lZ-002 o.nooo.ooo l.»»IO»0»3 Z.(I0»II3

Figure 13. All probe tips shorted S 2 2 magnitude and

phase with 95 percent confidence intervals

for four SMA occasions

-25-
i . o<.«.i. • a o j

•

!\»

4.76-H-OOl*

9.571.9-001* O.OOOOiOOO

1—KO

<* . • 3 Z 6.0000*0 02 1.20 0*00 3 FREQUENCY (MHz) 1.6000*003 ?. 00 J0» 00 J

2.t7'80*Q0Q*

8.3530-001*

-1.007<«*000*

-2. 8502*000*

I j:

.6929*000*

.0000*000 .00 00*0 02 1.20 00*08 3 FREQUENCY (MHz)

Figure 14. Thru-line S i2 magnitude and phase with

95 percent confidence intervals for

four SMA occasions

-26-
i.o,*so*ooo*

1.0«V>*000*

<• i.o?ia*ioa*

l.tOOJ>000>

t.Mri-ooi*

*.57ir-001*

0.0000*000 k. 0000*002 MI1IHI1

t.tztoooi*

L 4. 3910-001*

-4.I23J-001*

-i.n3»*ooo»

« f j-

-fc.SS5Z>000. 0.0000*000 •.. 0000*003 l.tOMtOI] Z.M0i«M3

Figure 15. Thru-line S 2 i magnitude and phase with

95 percent confidence intervals for

four SMA occasions

-27-
Pllll Of tjllN»Ul> jMN). .r -*-.. Ut llulll'WL ULTrRnltitTIONi f0« IM( SH H1GNIIU0E

J l.i»3f-002*

t*192B- J03*

t.5*.fc6-003* 1.6000*003 2.I000X03

J.ikfcs»QOa<

J 9.50Qt*-OJl«

5.1885-0J1 •

LOT OF ESMKaTEO STftNJ. SEV5. FOR I*0WIuUAL UETERMI hATIONS FOR THE Sll *NGCE

1.2Eei-001«

i..oo;c.Djf 8.0000*002 1. 2000*003 1.6000*003 2.1000*0(3

F lEQOEHCt (HHij

Figure 16. All probe tips shorted Sn magnitude and

phase standard deviation for four SMA

occasions

-28-
PLOT OF tSTIMST.O JT1N.1. OiWS. FOR HJIVMUtl UETERN 1 NftTl ON5 FOR TMF 522 HAGNITUOE

J 2.J6I.7-002*

1. ".722-002*

7.*H-.i>»

0.00)0*000 1.6000*001 J. IOII««ll

PLOT OF ESTl*«TEG sTJNJ. „:VS. FOR I ICIVIOUil uETERHImT IONS FOR IME S22 «NGLE 3.1729-002*

2.6199-002*

2.0669-002*

1.51*. 0-002*

9.6097-003*

.0799-003* 0.0000*000 .0000*302 1.2000*003 1.6000*003

FREQUENCY (MHe) 2.0000*003

Figure 17. All probe tips shorted S 2 2 magnitude and

phase standard deviation for four SMA

occasions

-29-
»L01 OF FSUHMtO SI«NO. OE«S. FO» Kulll'ML OCIimuTIMS Of tMC S12 H4CMI IUOC 1.IM-JI,1 '

;.Mii-i«;'

2.oro<>-oo2«

j i.<it2?-ao2*

7.3H2-003*

fc.717fc-00<.* • *

• .0000*000 *.. 0000*002 8.0000*002 1.2000*003 1.6000. 0(3 2.M00*II3

2.75r*.*iOI*

2.2(13*000*

>. 1.3291*000*

(.5210-001*

3.'Mt-001*

PLOT OF ESTIKITEO SI»N0. D£»S. FOR INDIVIDUAL OETERKI N*TI ONS OF IHE S12 4NCIE

Figure 18. Thru-line Si 2 magnitude and phase standard

deviation for four SMA occasions

-30-
10! Of EStlmtEO ST«NO. L)£»S. FOB INOMIDUtl OEtEKKINoT IOMS Of TME S21 HKNI TU9E

). 3611-00?*

2.rosi-oo2*

t.toM-ll?*

o 1.1111-002*

7.11-1-103.

».6J*i-10*.* •

•.•••0*111 t.lHOIIi l.llll'Ot; 1.2111*103 1.HIIINI

FREQUENCY (MB*)

PLOT OF ESMKlfEO SIINO. OE«S. FOR 1N0IVI0UAI OETEKHINtTIOttS OF THE S21 1WLE

I. • •«•••••

2.1111*111

2.2j««*ooo*

i.rriKiiy

l.HZIHH*

1.S3U-101*

1. SoU-Oll*

0.0090*000 0.0000*002 •.1000*002 1.2001*003 1.6010*003 2.M11*113

FRCQUtiNCV(MHz)

Figure 19. Thru-line S 2 i magnitude and phase standard

deviation for four SMA occasions

-31-
5.2 General Comments

All Probe Tips Shorted

Mag (Si!) 1. No evidence of bias is apparent.

2. The standard deviations seem to be sensitive to frequency, but the estimated value

of 0.04 at 1500 MHz is disproportionately

large. The next largest estimated standard

deviation is 0.02 at 1900 MHz.

3. Largest average value: 1.004 at 1700 MHz

Largest value recorded: 1.022 at 1500 MHz

Smallest average value: 0.980 at 1500 MHz

Smallest value recorded: 0.928 at 1500 MHz

4. The 7 mm values were close to the SMA

averages below 1400 MHz; largest positive

difference was 0.012. The largest positive

difference overall was 0.03 at 1800 MHz.

Mag(S 2 2) 1- As with the data for mag(Sii), there is no

evidence of any bias.

2. Again, there is evidence that the standard

deviation is sensitive to changes in frequency. The largest estimated value is

0.07 at 1500 MHz; the next largest is 0.03

at 1800 MHz.

3. Largest average value: 1.047 at 1500 MHz

Largest value recorded: 1.145 at 1500 MHz

Smallest average value: 0.990 at 1800 MHz

Smallest value recorded: 0.095 at 1800 MHz

4. The largest positive difference between the

7 mm data and the SMA averages is 0.0 5 at

1500 MHz. The other differences are within

0.01.

-32-
All Probe Tips Shorted ( contd .

)

Mag (Si 2) 1. Some evidence of bias can be seen,

especially for the higher frequencies.

2. The standard deviation tends to increase

with frequency; the largest estimated

standard deviation is 0.027 at 1500 MHz.

3. Largest average: 0.091 at 1500 MHz

Largest value recorded: 0.129 at 1500 MHz

Smallest average value: 0.002 at 400 MHz

Smallest value recorded: 0.0005 at 400 MHz

4. The 7 mm data are within 0.006 below

1500 MHz.

The largest positive difference (at

1500 MHz) is about 0.03.

Mag(S 2 i) 1. There is evidence of bias.

2. The standard deviation increases with

frequency. The largest estimate is

0.025 at 1500 MHz.

3. Largest average value: 0.093 at 1500 MHz

Largest value recorded: 0.128 at 1500 MHz

Smallest average value: 0.0015 at 400 MHz

Smallest value recorded: 0.0006 at 400 MHz

4. The 7 mm values of mag(S2i) are within 0.001

for frequencies less than 1400 MHz. At 1500

MHz the positive difference is 0.04.

Angle (Si 1) 1. Some evidence of an increasing negative bias

for frequencies above 1400 MHz is present.

2. There are also indications that the precision may be better for frequencies above

1200 MHz. The largest estimated standard

deviation was 22 degrees at 500 MHz; value

0.12 at 1600 MHz.

-33-
All Probe Tips Shorted (contd.)

Angle (Si i) (contd.)

3. Largest average value: 0.905 at 500 MHz

Largest value recorded: 4.18 at 500 MHz

Smallest average value: -2.23 at 1500 MHz

Smallest value recorded: -3.01 at 1700 MHz

4. The largest positive difference of the

7 mm values from the SMA averages was 2.1

degrees at 1600 MHz.

Angle (S2 2) 1- There is no evidence of any bias. This is in

contrast to what was noted about angle(Sii).

2. The standard deviation did not appear to be

sensitive to frequency and the precision

seemed two orders of magnitude better than

what was apparent for angle (S11). The

largest estimated standard deviation was

0.032 at 1500 MHz.

3. Largest average value: 0.010 at 30 MHz

Largest value recorded: 0.055 at 900 MHz

Smallest average value: -0.047 at 1700 MHz

Smallest value recorded: -0.092 at 1700 MHz

4. The largest positive difference from the

7 mm data was 2.8 degrees.

-34 -
Thru-Line

Mag (Si i): 1. There was some evidence of positive bias

for values of mag (Si i) above 1100 MHz;

but the values tended to rise with frequency.

2. On the basis of the estimated standard

deviations, the standard deviations of the

measured values of mag (Si i) did not appear

to be sensitive to frequency changes. The

largest standard deviation estimated was

0.03 at 1000 MHz.

3. Largest average value recorded: 0.063 at

1600 MHz

Largest value recorded: 0.082 at 1100 MHz

Smallest average value recorded: 0.01 at

200 MHz

Smallest value recorded: 0.003 at 600 MHz

4. The values of mag (Si i) obtained using the

7 mm connections tended to be less (but

greater than zero) than the average values

of mag (Si i) obtained using the SMA connectors. The largest positive difference is

0.033 at 1700 MHz. The largest value of

mag (Si i) recorded for the 7 mm data was

0.053 at 1600 MHz.

Mag(S 2 2): 1- As with mag(Sn), the values of mag(S2 2)

rise with frequency.

2. The estimated standard deviation of mag(S 2 2)

at 1500 MHz (.04) was relatively large.

The next largest value was 0.03 at 1000 MHz.

3. Largest average value: 0.07 at 1500 MHz.

Smallest average value: 0.009 at 200 MHz.

Smallest value recorded: 0.003 at 400 MHz.

-35-
Thru-Line (contd.)

Mag(S 2 2) (contd.)

4. The largest positive difference from the

7 mm data was 0.04 at 1500 MHz. The

largest 7 mm value for mag(S 2 2) is 0.044

at 1600 MHz.

Mag (Si 2 ) 1. No evidence of any bias was apparent

from the data.

2. There appeared, however, to be a tendency

for the standard deviation to increase with

frequency especially after 1100 MHz. The

largest standard deviation estimated was

0.034 at 1500 MHz; next largest was 0.008

at 1800 MHz. The instability exhibited here

and elsewhere at 1500 MHz appears to affect

only the first three SMA "occasions".

3. Largest average value: 1.012 at 1500 MHz

Next largest average value: 1.002 at

1700 MHz

Largest value recorded: 1.062 at 1500 MHz

Smallest average value: 0.985 at 1600 MHz

Smallest value: 0.979 at 1600 MHz.

4. The 7 mm values of mag (Si 2) were generally

within 0.01 of the average SMA values. The

largest positive difference 0.011 at

1500 MHz.

Mag(S 2 i) 1- No real evidence of bias was apparent.

2 . With respect to the estimated standard

deviations, those below 1000 MHz were

generally smaller than those above; range

of .0006 to .003 below and range of .004

to .008 above if one leaves out the value

of .034 at 1500 MHz.

-36-
Thru-Line (contd.)

Mag(S 2 i) (contd.)

3. Largest average value: 1.011 at 1500 MHz

Next largest average value: 1.004 at 1700

MHz

Largest value recorded: 1.061 at 1500 MHz

Smallest average value: 0.984 at 1600 MHz

Smallest value recorded: 0.979 at 1600 MHz

4. The 7 mm values were generally within 0.01

of the SMA averages. The largest positive

difference was 0.017 at 1700 MHz.

Angle (Si 2 ) 1. No evidence of bias apparent from the data.

2. Clearly there is a tendency for the standard

deviations to increase with frequency. The

low value of the estimated standard deviation of angle (Si 2 ) is 0.4 at 200 MHz, and

the high value is 2.8 at 1900 MHz.

3. Largest average value: 1.22 at 1600 MHz

Largest value recorded: 2.32 at 1700 MHz

Smallest average value: -1.47 at 1400 MHz

smallest value recorded: -4.41 at 1900 MHz

4. The 7 mm data were within two degrees of the

average SMA averages

Angle (S21) 1. Again, no bias is evident.

2. As with angle(S 2 i), standard deviations

increase with frequency.

3. Largest average value: 1.29 at 1600 MHz

Largest value recorded: 2.42 at 1700 MHz

Smallest average value: -1.47 at 1400 MHz

Smallest value recorded: -4.31 at 1900 MHz

4

The 7 mm data were within two degrees of the

average SMA values. The differences became

larger with frequency.

-37-
6. CONCLUSIONS

A measurement technique has been described that demonstrates the practicality of making accurate measurements on

integrated circuit devices up to 2 GHz with this probe assembly. The accuracy of this technique is best illustrated by

figures 20 and 21 that show plots of measured and corrected

data for the two test devices measured, i.e., all probe tips

shorted and thru-line.

20

10 180 -10- m

m -20

K

O -30

ill °-40

-50

-60

0.1

r

- S

22

- o "^CORREC'ED

- \ryr s

22

- S

11 \\- UNCORRECTED iii

0.5 1 .0 2.0 FREQUENCY (GHz)

Figure 20. All probe tips shorted measurements

CORRECTED

0.5 1.0 FREQUENCY (GHz)

Figure 21. Thru-line measurements

-38-
Early in the program, it was seen that a possible

limiting factor of this measurement technique was how

well we could achieve a good short circuit between the

probe tips and ground. This problem was solved by physically contacting the large copper short circuit to the

bottom of the probe ground plane, and removing some material

from the large copper short circuit to accommodate the probe

tips, as shown in figure 5.

Stray (probably capacitive) coupling between the

ungrounded conductors, probe tips 1 and 3, was shown to be

neglibigle and does not affect the measurement results.

7 . ACKNOWLEDGEMENTS

The authors wish to thank John Labrecque of the

Statistical Engineering Laboratory for his contribution

to the data analysis section. Also, a special thanks to

Gary Rosenberger for his help on the computer software.

-39-
8 . REFERENCES

1. Sawyer, D. E., Rogers, G. J., and Huntley, L. E.,

"Measurement of Transit Time and related

Transistor Characteristics," AFWL-TR-73-54

,

(October 1973) . Available from National Technical

Information Service, Springfield, Virginia 22151,

Accession No. 91428.

2. Rogers, G. J., Sawyer, D. E., and Jesch, R. L.,

"Measurement of Transistor Scattering Parameters,"

NBS Special Pub. 400-5, Semiconductor Measurement

Technology, January 1975.

3. Jesch, R. L. , Bailey, R. A., and Tausch, H. J.,

"Characterization of a HF Probe for Integrated

Circuits Measurements," 1974 GOMAC Digest of

Papers, pp. 120-121, June 1974.

4. Kerns, D. M. and Beatty, R. W. , "Basic Theory of

Waveguide Junctions and Introductory Microwave

Network Analysis," pp. 72-83, Pergamon Press,

New York, 1967.

-40-

i
APPENDIX I

LISTING OF COMPUTER PROGRAM WRITTEN IN BASIC

File

INSTRUCTIONS

I.10 110

120

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140

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ISO

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7D0

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Kcf'i REM REM

REM

REM REM

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REM

REM

REM REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

REM

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REM

I HIS Cfl SET !E COHTRi MS ALT. AND USING THE S/N 104 IRAN PROGRAMS & DATA FILES FOR CALIBRATING

' PROBE ASSEMBLY. THE FILE CONTENTS ARE:

10

11

50

51

INSTRUCTIONS

PROGRAM FOR uETTIHU DATA OFF TAFt RROGRAM FOR CALIBRATING ARMS fi & B DATA FOR CALIBRATING ARM A S-PARAMETERS FOR ARM A ZP VALUES FROM ARM A DATA FOR CfiLIBRhTl.NU ARM B S-PARAMETERS FOP ARM B AVERAGE ZP VALUES FROM ARMS A & B Tl INVERSE

T2 INVERSE PROGRAM FOR EVALUATING T EST ITEM (TRANSISTOR

DATA FOR EVALUATING TEST ITEM #1

- -PARAMETERS FOR TEST ITEM #1 DATA FOR EVALUATING TEST ITEM #20

S-PARAMETERS FOR TEST ITEM #26

INTO PROPER FILES

"HE PROBE ASSEMBL

?DER: DATA FOR CHLIBRFM1NG ARM H OF MUST BE LOREEE

INTO FILE 3 IN THE FOLLOWING

FREQ , HO .- F O i MS > PS j HZ r PZ - ML PL where the 1st letter

m=maghitijhe

p=phase in degrees

and where the 2nd letter

0=open circuit

s-short to ground

z=short to zp L=LOAD

UP TO 20 LINES OF BATR (DIFFERENT FREQUENCIES: CAN Bh STORtD IN hiLE ! USING A SEMIPRECISIOh DIMENSION STATEMENT: DS<20-9>

DATA FOR CALIBRATING ARM B IS LOADED INTO FILE 6 SAME AS FOR FILE 3

DATA FOR UP TO 23 TEST ITEMS IS LOADED INTO FILE 12 j 14) . „

> 50. THE DATA IN EACH FILE HAS : HE FOLLOWING ORDERS FREQ , MS 1 1 > PS1 i - MS 12

PSI 2: MS21 - PS21 , MS22 , PS22 WHERE MS11=MAGNITUDE OF Sit- PSH=PHRSE OF Sll IN DEGKEESi EjC.

UP TO 20 LINES OF DATA (FREQUENCIES) CAN BE STORED FOR EACH I EST ITEM. THE FREQUENCIES SHOULD CORRESPOND TO THOSE AT WHICH ARMS A t B HAVE BEEN CALIBRATED.

THE PROGRAM IN FILE CAN JSED TO LOAD DATA INTO THE FILES FROM PAPER TAPE IF THE DATA ON THE TAPE IS IN THE PROPER ORDER. SEE FILE 1.

TO CALIBRATE THE PROBE ASSEMBLY? FIRST LOAD THE DATA FOR ARMS A &_B INTO FILES 3 I: 6- AND THE DATA FOR THE TEST ITEMS INTO FILES 12) 14 -...50. LOAD FILE 2 AMD RUN. THE PROGRAM WILL ASK FOR THE VALUE OF THE STANDARD LOAD RESISTOR USED IN CALIBRATING ARMS A 8= B. TYPE IN THE VALUE; ASSUMED REAL. IT WILL THEN

ASK FOR THE * OF FREQUENCIES AND # OF TEST ITEMS TO BE EVALUAiED.

TO CALIBRATE ONLY) TYPE O FOR THE # OF TEST ITEMS. THE PROGRAM THEN CALCULATES Ti INVERSE 8, T2 INVERSE FOR hACH FREQUENCY

AND STORES THEM IN FILES 9 fe 13.

IF THERE APE TEST ITEMS TO BE EVALUATED- THIS PROGREM THhN LOADS IN PROGRAM 11 WHICH EVALUATES THE TEST ITEMS. S-PARHMETERS FOR TtSl ITEM #1 ARE STORED IN FILE 1.3 j FOR ITEM #2 IN 15- AND FOR ITEM #N IN FILE 11+2N.

TO EVALUATE THE TEST ITEMS WITHOUT RECALIBRATING- LOAD DATA FOP THE TEST

ITEMS INTO FILES 12- 14- . , . * 50 AS DESCRIBED ABOVE. THtN SCRATCH

1 COM F3»F9)QS(20)9))RS(2O)9))ZS(20)2>

L0AD11- 1O0-

PROGRAM 11 WILL GO TO FILE 9 & 10 TO GET EXISTING CALIBRATION CONSTANTS

AND THEN EVALUATE i HE TEST ITEMS.

-41-
File 1

10 REM: TAKING DATA FROM PAPER TAPE & STORING IN FILES

12 REM: TO READ IN PAPER TAPE TYPE PTAPE #7

14 REM

16 REM DATA ON PAPER TAPE SHOULD BEGIN AT THE FOLLOWING LINE NUMBERS:

18 REM

20 REM ARM A OPEN CIRCUIT DATA; 300 DATA FPEQ> MAGNITUDE* PHASE' DEGREES)

22 REM ARM A SHORT TO GROUND DATA! 400 DATA

24 REM ARM A SHORT TO ZP DATA; 569 DATA

26 REM ARM ri LOAD DATA! 600 DATA

23 REM

30 REM ARM B OPEN CIRCUIT DATA! 70S DATA FREQ> MAGNITUDE* PHRSE(DEGREE3

32 REM ARM B SHORT TO GROUND DATA! 889 DATA

34 REM ARM B SHORT TO ZP DATA? 900 DATA

36 REM ARM B LOAD DATA! 1000 DATA

38 REM

46 REM S-PARAMETERS OF PROBE ASSEMBLY CONTAINING TEST ITEM #1 IN THE ORDER:

42 REM 11W0 DATA FREQ> MSI 1 , PS1

1

> MS12? PS12> MS21 , PS21 j MS22; PS22

44 REM WHERE MSI 1=MAGHITUDE OF Sll> PS1 1=FHASE( DEG> OF SI 1 j ETC,

46 REM S-PHRAMETERS OF PROBE ASSEMBLY CONTAINING TEST ITEM #2 48 REM 120O DATA . . . 50 REM

52 DIM QSE 20>9]»C[ 19]»fl*r.20] 54 FORMAT F9, 3> F7. 3, F8. 1i.F7.3jF8. 1jF7.3j F3. 1i.F7.3jF8. 1 56 PRINT "TO STORE ONLY CALIBRATION DATA. ENTER 1" 58 PRINT 'TO STORE ONLY TEST ITEM DATA- ENTER 2" 60 PRINT

62 PRINT

64 DISP 'SEE NOTE ON PRINTER "j bb INPUT L 68 GOTO l Or 70, 1 14

70 REM: STORING CALIBRATION DATA

72 PRINT "READ ALL OF CALIBRATION TAPE (TYPE: PTAPE # 7>> THEN PRESS RUN 80' 74 PRINT

76 DISP ' SEE NOTE ON PRINTER"

78 STOP

30 DISP "NO. OF FREQUENCIES'. 1 TO 20>="j

82 INPUT F9

84 FOR F0=3 TO 6 STEP 3 36 FIND F0

88 K2=2

90 FOR K=l TO 4 92 K3=K2+i

94 FOR F=l TO F9

96 READ QCF> 1 ]>QCF;K2]jQ[FjK3]

98 NEXT F 100 K2=K2+2

102 NEXT K 104 GOSUB 154 106 STORE DATA F0,Q

108 NEXT F0

110 PRINT CALIBRATION DATA STORED

112 END

-42-
File 1 (contd.)

114 REM: STORING TEST ITEM DATA

116 DISP NO. OF TEST ITEMS = "5 US INPUT f- 120 LISP 'HO. OF FREQUENCIES'^ TO 20>="S

122 INPUT F9

124 F2=11+2*F3

126 F0=12

128 FIND FO

138 X=RB'r'TE7 132 IF X=S THEN 130

134 FOR F=l TO F9

136 ENTER C7j*)fl*[ 1, 10: 138 NEXT F 140 GOSUB 154

142 STORE DATA FOsQ

144 F0=FS+2

146 IF F0<F2 "THEN 128

148 PRIN T

"

fl LL STORED"

156 PRINT

152 END

;fork=ito9»qcfjK :..

154 PRINT

156 PRINT : 158 PRINT

166 FOR F=l 162 WRITE

164 NEXT F 166 PRINT

168 PRINT

170 PRINT

172 PRINT

174 PRINT

176 STOP

178 RETURN

DfiTA ABOUT BE OPEL IN F ILE"F0J "IS

1 5s 54 > Q[ F > 1 ], Q[ F t 2 1 , QC F s 3 3 s Or F ? 4 1 , Q[ F , 5 ] j Q[ F

].Q[Fi SCF

'IF DATA

TO REJEC

.OOKS OK > PRESS CONT"

' CAL DATA) START OVER, 10 REJECT R FES" IBM, PRESS CONT 139

-43-
File 2

1 COM F3> F9>QSC20<9 I>RSC20»9]>ZSC 26,2]

2 REM

188 REM! CALIBRATING TRANSISTOR PROBE ASSEMBLY, ONE ARM FIT A Tint

110 DIM XC 9 ] < YC 9 ] > M[ 9 ] > PC 9 ] , WS[ 20 1 9 ] 115 FORMAT F9.3iF7.3jF3. 1-F7.3.F8. 1jF7.3jF8. 1>F7.3»F8. 1 120 DEG

130 XI5D=1

140 YC53=YC6]=0

145 DISP "VALUE OF STANDARD LOAD = "J 150 INPUT X[6]

160 PRINT "STANDARD LOAD = "Xt 6

35 "OHMS"

170 DISP "NO. OF FREQUENCIES U TO 20)="

5

172 INPUT F9

174 DISP "NO. OF TEST ITEHSC1 TO 20)="

i

176 INPUT F3

19G

192

193

194

195

196

198 200

202

204

206

208

FOR F LOAD

PRINT

PRINT

IF FO PRINT

GOTO PRINT PRINT

PRINT PRINT

PRINT

0=3 TO 6 STEP 3 DATA F0jWT0 - 3 for Ara A, 6 for Arm B

=6 THEN 20g

"S PARAMETERS FOR ARM A' !02"S PARAMETERS FOR ARM B'

FREQ

Sll MAG ANG S12

1AG ANG MAC A Hi MAG ANC

509 FOR F=l TO F9

510 RESTORE 3000

550 FOR K=l TO 4 552 L=2*K

555 M=WCF»L3

560 P=WCFjL+1 ] 570 D=(1+M*M-2*M*C0S<P;

;80 ;:ck]=ci-m*m). d 590 YCK]=2*M*SIN(P). n 510 NEXT K

Converting reflection coefficient

magnitude (M) and phase (P) input

data to impedance Z - I, j^jr - * + jy

330 FOR L=l TO 15 340 GOSUB 1000

350 NEXT L 410 K=4

420 GOSUB 1200

430 MC4]=S0R(MC4]:

440 PC4]=PC4]/2

450 GOSUB 1275

460 FOR L=l TO 3 470 GOSUB 1000

430 NEXT L

Calculating the ABCD Cascading

Matrix Ti or T 2 ; and also IP

-44-
File 2 (contd.)

499

500 FOR 1=1 TO 2 510 FOR J=l TO 2 520 F.[ Ii J]=fl[ I,J] = X[K]

530 F[ I- J]=BC I. J]=YtK]

540 K=K+1

550 NEXT J 566 HE XT I

565 IF F0=6 THEN 958

Setting Ti or T» - I jr - A jB

For Arm B data, go to 950

570 ZEFil ]=XC7]

5:30 ZCF»2]=YC7]

Storing Z at frequency F in matrix 1

590 GOSUB 21O0

591 K=2

592 FOR 1=1 10 2 593 FOR J=l TO 2 594 QCFiK]=C[ I < J]

595 QCF-K+1 ]=D[ I, J]

596 K=K+2

597 NEXT J 598 NEXT I

Calculate T t inverse - C + jD

Storing Ti inverse at frequency F in matrix Q

660 GOSUB 1700

670 GOSUB 1600

690 GOSUB 2500

710 NEXT F

Converting Cascade parameters to S-parameters and printing results

715

716

720

730

740

750

760

770

780

790

800

810

820

830

840

845

852

854

856

PRINT PRINT

IF F0=6 PRINT " GOTO 76 PRINT " PRINT

PRINT " PRINT

FOR F=l K=7

XI 7 ]=ZC V[7]=Z[

GOSIJB 1 WRITE ( FORMAT NEXT F FOR 1=1 PRINT

NEXT I

Printing Z values

THEN 750

ZP FROM ARM fi" AVERAGE ZP FROM AKl'iS ft & B" FREQ REAL IMAGINARY MAGNITUDE PHASE"

TO F9

FjI ] F,2]

200 Converting Z - X + jY to magnitude and phaae

15-845:.'W[F< 1 ])XC7];Y.C7j!M[7.]jPC7] P F9.3.3F12.45F12.2

TO 4

-45-
File 2 (contd.)

860 STORE DhTh F0+1>W

S76 STORE DfiTFl F0+2-Z

880 NEXT FO

885 PRINT

898 STORE DHTfl 9.Q

906 STORE DflTfl 10j F 905 IF F3=0 THEN 93C

910 LORD 11> 100-245

920 END 930 PEW I IIH 940 END

950 i F. i XZCFn 1 J+XC7]

953 ZCF »2]=(Z[Fj2]+Y[7]

9 5 6 FOR \ =1 TO 4 960 PEflD J 965 L=2*K

970 PL F-L ]=J*:<[ K I 936 PIF.L+1 3=J*YEK]

990 NEXT K 999 GOTO 660

Storing S-parameters

Storing Z values

Storing all Ti &1 matrices in fila 9 Storing all T2 ~ l matrices in fila 10 Loading in program to evaluate test iti

Calculating average Z from Arms A and B

Calculating Tt inverse at frequency F, storing in matrix R.

-46-
File 2 (contd.)

Subroutines

1000 REN: COMPLEX +>->*>&/

1085 READ I, J;K 1010 IF 10 THEN 1075

1615 I=-I 1028 IF J>@ THEN 1055

1025 J=-J

1030 B=XC J ]*XC J ]+YC J ]*Y[ J J 1035 X=<X[ I ]*XC J ]+YC

]*YC J J), D 1040 YC K ]=CYC I ]*X[ J ]-X[ I ]*YC J ] 1045 XCK]=X

1050 RETURN

1855 X=XC I ]*X[ J]-Y[ I ]*Y'[ J] 1060 Y[ K ]=YC I ]*X[ J ]+XE I ]*Y[ J ] 1065 XCK]=X

1070 RETURN

1075 IF J/6 THEN 1100

1080 J=-J 1085 X[K]=X[ I ]-XC J] 1090 YCK]=Y[ I ]-Yt J] 1095 RETURN

1100 XCK3=X[ I ]+XC J] 1105 YCK ]=YC I ]+Y[J]

1110 RETURN

Vz

j Vz

j v^

z i+z.

Complex Math Subroutine

Code

I J z *-

+ + z

i + z

j + - z i

- z

j - + z

i

* z

j - - zy /z

j

12U0 REM: CONVERTING X+JY TO M 1205 X=XCK]

1210 y=yi:k.i 1215 mck]=sqr<x*x+y*y)

1220 P=flTH(Y/X) 1225 IF X>0 THEN 1250

1230 IF Y>0 THEN 1245

1235 P=P-180

1240 GOTO 1250

1245 P=P+180

1250 PCK]=P

12: RETURN

X neg, y neg

X neg, y poe

1275 REM: CONVERTING M & P Ti 1280 X[K:]=M[KJ*COS(p[KI)

1285 Y[KI=M[K]*SIN(p[K3)

1290 RETURN

,!*_ p « £-//•'

-P*l

>^ n

,„ P ,pc + ir»'

16O0 REM: CONVERTING

1610 MAT I=IDNC2.

1620 MAT E=(8.02::

1630 MAT A=E+I

1640 MAT B=(0.02;

1650 GOSUB 2100

1660 MAT R=E-I

1670 GOSUB 2000

1680 RETURN

TO Phi HMt'i'U GIVEN =E+JFj GIVES :;=E+JF

-47-
File 2 (contd.)

1700 PEN: 1710 REM: 1726 E2=EE

1 730 FC 1>2 1740 EC 1.2 1750 C0=E[

1760 MAT I 1770 MAT A 1780 MAT E 1790 EC2j1

1800 FC2> 1 1810 MAT C 1820 MAT D 1830 GOSUB

1840 RETUR

CONVERTING Z TO T OR T TO Z PARAMETERS

GIVEN Z=E+JF, GIVES T=E+JF. GIVEN T=E+JFi GIVES Z=E+JF

1 , 1 ]*EC2»2]-F[ 1j 1 ]*FC2j2]-EC 1i2]*E[2j 1 ]+FI 1>23*FC2> 1 ] ]=EC 1. 1 ]*Ft2>2]+FC 1j 1 ]*£[ 2<jJ-T£[ L, 2]*FC2, 1 ]-FC 1i23*EC2j 1 ] ]=E2

2. 1 ]*EC2i 1 ]+FC2- 1 ]*FC2; 1 ] =IDNC2j2]

= (E[2» 1 ]/C0>*I

=C-F[2>1]/C0>*I

]=1

] = =E=F20OO

N

20O0 REM*- MULTIPLYING 2 COMPLEX 2010 MAT G=B*D

2020 MAT E=fl*C 2030 MAT E=E-G

2040 MAT G=B*C

2050 MAT F=A*D

2060 MAT F=F+G

2070 RETURN

MATRICES E-UF=(A+JB <*'C+JD:

21O0

2110

2120

2130

2140

2150

2160

2170

2180

2190

REM: MAT G MAT H MAT C MAT C MAT C MAT

MAT RETUR

DIM A

INVERTING A COMPLEX MATRIX

=IHV(A>

=G*B

=B*H

=A+C =INVCC)

=H*C

=(-l>*D

N

[ 2> 2 I. B[ 2, 2 ]< CC ^ 2 ], D[ 2> 2 ]! E

C+JD=INVCfl+JB)

:]jFC-2j2]5G[2j2]jH[2j2]

25O0 REM: CONVERT ELEMENTS OF E+JF TO MAGNITUDE & PHASE

2520 K=l 2536 I- OR 1 = 1 TO 2 2540 FOR J=l TO 2 2550 !<=E[ I , J I 2560 Y=FC I » J]

2570 GOSUB 1215

25S0 L=2*K

2590 WCF,L]=MCK]

2600 W[FjL+1 ]=P[K]

2610 K=K+I 2620 NEXT J 2630 NEXT I 2640 WRITE (.15, 115>WCF, 1 ],MC 1 ]»P.C 1 ] » Ml 2 ], PC 2 ]> MC 3 1, PCS It M[ 4 ] > PC 4 ] 2650 RETURN

TORE IN Wj PRINT

H000 DATA 1i-4i"7j4»-3j4i3»-2»8»1i

3018 DATA -8i--3i3>-3»-7»3»-3>i»l!

3020 DATA 1,-1,-1,1

i9, 1,-3, 3, -7, 3,7,-4,9, 4, -7,-4, 7,-

• 3 s 4 - 1,-4)

4

j -5, -4 , 4, -1,4, 1,-2,4,; i 4, 3

-48-
File 11

100 lie

115 £00

210

220

226

230

240

245

256

255

260

262

264

266

26S

270

272

274 276

280

290

300

316

320

330

340

350

360

370

386

390

400

460

470

430

490

500

510

520

530

540

550

560

570

580

59.0 600

610

620

630

640

660

760

770

773

776

780

790

810

820

830

flHG MAG For each frequency F, set:

REM: EVALUATING TRANSISTOR IH PROBE ASSEMBLY

DIM M[4]>PC4 3sS[2i2]>T[2»2]jU[2j2 3O/C2j2])WS[20»9]

FORMAT F9.3»F7.3jF8. 1*F7.3iF8.. 1jF7.3>F8. 1jF7.3jF8. 1 LOAD DATA 3<Z LOAD DATA 9<Q LOAD DATA 10.R DISP "HO. OF FREQUENCIES';! TO 20) = "? INPUT F9 DISP NO. OF TEST ITEMS* 1 TO 20::' = ".: INPUT F3 DEG F2=11+2*F3

F4=0

FOR Fl=12 TO F2 STEP 2 F4=F4+1 PRINT "S PARAMETERS FOR TEST ITEM NO. "F4 N=3 GOSUB 1000 LOAD DATA Fl-W PRINT " .311 S12 PRINT " FREQ MAG ANG MAG PRINT

FOR F=l TO F9 FOR 1=1 TO 2 FOR J=l TO 2 S[I»J3=Q[-FjK]

TC I, J]=Q[F»K+1 ] IJ[ I»J3=R£F>K3

VEI. J3=RCFiK+13

EC I» J]=WCFiK]*COS<W[F'jK+1 i: F[ I)J]=W[F)K]*SIN(W[F ! K+1 ]; K=K+2

NEXT J NEXT I GOSUB 150O GOSUB 17O0 MAT A=E \ m ,

MAT B=F ( MAT C=U \ _ T -i MAT D=V / 2 GOSUB 2000

HAT C=E

MAT D=F

HAT A=S

HAT B=T GOSUB 2000 GOSUB 1709 HAT i>COH

ANG MAG ANG'

Ti _1 » S + jT

Tj -1 - U + jV

S-parameters of probe assembly E + jF

Convert S to T parameters

Cascade parameters of probe assembly » E + jF

« TTj

Tr

Calculate TTj -1 - E + jF

Calculate Tj^TTj -1 - E + jF = t s Converts T 9 to Z s , Impedance parameters

HAT IX2CF. 1 ]>*Cl HAT H=':Z[F,£];'*C/ Z.- G +1H

P MAT E=E-G

MAT F=F-H

GO SUB 1600 GOSUB 2500

NEXT F STORE DATA F1+1»W

PRINT

PRINT "STORED IN FILE "FI+ N=4 GOSUB 1000 NEXT Fl REWIND

END

- transistor Impedance parameters

Converts Z to S , S-parameters

Prints S-parameters

Store S-parameter of transistor

-49-
File 11 (contd.)

Subroutines

1000 REM: SKIPPING N LINES

1010 POR 1=1 TO N 1020 PRINT

1030 NEXT 1 1040 RETURN

1200 PEN: CONVERTING X+JY TO M 8< P 1285 X=XCK]

1210 Y=YCK]

1215 MCK]=SQRCX*X+Y*Y)

1220 P=ATH(Y- ::.' 1225 IF X>0 THEN 1256

1230 IF Y>0 THEN 1245

1235 F-P-180

1240 GOTO 1258

1245 P=P+180

1250 P[K] = P 1255 RETURN

1275 REM: CONVERTING M & P TO 1280 X[K]=MCK]*COS<R[K])

12S5 YCK]=t'1[K]*SIN(R[K]>

1290 RETURN

1500 PEN: CONVERTING

1510 MAT I=IDNC2i2]

1520 MfiT fl=I-E 1530 MAT B=<-1>*F

1540 GOSUB 2100

1550 MAT H=I+E

1560 MAT B=F

1570 GOSUB 20OO

15S0 MAT E=C50)*E

1590 MAT F=<50)*F

1599 RETURN

1 600 REM: CONVERTING

1610 MAT I=IDN[2.2]

1620 MAT E=(O.02>*E

ro z parameters; given s=e+jf< gives z=e+jf

TO PARAMETER GIVEN Z=E+JFj GIVES S=E+JF

1630 MAT A=E+I

1640 MAT B=<0.02)*F

1650 GOSUB 2100

1660 MAT H=E-I

1670 GOSUB 2000

1680 RETURN

1700 REM- CONVERTING Z TO P OR T TO Z PARAMETERS

1710 REM: GIVEN Z=E+JF, GIVES T=E+JF. GIVEN T=E+JFj GIVES Z=E+JF

1720 E2=E[-li 1 ]*E[2j2]-FC 1- 1 3*FC2j2 3-El i.2 3*E[2, 1 ] + FC 1,2]*F[2- 1 I 1730 F[ 1,23=E[ 1. 1 ]*FC2j2 3+F[ 1, 1 3*E[2<2 3-E[ 1>23*F[2j 1 3-FC 1j2]*E[2i 1 1 1740 EC 1>23=E2

1750 C0=EC2i 1 ]*EC2. 1 I+FC2, 1 3*FC2) 1 I 1760 MAT I=IDN[2<2 3 1770 MAT A=<EC2j 1 3/C0>*I

1730 MAT B=<-F[2s 1 ]/C0)*I

1790 E[2j 1 3=1 1S00 FC2'»1 3=0 1810 MAT C=E

1320 MAT D=F 1830 GOSUB 2O00

1840 RETURN

-50-
File 11 (contd.)

2000 REM: MULTIPLYING 2 COMPLEX MATRICES E+JF=<fi+JB)*<C+JD)

2010 MAT G=B*D

2020 MAT E=A*C

2030 MAT E=E-G

2040 MAT G=B*C

2050 MAT F=R*D

2060 MAT F=F+G

2070 RETURN

2100 REM: INVERTING A COMPLEX MATRIX C + JD=INV<: A+JEO 2110 mat g=inv<:a:>

2120 MAT H=G*B

2130 MAT C=B*H

2140 MAT C=A+C

2150 MAT C=INVCC)

2160 MAT D=H*C

2170 MAT D=C-1>*D

2180 RETURN

2190 DIM flC2»2].BC2j2].CC2.2].DC2.2] 3 EC2j2]»FC2»2]>GC2.2]»HC2.2]

2200 REM: PRINTING ELEMENTS OF E+JF not used

2210 PRINT "PARAMETERS (REAL 8, IMAGINARY) ARE" 2220 PRINT

2230 print "ud = "Ei l- 1 ];fe i. i j; "a 2.-' = "eci,2];fci.2]

2240 PRINT "C2D = "EI2, 1 ]:F[2, 1 ]! ' C22) = "EC 2, 2 ]j FC 2. 2 ] 2250 PRINT

2260 RETURN

2300 REM: READ MATRIX E+JF IN ORDER 11,12-21)22 not us«d

2310 FOR 1=1 TO 2 2320 FOR J=l TO 2 2330 READ ECI.J].FCI.J]

2340 NEXT J 2350 NEXT I 2360 RETURN

2500 REM: CONVERT ELEMENTS OF E+JF TO MAGNITUDE & PHASE. PRINT

2520 K=l 2530 FOR 1=1 TO 2 2540 FOR J=l TO 2 2550 X=EL I.J]

2560 Y=Ft I.J]

2570 GOSUB 1215

2580 L=2*K

2590 WCF.L]=MCK]

2600 WCF.L+1 ]=PCK]

2610 K=K+1

2620 NEXT J 2638 NEXT I 2640 WRITE (15. 115)WCF, 1 ]>M[ 1 ].PC 1 ]. MC 2 ], P[ 2 ]. HC 3 1, PC 3 ], MC 4 1. PC 4 ] 2650 RETURN

51-
form NBS-114A (1-71) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS TN-663

2. Gov't Accession No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Characterization of a High Frequency Probe

Assembly for Integrated Circuit Measurements

5. Publication Date April 1975

6. Performing Organization Code

7. AUTHOR(S) 8. Performing Organization

R. T. . Jp.qr-h anH C.

.

A^ Hner

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2764370

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Department of the Air Force

Air Force Weapons Laboratory

Kirtland Air Force Base, New Mexico

13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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

bibliography or literature survey, mention it here.) A detailed, applications-oriented description of

a measurement technique that characterizes a highfrequency probe assembly for integrated circuit

measurements is given along with the procedure that

extracts the parasitic effects of the probe assembly

from measurements made at the input connectors of

the probe assembly. The scattering parameters of

an integrated-circuit device or transistor can now

be extracted and accurately determined up to 2 GHz

at the wafer stage of assembly. This represents a

significant advance over conventional techniques

that enable only dc parameters to be measured. Measurement results using this technique are given along

with the precision of values obtained as well as the

nature of the measurement bias introduced by the

probe assembly.

17. KEY UORDS (Alphabetical order, separated by semicolons)

High frequency probe assembly; integrated circuit transistors;

parasitic element; S-parameters

.

18. AVAILABILITY STATEMENT

ZK UNLIMITED.

i I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

55

22. Price

$1. 10

USCOMM-DC 66244-P7
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