NBS MONOGRAPH 82

MICROWAVE IMPEDANCE

MEASUREMENTS AND STANDARDS

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U.S. DEPARTMENT OF STANDARDS

NATIONAL BUREAU OF STANDARDS
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UNITED STATES DEPARTMENT OF COMMERCE • John T. Connor, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Microwave Impedance Measurements

and Standards

Robert W. Beatty

National Bureau of Standards

Boulder Laboratories

Boulder, Colorado

National Bureau of Standards Monograph 82

Issued August 12, 1965

For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington, D.C., 20402 - Price 20 cents
Library of Congress Catalog Card No. 65-60054
Foreword

This publication is a tutorial review of microwave

impedance measurements and standards. It is not intended

to be comprehensive but to emphasize fundamental theory,

definitions, the conventional slotted Une, and reflectometer

techniques. Particular attention is given to discussion

of errors.

Sections 1 through 5 provide a theoretical introduction

to the subject, which is then followed by detailed discussions

of selected measurement techniques and impedance standards. A list of selected references is included.

A. V. ASTIN, Director.
Contents

Page

Foreword Ill 1. Definition of reflection coefficient i 2. Definition of impedance, normalized impedance 2

3. The Smith chart 3

4. Effect of change of position of terminal surtace 5

5. Voltage standing-wave ratio (VSWR) 6

6. The idealized slotted section 7

7. The actual slotted line... 8

7.1. Irregular variations in probe coupling 8

7.2. Probe loading of the slotted fine 9

a. Probe replaced by shunt admittance, generator nonreflecting 9

b. Probe replaced by shunt admittance, arbitrary generator 10

c. Three-arm junction representation of slotted line 11

7.3. Residual VSWR 12

7.4. Other sources of error associated with the slotted line 13

a. Change of characteristic impedance by slot 13

b. Slot waves 13

c. Attenuation or slope 14

d. Leakage 14

7.5. Still other sources of error 14

7.6. Conclusions 15

8. Rotating probe devices 15

8.1. Rotating probe — rectangular waveguide 15

8.2. Rotating probe — coaxial line 17

8.3. Rotating probe instruments — other 19

9. Resonance lines 19

9.1. The Chipman line 19

9.2. Squared VSWR response 21

10. Reflectometer techniques in general 22

10.1. Reflectometer for swept-frequency applications 22

10.2. Reflectometer for single-frequency operation 23

10.3. Single directional coupler reflectometer 23

a. Adjustment of the tuners 24

b. Approximate theory of tuning adjustments 25

c. "Exact" theory of tuning adjustments 27

d. Error analysis 29

10.4. Phase of reflection coefficient 30

11. Reflection coefficient standards 30

12. References 32

IV
Microwave Impedance Measurements

and Standards

Robert W. Beatty

A survey and discussion of well-known microwave impedance measurement techniques is presented. The discussion includes an introduction

[1] ^ which emphasizes basic concepts and reflection coefficient-VSWR

relationships. Sources of error in the various measurement techniques

are discussed and methods to reduce errors are presented. The discussion

of errors in slotted hne and reflectometer techniques is most thorough.

Methods using rotating loops and resonance lines are included and a brief

discussion of microwave impedance standards is given.

1. Definition of Reflection Coefficient

The propagation of electromagnetic energy can generally be regarded

as wave propagation.

A particularly simple type of wave is one which travels along a straight

hne, following a uniform path or waveguide. The wave has sinusoidal

time variation at a single frequency and may suffer attenuation due to

dissipation but is not reflected unless it encounters some discontinuity

in, or termination of, the path or waveguide.

This type of wave is the one to be considered, because other more

complicated types can be synthesized by proper combination of appropriate simpler types.

The reflection of a wave traveling in one direction may in general

produce a scattering, such that waves in different modes are set up in

different directions. However, for our purposes, only the wave coming

back along the same path in the same mode is regarded as the reflected

wave, the others being regarded as scattered wave components.

If the incident and reflected wave amplitudes are denoted by a and 6,

respectively, the reflection coefficient is the ratio of b to a. Since the

wave amplitudes are usually written in complex form to include phase

information regarding the sinusoidal time variation, the reflection

coefficient F as defined above is, in general, complex.

Thus, it is seen that the concept of reflection coefficient is applied to

the case of

(a) sinusoidal time variation,

(b) single frequency,

(c) single propagating mode.

' Figures in brackets indicate the literature references at the end of this Monograph.

1
(d) uniform path or waveguide having a termination or discontinuity

which causes reflection, and

(e) incident and reflected waves traveling the same path in opposite

directions.

In microwave circuit analysis, it sometimes happens that the waves

travehng in opposite directions in a waveguide are not clearly distinguishable as "incident" and "reflected." One can then make an

arbitrary choice and, in doing so, it may be convenient to define certain

reflection coefficients as the ratio of 6 to a and others as the ratio of

a to b. This happens because a is often chosen to designate the amplitude of a wave incident on a waveguide junction, and b the amplitude of

a wave emerging from the junction.

Thus it may happen that the wave emerging from a junction is the

wave incident upon a load. The reflection coefficient of the load would

then be the ratio of a to 6 in this case.

There is no concept of mutual reffection coefficient corresponding to

that of mutual impedance. If there were, this would be defined as the

ratio of the amphtude of a reflected wave in one mode or path to the

amplitude of an incident wave in another mode or path. These ratios

are called scattering coefficients rather than reflection coefficients. The

concept of reflection coefficients is thus seen to be a special case of

the concept of the scattering coefficient.

2. Definition of Impedance, Normalized Impedance

Impedance has been defined as the ratio of v to i, the generalized

voltage and current.

If one uses p as a mode index,

l + *£

Conversely,

Zp

rp=y—' (2)

±£.+ 1

The characteristic impedance Zop is a normalization constant whose

choice is arbitrary.

One may avoid or hide Zop by use of the normaUzed impedance con-
cept. The normalized impedance is

^Op A 1 p

(3)

The normalized impedance is a dimensionless ratio, and in common

usage the front superscript is dropped. Thus, there may occasionally

arise some misunderstanding as to the meaning of Zp, but this is relatively rare.

3. The Smith Chart

The relationship (2) may be written

z-i

zTT'

where it is understood that Z represents a normalized impedance for a

particular mode. This can be written

r=i Z+1 (4)

The transformation of lines of constant resistance to circles in the

F-plane is shown in figure 1.

The transformation corresponding to (4) is shown in simple steps,

starting with the dashed line of constant resistance r shown in the

Z- PLANE Z + l

r + l

0 0

z + l

r + l I

-2

Z+l

/

0^

r + l

/

0

R =

r + l

Figure 1. Steps in the transformation of a line of constant

resistance in the impedance plane to a circle in the reflection coefficient plane.

3
Z-plane, then in the Z+l plane, then the circle due to inversion, the

rotation and stretching caused by multiplication by — 2, and finally the

translation caused by the addition of unity.

Note that all hues of constant resistance r transform to circles in the

F-plane; the circles, having centers which lie on the real axis, have radii

equal to the reciprocal of r + 1 and pass through the point 1, 0.

A similar development for lines of constant reactance is shown in

figure 2.

It is seen that lines of constant reactance transform to circles in the

F-plane; the circles, having centers which lie on a Une perpendicular to

the real axis and passing through the point 1, 0, have radii equal to - and

X

pass through the point 1, 0.

If the transformation of (4) is apphed only to portions of lines in the

right-half Z-plane, we obtain the familiar Smith chart, shown in figure 3.

The same chart, rotated 180 degrees, can be used to represent the

transformation of normalized admittance y to reflection coefficient. This

is briefly proved as follows:

It is apparent that when y is substituted for Z in (4) we have minus

(5), so that the same chart, rotated by 180 degrees, can be used for

admittances.

(5)

0

z

r

0 Figure 2. Steps in the transformation of a

line of constant reactance in the impedance

plane to a circle in the reflection coefficient

plane.

4
_RESISTANCE

FlGVRE 3. The Smith Chart. COMPONENT

4. Effect of Change of Position of Terminal Surface

A change of position of the terminal surface, at which the terminal

variables v and i or a and b are determined, changes the reflection coefficient r in a simple manner, but the impedance Z is changed in a more

complicated way.

X| Xg

2

= 01 e"^-^, AND b| =

Figure 4. Diagram representing traveling waves on a transmission line as observed at two

terminal surfaces having positions Xi and X2.

The diagram shown in figure 4 appUes to the case where r2 is known

and we wish to determine Fi at a distance / toward the generator, which

is along a uniform waveguide having a propagation constant y = a-f;/3.

a2 = aie~^\ and bi = b2e~^^.

Therefore,

Y^=h = h ^-2yi = Y2e-^yK (6)

ai a2

The magnitudes are related by

\r,\ = \T2\e-'^\

and the phase of Fi equals the phase of F2 minus 2(31, or

l//l=l//2- 2/3/ + 2/177,

where n is an integer.

5

767-763 0-65—

2
One can derive the conventional transmission line formulas from

(6), remembering that

Z 1 + r

'^ —^— and e'>'' = cosh yZ + sinh yl.

One obtains

^ _ Z2 + tanh yl

^ I+Z2 tanh yT (7)

and for the special case of no losses,

^ _ Z2 +y tan f3l

'~l+yZ2 tan ^8/" (8)

5. Voltage Standing-Wave Ratio (VSWR)

The ratio cr is called the VSWR and may be defined in terms of the

reflection coefficient F by the equation

(T

= 1 + r

1- r

(9)

Accordingly, a VSWR may be associated with any reflection coefficient F.

If F can be determined, the corresponding VSWR can be calculated

from (9).

An alternative definition of VSWR requires the postulation of a lossless waveguide in which there is, in general, a standing wave produced

by the sum a + 6 of the incident and reflected waves. This standing

wave is f = a + 6, a standing wave of generalized voltage. As one examines diff^erent positions of a terminal surface as it moves along the

waveguide, one finds that fmax ~ l^^l + 1^1 ? and Vmm ~ 1^1

"

1^1 • Thus the

standing wave ratio of v is

(T

= ^max a + b 1 + lFl

^min a b 1-|F| (10)

If losses were present (as they always are), then the maxima of v would

vary, as would the minima. If we took the ratio of fmax to f^mm^ where

^^min ^as located approximately one quarter wavelength from the position

of fmax? measured toward the generator, then

orA

=

Vmax

Vmin

\a\ + \b\ 1 + lFl

\a\e 4 -\b\eAc l-|F|e"

(11)

6
One sees that the association of VSWR with a standing wave of v

leads to the ratio aa of (11), which involves both |r| and a in a fairly

complicated manner. It seems preferable to associate VSWR, cr, with

the reflection coefficient T as in (9).

6. The Idealized Slotted Section

The propagation of certain waveguide modes is not greatly disturbed

if a thin slot is made in the outer conductor of the w^aveguide in a direction parallel to the axis of the waveguide. Examples of these modes

are the TEM mode in coaxial line and the TEio mode in rectangular

waveguide.

A probe may be inserted in the slot to sample the fields, and movement

of the probe along the slot will provide data on the variation of the field

strength as a function of axial length.

Probes may sample either the electric or the magnetic field, or both,

and may sample either transverse components, axial components, or

both. The usual type of probe encountered in commercially available

instruments is one which samples the transverse component of the

electric field and does not respond to the magnetic field or to axial

components of the electric field (if present).

Ideally, the output level l^sl of the probe to the detector is proportional to the strength of the field sampled. For example, if the transverse component E< of the electric field is sampled,

|63|=/^i|E,|=/^2|F|=/^2|a + 6|=/^2|a| • |H-r|, (12)

where Ki and K2 are constants. Thus, the probe samples the standing

wave which is set up as the sum of the oppositely directed traveling

waves having amplitudes a and b.

Suppose that the probe is located at terminal surface 1, whose position

is variable, and the load (r2) is at terminal surface 2, whose position

is fixed. With reference to the diagram of section 4, the probe output

level is

l + |r2|e^'"''2-2r') • (13)

In the idealized slotted line, which is lossless {y=jfB, a =

0),

I 63 I = /^2 I

The corresponding vector diagram is shown in figure 5. As the probe

changes position, the smaller of the two vector components rotates,

and goes in and out of phase with the fixed vector component of unit

magnitude.

63|=A^2|ai| • |1 + ri| =/^2|a2|e'

(14)

7
Figure 5. Vector diagram pertinent to the probe output of an idealized slotted line.

Thus the ratio of maximum to minimum probe output is

= o-L(the VSWR). (15)

max

\bs min

1 +

1-

One sees from the diagram that as the probe moves in a direction

away from the load, the first minimum in its output occurs when

iljL-2f3lm =±7r. (16)

The phase angle of the reflection coefficient of the load is then

given by

\\fL

= 2film±7T. (17)

7. The Actual Slotted Line

Although the ideaUzed slotted hne is simple, any actual slotted hne

is quite compHcated, and a rigorous analysis of its performance is quite

difficult. Errors due to unavoidable mechanical irregularities in the

construction of slotted hnes have never been reduced to the point where

the complexity of a rigorous analysis was justified. Steps have been

taken in the direction of a more rigorous analysis of actual slotted hne

behavior, but these have found relatively httle appUcation in practice.

Sources of error will be hsted, and some of them will be discussed in

more or less detail in the following paragraphs.

7.1. Irregular Variations in Probe Coupling

The irregular variations in probe couphng caused by unavoidable

mechanical defects in the construction will cause corresponding variations in the probe output. These unwanted variations are superimposed

on the cychcal variations due to the standing wave, and they will cause

the observed standing wave ratio to diff"er from the actual standing wave

ratio. They may even mask the variation that one wishes to observe,

and this occurs approximately when the hmits of variation are the same.

8
For example, if the irregular variations in probe output have a maximum amplitude of ± 0.5 percent (a typical value for precision slotted

lines of high quality), they may begin to mask the cycUcal variations

from a load having a VSWR of 1.01, or less.

These irregular variations are most probably caused by variations

in the penetration of the probe in the slot as the probe and detector

move in an axial direction. Irregular transverse motions of the probe

within the slot will also contribute. Irregularities in the inside dimensions of the waveguide will also cause irregular variations in probe output

but wiU probably contribute less than the above causes.

A less obvious but often troublesome source of irregular variations in

probe output is the variation in contact resistance between the probe

carriage and the slotted line. This contact resistance is m series with

the rf current that flows into the probe circuit from the waveguide.

7.2. Probe Loading of the Slotted Line

An important source of error in slotted line measurements is the probe

loading effect. In the ideal situation, the probe is decoupled so as to

penetrate the waveguide only very sHghtly, and hence it does not disturb the fields within the waveguide.

In practice, however, one must have sufficient couphng so that enough

energy is extracted from the waveguide to operate the measuring or

indicating apparatus. As a practical approach to this problem, it is

recommended that one begin with more than adequate probe insertion

and note the change in observed VSWR as one gradually, in small increments, withdraws the probe. When the change in VSWR has become

negUgible, the probe has been sufficiently decoupled.

One might like to be able to estimate the error caused by probe loading

and obtain quantitative results. In some cases, it might even be

desirable to operate with a deeply inserted probe and make corrections

for the probe loading effects. These problems have been solved, but

the solutions have not been reduced to practice except in restricted

cases, for example, when it is assumed that the generator is nonreflecting.

Several analyses have been made, each progressively more rigorous

than the other. However, with more rigor comes greater complexity,

and the need must be great before the results of a rigorous analysis are

applied to a simple measurement.

In the following, three analyses will be briefly discussed.

a. Probe Replaced by Shunt Admittance, Generator Nonreflecting

One analysis has been made by assuming that the probe dimensions

are smaU compared with a wavelength and that its effect on the waveguide is that of a shunt admittance. In order to simplify the analysis,

it has also been assumed that the generator is nonreflecting.

9
Figure 6. Simplified equivalent circuit of a slotted line for analysis of probe loading

effects.

We can then draw a simple equivalent circuit as shown in figure 6.

In this circuit, normahzed impedances and admittances are used, and

the circuit is assumed to represent conditions at a terminal surface in

the waveguide located at the probe position. The admittance Yl is

related to the actual load admittance by (7), if one replaces Zi by

and Z2 by It is assumed that there are no losses in the waveguide.

The expression for fp is

1

Vp e

^ l + Fp + F^'

^^^^

It is assumed that the probe output level I63I is proportional to \vp\^ so

that the above equation gives the probe response.

In the ideal situation, Fp = 0, and

\^^\=Y^ = \^^^^l)^ (19)

where A: is a constant. This is similar to (12), and the ideal response is

obtained. However, the effect of the probe admittance Yp is to modify

the probe response so that the observed ratio of maximum to minimum

is no longer equal to the VSWR, and the distance to the first minimum

no longer gives by calculation from (17).

Corrections to these observed values have been calculated and some

information on them is given by Ginzton [2] . One must know Yp in

order to apply these corrections. It is difficult to calculate Yp or to

measure it, but this need not be done, since it can be obtained by

analysis of the response curve [3]

.

b. Probe Replaced by Shunt Admittance, Arbitrary Generator

If one desires a httle more rigor and takes into account the fact that

the generator may not be matched to the waveguide, the analysis becomes

a bit more comphcated in that one more variable, Yg, the generator

admittance, is involved.

10
Following the same prodecures used to obtain (18), we now obtain,

taking into account Fg,

= ^'Cr = 1 ^

Y'c + Yp-^Yi l^r'c'Y'f,+ Yp^Y'^' ^^^^

where be is the amplitude of the wave emerging from the generator when

it is terminated by a nonreflecting load.

In the above equation, the prime indicates that the quantity indicated

is referred to the terminal surface located at the probe position.

Since (20) is similar to (18), it is to be assumed that a similar distortion

of the probe response occurs, but this distortion is a Uttle more complicated and the analysis has not been carried as far, mainly because

of the difficulties one would have in graphically presenting the results.

If one knows Yg and Yp, it is possible to determine their effect on the

probe response from (20). However, the more practical problem, that

of finding Yl given the probe response, Yg and Fp, has not been solved

at present.

It should be noted that the foregoing analyses may take simpler forms

if the probe loading is small. It can then be assumed that reflections by

the probe interact with reflections by the generator and the load, going

in and out of phase with each other as the probe changes position.

It is also interesting to observe that, even when the load is nonreflecting

(F[ = 1) , one can observe a VSWR if Yg ^

1. This observed VSWR is

not related to the load in any way, however.

c. Three-Arm Junction Representation of Slotted Line

If more rigor is desired, the slotted line may be considered as a threearm waveguide junction as shown in figure 7.

This approach is necessary if the probe dimensions are not small

compared to a wavelength or cannot, for some other reason, be represented by a simple admittance shunted across the waveguide.

DETECTOR

Figure 7. Representation of a slotted line as a three-arm waveguide junction.

11
D. M. Kerns has obtained the characteristic equation giving the detector response for this case [4]. The equation is as follows:

c e-j^^G

"

1 + Fp + mTGe-^^^'G + [1 + nTce-^^^WiKTL, pk) ' ^^^^

where

and c, Fp, m, fi, and K are constants independent of Ig and U.

It is worth noting that four characteristic constants, Yp, t/iFg, JiTg',

and jSl, are associated with the characteristic equation, instead of only

two, Yg and Fp, as before. If the generator is matched to the waveguide,

two of these constants vanish, and if the junction is lossless, |/^| = I.

In this case, (21) reduces to the same form as (18).

Further analysis has not been performed but could be completed if

desired. The practical problem is to obtain the reflection coefficient of

the load given the response curve of the detector and any additional data

that are required, such as the four characteristic constants above.

7.3. Residual VSWR

The residual VSWR of a slotted fine is the VSWR within the slotted

section when the load is nonreflecting. It is caused by reflections from

discontinuities such as occur at the end of the slot, at tapered sections,

at beads which support the center conductor (when used), and at connectors.

All of these reflections add to the reflection from the load, and since

the phase difference is usually unknown, this represents a source of

error.

Assuming that the residual reflection coefficient Fr corresponding to

the residual VSWR is smaU, as is usually the case, one can write

F-F. + Fl, (22)

where F is the reflection coefficient in the slotted fine, and Fl is the reflection coefficient of the load. If only the magnitudes are known, we

can say that

|F|-|Fr| ^

|Fl|

^ |F| + |Fr|. (23)

For example if the residual VSWR is 1.04 (|Fr|

^

0.02) and the VSWR

in the slotted line is 2.50 ( |F| 0.429), the VSWR of the load is between

2.38 and 2.63 (0.409

^

IFlI

^

0.449).

12
It should be noted that the choice of terminal surface at which Tl is

to be specified is somewhat arbitrary and that the residual VSWR is

then also somewhat arbitrary. For example, the terminal surface can

be chosen on either side of the connector. In one case the reflection

from the connector would be included in the residual VSWR, and in the

other case it would not.

7.4. Other Sources of Error Associated With the Slotted Line

A number of other sources of error as foUows are associated with the

slotted line, and while these normally produce negligible errors in welldesigned apparatus, one cannot always assume that they are negligible.

a. Change of Characteristic Impedance by Slot

In general, the characteristic impedance of the slotted waveguide is

different from tl^^t of the unslotted portions at the ends. The normalized

impedance one measures is thus referred to a base other than the desired

one.

However, the error caused by this source is usually far less than that

from the other sources and may be neglected. In case of a very wide

slot, however, it may be desirable to check this source. The increase

in characteristic impedance in ohms caused by a slot in a coaxial line,

TEM mode is

AZo ^ 0.03^2^ (24)

where 6 is the angular opening of the slot in radians. A slot opening of

0.1 rad (5.73 deg) will produce an impedance change of less than 0.0003

ohms, for example [5]

.

b. Slot Waves

The presence of the slot makes possible the propagation of modes

other than those which propagate in an unslotted waveguide. These

can be excited by the discontinuities at the ends of the slot or by asymmetrical location or construction of the slot as well as by the probe. At

certain frequencies, a slot mode may resonate, increasing its strength

and effect. If the probe responds to the fields in the slot mode, its

response will be distorted and errors produced. The presence of slot

waves may sometimes be observed as this distortion effect, but sometimes their presence is unnoticed.

They can be reduced by tapering the ends of the slot, symmetrical

construction and location of the slot, and damping of the resonances by

judicious placement of absorbing material.

767-763 0-65—

3

13
c. Attenuation or Slope

In any slotted line, the amplitude of the standing wave decays because

of losses as one proceeds in an axial direction. Thus, one maximum is

not as large as the next one. If the ratio is taken of two maxima to the

minimum response between them, shghtly different results will be

obtained. This effect is described by (11).

If the attenuation is small, as is usually the case, this effect may be

neglected, especially if one takes the average of the two ratios mentioned

above. If one denotes the average by r, the VSWR (ctl) of the load is

approximately

where a is the attenuation in nepers per unit length and / is the distance

from the terminal surface of the load to the probe position for minimum

response.

Leakage to the detector from the slot or from end connectors of the

slotted hne may cause difficulty in cases where the probe is decoupled

and the detector has high gain. It can cause errors in the measured

ratio of maximum to minimum response.

A number of other sources of error can be mentioned. Some are

normally small, while others require special precautions in order to

keep them small.

Appreciable harmonic content or spurious modulation of the signal

source can cause large errors. Pulling of the oscillator caused by variations in loading as the probe changes position can be troublesome.

Instabihty and noise, both in the signal source and the detector, can

cause errors. The apparatus used for measuring ratios can contribute

to error if not accurate. The solutions to these possible sources of

trouble are fairly obvious.

Measurement of the phase angle of reflection coefficient or impedance

is subject to many sources of error, such as error in measuring the displacement of the probe, error in measuring frequency, difference in

wavelength in the slotted and unslotted portions of the waveguide, probe

loading effects, etc.

(25)

d. Leakage

7.5. Still Other Sources of Error

14
7.6. Conclusions

The slotted line is a convenient instrument to use and measurements

can be made of VSWR and phase angle of reflection coefficient with fair

to good accuracy.

However, the possibilities for making errors are many, and a skilled

operator is a valuable accessory. The nature of the error sources is

such that the refinement of slotted lines for highly accurate measurements is difficult and expensive. It has been found that the tuned single

directional coupler reflectometer to be described has more promise for

single-frequency operation.

Due to convenience of operation, reasonable size, ease of obtaining

phase information, ease of retuning when changing frequency, rapidity

of measurement, etc., the slotted line is the most popular instrument

for measuring reflection coefficient and impedance at microwave frequencies. However, its refinement for measurements of higher accuracy appears to be unprofitable.

8. Rotating Probe Devices

Instead of sHding a probe which couples to the electric field in an

axial slot to make a measurement of reflection coefficient, one can obtain

a similar response and make similar measurements with a rotating probe

which couples to the magnetic field.

Two versions will be described, one for rectangular waveguide and

one for coaxial line.

8.1. Rotating Probe — Rectangular Waveguide

The rotating probe is located in the top or broad wall of the waveguide,

off center, where the axial and transverse components of the magnetic

field for the dominant mode have equal magnitudes. This can be shown

to occur when x = d^ and

<f

=-tan-i^, (26)

TT Ac

where Kg is the guide wavelength, \c is the cutoff wavelength, and d,

and a are shown in the diagram of figure 8.

The two components of the magnetic field in a progressive wave

travehng in the Z-direction are, at x = d^ not only equal in magnitude,

but are at right angles in space and in time quadrature. These conditions produce a circularly polarized magnetic field which can be coupled

out by a circular waveguide placed as shown. The diameter of the

circular waveguide is such that it is below cutoff" for the dominant mode.

15
Figure 8. Rotating probe coupling to magnetic fields in a rectangular waveguide.

Figure 9. Orientation of coupling loop relative to axis of waveguide.

This results in low probe loading of the rectangular waveguide, which is

desirable.

The effect of a reflected wave travehng in the opposite direction in

the rectangular waveguide is to couple out a circularly polarized component having opposite rotation. The result is an eUiptically polarized

wave in the circular waveguide. Rotation of the probe will give a cycHcally varying output similar to the slotted Hne response, except that angular displacement takes the place of Hnear displacement.

It can be shown that

Ha:=jHoil-\TL\ej^L),

and

Hz = Hoil-\-\TL\ei^L),

^27)

where Hq = B — A sin — , and A is an amplitude factor.

a a

The couphng loop is oriented as shown in figure 9.

16
The output level \bp\ of the coupling loop is

K\Hz cos d-^Hx sin d

= KHo\l-\-\rL\e^^^L-^^^ (28)

This is of the same form as (14), showing that 6 plays the same role in

this instrument that j8/ plays in the slotted hne. The procedure to

measure Tl is, therefore, similar to that used with the slotted line, if

one substitutes rotation for linear displacement.

Since the correct location of the probe varies with frequency, one

would expect errors to be introduced when not operating at the design

frequency. Probe loading effects would be present but differing from

those in the slotted hne. Some error might be expected if the probe

couples to the electric as well as the magnetic fields. Any axial variation of the probe during rotation will cause error. However slot effects

have been avoided. A detailed description of an actual instrument is

given by Hopfer and Nadler [6].

Although this instrument is commercially available in some waveguide sizes, it has not yet replaced the slotted hne in popularity.

In coaxial hne, an instrument using a rotating probe coupled to the

magnetic field has been developed and is commercially available. Such

an instrument operates below 1 GHz (Gc/s) and at these frequencies is

smaller than a slotted line and has comparable accuracy.

As shown in the diagram of figure 10, it consists of a coaxial tee junction with a circular waveguide, below cutoff, coupled at the branch point.

8.2. Rotating Probe — Coaxial Line

DETECTOR

Figure 10. Diagram of a standing wave indicator for coaxial line.

17
The rotating probe is located within the circular waveguide incorporating

a mode filter so as to permit coupling only to the magnetic field and not to

the electric field.

In deriving the working equation of the instrument, it is assumed that

the transverse magnetic field components of the TEi,i mode in the circular waveguide are excited by, and have magnitudes proportional to,

the branch currents /r, /i, and Ii- One can then write

(29)

Referring the unknown admittance Yy and that of the standard Ys to

the branch point, and denoting these referred admittances by primes,

we have

^ Hx = CMY',-Y:)

[Hy = C2v{Yl+Y',),

(30)

where v is the voltage at the branch point.

The output level, denoted by of the probe (coupling to the magnetic field, and having an angular position 6 as shown in figure 11) is

\bp\ =K\Hx sin S — Hy cos d\. (31)

If one assumes that Ci = C2 = C, and that Yg=—jYo, where Yo is the

characteristic admittance of the coaxial Hne, it can be shown that

KCvYoV2

'^^1 ii + n

i + |r:|e

+26)

(32)

This is of the same form as (14), showing that (d—^in this instrument

plays the same role that (31 does in the slotted line. The measurement

technique is then analogous and needs no further discussion.

PLANE OF LOOP

Figure 11. Orientation of coupling loop relative to axes of coaxial lines.

18
Errors will result from inability to satisfy the assumptions made in

deriving (32), but, below 1 GHz, these errors can be kept small. A detailed description of an actual instrument is given by Hopfer and

Finke [7].

8.3. Rotating Probe Instruments — Other

Other instruments using rotating probes have been developed [8] in

which the principle of operation is similar to, or a variation on, those

described above.

9. Resonance Lines

Microwave impedance measurements may be made by observing

resonance phenomena produced by sUding short-circuiting plungers

or otherwise varying susceptances of coaxial lines and other types of

uniform cyhndrical waveguide.

9.1. The Chipman Line

An early resonance line technique was developed by R. A. Chipman

[9], and refined by Meier and Summers [10].

This technique is characterized by a response which is the inverse

of that from a slotted fine, and both generator and probe are loosely

coupled to the waveguide (which is often a coaxial Hne).

As shown in the diagram of figure 12, the generator is loosely coupled to the waveguide at a fixed position, while the detector is loosely

coupled to respond to the current in a sliding short-circuit. Measurements are made by sliding the short-circuit and observing the detector

response curve. A simplified analysis based upon an ideahzed model

yields the equations of basic interest. It is convenient and appropriate

to assume that the line is lossless, that the generator couphng introGEN

A

DET

COUPLING

LOOP

SLIDING

SHORT-CIRCUIT

Figure 12. Diagram and simplified equivalent circuit for a form of resonance line

developed by Chipman.

19
duces no discontinuity and does not appreciably load the line, and that

\Zg\ is great enough so that ic may be considered constant.

The current on a short-circuited lossless hne is known to be sinusoidally distributed, or

is =I cos f3d.

From KirchhofF's law,

iG — is-^iL or is = iG~ il,

cos fid

However, from elementary circuit theory,

• 1 . Zp

where

7 =

The amplitude of the probe output is proportional to

iG /i Zp\ ic

/ = —^

1-^ =

cos (3d \ Z'J cos pd Z'^

r-w i ' J- 7'

This equation yields the response, but it is desirable to convert to

another form in which d and / are expHcitly involved. Replacing Z'^

and Z'l^ by their corresponding reflection coefficients and F^,

where F^ = F^e'-'^^^ and F^ = Fz.e--'^^^

l^^G

y Y-\-e-^^^^ j

(1 + Flc ^2/3^)

-j^_p.^p^^_j-2^(^^f)- (33)

Assuming that the detector is loosely coupled to a perfect shortcircuit (|F5| = 1), and that d is the independent variable, the observed

ratio r of maximum to minimum probe output level is

r = 1 + 1ITlI

ITlI

o-L, the VSWR. (34)

20
Usually / is less than one quarter wavelength, and the first maximum

probe output as d increases from zero occurs when

or

lPL

= 2p{dm-^l)±7T. (35)

Instruments based upon this principle are not commercially available

but have been constructed for special applications. Such instruments

are mechanically more awkward than slotted Unes, have greater loss

between generator and detector, and afford little or no increase in accuracy because it is difficult to maintain constant probe coupling. The

absence of a slot is an advantage and the inverse response is useful in

special apphcations such as the determination of the line attenuation.

In order to make accurate measurements, the assumptions made in

deriving (33) have to be satisfied, and the reflection coefficient Ts of the

short-circuit has to be determined. In addition, great care is needed

in the design and construction of the fine, insuring its uniformity and

the constancy of the detector probe coupling.

9.2. Squared VSWR Response

It is interesting to consider the response from another type of resonance Hne having fixed probes and variable short-circuit. Referring to

a diagram and model, as shown in figure 13, and making simphfying

assumptions as above, a simple equation may be derived for the response.

We assume that the detector is coupled to respond to v and that d is

how fixed while / or is variable. In a manner similar to before.

Figure 13. Diagram and simplified equivalent circuit of a form of resonance line which

can have squared VSWR response.

21
If d =—r, Z's

= <x) (lossless case), and

(36)

As either or / is varied, the ratio r of If max to

r

=

(37)

As / is increased, the first minimum l^l occurs when — 2)3/m ==t7r,

so that

It is interesting to note that squared VSWR response [11] may be obtained from other arrangements than the one shown.

10. Reflectometer Techniques in General

It is commonly understood that a reflectometer is an instrument used

to determine the magnitude |r| of the reflection coefficient, or the corresponding VSWR. Phase information is usually not provided, but can

be obtained by appropriate modifications of the instruments and

techniques.

10.1. Reflectometer for Swept-Frequency Applications

One form of reflectometer widely used for swept-frequency measurements consists of two directional couplers connected as in the diagram

of figure 14.

The detectors Di and Dr couple loosely to the incident and reflected

waves, respectively, so that the ratio of their input levels ideally equals

IFlI, the magnitude of the reflection coefficient of the load. Ratio meters

have been developed to make this a direct-reading instrument, which

(38)

GENERATOR LOAD

Figure 14. Simple diagram of conventional reflectometer.

22
is calibrated by replacing the load by a short-circuit, and adjusting the

detectors and ratio meter to indicate |r| = 1. In addition to the advantage of covering a broad frequency range with little or no adjustment,

this form of reflectometer is relatively insensitive to amplitude changes

of the generator such as those associated with instabiUty.

In order to obtain best accuracy, the directional couplers should have

high directivity, loose coupUng, and excellent VSWR characteristics.

In addition, the generator as seen at the plane of connection of the load

should be essentially non-reflecting over the frequency band [12].

With equipment presently commercially available, one can expect

to make measurements of IFlI over the range- 0.1 to 0.35 with an uncertainty of less than 5 percent at frequencies up to 140 GHz.

10.2. Reflectometer for Single-Frequency Operation

Methods have been developed [12] for reducing errors in reflectometer

measurements caused by imperfect directivity and multiple reflections

between load and generator by use of auxihary tuners placed as shown

in figure 15.

The tuners are carefuUy adjusted before making a measurement.

The adjustment [12] is such as to make the ratio of the detector output

levels very closely proportional to IFlI- It is possible, also, to estimate

the limits of error caused by imperfect adjustment of the tuners from

data obtained during the adjustment process.

By this technique, one obtains improved accuracy at the sacrifice

of swept frequency operation and ease of operation, since the tuning adjustments can be tedious. The measurement remains insensitive to

changes in level of the generator, however.

10.3. Single Directional Coupler Reflectometer

If a stable generator is available, the use of a single directional coupler

with two tuners will permit accurate measurements at a single frequency,

and reduces the number of tuners to be adjusted. Instead of simultaneously observing the ratio of two detector outputs, one alternately

connects the unknown and then a standard of reflection coefficient at

GENERATOR- TUNER

I—

D,

TUNER TUNER LOAD

Figure 15. Diagram showing the addition of tuners to a conventional reflectometer to

improve its performance for single-frequency operation.

23
DR

GEN CALIBRATED

ATTENUATOR

TUNER

•2i ^

TUNER LOAD

Figure 16. Simple schematic diagram of a tuned, single-directional coupler refiectometer.

the plane of the load. A calibrated attenuator is used to return the

dtetector output to the same value, and the ratio of levels can be read from

the attenuator dial.

The arrangement of apparatus is as shown in figure 16.

Ideally, the change in attenuation under the above conditions

equals the change in return loss when the unknown load Ir^l is substituted for the standard |rs|. This is expressed as

A^=201ogio|^4- (39)

In the special but usual case in which a short circuit is used as the

standard, and the attenuator is initially set on zero,

^ = 20 logio -rp-j- . (40)

Tables of return loss [13, 14] are available to facilitate the determination of \Tv\ once A has been measured.

a. Adjustment of the Tuners

The purpose of adjusting the tuners [15] is to obtain two conditions,

(a) infinite directivity, and (b) eUmination of multiple reflections at the

plane of the load. It will be shown later that achievement of these two

conditions will result in ideal behavior of the refiectometer, in that the

side arm output level will be proportional to IFlIInfinite directivity would be obtained if the side arm output were zero

when the load was nonreflecting. In principle, one could connect a

nonreflecting load and adjust the tuner near the load until the side arm

output was reduced to zero. In practice, however, it is difficult to obtain

a load having no reflection, and another method is recommended.

Referring to the above diagram, it is assumed that there is a section

of waveguide between the load and the tuner, and that this is sufficiently

long so that one can shde a termination within it for a distance of at

least one-quarter wavelength. This waveguide section is attached to

the tuner and is regarded as a part of the reflectometer.

A termination having a low reflection, for example VSWR less than

1.02, is slid back and forth in this waveguide and one observes cyclical

24
variations in the level of the side arm output. The adjacent tuner is

then adjusted until these cyclical variations have been eliminated or

reduced to a low amount, say ±0.5 dB.

The adjustment of the other tuner then follows in a similar way

except that instead of using a sliding termination having a low reflection,

one shdes a short-circuit, and instead of adjusting to a Umit of ±0.5 dB,

one does not stop adjusting until the cyclical variation in the side arm

output is less than ±0.01 dB. This second adjustment will satisfy or

closely approximate the second condition mentioned above, in which

multiple reflections at the plane of the load are eliminated. In figure 16,

this condition impHes that r2i = 0 at the plane L.

b. Approximate Theory of Tuning Adjustments

It can be shown that the amphtude 63 of the emergent wave from the

side arm of the directional coupler may be written [1] in the form

b^ = C

1 - T2iTL (41)

where

(i-Siirc) SisTl

SsiTg (l~533r£))

K =

S21S22

S31SS2

and

r2i=-

-d SuTg)

S21TG

Ssi^G

>31

S12

S22

S32

S23TD

(i-Snrc)

Ssi^G (I-SssFd)

The above terms include the amplitude 6g of the generator wave;

the scattering coefficients of the form Sij of the three-arm waveguide

junction representing the directional coupler, tuners, and waveguide

section; and the reflection coefficients Tg, Td, and Tl of the generator,

detector, and load, respectively. The reflection coefficient is that of

the equivalent generator as seen at the plane of the load.

The r2i is obtained as follows: By assuming that ai^^iFc, b2 = a2Ti^

a3 = bsTD^ and solving the scattering equations for a three-arm waveguide junction.

25
The scattering equations are

0=— (1 — SiirG)6i + Si2a2 +5i3rz)63,

62 = S2iTGbi + 8220,2 + SosTobs,

0 = SsiTcbi -f 532^2 — ( 1 — SssTd) bs,

and the solution for using Cramer's rule is the expression shown

above.

It is helpful to note that the above expression for K is closely related

to the directivity

S 9

D = 20 logioj^^- (42)

One sees that for infinite directivity, 531 = 0, and K

r2i = 0, then (41) becomes

^'~(i-SnrG)(i-533rz,)^'"

and the sidearm output level I63I is proportional to IFlIOne can see how the tuning adjustments described above lead to this

condition as follows: If Tl in (41) is the reflection coefficient of a sHding

termination having a VSWR less than 1.02, then IFlI < 0.01. With the

tuning stubs withdrawn, one can say that |r2i| < 0.1 and \K\ > 100, for

components easily obtainable. Thus |r2iTL| < 0.001, and I^^FlI > I.

Referring to (41) one sees that changes in phase of Tl caused by shding

the load will cause cychcal variations in I63I mainly because of the

numerator. It is also evident that these variations can be greatly

reduced by increasing which can be effected by adjusting the tuner.

When the variations have been reduced to ±0.5 dB, then \K\ has been

increased to approximately 3400.

The adjustment of the other tuner now proceeds after replacing the

shding termination by a shding short-circuit. Note that IFlI ~ 1, and

|i^|=3400 in (41), while |r22| is essentially unchanged. Thus I^FlI

= 34(X) and |F2iFL| < 0.1. As the short-circuit shdes, the variation in

Ibsl is now caused mainly by the denominator. Adjustment of the other

tuner wiU affect F2i without much effect on |if^| which is now large.

When the variation in I63I has been reduced to ±0.02 dB, then |F2i|

-0.001.

The estimation of the above quantities \K\ and |F2j| from the residual

variation in {bsl after the tuning process is stopped, as facihtated by the

graphs of figures 17 and 18.

= 00. Also if

(43)

26
c. "Exact" Theory of Tuning Adjustments

While the approximate theory of the tuning adjustments is probably

sufficient for most practical purposes, it may not suffice for the more

critical experimenter, and a 'more exact theory is then of interest.

Assuming that (41) is sufficiently exact, the conditions for no cyclical

Ll_ o

Figure 17. Graph showing effective directivity ratio K obtained in tuning process, versus

the residual variation when tuning ceases, for sliding terminations having VSWR's

from 1.0005 to 1.02.

27
Figure 18. Graph showing magnitude of reflection coefficient of equivalent generator at

terminal surface No. 2, versus residual variation when tuning ceases, for the sliding

short-circuit termination.

variation of I63I as we change the phase of Tl are as follows:

(1) K=cc^ r2i=o

(2) ^=-r*,r*

(3) K=-T2i

(4) r^^o.

Although the first condition is the one finally desired, it is unhkely

that we will obtain it in the first adjustment. We choose terminations

for which Tl^ 0 and avoid the fourth, while the third is an undesirable

condition that would reduce \K\ rather than increase it, and is unlikely

to result from normal adjustments of the tuners.

Thus the second condition is the one most Ukely to be obtained, or

at least closely approached. If IFlI — 0.01, and |r2i| — 0.1, then condition (2) would require that \K\ = 10^. This might be the result of

28
adjusting the first tuner. Then if IFlI^I, and |/^| = 10^, condition

(2) would require that |r2i| = 10~^. This might be the result of adjusting the second tuner.

If a higher \K\ or lower |r2i| were then required, the adjustments

could be repeated in sequence, although it seems probable that two or

three adjustments would suffice for most purposes.

d. Error Analysis

Once \K\ and |r2i| are determined from the residual variations in

1 63 1 after the tuning adjustments, the error in measuring the reflection

coefficient \Tv\ of an unknown can be calculated. Curves are available [15] to determine hmits of these error components directly from

the residual variations in \b3\.

In a typical example, the uncertainty in measuring iFul — 0.2 is less

than 0.1 percent if the residual variation in I63I is less than 0.5 dB

when shding a termination having a VSWR less than 1.01, and less

than 0.02 dB when sliding a short-circuit.

In this case, errors from other sources are hkely to be larger. Some

of the other important sources or error are

(1) Error in measuring ratio of side arm outputs when substituting an

unknown for a standard load. (This can be due to the error in the

calibrated attenuator, if this technique is used.)

(2) Uncertainty caused by reflection from a waveguide joint or

connector.

(3) Uncertainty in knowledge of the reflection coefficient IF^I of the

standard load.

(4) Instabilities of source, detector, or other components.

GENERATOR

SLIDING SHORT-CIRCUIT

PHASE SHIFTER

DETECTOR

^

TUNED

I REFLECTOMETER

X

LOAD

Figure 19. An arrangement for obtaining phase information with a refiectometer, using a

sliding short-circuit and tuned directional coupler as a standard phase shifter.
10.4. Phase of Reflection Coefficient

A number of arrangements and techniques have been suggested for

obtaining phase as well as amphtude information with reflectometers.

One of these [16] is shown in the diagram of figure 19.

One adjusts both the attenuator and phase shifter to produce a detector

output nuU. This is done alternately with the standard and the unknown

connected at the plane of the load.

Ideally the difference in readings equals the difference in phase or

amphtude, as the case may be.

A more refined version capable of greater accuracy is possible [17],

but unless greater accuracy is really required, it would be well to avoid

the tedious tuning operations required.

11. Reflection Coefficient Standards

In rectangular waveguide, many reflection coefficient standards have

taken the form of waveguide discontinuities of simple geometry. The

reflection is calculated from the geometry. Examples of these are the

step in the narrow wall and the half-round inductive obstacle.

Most commercially available reflection coefficient standards employ

a step in the narrow wall, making this occur at the waveguide joint, so

that essentially a reduced height waveguide is joined to one having

standard dimensions. The VSWR is, to a good approximation, equal to

the ratio of the narrow wall inner dimensions, and is insensitive to

frequency. There is a frequency-dependent, second-order correction

for the discontinuity capacitance, but this is small if the reflection

coefficient is 0.2 or less, which is usually the case. A shding termination of small reflection usually is included, so that its effect on the total

reflection can be taken into account and subtracted. Although these

types of standards are convenient and have good accuracy and stabihty,

there is no separation of the reflection from the discontinuity and that

from the waveguide joint, and the effects of losses are neglected. Thus,

more accurate standards can be constructed such as the half-round

inductive obstacles.

The half-round inductive obstacle reflection coefficient standard

[18, 19, 20] was designed to avoid sharp inside corners when electro

formed, and accurate, calculated values are available. The reflection

from the joint is separate, and nonstandard waveguide is not required.

Corrections for finite conductivity of the metal are possible, but not yet

available. The reflection from this type of standard is frequency

sensitive.

Perhaps the most accurate reflection coefficient standard is the shortcircuit, or more specifically, the quarter wavelength section of shortcuited waveguide [18]. This standard is frequency-sensitive, but is

30
AXIS OF

WAVEGUIDE

PLANE OF

SHORTCIRCUIT

PLANE OF JOINT

(a)

PLANE OF

SHORT-CIRCUIT

MAGNITUDE

OF CURRENT,

-PLANE OF

JOINT

(b)

Figure 20. Diagrams showing current distribution in short-circuited sections of (a) rec- tangular waveguide (TEi, o mode), and (b) coaxial line.

not sensitive to small dimensional errors, or to reflections or losses at

the waveguide joint. This freedom from losses at the joint is a result

of the vanishing of the axial component of current at the joint, as shown

in figure 20. Although the nominal reflection coefficient is unity, the

actual reflection coefficient can be determined to very good accuracy

from a knowledge of the microwave conductivity of the waveguide walls.

These data are obtained from independent measurements. The actual

reflection coefficient has also been determined by two other independent

methods, giving close agreement. These methods are (1) measuring

the ^ of a cavity which incorporates the quarter wavelength reflection

coefficient standard, and (2) measuring the losses of the standard by

means of a microcalorimeter.

When using this type of standard to measure an unknown having a

small reflection, the difference in return loss may be large, say 60 dB,

and consequently difficult to measure accurately. However an adjustable load may be used as an intermediate source of reflections, making

the measurement in two smaller steps, say 30 dB each.

In coaxial hne, microwave reflection coefficient standards of the

resistive type, have been constructed and also, the quarter wavelength

short-circuit is used [16]. It is anticipated that further developments

wiU be forthcoming now that a low reflection coaxial connector is

generally available [21].

The present state of the art, regarding the accuracy of calibration of

microwave standards of reflection coefficient at NBS, is described in an

article [22] which is part of a series on high-frequency and microwave

caHbration services.

The constructive suggestions of Robert C. Powell, Bill C. Yates, and

Harvey W. Lance of NBS for improving the presentation are gratefully

acknowledged.

31
12. References

[1] Additional theoretical background will be found in Basic Theory of Waveguide

Junctions and Introductory Microwave Circuit Analysis, by David M. Kerns and

Robert W. Beatty, to be published.

[2] E. L. Ginzton, Microwave Measurements (McGraw-Hill Book Co., Inc., New York,

N.Y., 1957), pp. 244-245.

[3] W. Altar, P. Marshall, and L. Hunter, Probe error in standing-wave detectors, Proc.

IRE 34, No. 1, 33^ (Jan. 1946).

[4] A. C. MacPherson and D. M. Kerns, A new technique for the measurement of microwave standing-wave ratios, Proc. IRE 44, No. 8, 1030 (Aug. 1956).

[5] IT&T Corp., Reference Data for Radio Engineers, 4th ed. (New York, N.Y., 1957),

p. 594.

[6] S. Hopfer and L. Nadler, Waveguide rotary standing-wave indicators, PRD Repts. 6,

No. 1,1-6 (Jan. 1959).

[7] S. Hopfer and H. Finke, Impedance measurements in the 50-1000 Mc/sec range with

a new standing-wave indicator, PRD Repts. 3, No. 2, 1-7 (Jan. 1955).

[8] E. L. Ginzton, Microwave Measurements (McGraw-Hill Book Co., Inc., New York,

N.Y., 1957), p. 298.

[9] R A. Chipman, A resonance curve method for the absolute measurement of impedance at frequencies of the order of 300 Mc, J.A.P. 10, 27-38 (Jan. 1939).

10] A. S. Meier and W. P. Summers, Measured impedance of vertical antennas over

finite ground planes, Proc. IRE 37, No. 6, 609-616 (June 1949).

"11] R. W. Beatty, Magnified and squared VSWR responses for microwave reflection

coefficient measurements, IRE Trans. Microwave Theory Tech. MTT-7, No. 3,

351-355 (July 1959).

12] G. F. Engen and R. W. Beatty, Microwave reflectometer techniques, IRE Trans.

Microwave Theory Tech. MTT-7, No. 3, 351-355 (July 1959).

13] R. W. Beatty and W. J. Anson, Table of magnitude of reflection coefficient versus

return loss (La = 20 logioiYrp), NBS Tech. Note 72 (Sept. 19, 1960).

14] R. W. Beatty, Decibels return_loss to magnitude of voltage reflection coefficient,

Microwave Engineer's Handbook and Buyer's Guide, pp. TD188-192 (1961-62);

pp. T221-225 (1963-64).

15] Wilbur J. Anson, A guide to the use of the modified reflectometer technique of

VSWR measurement, J. Res. NBS 65C (Eng. and Instr.), No. 4, 217-223 (Oct.-Dec.

1961).

16] R. W. Beatty and W. J. Anson, Apphcation of reflectometer techniques to accurate

reflection measurements in coaxial systems, Proc. lEE 109 (Pt. B), No. 46, 345—

348 (July 1962).

17] R. W. Beatty, A microwave impedance meter capable of high accuracy, IRE Trans.

Microwave Theory Tech. MTT-8, No. 4, 46W63 (July 1960).

18] R. W. Beatty and D. M. Kerns, Recently developed (Aug. 1958) microwave impedance

standards and methods of measurement, IRE Trans. Instr. 1-7, Nos. 3/4, 319-321

(Dec. 1958).

19] D. M. Kerns, Half-round inductive obstacles in rectangular waveguide, J. Res. NBS

64B (Math, and Math. Phys.), No. 2, 113-130 (Apr.-June 1960).

20] Precision Measurement and CaUbration — Electricity and Electronics, NBS Handb.

' 77, Vol. 1 (Feb. 1,1961).

21] A. E. Sanderson, A radically new coaxial connector for high-precision measurements.

The General Radio Experimenter 37, Nos. 2 and 3, pp. 1-6 (Feb.—Mar. 1963).

^22] RSL Engineering Division (NBS), Microwave and high-frequency calibration services

of the National Bureau of Standards — Reflection coefficient and immittance,

IEEE Trans. Microwave Theory Tech. MTT—12, No. 6, correspondence (Nov.

1964).

U.S. GOVERNMENT PRINTING OFFICE : 1965 OL—767-763

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