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Jta
REFERENCE

N B S

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*\ Ai-2. \

6

°»£ AU 0* * NBS TECHNICAL NOTE 673

NBS

Publications

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

/9 75
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards 1 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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OP STANDARDS

NOV 2 S 1975

Using Six-Port and Eight-Port Junctions

To Measure Active and Passive

Circuit Parameters

Cletus A. Hoer

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

#** or / w \

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

John K. Tabor, Under Secretary

Dr. Betsy Ancker-Johnson , Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

Issued September 1975
NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 673

Nat. Bur. Stand. (U.S.), Tech Note 673, 29 pages (Sept. 1975)

CODEN: NBTNAE

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

(Order by SD Catalog No. C13. 46:673) $0.80
CONTENTS

Page

ABSTRACT 1

I. INTRODUCTION 1

II. PHASE FROM AMPLITUDE MEASUREMENTS - IDEAL CIRCUITS 3 Basic Idea 3 Correlator 3 A Vector Voltmeter 5 Six-Port Ref lectometer 5 Eight-Port Ref lectometer 7 Limitations of Ideal Circuits 8

III. ARBITRARY SIX-PORT AS A VECTOR VOLTMETER 9 General Theory 9 Complex Voltage Ratios 11

Self-Calibration Procedure 11

Broadband Two-Position Insertion Device 13

Six-Port Design Criteria 13 Experimental Setup 17 Results 17

IV. ARBITRARY SIX-PORT AS A REFLECTOMETER 18

General Theory 18

Calibration Techniques 19

Design Criteria 21 Experimental Results 21

V. FUTURE APPLICATIONS 22

VI. BIBLIOGRAPHY 22
ILLUSTRATIONS

Figure Pag e

1. Getting the phase angle $ from the law of cosines 2

2. Using a 180° hybrid (H) and a quadrature (90°) hybrid (Q) to get the sum and difference vectors shown in Figure 1 2

3. Correlators constructed from hybrid junctions (H) , quadrature

hybrids (Q) , and in-phase power dividers (D) 2

4. Using the four outputs of a correlator to display a dot indicating

phase angle <j> and the amplitude |aia2| 4

5. Adding two power dividers (D) and detectors P3 and P4 to the

correlator to make an eight-port vector voltmeter 4

6. Experimental eight-port vector voltmeter for the 8-12 GHz range .... 4

7. Combining quadrature hybrids (Q) and a power divider (D) to make an an eight-port vector voltmeter having two input ports and six output

ports which are terminated with diode detectors. The signals labeled

at different parts of the junction are those one would obtain from

ideal components if the two input signals are 2 2a 1 and 2 2a£ .... 4

8. A four-probe ref lectometer consisting of four identical voltage probes

spaced an eighth of a wavelength apart beginning at a distance nX/2

from the reference plane 6

9. Using two directional couplers with a correlator to get the same outputs as the four-probe ref lectometer 6 10. Eight-port ref lectometers capable of displaying T, Z or Y directly on a scope 6 11. An abritrary six-port junction with power meters on four of the six

ports, being used as a vector voltmeter 9 12. Setup for calibrating and using a six-port junction to measure

complex voltage ratios 12

13. Using a quadrature hybrid (Q) and a power divider (D) to make an insertion ratio of 3 dB with 45° phase shift 12

14. Experimental six-port junction and power detector mounts 14

15. Experimental six-port X-band vector voltmeter setup. From left

to right: Programmable calculator, Input/Output Expander,

DVM and Scanner, four power meters, six-port junction (on

white paper) , and two input signal lines 15

16. An arbitrary six-port junction with power meters on four of the six

ports being used as a ref lectometer 16

17. Six-port ref lectometers which satisfy the design criteria in Table 4 . . 20
TABLES

Table Page

1. Summary of equations for generalized six-port junctions and also two corresponding ideal eight-port junctions. The coefficients of the

power readings P3 . . . Pg are constants which are determined by

calibrating the junction for the intended application vi

2. Outputs of an ideal eight-port vector voltmeter, used as a guide in

designing a six-port vector voltmeter 16

3. Amplitude and phase change in the two-position step attenuator as measured by the six-port with diode power meters and by the NBS

Automatic Network Analyzer 16

4. Outputs of an ideal eight-port ref lectometer, used as a guide in

designing a six-port ref lectometer 20
Table 1

PHASE INFORMATION FROM AMPLITUDE MEASUREMENTS

Bneralized Six-Port Vector

Voltmeter

Generalized Six-Port Reflectometer

U CM U) U.

SIX-PORT JUNCTION A* , *

a 2 b 2

pU CP<J UJ U

0. SIX-PORT JUNCTION ±

a i - Ep±p

±

|a 2 | 2 =Eo,Px x

iia2 I cos <J) = "/, x.P. i 1

iia 2 | sin <j) = Eyip

i

i = 3

a 2 E

(x

i + J Vp

i E pi

p

i

|a| 2 -SVi

ab I cos ill =y*— c.P.

' x x

ab | sin ty =^T s .P.

b E

(c

i +

* s

i )pi r = E

a

ipi

|v| 2 = £v.P. " 1 1

P = Ivil cos =y q.P,

»" = Ivil sin =V r.P. V(q. + j r.)P4 V ^-> X

J X X

Z = IVi

leal Eight-Port Vector Voltmeter

|a 1+a

2

| 2

|a x-a

2

| J

I'll'

CORRELATOR

l*2

l'

2 -4=

l» 1 -J a

2

| 2

l a

l + 3 a2

I 2

aiM = k P ;

|a 2 | 2 = k P„

a!a 2 I cos (f> = k (P 5 - P7)

aia 2 I sin cf> = k (P 6 - P 8 )

, - (P5- P7) + .1 (P 6 ~ Pa ) P3

Ideal Eight-Port Reflectometer

| a + bl ' la - b! 2 GH EIGHT-PORT VECTOR VOLTMETER &

V^/> *rT-> |a-jb|' |a-jb| J

Ibl* K3

X

|a|" = K P 3

|b| 2 = K P„

|ab| cos ty = K (P 5 - P 7 )

[ab I sin ij) = K (P 6 - P 8 )

r = (Ps - P 7 ) + .1 (Pe - Pa ) P3

|v| 2 = 4K P 5

iZ | 2 = 4K P 7

|viZ | cos 9 = K (P 3 - P^)

|viZ | sin = 2K (P 6 - P 8 )

Z m

(P 3 - Pi») + 2j(P 6 - Pa ) Zo 4 P 7

mmary of equations for generalized six-port junctions and also two corresponding ideal eight-port

notions. The coefficients of the power readings P3 ... P 8 are constants which are determined by

calibrating the junction for the intended application.
USING SIX-PORT AND EIGHT-PORT JUNCTIONS TO MEASURE

ACTIVE AND PASSIVE CIRCUIT PARAMETERS

Cletus A. Hoer

This review paper brings together a number of old and new methods for

measuring voltage, current, power, impedance, and phase angle using

only amplitude type detectors. Vector voltmeters and ref lectometers

can be constructed to measure all of these quantities in terms of four

amplitude measurements made on four arms of a six-port junction. Whereas previous uses of this type of instrument depended on precision components for accuracy, new equations switch this dependence primarily to detector linearity and only secondarily on the properties of the measuring

device itself.

KEY WORDS: Admittance; automated precision measurements; correlator;

current; impedance; microwave circuit parameters; microwave measurements;

phase angle; power; ratio; reflection coefficient; reflectometer; selfcalibration; six-port; vector voltmeter; voltage.

I. INTRODUCTION

Perhaps the greatest impact in the field of UHF and microwave measurement in recent

years has been the introduction of the Automatic Network Analyzer. In contrast with the

prior art where the key to improved accuracy was usually an improved hardware item, the procedure now is to measure the hardware imperfections and adjust the measurement results in

such a way as to account for them. The key to this correction process is in the measurement

of the phase as well as amplitude of the complex parameters involved. The measurement of

this phase has generally involved conversion to a lower frequency which complicates the detection process. Although phase detection circuits which operate directly at the UHF and microwave frequencies are well known, these have generally assumed ideal components, and are not

particularly suitable for automation.

Recent theoretical studies of an arbitrary six-port junction have provided an alternative

method of obtaining the phase information without requiring either frequency conversion or ideal components. The theory shows that any six-port junction which has four linearly independent ports terminated with power detectors can be used to measure active and passive circuit parameters such as voltage, current, power, impedance, phase angle, and complex voltage

ratios. Phase angle as well as amplitude of the desired circuit parameters are determined

by the four power readings. Accuracy of the measurements is primarily a function of the

linearity of the power detectors, and only slightly dependent on the properties of the sixport junction itself. Precision components are not required to make precision measurements.

Components are available to build six-port junctions up to 200 GHz.

One of the unexpected results of this study is that most of the earlier designs for

getting phase information from simple amplitude measurements provide a set of data which is

ill conditioned from the viewpoint of the more general theory. Fortunately, the theory also

suggests how these designs can be modified to eliminate this condition. Some of these earlier

phase detection circuits will be reviewed to show how one can obtain phase information directly

at the measurement frequency using only amplitude (e.g. power) detectors. This review of ideal

circuits will lay the groundwork for understanding how a properly designed linear six-port junction can be used to make the same measurements more accurately without requiring the use of

precision components.

Section II discusses six-port junctions which have been used in the past to make voltage

ratio measurements and measurements of impedance. Some new ideas are added to make these old

circuits more useful, leading to the design of a vector voltmeter and a reflectometer each

having eight ports. Section III goes into the generalized six-port theory, showing how an arbitrary six-port junction can be used to measure complex voltage ratios. Section IV shows

how an arbitrary six-port junction can be used to measure complex impedance or reflection

coefficients. Equations for the generalized six-port are summarized in Table 1 which also

gives examples of corresponding ideal eight-port junctions and their equations.

Partial support of this work by the Naval Sea Systems Command, USAFSAM, and the

Army Metrology & Calibration Center is gratefully acknowledged.
a 2

a, - a.

(a)

D a :

a i " D* 2

(b)

Figure 1. Getting the phase angle (j) from the law of cosines,

a 2

H

_

~*"a i

a! + a 2 a 2

Q

"*" a i

a, - ja.

a i " Da.

(a) !b)

Figure 2. Using a 180° hybrid (H) and a quadrature (90°) hybrid (Q) to get the sum and difference vectors shown in Figure 1.

a, + a. a, - a. |a x + a 2 Qh-x@ Gh-s®

(a)

b, a-

(b)

/vw-—

I

a, b.

a, - ja 2 I 2 |a, + ja.

D a2 b2

6

Da I a, + ja2

Figure 3. Correlators constructed from hybrid junctions (H)

,

quadrature hybrids (Q) , and in-phase power dividers (D)

.

-2-
II. PHASE FROM AMPLITUDE MEASUREMENTS - IDEAL CIRCUITS

Basic Idea

Consider two sinusoidal voltages ai and a2 having the same frequency and related in phase

as shown in figure la. The phase angle <j> between a 2 and aj can be determined by measuring the

amplitude of a i5 a 2 , and either ai - a 2 or ai + a 2 and calculating the angle from the law of

cosines;

|ai - a2 | 2 = |ai| 2 + |

2 | 2 - 2|aia2 | cos (1)

lai + a 2 | 2 = | a.!

| 2 + |a 2 | 2 + 2|aia 2 | cos (2)

If the amplitude of both the sum and difference vectors are measured, the phase angle can be

obtained from

4|aia 2 | cos <j> = ai + a 2 | - |ai - a 2 1 (3)

which is (2) minus (1). One disadvantage of calculating <j> from any one of these three equations is that cos <j) is sensitive to angles near ±90° but insensitive to angles near 0° and

180°. Also, the cosine does not give the sign of the phase angle, only its magnitude. What

is needed in addition to cos (J) is the sin <j> which is sensitive to angles near 0° and 180°

and which also gives the sign of the phase angle.

One way to get sin <j> is to shift either ai or a 2 90° and then combine to get the sum and/or difference. Figure lb shows the result of shifting a 2 90°. The sum and difference

amplitudes are

|ai + ja 2 | 2 = |ai 2

| + |

2 | 2 - 2|aia 2 | sin (4)

ai - ja 2 | ai + a 2 + 2 aia2 sin (5)

which combine to give

4|aia 2 | sin = ai - ja 2

2 - |a x + ja 2 | 2 (6)

To get the sum and difference of two signals, a 180° hybrid junction or magic tee can be

used as shown in figure 2a. To shift one of the signals 90° relative to the other and then

combine to get the sum and difference, a quadrature (90°) hybrid can be used as shown in

figure 2b.

Correlator

Quadrature hybrids and 180° hybrids can be combined in different ways to make a device

called a correlator or phase-discriminator [1] whose outputs give both cos (j> and sin (j) from

amplitude measurements. Two correlators are shown in figure 3. Both have the same output

amplitudes, but the one in figure 3b is more practical at frequencies above about 1 GHz where

quadrature hybrids are less expensive than 180° hybrids. The boxes labeled "D" are power

dividers which split an input signal into two output signals each having the same amplitude

and phase angle relative to the input signal. The amplitudes of the four output signals are measured with power detectors P5 ... P 8 . The phase angle <j> between the two input signals

ai and a2 is calculated from (3) and (6) which can be written

|aia 2 | cos <J) = R (P 5 - P7) " X.

|aia 2 | sin (J) = R (P 6 - P B ) * Y,

(7)

(8)

-3-
+

+

Y-axis

X-AXIS

SCOPE

Figure 4. Using the four outputs of a correlator to display a dot

indicating phase angle <j) and the amplitude |aia 2 |.

a.- D a. a 1+ ja

2 Figure 5. Adding two power dividers (D) and detectors P 3 and P 4 to the correlator to make an eight-port vector voltmeter.

Figure 6. Experimental eight-port vector voltmeter for the 8-12 GHz range,

CORRELATOR

A

a 2 -a i

ja 2

-ft

a2 " Dai 2

ai-]a 2

-IG —WV

1 ' -D2a x

REFERENCE

SIGNAL

Figure 7. Combining quadrature hybrids (Q) and a power divider (D) to make an eightport vector voltmeter having two input ports and six output ports which are terminated

with diode detectors. The signals labeled at different parts of the junction are those one would obtain from ideal components if the input signals are 2 • 2a j and 2. 2a2 .

-4-
where each detector is assumed to have the same input resistance R. If each power detector

has an output voltage proportional to the rf input power, these voltages can be combined as indicated in (7) and (8) to get two voltages X and Y . When X and Y are connected to the

horizontal and vertical inputs of a scope, it will display a dot which indicates both the

phase angle (f> (0 to 360°) and the amplitude |aia2 | as shown in figure 4.

A Vector Voltmeter

The correlator is unable to measure | a i

| or |a 2 |, only the product |aia|. To separate

|ai| and |a2 | , one can add two more power dividers and detectors to the correlator as shown

in figure 5. This circuit acts like a vector voltmeter in that it measures the amplitude of

the two input signals as well as the phase angle between them. If P 3 is used to level the

generator so that |ai| is held constant, the scope display in figure 4 indicates the amplitude

and phase of the complex voltage ratio a 2 /ai . Amplitude and phase information are calculated

from the following equations which are for an ideal eight-port vector voltmeter.

ai

2 _ 2RP;

|a 2 | 2 = 2PJ\

|aia2 | cos <f> = 2R(P 5 - P 7 )

|a!a 2 | sin $ = 2R(P 6 - Pe)

The complex voltage ratio a 2 /ai is given by

(9a)

(9b)

(9c)

(9d)

a 2 ai

|aia2 [(cos (j) + j sin <{)) ^7P

(P 5 - P 7 ) + J(P 6 - Pe)

(10)

Figure 6 is a photograph of an eight-port vector voltmeter constructed from commercially

available miniature coaxial X-band quadrature hybrids and a power divider. Back diodes are

used for power detectors. The components in the photograph are identified in figure 7 which

also shows how the signals are combined to get the six desired outputs.

Six-Port Ref lectometer

The four-probe ref lectometer [2] shown in figure 8 is a six-port junction used to display

complex reflection coefficients in the same way that a correlator is used to display complex

voltage ratios. The reflection coefficient, T, is a complex voltage ratio, the ratio of the

voltage wave, b, reflected from a device to the voltage wave, a, incident on the device,

r =

'a 1 (ID

where the angle ¥ between a and b is the phase angle of the reflection coefficient. Equations

for getting ¥ in terms of amplitude measurements are identical to (1) through (6) if a\ is

replaced by a, a 2 by b', and <}), by ¥. Equations (3) and (6) then become

4 | ab | cos ¥ = | a + b| 2 - |a - b|

4 ab sin <F - jb| 2 - |a + jb|

(12)

(13)

The four amplitudes on the right of (12) and (13) can be obtained with four identical voltage

probes spaced an eighth of a wavelength apart in a uniform lossless transmission line as shown in figure 8. If the outputs from these probes are measured with power detectors

P5 ... P 8 , equations (12) and (13) become

|ab|cos V = K(P 5 - P 7 ) -> Xy

lab I sin T = K(P 6 - Pe) * Y

¥

(14)

(15)

where K is determined by the coupling between the probes on the transmission line. If the

voltage Xy and Y^ are connected to a scope, it will display a dot indicating the phase angle

'F, and the amplitude |ab| which is proportional to |r|.

-5-
G>

p 8 p 7 u p

2

A/W

b a

r = 1—h e a

Figure 8. A four-probe ref lectometer consisting of four identical voltage probes spaced

an eighth of a wavelength apart beginning at a distance nA/2 from the reference plane.

a + b P 7

) I

0" WvA^ x

CORRELATOR

P 6 )

I Pa-jb|-2 |a+jb|

a->a b

X

--VW

a

Figure 9. Using two directional couplers with a correlator to get the same outputs as the four-probe ref lectometer

.

la + bl 2 la - bl 2

EIGHT-PORT VECTOR VOLTMETER

a, a a

£>

vwv- X

a-jb| 2 |a+jb|

A a

2 a b

X

VW

(a) A/W

AAA^ X X

^vw

Pe) (Ps.

(b) rA

2

Figure 10. Eight-port ref lectometers capable of displaying

T, Z or Y directly on a scope.

-6-
Another way to make a six-port ref lectometer for measuring complex reflection coefficients in terms of amplitude measurements is to use a correlator with two directional

couplers as shown in figure 9. The outputs of the two (ideal) couplers, which become the

inputs to the correlator, are proportional to a and b;

ai = l

1^ a , a 2 = S 29 b (16) ^90

where the S's are scattering coefficients between ports indicated by the subscripts. If

the scattering coefficients satisfy

I

1-2- = S 29 , (17)

then the correlator measures the ratio a 2 /ai = b/a which is T. Equation (17) is satisfied

by adding attenuation and phase at the output of one of the couplers. Equations for calculating or displaying f and |ab| are identical to (14) and (15) with K = R/|s 2 g|

2

. One

advantage of the correlator-coupler design is that broadband components can be used in its

construction, whereas the four-probe design has the correct probe spacing only at one

frequency.

Eight -Port Ref lectometer

An eight-port ref lectometer can be constructed by connecting the eight-port vector

voltmeter of figure 5 to the output of two directional couplers as shown in figure 10. This arrangement has several advantages over the six-port reflectometers in figure 8 and 9. The additional two detectors P 3 and Pit make it possible to separate |a| and |b| and also to display impedance, Z, and admittance, Y, as well as T directly on a scope.

If (17) is satisfied, the six outputs of the ideal eight-port ref lectometer give a set

of equations similar to those in (9) and (10) for the ideal eight-port vector voltmeter;

|a| 2 = K P 3 (18a)

|b| 2 = K F k (18b)

|ab|cos V = K(P 5 - P 7 ) (18c)

|ab|sin Y = K(P 6 - P 8 ) (18d)

where

K = l^T^ (19)

IS 29

The reflection coefficient can be written

r = ' ab ' (C ° S ^ 8lny ) (20a)

= (P5 - P7) ^

(P6 -

Pfi)

. (20b)

Leveling the generator with P 3 so that |a| is held constant at the reference plane will give

a scope display (using X„, and Y as before) whose radius is proportional to |r|.

Recall that the voltage, v, and the current, i, at the reference plane are related to the incident and reflected waves by

-7-
v = a + b (21)

iZ = a - b . (22)

where Zo is a constant usually chosen equal to the characteristic impedance at the reference

plane. With the help of (21) and (22), one obtains a set of equations similar to (18) giving

v, i, and the phase angle between v and i in terms of the six amplitude measurements*:

|v| 2 = 4KP 5 (23a)

|iZ | 2 = 4KP 7 (23b)

|viZ |cos 6 = K(P 3 - PO (23c)

|viZ |sin 6 = 2K(P 6 - Pe) (23d)

Equations for Z and Y are similar to (20) for T.

Z _ (P 3 - PO + 2.1 (P 6 ~ Pe)

Z 4 P 7 (24)

YZ = (P3-P^

4

-p

2 ,i(P 6 -P B ) (25)

If Xfl is a voltage corresponding to (P3 - Pi»)/2, and Y

fl (=YV)/ ) is a voltage corresponding

to P6 - Pe> these two voltages can be applied to the X and Y axis of a scope to display a dot

indicating the phase angle 9 and the amplitude | viZ | • Leveling the generator with P7 will

hold the current constant at the reference plane, and give a scope display whose radius is

proportional to |z|. Leveling the generator with P5 will hold the voltage constant at the

reference plane, and give a scope display whose radius is proportional to |Y|. Since the

phase angle of Y is -0, the voltage Y on the Y axis of the scope must be reversed to get

the correct sign of the admittance phase angle.

Another way of making an eight-port ref lectometer is by adding two directional couplers

to the four-probe ref lectometer as shown in figure 10b. If (17) is satisfied for the

couplers, and if each probe coupling is 6 dB less than the coupler coupling, S29, all of

equations (18) - (25) apply to figure 10b also. The design in figure 10b is easier to construct than that in figure 10a, but the above equations will hold only at the frequency

where the probe spacing is as indicated.

Limitations of Ideal Circuits

One problem with all of the previous circuits is that it is difficult to get components

good enough for precision measurements. Tuners and other hardware can be added to force one

or more of the outputs to read exactly as desired [3] , but that requires time and patience,

and is usually correct at only one fixed frequency.

In attempting to correct for non- ideal components, a detailed circuit analysis of some

of the preceding networks was performed at NBS several years ago. This analysis led to the

surprising result that, with few exceptions, any linear six-port junction with four ports

terminated with amplitude measuring detectors (e.g. power detectors) can be described by

* Since (17) must be satisfied for (23a) and (23b) to hold true, these equations provide

an easy way of determining when (17) is satisfied. With a short at the reference plane

so that v=0, attenuation and phase are added to the output of one of the couplers until

P5=0. Likewise, P7 must equal zero with an open at the reference plane.

-8-
Figure 11. An arbitrary six-port junction with power meters on four

of the six ports, being used as a vector voltmeter.

the same set of rather simple but exact equations. The contents of the junction do not

matter. It is not necessary to have precision components to make precision measurements.

The remainder of this paper will derive the general six-port equations and describe techniques for calibrating an arbitrary six-port for several different applications. An arbitrary six-port will first be analyzed as a vector voltmeter, and then as a reflectometer.

III. ARBITRARY SIX-PORT AS A VECTOR VOLTMETER

In this section we will show that it is possible to use an arbitrary six-port junction

as a vector voltmeter, measuring the amplitude of two input signals as well as the phase

angle between them in terms of power measurements made on four of the six ports [4]

.

General Theory

Consider the arbitrary six-port junction shown in figure 11, where four ports are terminated with power meters. If the junction is linear and only one mode is present at each port, the scattering equations for the junction can be written

>i -£

j=i

S. .a. ij 3 i = 1 6, (26)

where a. and b, are the complex incident and emergent wave amplitudes and the S.. are the

j i &

ij

scattering parameters of the junction. Assuming that the power meters on arms 3 ... 6 are permanently connected,

a.

3 b. r.3 3

3 = 3 (27)

where Y. is the reflection coefficient of the power meter on port j. Equations (26) and (27)

represent a collection of ten linear equations in terms of the twelve variables a., b.,

i = 1 ... 6. This system of equations may be solved for any ten of these variables as functions of the remaining two. In particular, it is possible to write

b. = A.ai + B.a2 , i = 3 ... 6, i l l (28)

where A. and B. are functions of the scattering parameters of the junction and the reflection

coefficients or the power meters. Multiplying (28) by its complex conjugate yields

lb. I 2 = |A.| 2 |ai| 2 +A.B.a 1 a 2 + A.B.a!a2 + IB.

|

2 la 2 I

' i

1

' l

1

. ' ' li li ' i

1

' 1 = 3 ... 6 (29)

where (*) indicates complex conjugate.

If the phase angles <j>i, <b 2 and (j) are defined such that

ai = ai e

J<Pi a2 a 2 e

JtP2 (30)

-9-
and <j) = cf>2 - (jii, then (29) becomes

P-^ = |A.| 2 lai| 2 + (A.B. +A.B.) la^l cos <)> 1

+ |B

±

| 2 [a 2 | 2 + J(A

±B - A.B ) |aia2 | sin <|> , i = 3 ... 6 (31)

where P. = K. |b. |' is the power indicated by the meter on the i port, and K. is a constant.

This expression represents a linear system of four equations in the four unknowns |ai| 2

,

|

a

2 1 » |aia2| cos <}) and |aia2| sin <|>. If these equations are independent^, they may be

inverted to obtain each of the four unknowns as a linear function of the four P. (i = 3 ...6).

The result is

a

2

1

I 2

= Z P-^ (32a)

= £ a. P. i = 3 ... 6 (32b)

la a I cos $ = y x.P. (32c)

' i 2' ^ i i

la a | sin <J> 1 = V y.P. (32d)

i 2

1 ^

'i i

where each sum in (32) and throughout this paper is over the four sidearm power readings.

The coefficients of P. are real numbers which are functions of the parameters S.. and I*.. i ij 3 Equations (32) constitute the desired result and are valid for any linear six-port junction

subject to the conditions mentioned.

Note that it is not necessary to measure absolute power at the sidearms. As long as P indicated by the sidearm power detector is proportional to the absolute power, the proportionality constant is absorbed in the coefficient of each P. in (32).

Using (32) in (10a) gives

T(x, + jy,)P,

(33)

V (x. jy.)P.

a 2 *-> 1 1 1 £ p

i pi

Equations (32) and (33) should be compared with (9) and (10) for the ideal eight-port vector

voltmeter.

A more useful form of equation (33) for calibration purposes is obtained by factoring x + iy out of the top sum and factoring p out of the bottom sum to get m

J m n

ajL = k Z

Z iP

i (34)

E

W.P.

X 1

where k, z., and w. are new constants such that z. = 1 when i = m, and w. = 1 when i - n, so that only f.hree complex z. and three real w. need to be determined by some calibration process,

For many applications the complex constant E does not need to be known.

This condition is not satisfied by the ideal correlation discussed in section II. For any correlator, the matrix to be inverted in (31) is either singular or nearly so, leading to the ill condition mentioned in the introduction. The "Six-Port Design

Criteria" below shows how to modify the correlator to eliminate this ill condition.

-10-
Complex Voltage Ratios

Using (21) , the voltage at the two input ports can be written

v 111 . = a . + b .

= a.(l + r.)

where V. is the complex ratio b./a. at port i; 1 11

r = s + s ^

i ii 12 ai

r = s + s ai

i = 1, 2

22 21 32

(35)

(36)

(37)

(38)

The scattering parameters in (37) and (38) are those of the equivalent two-port obtained by

terminating the four sidearms of the six-port with power meters. The ratio of the two input

voltages is

212. vi

a 2 (i+r 2 ) aid+ro (39)

The voltage ratio will be proportional to a2/ai provided that there is sufficient isolation

between input ports 1 and 2 so that any change in T\ or r 2 due to a change in ai or a2 is

negligible.

Self-Calibration Procedure

All of the constants in (34) except k can be determined by a self-calibration technique

which does not require any standards. A calibration circuit such as shown in figure 12 is

used. A signal is divided into two channels which are connected to the inputs of the six-port.

The signal a\ in one channel is held constant by internally leveling the generator and

isolating it from the signal a 2 in the other channel which contains a level set attenuator,

ao» phase shifter, <j)o, and a two-position insertion device. Data for calibrating the sixport is obtained by noting the value of all P. for the two positions of the insertion device

at different settings of ao and (f>o. The value of the insertion device does not need to be

known, but it must be highly reproducible and independent of signal level.

The initial value of a 2 relative to aj is determined by the setting of ao and <J>0 , which

also need not be known. When the insertion device is switched to its second position, a 2 changes to a 2 and the power readings change from P. to Pi. Assuming that aj is constant

during the time it takes to read P. and Pi

i l

i i (32a) gives

ULL Z) w - p - = Y, w.p! *-* ii *—' ii (40)

The ratio of a2 /a 2 obtained from (34) is

y z.p!

*-i i i £ z

ip

i

'

This L is the change in insertion ratio of the two-position insertion device.

(41)

-11-
AA/V

/\y

ISOLATOR

t

DVM

SCANNER

SIX-PORT JUNCTION

CALCULATOR

INSERTION

POINT

»

TWO-POSITION

INSERTION DEVICE

Figure 12. Setup for calibrating and using a six-port

junction to measure complex voltage ratios.

-V\A—

I

IN s=*

\/ 3 dB /45° + 9

'

OUT

dB /

Figure 13. Using a quadrature hybrid (Q) and a power divider (D) to make

an insertion ratio of 3 dB with 45° phase shift.

-12-
The measurements of P. and P! are repeated for four or more different settings of ao and <J>o. Each different setting gives additional equations like (40) and (41) where L is the same for each measurement . These two sets of equations can be solved for the calibration

constants z., w. and also for L. If L is known it can be thought of as the standard in the

calibration process. However the calibration process works equally well if L is not known.

To assure that L remains constant when ao and $o are changed, and that a x remains

constant at the two position of L, isolators are added as shown in figure 12.

The constants p , and x + jy cannot be determined by this calibration process. However, for measuring complex insertion ratios, these constants are not needed. Complex

insertion ratios of a 2 /a 2 can now be measured using the known z. in (41). Using the z. and

w. in (34), ratios of a 2 /ai can be measured to within a constant k.

Broadband Two-Position Insertion Device

In calibrating the six-port, the complex insertion ratio, L, of the repeatable twoposition insertion device must not have a phase angle of 0° or multiples of 90°. A phase

shift of 45° works well and is easy to generate. One way of getting 45° phase shift over

a broad frequency range is shown in figure 13. The two outputs of the quadrature hybrid

(Q) are equal in amplitude but 90° out of phase. Adding these two signals with an in-phase

power divider (D) gives a signal that is shifted 45° relative to the input signal. In addition to this 45° there will be some phase shift 6 due to the lengths of line. The

length of the lower path can be adjusted to give a phase shift equal to 0. The phase difference in the two switch positions will be 45° over the complete frequency range of the hybrid

and divider, which can be the same as the frequency range of the six-port. The amplitude

of the insertion ratio will be 3 dB.

The optimum value of |l| to calibrate the six-port has not been determined. Values near

3 dB and 8 dB have been used with no noticeable difference in results.

Six-Port Design Criteria

Comparing (32) and (9) leads one to expect that the four outputs of a practical six-port

vector voltmeter would be some combination of the six outputs of the ideal eight-port vector

voltmeter shown in figure 5. This is indeed the case. These six outputs are listed in

Table 2. It can be shown that a practical set of four outputs includes one from each group

in Table 2. The fourth output can be any one of the six not already used. For example, if

| a.i | - | a.2 | , a practical six-port vector voltmeter could have outputs approximately proportional to

|ai| 2

, |ai + a 2 | 2, |ai - ja 2 | 2

, and |a 2 | 2

. (42)

Or if | a^ | << | a-i | one might design the outputs to approximate

|ai -a2 | 2

|ai| 2

, |ai + a 2 | 2, |ai - ja 2 | 2

, and / or I (43)

|ai + ja 2 | 2

Here |ai - a 2 | or |ai + ia 2 | 2 is used instead of |a 2 | 2 because |a 2 | 2 might be too small

to measure, but |aj - a 2 | or |aj + ja 2 | 2 would still contain useful information about a 2 .

It should be emphasized that the outputs listed in Table 2 are only design goals. The

actual outputs of a six-port can depart considerably from these values and still be quite

useful. When the outputs depart greatly from those in Table 2, the coefficients of P. in

(32) become large so that the desired information is obtained from the difference between

large terms in the sum. As the individual terms in the sum become significantly larger than

the quantity on the left of the corresponding equal sign in (32), greater precision is

required in measuring each P. to obtain a given accuracy.

-13-
» w

<-t

~"*; »<Mj §MO

•UO

(D

J-i 0) T)U

atICmeono

a.

•H

05 J

a>

(UM3

60 •H

Fn - 14 -
60

U

•H 0)

0)

O E u

(1)

0)

ts • O 0) ft 01 6 H -H O 3 i-H u o

P^ 14-1 rH

cd - s • ^ 60

ft 0> -H 3 fi ID

4-1

C

0) Cfl 4-1 CO CJ 3

C/3 ft

H

C

CU 13 -H

4J

C

oi cd o

4-> 2 4-1 •H > o n t3 >

*> £CO

O CD •> T3 ^"^

CJ S M

01 CO 0) > &£ •oh a

CO f

4-1 0) 3 4-1 ft -H

X 4-1 ,C O ao

ft 3 i ft oH

COC cO i-)

CD <-{ 6 3 4-1 •H O !-i M <-f O

41 5) ft

ft

O I X X W 01 -H • CO in g

i-H e

CO

a)M

Jj 60 3 o

60 ^

•H ft - 15 -
Group 1 Group 2 Group 3

|a,| 2

|a 2 | 2

|ai + a 2 | 2

|ai - a 2 | 2

|ai - ja 2 | 2

|ai + ja 2 | 2

Table 2. Outputs of an ideal eight-port vector voltmeter,

used as a guide in designing a six-port vector voltmeter.

FREQUENCY, GHz, 8 9 10 11 12

ATTENUATION DB

SIX-PORT

ANA

DIFFERENCE

7.82

7.75

7.58

7.57

7.52

7.48

7.91

7.92

8.53

8.36

.07 .01 .04 -.01 .17

LU - < LU X Q

D.

SIX-PORT

ANA

DIFFERENCE

38.15

38.09

34.13

34.81

33.19

32.45

31.49

31.73

31.00

30.91

.06 -.68 .74 -.24 .09

Table 3. Amplitude and phase change in the two-position step attenuator as measured

by the six-port with diode power meters and by the MBS Automatic Network Analyzer.

b 3 ©® © ©

a 3f

bl* n

a., f

b5

-t_

a 5

,r

b 6 .

a 6 T

r*- i

/0_ SIX-PORT JUNCTION \Z>

b, a, a 2 b 2wv

Figure 16. An arbitrary six-port junction with power meters on four of

the six ports being used as a reflectometer

.

-16-
Note that the correlator by itself does not satisfy the above design criteria. It has

no output in group 1 of Table 2. Although the correlator is a six-port device, the equations

in (32) do not apply in the limit when the correlator becomes ideal because the four outputs

are not linearily independent. To see this, add (1) and (2) and also add (4) and (5) to get

2 | ai| 2 + 2|a 2 | 2 = |ai + a 2 | 2 + |ai - a 2 | 2

= |ai + ja 2 | 2 + |ai - ja 2 | 2 (44)

This equation shows that the ideal correlator has only three independent outputs since any one output can be obtained from the other three. In a sense, the ideal correlator is only

a five-port junction. One more independent output must be added to the correlator to have

(32) apply. That output should be one of those in group 1 of Table 2.

Experimental Setup

Several six-port measurement systems have been constructed at NBS, Boulder. In one experiment, the eight-port vector voltmeter shown in figure 6 was changed to a six-port by

terminating ports 7 and 8 with 50 Q loads. The remaining four outputs are proportional

(roughly) to those in (42). The back diodes were replaced with diode type power meters

having a linearity of ±1% from 10 nw to 10 uw. The power level into each diode was kept

less than 10 yw to assure square-law operation. Figure 14 shows the six-port and detectors.

Since the six-port calibration and measurement process requires taking many sidearm

power measurements, it is most desirable to have the data read directly into a computer

which can then process the data. A programmable calculator is capable of taking the necessary sidearm power readings under program control, and then processing the data to give

the calibration constants and measurement results.

Basic language programs have been written for calibrating the junction as a microwave

vector voltmeter, and also for using it to measure complex insertion ratio. After calibrating the six-port using the setup in figure 12, the same setup is used to measure complex

insertion ratios by either changing or inserting something in the test (lower) channel, and

using (41) to calculate the ratio.

A picture of the setup is shown in figure 15. The same setup can be used with any type

power detectors that have an output dc voltage which is a known function of the input power

level

Results

Measurements were made on this setup at 8, 9, 10, 11, and 12 GHz. The complex insertion

ratio of the two-position step attenuator L, was measured with the six-port and then measured

by the NBS Automatic Network Analyzer. The results are shown in Table 3. The agreement is

within what one would expect using detectors accurate to 1%. Better power detectors should

give greater accuracy. The comparison shows that the theory of using an arbitrary six-port

junction as a vector voltmeter is correct. It also shows that the six-port junction can be

calibrated without using any standards. The only precision component in the setup is the

two-position step attenuator whose change in insertion ratio is repeatable to ±.001 dB.

-17-
IV. ARBITRARY SIX-PORT AS A REFLECTOMETER

General Theory

An arbitrary six-port junction can be analyzed as a reflectometer in much the same way that it was analyzed as a vector voltmeter in section III [5]. Again consider the

arbitrary six-port junction shown in figure 11. Let a signal be applied to port 1, and

let port 2 be a reference plane at which we wish to make measurements of a, b, and Y (or v, i, and Z), as shown in figure 16. The derivation of the six-port reflectometer

equations follows the same steps used in (26) through (32), except that in (28) b. is

written in terms of a and b instead of ai and a2 ',

b. = C.a + D.b, (45)

where C.iiand D. are constants which are functions of S.. and T.. Multiplying (45) by its

ij J complex conjugate yields four equations similar to (31) only in terms of the four unknowns

|a| , |b| , |ab| cos ¥ , and | ab | sin Y. If these equations are independent,* they can be

inverted to obtain each of the unknowns in terms of the four sidearm power readings. The

desired result is

E-i (46a)

N'-EB!*!

lab I cos ¥ =y c. P.

lab I sin V =Y\ s. P.

(46b)

(46c)

(46d)

where each sum is over the four sidearm power readings. The coefficients of P. are again

real numbers. The set of equations in (46) is valid for any linear six-port, subject to the same conditions mentioned in arriving at (32). Using (46) in (20a), the reflection

coefficient at the reference plane becomes

r = E(c

i + J si )p

i Ea.P.i i

(47)

Equations (46) and (47) should be compared with (18) and (20) for the ideal eight-port

reflectometer.

A set of equations similar to (46) can be obtained in terms of v, i, and 9 instead of

a, b, and Y. Using (21) and (22) in (45) gives

C. + D. C. - D.

E.v + F.i

i l i = 3 (48)

where E. and F. are new constants playing the same roll as A. and B. in (28). Multiplying

(48) by its complex conjugate and solving the resulting four equations yields

* Like the correlator, the outputs of the four-probe reflectometer are not linearly independent and lead to a singular or nearly singular matrix in solving these equations.

See "Design Criteria" below.

-18-
M

2 =LVi (49a)

|i| 2 = £u

±Pi (49b)

P = |vi| cos 9 = ]Tq.P. (49c)

P" = |vi| sin =J2 r. P. (49d)

The coefficients of P. are again real constants. Equation (49c) is recognized as the real

net power, P, at the reference plane, and (49d) is the reactive power P" . Equations similar

to (47) are obtained from (49) for the impedance and admittance;

2>i + jr.) P.

£(q i ~ J r

±> P

i Y = ^ f ..p.1 (5D

One can show that the constants in (49) and (46) are related by the following equations

v.ill = a. + 3. + 2c. (52a)

i

Z

2

ii. = a. + 6. - 2c. (52b)

Z q

± = a± - 3± (52c)

Z r. = 2 s. (52d)

i l

Calibration Techniques

The simplest calibration proceedure is that for obtaining the q. in (49c) so that the

six-port can be used to measure net power P [6]. Referring to figure 16, port 2 is first

terminated with a power standard so that P = P , is known. The corresponding values of

P3 ... P6 are noted and used in (49c) to get

P . . = £q.P. . (53) std *-* 1 1

This proceedure is then repeated with the power standard replaced by three or more different

offset shorts (sliding short or variable lossless reactances) for which P = so that (53)

becomes

= Vq.P. (54)

equation (53) and three or more equations like (54) may be inverted to obtain the four q..

It should be noted that the standard power meter may be of arbitrary and unknown impedance. In addition, the arguments of the offset shorts are not required, although it is

obvious that multiples of A/2 must be avoided.

-19-
Group 1 Group 2 Group 3

|a| 2 -

|b| 2

|a + b| 2

|a - b| 2

|a - jb| 2

|a + jb| 2

Table 4. Outputs of an ideal eight-port reflectometer , used as a guide in designing a six-port reflectometer.

GHZH

©

V>A^-

CORRELATOR -TlKS

X

^r-7 W/V X

(a)

0-!

© © © ©

1 1 x

-*vw

vv\A/

(b)

Figure 17. Six-port ref lectometers which satisfy the design criteria in Table 4.

-20-
With the q. known, the net power into any unknown impedance can be measured using (49c).

Since the impedance of the load does not have to be known, mismatch errors [7] usually

associated with power measurements are eliminated.

Calibrating the six-port to measure T is only slightly more difficult. In addition to observing the P. for three or more different positions of an offset or sliding short, the P. are also observed for two or more positions of a low reflection termination. With this set

of measurements, all of the constants needed to calculate T may be determined. Details are given in reference [8]. The minimum of five measurements needed to calibrate a six-port

reflectometer should be compared with a minimum of three measurements required to calibrate

a four-port reflectometer having a complex ratio detector on its sidearms

If the measurement with a power standard is included in the above set all 16 of the

coefficients of P in (46) can be determined. The coefficients of P. in (49) can be obtained

from (46). The six-port reflectometer is then completely calibrated for measuring voltage,

current, power, impedance, and phase angles.

Design Criteria

The goals to strive for in designing a six-port reflectometer are similar to those for

designing a six-port vector voltmeter. It can be shown that a practical set of four outputs

includes one from each group in Table 4 plus a fourth which can be any one of the six not

already chosen. As with the six-port vector voltmeter, the actual outputs of a six-port

reflectometer can depart considerably from its design goals and still be quite useful. Two

examples of six-port reflectometers which satisfy the above design criteria are shown in

figure 17. Both were obtained from figure 10 by terminating ports 7 and 8. The design in

figure 20b is particularly interesting, whereas the design in figure 10b is useful at only

one frequency when using equations (18) - (25), the design in figure 17b is useful over at least a full waveguide band when using (46) - (52). This is because the A/8 spacing now

needs to be satisfied only approximately at the center of the band. Also the distance from

the probe to the reference plan, and the relative probe couplings are all of secondary

importance.

The design in figure 17a can be constructed to have a useful frequency range of four or more octaves. Precision components are not required, and components can usually be used

considerably outside of their normal specified frequency range.

In trying to apply (46) and (49) to the four-probe reflectometer in figure 8, one finds

that it has the same problem as the correlator in that its outputs are not all independent.

The identity

|a + b| 2 + |a - b| 2 = |a + jb| 2 + |a - jb| 2 (68)

shows that the four-probe reflectometer has only three independent outputs. Just like the

correlator, the four-probe reflectometer is, in a sense, only a five-port junction requiring

one more independent output for (46) and (49) to apply. The output needed is one from

Group 1 in Table 4'.

Experimental Results

The first application of the six-port concept was at NBS-Boulder using an X-band waveguide six-port reflectometer to measure net power [6]. To verify the theory, a six-port

reflectometer was placed in series with a tuned four-port reflectometer, the most accurate

instrument for measuring net power. Both instruments were calibrated to measure power at the same reference plane so that both instruments could measure the same power at the same

time. The power into a variable impedance load was measured at 10 GHz. The agreement

between the two instruments was .1% for |r|<.l and .25% for |r|<.2 at any phase angle.

These results showed that a six-port could be used to calibrate power meters (whose |r|

seldom exceeds 0.2) almost as accurately as a tuned four-port reflectometer without the

need to tune the measuring instrument at each frequency.

At the present time work is continuing at NBS to improve and evaluate the design

shown in figure 17b and to simplify the calibration software for using the six-port to measure T . -21-
V. FUTURE APPLICATIONS

One obvious application of the six-port concept is in computer controlled measurement

systems. If diodes or other power detectors are used which have an output dc voltage proportional to the input rf power, all desired information is obtained from four dc voltage

measurements. Adding a scanner, DVM, and a programmable calculator or minicomputer to the

setup such as shown in figure 12 makes an automated measurement system. All components

used to calibrate the six-port vector voltmeter can be controlled by the calculator so that

there is no operator involvement. In calibrating a six-port reflectomater , the operator

must connect the different loads but that is required to calibrate other automated reflectometers also.

Since it is not necessary to heterodyne the signal down to a lower frequency to measure phase angles, only one signal source is required and it need not be a phase-locked

source as is required in some rf measuring systems. The source could be a programmable

sweep oscillator which should be accurate enough for most applications.

Another application of the six-port concept is in the millimeter wave region where

it is much more difficult to get phase information by other techniques. Components are commercially available for constructing the six-port reflectometer in figure 17b up to about 200 GHz.

Finally, it should be possible to use two six-port reflectometers to measure all of

the scattering parameters of a two-port device by connecting one six-port on each side of

the two-port. Preliminary studies indicate that it may be even simpler to calibrate two six-ports than one.

VI. BIBLIOGRAPHY

1. S. B. Cohn and N. P. Weinhouse, "An Automatic Microwave Phase Measurement System,"

Microwave J., Vol. 7, pp. 49-56, Feb. 1964.

2. D. C. Thorn, J. S. Potts, and T. R. Erney, "An investigation of the Four-Probe

Reflectometer," University of New Mexico Technical Report No. AFWL-TR-73-5,

June 1973, 89 pages.

3. Cletus A. Hoer, "The six-port coupler: A new approach to measuring voltage, current,

power, impedance and phase," IEEE Trans. Instrum. Meas . , Vol. IM-21, No. 4, pp. 466-470, Nov. 1972.

4. Cletus A. Hoer and Keith C. Roe, "Using an arbitrary six-port junction to measure complex voltage ratios," presented at the 1975 International Microwave Symposium,

May 1975. To be published in IEEE Trans. Microwave Theory and Techniques.

5. C. A. Hoer and G. F. Engen, "Analysis of a six-port junction for measuring v, i, a, b, z, T, and phase," presented at the Proc. IMEKO Symp. Acquisition and Processing

of Measurement Data for Automation, Dresden, Germany, June 17-23, 1973.

6. G. F. Engen and C. A. Hoer, "Application of an arbitrary six-port junction to power

measurement problems," IEEE Trans. Instrum. Meas., Vol. IM-21, pp. 470-474, Nov. 1972.

7. R. W. Beatty and A. C. Mac Pherson," Mismatch errors in microwave power measurements,"

Proc. IRE, Vol. 41, No. 9. pp. 1112-1119, Sept. 1953.

8. G. F. Engen, "Calibration of an arbitrary six-port junction for the measurement of

active and passive circuit parameters," IEEE Trans. Instrum. Meas., Vol. TM-22,

pp 295-299, Dec. 1973.

-22-
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-6732. Gov't Accession

No.

4. TITLE AND SUBTITLE

Using Six-Port and Eight-Port Junctions

To Measure Active and Passive

Circuit Parameters

3. Recipient's Accession No.

5. Publication Date September 1975

6. Performing Organization Code

276.03

7. AUTHOR(S)

Cletus A. Hoer

8. Performing Organ. Report No. NBS TN-673

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2763146

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Same as Item 9.

13. Type of Report & Period Covered

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.)

This review paper brings together a number of old and

new methods for measuring voltage, current, power, impedance,

and phase angle using only amplitude type detectors. Vector

voltmeters and reflectometers can be constructed to measure

all of these quantities in terms of four amplitude measurements

made on four arms of a six-port junction. Whereas previous uses

of this type of instrument depended on precision components for

accuracy, new equations switch this dependence primarily to

detector linearity and only secondarily on the properties of

the measuring device itself.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons) Admittance; automated precision measurements; correlator;

current; impedance; microwave circuit parameters; microwave measurements; phase angle;

power; ratio; reflection coefficient; ref lectometer ; self-calibration; six-ports;

.vector voltmeter; voltage.

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