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NIST Technical Note 1379

Technical Note 1379

Direct Comparison Transfer of

IVIicrowave Power Sensor Calibrations

M.P. Weidman

Electromagnetic Fields Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

January 1996

Tes

U.S. DEPARTMENT OF COMMERCE, Ronald H. Brown, Secretary

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

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

Natl. Inst. Stand. Technol., Tech. Note 1379, 20 pages (January 1996)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1996

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
Contents

1. Introduction 1

2. Basic Theory 3

2.1 Efficiency Definitions 3

2.2 Transfer without Directional Coupler 3

2.3 Transfer with Directional Coupler 4

3. Applications 5

3.1 Measurement of Fq without a Directional Coupler 6

3.2 Measurement of Fq of a Directional Coupler 6

3.3. Other Types of Directional Couplers 7

3.3.1 VSWR Bridge 7

3.3.2 Resistive Power Splitter 8

5. Uncertainty Analysis 9

6. Conclusions 10

7. References 10

Appendix A. Uncertainty in Mismatch Factor 12

111

DIRECT COMPARISON TRANSFER OF MICROWAVE POWER SENSOR

CALIBRATIONS

M. P. Weidman

National Institute of Standards and Technology

Boulder, Colorado 80303

This report describes a basic, but potentially accurate, transfer technique for comparing

microwave power sensors. The technique is not new, but the specific applications are.

This report is written to supplement the existing literature. The method transfers the

effective efficiency of a standard power sensor to an unknown (uncalibrated) power

sensor. The power sensors may be bolometric (thermistor mounts), thermoelectric, or

diode types, and each type will have inherent limitations. The technique can be

implemented with a variety of commercial coaxial and rectangular waveguide

components. Measurement uncertainty is discussed in this report so that a potential user

can quantify transfer uncertainties.

Key words: direct comparison; effective efficiency; microwave metrology; mismatch

uncertainty; power sensor; power meter; power transfer

1. Introduction

This paper shows how to use direct comparison over broad frequency ranges with low uncertainties. In

this report, the generic term, power sensor is used to describe several types of microwave sensor in common use. Although the most nearly linear power sensor is the thermistor mount, thermoelectric and

diode sensors can also be used (with limitations). All sensors are used with some type of instrumentation

or power meter indicator. The indicated power is proportional to the net radio frequency (rf) or microwave power absorbed by the sensor. The purpose of calibration of the sensor is to determine this

proportionality.

The direct comparison measurement technique is based on alternate connections of a standard and

unknown power meter to a source of rf or microwave power (figure 1). The source can be a signal

1
generator, a generator with an isolator or attenuator, or may include a sensor-directional coupler monitor

at the generator output. Direct comparison is one of the oldest and most basic of microwave power

transfer techniques. References describing this technique as a calibration method date back to 1953 [1].

Other references describe different aspects of this method [2,3]. A good reference for the general topic

of power comparison techniques is Part C of [4]. Other calibration techniques, such as the use of the sixport [5] or tuned reflectometers [6], are more complex and are not discussed in detail here.

One of the main sources of uncertainty in any power transfer is caused by the impedance mismatch

between the source and the power sensors connected to the source. Figure 1 shows the alternate

connection of two sensors to a source. The power

sensors in a direct comparison are of the

terminating type and usually consist of a standard

sensor and one or more unknown sensors.

Historically, the direct comparison method was

used for single frequency or narrow-band

measurements or for measurements where a low

uncertainty was not required. The reasons for

using the direct comparison instead of other

methods are speed and simplicity. There are

several options for using the technique depending

on the accuracy required. The higher accuracy unknown detectors to a generator.

implementation uses high directivity waveguide

directional couplers, or in the case of coaxial sensors, VSWR bridges. Full evaluation of the uncertainty

in the direct comparison technique requires separate measurements of the complex reflection coefficients

r^, r^, and r^. These reflection coefficients apply to the power standard sensor, the equivalent

generator, and the device under test (DUT) sensor. The reflection coefficient measurements can be

determined using a commercial vector automatic network analyzer (VANA) with appropriate speed and

accuracy.

f^

Standard

Sensor

h-^r

s

Unknown

Sensor —*rU

Figure 1. Alternate connection of standard and
2. Basic Theory

2.1 Efficiency Definitions

The calibration quantity used to characterize terminating power meters is effective efficiency rj^ for

thermistor sensors and efficiency factor r; for the other types of sensors. Efficiency -q^ is defined as

^DC^^RF ' ^^^^^ ^DC *^ ^^^ substituted dc power and Pj^ is the net radio frequency (rf) or microwave

power dissipated in the sensor. Substituted dc power is the change in direct current (dc) or low frequency

power necessary to maintain the thermistor element or elements at a constant resistance when rf or microwave power is applied to the sensor.

Thermoelectric sensors convert the absorbed rf power to heat, then to dc, and instrumentation amplifies

the low level dc and displays the result. Diode sensor-power meters convert rf voltage to dc voltage and

display the result. In the square law region, the diode sensor-meter displays a response proportional to

rf power (voltage squared). The efficiency factor r; of thermoelectric or diode sensors is P^/Pj^f , where

Pj^ is the indicated or displayed power meter reading and Pj^p is the net rf or microwave power

dissipated in the sensor.

2.2 Transfer without Directional Coupler

Effective efficiency t;^ from a standard thermistor (rj for other sensors) to a DUT sensor is transferred

using

^ £1/ = n £S X PRATIO ^ ^^ ' ^^^

where rj^jj is the effective efficiency of the DUT and rj^^ is that of the standard. When the power

sensors are not thermistors, effective efficiency is replaced by efficiency defined in eq (1). Pj(^jjq is

the ratio of two substituted dc or indicated powers,

p

^ ^^DC>U

(2) '^ RATIO (J> \ '
where P(d£)s is the dc power in the standard and P(dq)u is the dc power in the DUT. For

thermoelectric or diode sensors, the Pj)q are replaced by the indicated powers Pj^. The mismatch factor

MM is

MM = (i-|r„p)^i-rr 1^

(3)

where T^, F^, and Tq are the respective complex reflection coefficients of the DUT, the standard, and

the generator. Application details are described in section 3.

2.3 Transfer with Directional Coupler

A source which includes a generator and directional coupler-sensor on its output has several desirable

features. Figure 2 shows the coupler system. The directional coupler samples the incident power from

the generator and can be used for power leveling. Recording the side arm and main arm powers

simultaneously is the same as leveling. Another feature of the coupler system is that Fq at the output of

the coupler is a function of only the coupler

parameters and not of the generator driving the

coupler [2].

A given application may include a waveguide

coupler, a voltage standing wave ratio (VSWR)

bridge, a power splitter, a quadrature hybrid, or some other type of directional coupling device. In

a typical system, a power sensor is permanently

attached to the incident-side-arm of the coupler.

Signal

Source

incident

Sensor

Test

Port

Figure 2. Directional coupler port numbering.

Effective efficiency rj^ from a standard thermistor

to a DUT with a directional coupler is transferred with eq (1). When the power sensors are not

thermistors, effective efficiency is replaced by the efficiency factor tj. Let R be the ratio of substituted

dc powers, PsiDE^^MAIN' ^^^'"^ ^SIDE '^ ^^^ ^^ power in the sensor on the side arm of the coupler,

and ^^^yy is the dc power in the power sensor on the main arm. In addition, let R^ be that ratio with
the standard connected and Rjj be the ratio with the DUT connected. Then a new Pj^jjq is

i> = -^

(4) 'RATIO D '

which involves four dc powers. It is not necessary to control the power level of the source if P^^^^^ and

^SIDE ^^ measured simultaneously. If any of the sensors are not thermistors, the dc powers are replaced

by the power meter indicated powers. Mismatch factor MM is the same as shown in eq (3), where Tjj

and Tr are the same, and Tq is the complex reflection coefficient of the coupler equivalent generator.

The definition of Tq for a directional coupler comes from ref. [2] and is

r - 5 _fl2^ (5)

•^13

where the 5- • are the scattering parameters (S-parameters) of the directional coupler used in the power

transfer. Figure 2 shows the port numbering for the S-parameters of the coupler.

3. Applications

The value of ij£^ of a standard thermistor or i; of a standard thermoelectric (or diode) sensor must be

icnown for a power transfer. Efficiency tj^^ may come from a national laboratory, a calibration

laboratory, or a manufacturer.

The other information necessary for an accurate power transfer is MM. The complex values of Tq, T^,

and Fj^ are required for best accuracy. If it is possible to measure only the magnitude of the reflection

coefficients, then there is an uncertainty in percent in MM of

A(MM) = 2oo(|rc||r,-H|rGl|rj). (6)

For typical values of F^ F^, and F^, the uncertainty in MM can range from 1 percent to 15 percent if

only magnitudes of F are measured. Equation (6) comes from a first-order approximation to the derivative

ofeq(3).
3.1 Measurement of Fq without a Directional Coupler

Tq for an active source is difficult to measure, although a technique has been suggested if the source can

tolerate high reflected power [7,8]. A better way to use a source without the directional coupler is to put

an isolator or attenuator on its output. If low power is a problem, then the isolator would be preferable,

but isolators are limited in frequency range.

An approximation to Tq with an attenuator or isolator on the output of the generator is T looking back

into the output of the attenuator or isolator. This T can be measured without the generator turned on. The

uncertainty of this measurement depends on the F looking back into the active generator and the amount

of attenuation or isolation. Every 10 dB of attenuation or 20 dB of isolation will reduce the effect of the

active source F by an order of magnitude. The approximation to F^ is due to the fact that the

measurement looking back into the attenuator (or isolator), toward the generator, is performed with the

generator off and is typically negligible.

As an example, for an active generator with F = 0.3 ±0.3 and 20 dB of attenuation or 40 dB of

isolation, the uncertainty in F^would be 0.003. The estimate of uncertainty for the generator F^ (±0.3)

applies to most known signal generators. The approximation uncertainty in F^ must be propagated

through MM. The propagation of uncertainty in MM due to uncertainties in reflection coefficient is

analyzed in Appendix A.

3.2 Measurement of Fq of a Directional Coupler

The definition of F^ is given in eq (5). F^ is a function of the S-parameters of the coupler only and is

not affected by the generator. Reference [2] describes one way to measure F^, but this method requires

a tuning adjustment at each measurement frequency.

An approximate measurement method, which can be done over a broad frequency range with a vector

network analyzer, is to measure only the S22 term for the coupler. The second term in eq (5) involves

the directivity 20*log(\S2^\/\Sj^\) and the main line loss 20*log(\Sj2\). S-parameters are defined as

voltage ratios, so that decibel (dB) values are 20*log(S). The second term on the right side of eq (5) can

be ignored if the directivity is high. The magnitude of the directivity term is shown in the examples.
S22 is the r looking into port 2 (fig. 2) with the other ports terminated in nonreflecting loads. There are

three elements to the uncertainty in Tq when approximating it by S22-

(1) The finite directivity of the coupler or bridge.

(2) The assumption of a matched load on port 1 when measuring T at port 2. Attenuation between

port 1 and port 2 reduces the effect of not having a matched load on port 1 by | Sj2 \ * \ S21 \ This is

the same order of magnitude reduction for each 10 dB of attenuation as described in section 2.1.

(3) An imperfect load on port 3.

Some examples should clariiy the measurement of Vq. If the directivity of the coupler is 40 dB, the

uncertainty in |r^| from element (1) is 0.01. With an isolator of 20 dB, or a 10 dB attenuator on port

2, (along with 40 dB directivity) the uncertainty in |r^| due to element (1) would be 0.001, which is

negligible for most purposes.

For a 3 dB coupler (without an attenuator or isolator) with a 0.02 load on port 1, element (2) would

result in an uncertainty of 0.01 . A better condition would be to add a 10 dB pad or 20 dB isolator on port

2, then element (2) would result in an uncertainty of 0.002.

Element (3), which is a function of the load on port 3 involves the two-way loss firom port 2 to port 3

and for a 40 dB coupler directivity and 3 dB forward coupling, the effect of the T on port 3 is reduced

by 0.00005. Even a short circuit on port 3 has little effect on 822-

All of the uncertainties in Vq must be propagated through MM to get the uncertainty in the power

transfer, which is described in Appendix A. The previous examples should help explain how to calculate

an uncertainty in MM for different combinations of hardware.

3.3. Other Types of Directional Couplers

Figure 2 and the general description so far correspond to waveguide directional couplers. Other types of

couplers are useful for the direct comparison power transfer method.

3.3.1 VSWR Bridge

Figure 3 shows the rf hardware for one possible coaxial power calibration system. The VSWR bridge
is the same as the directional coupler. The

VSWR bridge was originally designed for

measuring VSWR with the generator on arm 2,

the test port on arm 1 and a sensor on arm 3. The application of this device to a power transfer

"-^ is a new innovation. The 3 dB attenuator on arm

2 of the bridge provides 6 dB of return loss

isolation for the S22 measurement. S22 is defined

with matched loads on all other ports. In the

Incident

Sensor

Signal

Source "•

VSWR

Bridge

3db

Atten.

_L Test Port

example of figure 3, a nonideal load with r =0.02 F'gure 3. VSWR bridge used as directional coupler

for power transfer,

connected to port 1, when measuring 822^ will

create an uncertainty in S22 of 002 times 0. 1259 or 0.0025. The 0. 1259 term comes ft"om the two-way

loss through the sum of the 3 dB attenuator and the 6 dB coupling inherent to the VSWR bridge (9 dB

corresponds to a voltage rafio of 0.1259). The uncertainty due to finite directivity is \S23*S]2\/\S]j\

or 0.00355. The uncertainty due to finite directivity, for this example, is based on a directivity

i\S2ySjj\) of 40 dB plus the 9 dB loss ft-om port 1 to port 2 (6 dB coupling + 3 dB attenuator).

3.3.2 Resistive Power Splitter

Another type of coaxial directional coupler is the resistive power splitter shown schematically in figure

4. This device has a nominal coupling of 6 dB between ports 1 and 2 and ports 1 and 3. If this device

is perfectly symmetrical with no parasitic

reactances, 5*22 = 0.25, $22 = 0.25, and

Sjj = Sj2, so r^ ft-om eq (5) is zero. 5*22 for a power splitter is not a good approximation to Tq,

so even though Tq may be small, a measurement

of its value is difficult but necessary for a

thorough uncertainty analysis. One way to

measure Tq is to use a VANA to measure all the

complex S-parameters in eq (5) and calculate Tq.

A slight modification to this takes advantage of

the approximation, S2J = S^j, so that from eq

(5) r^ = ^22-^23' ^^^ *^'^ method still requires

^inc

/ '

Gen • <C

Power

iSOCk

- 50 fl

Splitter

^ Test Port ^2

^

Figure 4. Schematic representation of coaxialresistive power splitter.
measurement of complex S-parameters. A third way is to use a sliding short coupled to a slotted line

[7,8], but since this is a single frequency method, it would be just as easy to use the method described

in ref. [2]. A comparison of the second and third methods for measuring Tq on power splitters show a

range of uncertainties of 0.01 to 0.03 in r^ [9]. As in the preceding sections, any uncertainty in r^must

be propagated through MM (eq (3)) to determine the uncertainty in the power transfer.

5. Uncertainty Analysis

This section is intended as a general guide in determining the uncertainty for a power transfer using the

techniques described in the previous sections. The method of combining uncertainties, root sum of squares

(RSS), for example, or probability considerations (coverage factors) are left to the user.

The uncertainty in measuring rj^^ for an unknown device (DUT) is a combination of the uncertainties

in the elements in eqs (1) to (3). The following list of uncertainties can be used as a guideline.

Power Standard rj^-^ Uncertainty:

The first element on the right side of eq (1) is the effective efficiency t;^.^ of the standard

thermistor mount. The value of this uncertainty normally comes from the standards or calibration

laboratory which provides the efficiency for the working standard.

^ratio Uncertainty:

Sources of uncertainty include, but are not limited to, power and frequency instability and

connector repeatability. Instrumentation uncertainties such as resolution or offsets also occur here.

These uncertainties are determined experimentally, using the actual hardware, by repeating the

process and calculating the variability (standard deviation).

Mismatch Factor Uncertainty:

Mismatch factor MM in eq (3) has an uncertainty based on the VANA measurement of the

reflection coefficients F and the approximations described in the basic theory above. The VANA

uncertainty is dependent on the calibration technique, for example, sliding load or TRL. Equation

(3) shows that the effect of the F measurement on the power measurement is of second order.

The differential of eq (3), expressed as partial derivatives, can be used to determine the

uncertainty in the power transfer. Appendix A gives the equations.
6. Conclusions

Several relatively simple calibration procedures which yield a power sensor transfer with an uncertainty

which can be fully characterized have been described. The transfer system can be constructed from

commercially available hardware.

The author thanks Fred Clague and Marilyn Packer for their encouragement and suggestions. Thanks also

to Claude Weil and Thomas Scott for their suggestions.

7. References

[1] Beatty, R.W.; Macpherson, A.C. Mismatch Errors in Microwave Power Measurements. Proc.

IRE, 41(9): 1112-1119; 1953 September.

[2] Engen, G.F. Amplitude Stabilization of a Microwave Signal Source. IRE Trans. Microwave

Theory Tech., MTT-6(2): 202-206; 1958 April.

[3] Desch, R.F.; Larson, R.E. Bolometric Microwave Power Calibration Techniques at the National

Bureau of Standards. IEEE Trans. Instrum. Meas., IM-12(1): 29-33; 1963 June.

[4] Fantom, A.E.; Radio Frequency and Microwave Power Measurement. Peter Perigrinus Ltd.,

London, United Kingdom, 1990.

[5] Engen, G.F.; Hoer, C.A. Application of an Arbitrary 6-port Junction to Power Measurement

Problems. IEEE Trans. Instrum. Meas., IM-21(4): 470-474; 1972 November.

[6] Engen, G.F. A Transfer Instrument for the Intercomparison of Microwave Power Meters. IRE

Trans. Instrum., IM-9: 202-208; 1960 September.

[7] Sorger, G.U.; Weinschel, B.O.; technique presented at IMEKO Symposium on Microwave

Measurements; October, 1966.

10
[8] Alford, A. Measurement of Generator Impedance Using a Sliding Short Circuit. Microwave J.,

29(8): 117-118; 1986 November.

[9] Ulriksson, B.A.; Lucas Weinschel internal report. Lucas Weinschel, Gaithersburg, Maryland.

11
Appendix A. Uncertainty in Mismatch Factor

This appendix shows the derivation of the equations necessary to calculate the uncertainty in MM defined

in the Basic Theory section 2.

Equation (3) is repeated here as eq (Al),

MM = -—^-^^ ^-^ , (Al)

where the mismatch factor is MM. The differential of MM is

^I^gI ^irj aiFyi 34.^5 3<|)o„

where the partials are with respect to the magnitudes of the three Fs, and ^qv, and ^qu are defined by

where $^, f*^, and $^ are the phase angles of Tq, F^, and Fj^.

In order to simplify the algebra, the second ratio in MM in eq (Al) was changed to

|i-r^j2 i_2|r^^|co5($^-H*^)+|r^i;l

(A5)

This simplification gets rid of the complex terms in eq (Al) and leads to the use of $^^ and ^qu in

12
eq (A2).

Equations (A6) through (A 10) follow from eqs (A2) through (A5).

dlTJ

(MMd)Bil-C\AB-D)-iMMn)C(l-B^)(AC-E)

(MMdf

(A6)

d(MM) ^ 2

air„i

A(l -C^)(AB-D)+(MMn)B/il -B^)

iMMd)

(AT)

djMM)

airj

= -liMMn) Ail-B^)iAC-E)+(MMd)CKl-C^)

(MMdf

(A8)

-2ABil-C^)

(MMd)

d(MM) 2(MMn)AC(l-B^)

d(E) (MMdf

(A9)

(AlO)

Definitions for the shorthand terms in eqs (A6) through (AlO) are

MMn = numerator of MM ratio.

MMd = denominator of MM ratio.

A=\T^\,B=\T^\, and C=\T,\,

D=C05((|)g+(|)y), and £=C05(<|)(j+(J)j).

(All)

(A12)

(A13)

(A14)

13
The phase angle uncertainties which are needed along with eqs (A9) and (A 10) are defined in eq (A 15).

The partial derivative of MM with respect to D and E are multiplied by d(D) and d(E) and then replace

the last two terms in eq (A2):

diD)= -SIN(<^^^)d(<^^^) and d(E)= -5/A^((t)c^d((l)^,), (A15)

where d(^) is the uncertainty in ^Qr and ^qtj in radians. In reflection coefficient measurements, the

uncertainty in the phase of F is inversely proportional to the magnitude of F. As the magnitude of F

approaches zero, the uncertainty in the phase of F approaches ±7r rad, but the product AB in the

numerator of eq (A9), or AC in the numerator of (AlO) approaches zero at the same time, so the partial

derivatives of MM times the differentials, d(^), approach zero.

Equations (A6) through (A 15) are used in the calculation of the uncertainty in the power transfer caused

by uncertainties in the reflection coefficient measurements.

14


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