National Bureau of Standards

Library, E-01 Admin. Blclg. NOV 2 3 1970

NBS TECHNICAL NOTE 393

National Bureau of Standards

JUL 2 8 1^72

U.S.

PARTMENT

OF

OMMERCE

National

Bureau

of

Standards

A Method

for Designing Multi-Screw

Waveguide Tuners
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NBS TECHNICAL NOTE 393

ISSUED OCTOBER 1970

Nat. Bur. Stand. (U.S.), Tech. Note 393, 20 pages (Oct. 1970)

CODEN: NBTNA

A Method for Designing Multi-Screw

Waveguide Tuners

M. P. Weidman and E. Campbell

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

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CONTENTS

Page

Abstract 1

I . Introduction 1

II

.

Tuner Requirements 3

III

.

Tuner Analysis 3

IV. Design Technique 7

V. References 12

Appendix A 19

Appendix B 20

in

A METHOD FOR DESIGNING MULTI-SCREW

WAVEGUIDE TUNERS

By

M. P. Weidman and E. Campbell

Capacitive screw, waveguide tuners are commonly

used in microwave measurement systems and as devices

for adjusting the impedance of various waveguide terminations. The design of a broadband tuner of this

type has been a problem in the past.

This paper describes a method for designing

tuners which will work effectively for relatively

wide ranges of frequencies.

Key Words: Impedance transformer; waveguide tuner;

capacitive screw tuner.

I. INTRODUCTION

The capacitive screw or stub tuner is a familiar device

to many who work with rectangular waveguide measurement systems

This tuner consists of one or more cylindrical screws or

stubs which can be mechanically inserted into the center of

the broad wall of a rectangular waveguide. The stub is then

parallel to the electric field for the dominant TE

1f)

mode of

propagation and appears as a shunting capacitive susceptance

for stubs with diameters an order of magnitude less than the

wide waveguide dimension [2], [3],
There are basically two forms of capacitive screw tuners.

One form is the slide screw tuner which has a single screw

that can be adjusted into or out of the waveguide and also

moved along the length of the waveguide. The slide screw

tuner is useful over a full waveguide bandwidth, but for

critical measurements it has too much RF leakage. The other

form of capacitive screw tuner is the multi-screw type with

fixed position screws. The problem in designing the multiscrew tuner is the establishment of a screw spacing such

that the tuner is useful over a broad range of frequencies.

The following is a description of a method for determining a spacing of screws in a multi-screw tuner which will

be useful at any frequency in a full waveguide bandwidth. To

the writers' knowledge, this has never been done before except

at NBS. The design technique described here is meant to be

an improvement over techniques which have been used at NBS

in the past. Tuners have been built in several waveguide

bands using general criteria similar to the one described

here and have functioned well in many waveguide measurement

systems at frequencies throughout the waveguide band. Tuner

spacings which do not follow these criteria are, in general,

not usable at all frequencies.
II. TUNER REQUIREMENTS

Tuners are used in refined measurement systems to establish idealized impedance conditions. Consider the tuner as a

two port waveguide network. If the output port is terminated

in a nonreflecting load, and the input port reflection coefficient can be adjusted to any magnitude and phase, then the

tuner can be used to achieve any desired impedance condition

in a waveguide system.

III. TUNER ANALYSIS

A rigorous mathematical analysis of a single cylindrical

stub of variable length extending from the broad dimension of

rectangular waveguide is a difficult problem. Mathematical

and experimental analyses of this problem can be found in

the literature [1], [2].

The analysis used here applies to a multi-screw tuner.

Because of the complexity of the multi-screw tuner, several

simplifying assumptions will be made:

1) Dominant mode propagation exists in the waveguide

everywhere except in the near vicinity of the tuning

screws. That is, higher order waves set up by one

tuning screw are sufficiently attenuated before

reaching another tuning screw.

2) The multi-screw tuner is lossless. This is a good

approximation for analytical purposes.

-3
3) Reflection coefficients to be realized at the input

port are small in magnitude (less than 0.5).

The model of the cylindrical stub to be used in this

analysis is that of a shunting capacitive susceptance. This

model was determined experimentally by assuming an equivalent

T -- lumped element circuit and then measuring values for the

three lumped elements [2]. This equivalent circuit was then

converted to an input reflection coefficient (assuming a matched line on either side of the stub) which was then

plotted on a normalized Smith admittance chart. The admittance at a single frequency, plotted on a normalized Smith

admittance chart, follows the semicircle of unit conductance

clockwise as the screw is inserted into the waveguide [3]

.

This is shown in figure 1. In figures 1-3 it is assumed that

only admittances inside the |r| = .5 circle can be realized.

This is done to reduce screw interaction, and more closely

approximate the shunt capacitance model for the screw.

Tuning also becomes critical as the screw approaches the

resonant point (quarter wave insertion) [3].

If the screw is adjusted longitudinally in the waveguide (as can be done with the slide screw tuner) the semicircle of figure 1 is made to rotate through 360 degrees

for a longitudinal movement of one-half guide wavelength.

From this it can be seen that the slide screw tuner can

produce the required range of reflection coefficients.
The multi-screw tuner can be analyzed using the Smith

chart along with the three simplifying assumptions mentioned

above. A useful multi-screw tuner for a single frequency is

one with three screws spaced one-sixth guide wavelength apart.

The actual spacings can be one-sixth guide wavelength pl'us

integral multiples of one-half guide wavelength. The range

of admittances that can be realized at a single frequency

for this three screw tuner is shown in figure 2. In figure

2 the screws are numbered one through three, and the admittances which are realized by adjusting any two screws are

those seen at the plane of screw number one or an integral

number of half -guide wavelengths from screw number 1. An

example of how one admittance would be produced is shown

in figure 2 in the region where screws 1 and 2 are used.

Screw number 2 is inserted until point B is reached and then

screw number 1 is inserted until point C is reached. The

reader is referred to Ragan [3] for an explanation of the

details of this technique. It can be seen from figure 2 that

the requirements for a waveguide tuner, operating at a single

frequency, have been met by the three screw tuner with a screw spacing of one-sixth guide wavelength.

Up to this point the analysis has been limited to a single frequency. Figure 3 shows the Smith chart representation of the tuner in figure 2 at a higher frequency. Screws

1 or 3 can be inserted into the waveguide in order to approach
admittances in the unper half of the Smith chart, but then

screw number 2 will move the admittance away from the area

above the screw 1 semicircle. The tuner design shown in

figure 2 will be even less useful at still higher frequencies.

The limits on the spacing of a set of screws to be used

at any one frequency are then conveniently analyzed with the

aid of the Smith chart. In order to be able to converge on

an arbitrary admittance by alternate adjustments of two screws,

it is desirable to have the locations of the semicircles for

individual screw insertions spaced symmetrically around the

Smith chart. For good tuner nerf ormance , the spacing should

be at least as close as that illustrated in figure 2. This

would mean that for a broadband tuner there should be no

frequency in the band for which there are less than three

screws spaced equally around the Smith chart. For actual

design this requirement can be altered somewhat.

Another way of specifying tuner spacings is to represent

each screw by a phasor. The angular spacings of these phasors

would then be

720d

n n X g

where d is the distance of the nth screw from some reference

point, 9 is the angular location of the phasor and X is the

guide-wavelength at a particular frequency. The design requirement for a broadband tuner is then that at every

6-
frequency in the design band there should be no more than

120 degrees between any two adjacent phasors representing

points where screws are located. In actual practice this

value can be increased to 130 degrees without degrading the

performance of the tuner beyond usefulness. It is assumed

that the 9 angles have all been reduced to less than 360

n - degrees before plotting on a phasor diagram.

IV. DESIGN TECHNIQUE

The design technique described here is only one of many

which could be used and still meet the established criterion.

Other techniques at the NBS have been used to design tuners

which meet the spacing criterion and have been used extensively

over the frequency range at which they were designed to

operate. These tuners have performed well for various applications. The older techniques did not assure true broadband

usefulness; whereas this one does.

In applying the technique suggested here the highest

frequency of the design band is considered first. Four

stubs are spaced at 120° intervals. Physically this means

A /6 + nX /2 at the highest frequency. The nX /2 or integral

number of half wavelengths more than X /6 spacing depends

on the physical characteristics of the tuner. In most

applications above 4 GHz X /2 must be added to X /6 for

-7-
spacing since the drive mechanisms used on these stubs cannot physically be spaced any closer together. At even higher

frequencies X or more may be needed.

Figure 4(a) shows the stub spacing and figure 4(b) shows

a plot of the angular spacing of the first four stubs at the

highest frequency. In figures 4(b) - 4(d) the phasor number

corresponds to the stub number. Stub number one is always

assumed to be at zero degrees (everything is referenced to

stub 1)

.

As the frequency considered becomes lower, the angles

between phasor representing stubs are reduced in a clockwise

manner as in figure 4(c) until the spacing between phasors

1 and 4 is the maximum 130 degrees. At this frequency, stub

5 is placed so as to be at zero degrees . Stub 5 is placed

as close as physically possible to the right of stub 4 in

figure 4(a) and is still nX /2 distance from stub 1. It

should be noted here that the smallest possible spacing should

always be used since the rate of change of angle with respect

to frequency increases with increased spacing.

The preceding procedure is now continued down to a frequency where phasors 2, 3, or 4 may pass through zero

degrees into quadrant IV. Up to this point the angles between phasors 2 and 1, phasors 3 and 2, phasors 4 and 3, etc.

are all decreasing angles and are less than 130°. At the
frequency in which a phasor crosses from quadrant I to quadrant

IV, it is necessary to analyze the position of the last stub

to be added to the design. If the smaller angle is greater

than 130 degrees, another stub must be added at zero degrees.

If the angle is less than 130 degrees, the progress of the

last stub added is followed down in frequency until the

condition in figure 4(d) exists. Note that figure 4(d) is

only an example of what can happen. The situation in figure

4(d) is typical of what happens in waveguide bands from WR187

(3.95 - 5.85 GHz) to WR28 (26.5 - 40.0 GHz) with the exception of possibly one less stub involved. Now phasor 8 is

moving away from 4 as the frequency decreases . This means

another stub (9) must be placed nX /2 from stub 4. Stub 9

will be located as close as possible to stub 8 and still be

an integral number of half-guide wavelengths from 4.

Lower frequencies are considered again until another

opening of 130 degrees occurs between phasor 9 and the

closest following phasor. It is then necessary to add

another stub. Eventually the lowest frequency of the band

will be reached. Other phasors will rotate into problem

areas thus eliminating the necessity of adding certain stubs.

At the lower end of the band, stubs 1 through 4 become sufficient to meet the requirements in the waveguide bands from

WR187 to WR62. Above WR62 stubs 1 through 6 play the same

role. There will be more stubs than necessary to cover most
frequency ranges using this technique, but if true broadband

usage is desired, all the stubs are necessary.

An example of the design technique for WR90 (8.2 - 12.4 GHz)

is now given. Figure 5(a) shows the first step with the

associated spacing of stubs in inches. It has been assumed

that stubs cannot be placed any closer together than 1/2 inch

due to mechanical considerations. Figure 5(b) shows the

addition of stub 5 to fill the gap at 11.6 GHz. Figures 5(c)

through 5(e) show additional stubs. At 9.87 GHz the conditions of figure 5(f) exist and stub 9 is added. Figure 5(g)

shows the conditions at 9.53 GHz where stub 10 is added.

At approximately 9.21 GHz, phasor 10 is just crossing into

the fourth quadrant at zero degrees. At this frequency

phasor 6 is at 130 degrees and closing the angle with phasor

1. Figure 6(a) shows this condition. No additional stubs

are needed at this point. If the progress of the phasors

are now followed down in frequency it is found that no additional stubs are needed to finish the design. Figures 6(b) -

6(f) show the locations of the phasors for increments down

to 8.2 GHz.

This then completes the WR90 design. There will be no

frequency in the range of frequencies from 8.2 to 12.4 GHz

where an angle of greater than 132 degrees exists between

adjacent phasors representing stub locations. There may be

10-
one frequency in this design where an angle of 132 degrees

between phasors occurs, but the use of an additional stub

here is not necessary since it would only mean a small benefit

at that one frequency. The tuner will still be usable at

that frequency.

A time-shared computer, and BASIC programming language,

was used as an aid in the previous design technique. A program (Appendix A) was written which calculates angles for

screw spacings and reduces them by integral multiples of

360 degrees to be less than 360 degrees. The output is a print out of these angles, T(I,J). This program needs, as

data, the distance of each screw from screw number 1 in

inches, B(I), the waveguide width in inches, W, the number

of screws, N, and the frequencies (in GHz) at which phasor

diagrams are required, F(I). K is the number of frequencies

required. A second program (Appendix B) steps through small

increments, A, of a desired frequency range, Fl to F2, calculating the difference angles, D, between adjacent screw

phasors and lists the value of this angle if it exceeds some

predetermined value, C, (for example 130 degrees). The output is a print out of the frequency, F, and the angle, D, if

D is greater than C. Frequencies are in GHz. The second

program is useful for checking tuner designs or analyzing

tuners which have already been built.

-11
V. REFERENCES

[1] Lewin, L. (1951), Advanced Theory of Waveguides, Chapter

4, (Iliffe and Sons, Ltd: London, England).

[2] Marcuvitz, N. (1951), Waveguide Handbook, Chapter 5,

(McGraw-Hill Book Co., Inc., New York, N. Y.).

[3] Ragan, G. L. (1948), Microwave Transmission Circuits,

Chapter 8, (McGraw-Hill Book Co., Inc., New York, N. Y.)

-12-
0.125

Guide

wavelengths,

towardd ' generator

0.375

0,25

Figure 1. Normalized Smith admittance chart representation

of a screw in a uniform waveguide.

13
0.125

1

Guide . wavelengths,

toward/

generator/ Range of admittances which

screws I and 2 can produce

Screw I inserted into

uniform guide

o 0.25

0.5

Screw 2 inserted into^

uniform guide

3,0 «° Range of admittances which screws I and 3 can produce

Range of admittance which

screws 2 and 3 can produce

Screw 3 inserted into

uniform guide

0.375

Figure 2. Normalized Smith admittance chart representation

of the tuning capabilities of 3 screws spaced

one-sixth guide wavelength apart at design

frequency and reference plane at 1st screw.

-14
in = 0.5,

Screws I and 3A inserted into,

uniform guidea

Screw 2[

inserted intOi

uniform guidel

Figure 3. Normalized Smith admittance chart representation

of the tuning capabilities of 3 screws spaced

one-fourth guide wavelength apart.

15
oO

—^ <\J oO

00

I/) S

?H

o3 • HO

Q

UJa

UJhi < 2

o> CO

y< < + ; CM \^ 00

o> •" ^< » c O II ii x» c m

u

bfl •H

UJ

16
PHASOR DIAGRAMS FREQ. (GHz) SCREW LOCATIONS (INCHES)

2

120°

120°

-} 1,4 (a) 12.4 STUB I 2 3

LOC. O 0.748 1.495 2.243

j——1,5 (b) 11.6 STUB 5

LOC. 3.084

j -1,6 (c) 11.05 STUB 6

LOC. 3.981

j -1,7 (d) 10.625 STUB 7

LOC. 4.941

2 (e) 10.29 STUB 8

LOC. 5.953

(f) 9.87 STUB 9

LOC. 7.042

4,9

130°

5,10

1 (g) 9.53 STUB 10

8 LOC. 8.204

6 3 7

Figure 5. Phasor diagrams

17'
* M.10

(a) FREQ* 9.216Hz (b) FREQ = 9.06Hz

7-10 OMITTED

(c) FREQ = 8.8GHz

5-10 OMITTED

(d) FREQ = 8.6GHz

5-10 OMITTED

6 ?

(e) FREQ = 8.4GHz

7-10 OMITTED

(f) FREQ = 8.26Hz

7-10 OMITTED

Figure 6. Phasor diagrams

-18-
APPENDIX A

10 DIM B(15), T(15,20), F(20), G(20)

2 READ N, K, W

30 FOR I = 1 TO N

40 READ B(I)

50 NEXT I 60 FOR J = 1 TO K

70 READ F[J)

75 LET G(J) - l/SQR((F(J)/11.8027)+2-l/ (4*Wt2))

80 FOR I = 1 to N

90 LET T(I, J) = 720*(B(I)-B(1)) /G(J)

100 IF T(I,J) > 360 THEN 130

105 LET TCI, J) = INT(T(I,J)+.5)

110 PRINT TCI ,J)

120 GO TO 150

130 LET TCI ,J) = TCI ,J) -360

140 GO TO 100

150 NEXT I 160 PRINT

170 NEXT J

19-
APPENDIX B

10 DIM B (15) , T (15)

20 READ N, W, C

30 READ Fl, F2 , A

40 FOR I = 1 TO N

50 READ B(I)

6 NEXT I 70 FOR F = Fl TO F2 STEP A

80 LET G = l/SQR((F/11.8027)+2-l(4*Wt2))

90 FOR I = 1 TO N

100 LET T(I) = 720*(B(I) -B(l))/G

101 IF T(I) > = THEN 110

102 IF ABS (T(I)) > 360 THEN 105

103 LET T(I) = 360+T(I)

104 GO TO 110

105 LET T(I) = T(I)+360

106 GO TO 102

110 IF T (I) > 360 THEN 140

120 LET T(I) = INT (T(I)+.5)

130 GO TO 160

140 LET T(I) = T(I)-360

150 GO TO 110

160 NEXT I 170 LET K = N

180 LET S = 360

190 FOR I = 1 TO K

200 IF T(I) > S THEN 230

210 LET S = T(I)

220 LET II = I 230 NEXT I 240 LET T(I1) = T(K)

250 LET T(K) = S

260 LET K = K-l

270 IF K > THEN 180

280 FOR I = 1 TO N-l

285 LET J = 1+1

290 LET D = T(I)-T(J)

300 IF D < C THEN 320

305 PRINT "FREQ" F

310 PRINT D

320 NEXT I 330 LET D = T(N)+360-T(l)

340 IF D < C THEN 370

345 PRINT "FREQ" F

350 PRINT D

360 PRINT

370 NEXT F

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