NBSIR 81-1650

WR-10

SINGLE SIX-PORT

MEASUREMENT SYSTEM

M. Weidman

Electromagnetic Technology Division National Engineering Laboratory

Norionol Bureau of Srondords

Boulder, Colorado 80303

September 1981

NATIONAt* or stakoaRM

librart

NOV 1 6 1981

NBSIR 81-1650

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WR-10

SINGLE SIX-PORT

MEASUREMENT SYSTEM

M. Weidman

Electromagnetic Technology Division Norionol Engineering Laborarory

National Bureau of Srandards

Boulder, Colorado 80000

September 1981

U.S. DEPARTMENT OF COMMERCE, Malcolm Daldrige, Secrerary

NATIONAL BUREAU OF STANDARDS, Ernesr Ambler, Director

WR-10 SINGLE SIX-PORT MEASUREMENT SYSTEM

M. Weidman

Electromagnetic Technology Division

National Bureau of Standards

Boulder, Colorado 80303

A six-port system has been developed and used to measure

effective efficiency (r) ) and complex reflection coefficient

(F) in WR-10 (75-110 GHz) waveguide at frequencies in the 93.5-

96.5 GHz range. The system is automated except for the control of the mm-wave klystron source. This report includes a brief description and background of the measurement system

and a preliminary analysis of uncertainties.

1.0 Introduction

The design of the WR-10 single six-port system is based on a previous system in WR-15 waveguide [1] and the work of C. Hoer and G. Engen

[2 5 3] • The WR-10 system utilizes a commercially built, integrated,

dielectric waveguide circuit as part of the six-port network. In the

WR-15 system, the six-port network was built up from discrete commercial,

metallic waveguide components (directional couplers) . The integrated

dielectric waveguide circuit appears to give better performance, although over a limited bandwidth—approximately 10 percent. The remainder of the system (source type, instrumentation, and software) is

the same as the WR-15 system. Thermistor mounts are used as detectors

along with NBS Type IV power meters. Sliding and fixed terminations

together with calibrated (microcalorimeter) thermistor mounts are used

to calibrate the six-port for measurement of reflection coefficient,

F, and effective efficiency, n , of thermistor mounts. Figure 1 is a

block diagram of the measurement system, and Figure 2 is a schematic of

the six-port network.
2.0 Measurement Results and Error Analysis

2 . I Random Errors

A series of nine separate, complete calibrations were performed on

the system at 94.5 GHz with one of the working standard thermistor

mounts (measured in microcalorimeter) used as a standard for effective

efficiency and a quarter-wave short as the standard for reflection

coefficient. A second working standard thermistor mount, which had also

been measured in the microcalorimeter, was treated as an unknown.

The unknown was reconnected and measured three times on each of

nine occasions over a period of two weeks. Estimates of the betweenoccasion and within occasion standard deviations were obtained from a

one way random effects model. The estimated standard deviations for

ri are 0.00124 within occasions and 0.00192 between occasions. The resepective values for T magnitude are 0.00105 and 0.00296, The estimated

standard deviation of a single measurement is obtained by adding the

component standard deviations in quadrature. These estimates are 0.00229

with approximately 12 degrees of freedom for r) and 0.00314 with approximately nine degrees of freedom for V magnitude. Using Student’s t value

with a conservative eight degrees of freedom at the 99% confidence level

times the single measurement standard deviations yields the reported

limits to random error. These limits are 0,00768 for ri and 0.01053 for

e

T magnitude.

The random uncertainties are reported in Table I along with the

systematic uncertainties.

The estimated offset between the mean value of T] as measured on

e the six-port for the thermistor mount used as the unknown and the mean

value from the microcalorimeter is 0.002%. The estimated systematic

uncertainty for the possible offset based on 2 times the standard error

of the difference between the two mean values is 0.25%. (Therefore, the

estimated offset is not statistically significant).

2
2.2 Systematic Errors

For ri measurements using the six-port system, the systematic error

results from the error in the microcalorimeter measurement of rj for

e the two working standards and a mismatch loss uncertainty resulting from

a systematic error in T. The ±1.2% error from the microcalorimeter in

Table I includes both random and systematic components (see WR-10 microcalorimeter paper) . The two components have been added algebraically here

and are treated as a systematic uncertainty for the six-port system.

(The conservative approach has been used since the random errors are

based on limited sample size)

.

Although no definite offset showed up in the mean of the nine

measurement occasions for r) on the six-port, compared to measurements

on the microcalorimeter, there could be an uncertainty, for other F's,

caused by the fact that there is a systematic error in the measurement

of T. This error in F reflects itself through the measurement of mismatch

( 1 )

where g and £ denote generator and load respectively.

The effective efficiency for a device under test is calculated

using the equation

(i-| r | 2

) (i- | r | 2 /|i-r r | 2

Si,

1 s' ' g s' . k

(i-| r

| 2) (i- I r | 2

) /

|

!_r r | 2 g U

1

1 g U1 ( 2 )

3
In eq (2), n is the effective efficiency of the device under

eu test. M and M are the respective mismatch losses for device under

gu gs

test and standard* and K is a function of the substituted dc powers and

the value of T] for the standard,

e Using the values from Table I for T magnitude systematic error, it

can be shown that for typical F^ and F^, this results in a ±0.16 percent

g

uncertainty in M

^ and also in ri e

» since T]^ is directly affected by

M „ . This uncertainty was calculated using worst case phase conditions

g*-

for r and r. and with |T I * 0.07 and |rJ - 0.25. The systematic

g

i g error in f] for a device under test caused by a systematic error in

shows up in the ratio of M ^’s f°r standard and device under test. The

numerators of the two M^'s ratios in eq (2) (£ is u or s) will go in

the same direction (high or low) , whereas the denominators can go either

direction. To be on the safe side and include all possibilities, the

value for estimated systematic error in M

^ in Table I is double the

±0.16 percent value for one determination of M^.

The primary source of systematic error in the measurement of

reflection coefficient (D is caused by the fact that the section of

waveguide used for the sliding termination does not have perfect WR-10

dimensions. Using the dimensional tolerances for the mandrel on which

this precision waveguide section was electroformed and eq (14) from [4],

Ar = 2

(1 + 0)‘ ifd. (3)

i + r where A^ = A^ = ±2.5 ym, a = 2.54 mm, b = 1.27 mm, 0 = VSWR -

^ _ p

•

4
In this case, Ar is approximately ±0.0013 for j T j near zero. The

uncertainty decreases for higher reflection coefficients. Another source

of uncertainty is the fact that the quarter-wave short is not perfect.

If | r | for the quarter-wave short is assumed to be 0.998 ±0.002 (conservative assumption), the uncertainty in | T j would be ±0.002 times | T

j

.

No claim for T phase (systematic uncertainty) is made here, but dimensional considerations again apply. Phase of T is not normally used in

single six-port applications.

Conclusion

The WR-10 single six-port system appears to be in a satisfactory

operating state, and ongoing measurements with both working standards

and two check standards will be used to obtain more long-term data for

the system, for purposes of establishing statistical control.

References

[1] Weidman, M. P., A Semiautomated Six-Port for Measuring Power and

Complex Reflection Coefficient, IEEE Trans. Microwave Theory Tech.,

vol • MTT-25, No. 12, Dec. 1977.

[2] Engen, G. F., An Improved Circuit for Implementing the Six-port

Technique of Microwave Measurements, ibid.

[3] Engen, G. F., Calibrating the Six-Port Ref lectometer by Means of

Sliding Terminations, IEEE Trans. Microwave Theory Tech., vol.

MTT-26, No. 12, Dec. 1978.

[4] Yates, B. C. and Larson, W. , Millimeter Attenuation and Reflection

Coefficient Measurement System, NBS Tech Note 619, July 1972.

5
TABLE 1

Measurement Uncertainties for Single Six-Port

Uncertainty

Systematic

Microcalorimeter

M

^ (From T)

Possible offset between

mean of calorimeter

and mean of 6-port

Precision Section

A/4 Short

Total Systematic

± 1 . 20%

±0.32%

±0.25%

±1.71%

Random:

(t

For 0

.005,8) x s 0 „ x 100

and for |r| (t_ 005>8 ) x s

Six-port

Total Random and Systematic

± 0 . 86%

±2.63%

±0.0013

±0.0020 x j r |

±(0.0013 + 0.0020 x | T | )

±0.0105

±(0.0118 + 0.0020 x | T | )

6
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Figure

1.

Block

diagram

of

single

six-port

system.
Votted ARi A is lwrrGSATeC! PirLecTftic *Mvr6u?pr

Couple ^

Figure 2. Schematic of six-port network.

I E ST

8
NBS-114A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 81-1650

2. Performing Organ. Report No 3. Publication Date

September 1981

4. TITLE AND SUBTITLE

WR-10 Single Six-Port Measurement System

5. AUTHOR(S)

Manly P. Weidman

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8 . Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

10.

SUPPLEMENTARY NOTES

[3J Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

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

bi bliography or literature survey, mention it here)

A six-port system has been developed and used to measure effective efficiency ( n

e

)

and complex reflection coefficient (T) in WR-10 (75-110 GHz) waveguide at frequencies in the 93.5-96.5 GHz range. The system is automated except for the control of

the mm-wave klystron source. This report includes a brief description and background of the measurement system and a preliminary analysis of uncertainties.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

mm wave measurements; reflection coefficient; six-port measurement system;

thermistor mount calibration.

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