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If) NBS TECHNICAL NOTE 657

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

Calculated and Measured S n

, S

21 ,

and Group Delay for Simple Types of

Coaxial and Rectangular Waveguide

2-Port Standards
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;

' fJOARDS

r

11' 2V

and Group Delay for Simple Types of

Coaxial and Rectangular Waveguide 2-Port Standards

R. W. Beatty

Electromagnetics Division

Institute for Basic Standards

(^ r S, National Bureau of Standards

Boulder, Colorado 80302

-t,

leaU^itLai fls-hs. no , k^>7

.t-" <"

l \ Jo

U.S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS Richard W Roberts Director

Issued December 1974
Library of Congress Catalog Card Number: 74-600191

National Bureau of Standards Technical Note 657

Nat. Bur. Stand. (U.S.), Tech Note 657, 67pages (Dec. 1974)

CODEN: NBTNAE

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

(Order by SD Catalog No. C13. 46:657) $1.25
CONTENTS

Page

1. INTRODUCTION 1

2. FORMULAS FOR CALCULATION 2

3. COMPUTER PROGRAMS 3

4. EXAMPLES OF CALCULATED AND MEASURED DATA 4 4.1 Reduced IDOC Coaxial 2-Port 4 4.2 Increased ODIC Coaxial 2-Port 4 4.3 Reduced Height Rectangular Waveguide 2-Port 4

4 . 4 Discussion 5

5- DISCUSSION OF ERRORS 6

6. DESIGN INFORMATION 8

7. CONCLUSION 9

8 . ACKNOWLEDGMENTS 9

9. APPENDIX 9

10 . REFERENCES 11

APPENDIX : 5 3

LIST OF TABLES

Page

Table I. Additional parameters used in calculating S

1

, , S

21 , and T r of rectangular waveguide and coaxial line 2-ports 12

Table II. Reduced height h

R versus magnitude of S,1 for quarter-guide

wavelength WR90 (R-100) rectangular waveguide 2-ports 13

Table III. Increased ODIC and reduced IDOC versus |S 11 | for 9/16 inch

(14 mm) quarter-wavelength coaxial 2-ports 14

Table IV. Increased ODIC and reduced IDOC versus | St -i

J for 7 mm quarter-wavelength coaxial 2-ports 15

Table V. Approximate step capacitances versus |S,,| for quarter

wavelength 7 mm and 9/16 inch (14 mm) coaxial 2-ports using

either increased ODIC or decreased IDOC 16

in
LIST OF FIGURES

Page

Figure 1. Examples of 2-port standards incorporating simple discontinuities in coaxial line (a-h) and rectangular waveguide

(i-j). Regions A and C denote coaxial cross -sectional

dimensions specified by well-known standards, and region

B denotes the 2-port sections having modified dimensions 17

Figure 2. Equivalent circuit for dominant node propagation in coaxial

or rectangular waveguide 2-port standards of the types shown

in figure 1. The characteristic admittances YQN and YQ^ are

for the nominal standard waveguide and the 2-port section,

respectively. The equivalent discontinuity susceptance is

B, and the real part of the propagation constant is denoted

by a R. 18

Figure 3. Photograph of reduced IDOC coaxial 2-port designed to be

inserted into a 9/16 inch (14 mm) 50-ohm coaxial system 19

Figure 4. Computer printout of program CS11 for reduced IDOC coaxial

2-port 20

Figure 5. Computer printout of program CS21 for reduced IDOC coaxial

2-port 21

Figure 6. Polar plot of calculated and measured S, , of reduced IDOC

coaxial 2-port for frequencies from 0.1 to 0.5 GHz 22

Figure 7. Calculated and measured return loss = -20 log,

n

| S,

1

| versus frequency for reduced IDOC coaxial 2-port 23

Figure 8. Calculated and measured arg (S, , ) = ij>, - in degrees versus frequency for reduced IDOC coaxial 2-port 24

Figure 9 . Polar plot of calculated and measured attenuation in decibels

= -20 log, „ |S_, | and arg (S,,,) = if/_, at frequencies from 0.1

to 0.5 GHz for reduced IDOC coaxial 2-port. ; 25

Figure 10. Calculated and measured |S-,| versus frequency for reduced

IDOC coaxial 2-port 26

Figure 11. Calculated and measured arg (So-i) = iK, versus frequency for

reduced IDOC coaxial '2 -port 27

Figure 12. Calculated and measured group delay versus frequency for

reduced IDOC coaxial 2-port 28

Figure 13. Photograph of increased ODIC coaxial 2-port designed to be

inserted into a 9/16 inch (14 mm) 50-ohm coaxial system 29

Figure 14. Computer printout of program ICS11 for increased ODIC

coaxial 2-port 30

Figure 15. Computer printout of program ICS21 for increased ODIC

coaxial 2-port 31

iv
LIST OF FIGURES (Continued)

Page

Figure 16. Polar plot of calculated and measured S, , of increased ODIC

coaxial 2-port for frequencies from 0.1 to 0.5 GHz 32

Figure 17. Calculated and measured return loss = -20 log,

n |S,,| versus frequency for increased ODIC coaxial 2-port 33

Figure 18. Calculated and measured arg (S,,) = iK , in degrees versus frequency for increased ODIC coaxial 2-port 34

Figure 19 . Polar plot of calculated and measured attenuation in

decibels = -20 log 1Q l s 21 l and ar9

(S 21 ) = ^21 ° f increased

ODIC coaxial 2-port for frequencies from 0.1 to 0.5 GHz. 35

Figure 20. Calculated and measured |S~,| versus frequency for increased

„ ODIC coaxial 2-port 36

Figure 21. Calculated and measured arg (S

?

-,) = i> 7

-, versus frequency for

increased ODIC coaxial 2-port 37

Figure 22. Calculated and measured group delay versus frequency for

increased ODIC coaxial 2-port 38

Figure 23. Photograph of reduced height rectangular waveguide 2-port

designed to be inserted into a WR90 (IEC-R-100) waveguide

system 39

Figure 24. Computer printout of program WS11 for rectangular waveguide

2-port 40

Figure 25. Computer printout of program WS21 for rectangular waveguide

2-port 41

Figure 26. Polar plot of calculated and measured S.. , and S~, of rec- tangular waveguide 2-port for frequencies from 8 to 13 GHz 42

Figure 27. Calculated and measured return loss = -20 log,

n |S,,| versus frequency for rectangular waveguide 2-port 43

Figure 28. Calculated and measured arg (S,,) = iK , in degrees versus frequency for rectangular waveguide 2-port 44

Figure 29. Calculated and measured attenuation = -20 log,

n |S?

, | versus frequency for rectangular waveguide 2-port 45

Figure 30. Calculated and measured arg (S

?

-,) = ip~, in degrees versus frequency for rectangular waveguide 2-port 46

Figure 31. Calculated and measured group delay time versus frequency

for rectangular waveguide 2-port 47
LIST OF FIGURES (Continued)

Page

Figure 32. Percent change in |S , | versus |S,,| of ^ G /4 2-port standards

corresponding to a change of 0.001 inch in the increased

ODIC or reduced IDOC of 9/16 inch (14 mm) coaxial 2-ports

or reduced height rectangular waveguide 2-ports 48

Figure 33. Percent change in | S, ,| versus |S,,| of X„/4 2-port standards

corresponding to a change of 0.0001 inch in the increased

ODIC or reduced IDOC of 9/16 inch (14 mm) coaxial 2-ports,

or reduced height rectangular waveguide 2-ports 49

Figure 34. Calculated |S,,| versus frequency for various reduced height

WR90 (IEC-R-100) rectangular waveguide 2-port standards all

having a length of 0.4052 inch 50

Figure 35. Calculated | S, ,

| versus frequency for various reduced height

WR90 (IEC-R-100) rectangular waveguide 2-port standards all

having a length of 0.3150 inch (80 mm) 51

Figure 36. Plot of L = (2n-l) A r /4 versus frequency for TEM mode propagation in coaxial line 52

VI
CALCULATED AND MEASURED S n , S 21 , AND GROUP DELAY FOR

SIMPLE TYPES OF COAXIAL AND RECTANGULAR WAVEGUIDE 2 -PORT STANDARDS

by

R.W. Beatty

ABSTRACT

Formulas, simple computer programs, graphs and tables are given to aid in the design and construction of 2 -port standards

for rectangular waveguide and coaxial line. Only standards con- sisting of reduced height waveguide, increased ODIC (outside

diameter of inner conductor), or reduced IDOC (inside diameter

of outer conductor) coaxial line are considered. Examples of

the calculation of S

1

, , S„, and group delay, and their measurement with automatic network analyzers are given. Some of the

important sources of error in the standards are discussed and

design data are presented for specific standards

.

Key words: Automatic network analyzers; coaxial; coaxial line

step discontinuities; group delay; scattering coefficients;

standards; 2 -ports; waveguide; waveguide discontinuities.

1. INTRODUCTION

One can calculate the complex scattering coefficients S, .. and S ?? and

the group delay x of 2-port standards having simple geometries. These

standards are useful for monitoring the performance of computer-controlled

automatic network analyzers (A.N. A.) and for evaluating the accuracy of

their measurements over broad frequency ranges. They may have additional

uses in future developments.

There are many possible types of 2-port standards for which the above

parameters may be calculated. Some examples of simple steps in diameters

of inner and outer conductors of coaxial line and in the heights of rec- tangular waveguide are illustrated in figure l(a-j). However, only three

types are considered here [1] . They are the reduced IDOC (inside diameter

of outer conductor) type of figure 1(b), the increased ODIC (outside

diameter of inner conductor) of figure 1(c), and the reduced height (h

R

) type of figure l(j). These three types are chosen for their simplicity,

ease of construction, and accuracy. For a given value of |S,,| in the

range > | S, ,

| > 0.6, the increased ODIC type of 2-port (used by Whinnery

and Jamieson in 1944 [2]), has a somewhat greater sensitivity to dimensional

error than the reduced IDOC type but is easier to make and more economical.

In use, the 2-port standards are inserted into a standard coaxial line

or rectangular waveguide system at the output of an A.N. A. and their parameters measured over broad frequency ranges . One then compares the calculated and measured values in order to assess the performance and accuracy

of the A.N. A.
In the following, formulas and simple computer programs are given, as well as some examples of calculated and measured results.

The accuracy of the calculated results are discussed. Means of estimating uncertainties due to the more important sources of error are described. Finally, design data is given for specific standards.

2. FORMULAS FOR CALCULATION

As shown in figure 2, an equivalent circuit for the above types of

2 -port standards includes the normalized equivalent discontinuity susceptance

^— and the attenuation a D of the section of coaxial line or waveguide.

OR Using straightforward circuit analysis [3] , one can derive the following

formulas for S, , and S-, .

11

21

(1 + r - jbr)(l - ^ - jb)e

" 2yL

+ (1(1 -- r - jbr)(l ibrl (1 + - + jb)

(1 r + jbr)(l - i- - jb)e -2yL +

4e" YL

(1 + r + jbr)(l + - + jb)

(1 - r + jbr) (1 - jb)e -2yL + (1 + r + jbr) CI + |

+ jb)

(1)

(2)

where

r = OR

Y ON

b = Y = a. OR

. 2-n +

J —

.

L = length of 2-port,

r = the ratio of the characteristic admittances of the 2-port 's waveguide and of the external waveguide system,

and A„ = waveguide wavelength.

Additional parameters used in calculating S, -, and S

?

, for rectangular waveguide (TE,

n mode) and for coaxial line (TEM mode) are given in table 1.

The group delay parameter, x r , is defined in terms of \Jj--i i the argument

of S

?

, , as follows

.

-d ij> 21

dco

-1

2-n

d i> 21

(3)

df

Alternately, we can write

-1 .. .JA *21

x r

= — limit

b

2t\ Af->0^ Af

(4)
where A i|> 21

is the increment in 4> 21 ±n degrees corresponding to a given

increment Af. For finite Af,

G

' l5J

where

360 (fH

- f

L

)

f„ = f + 1/2 (Af), fT = f - 1/2 (Af) , and Af << f,

We use eq (5) in calculating t„ for 2 -port standards, choosing Af < 0.1 f.

(One can test whether or not Af has been chosen to be sufficiently small by

recalculating with a still smaller Af and comparing the differences in the

t 's obtained in the two calculations. Of course, if Af is made too small, errors in calculation will result as one reaches the limits of computer

capability. It is not usually difficult to tell when this happens.)

3. COMPUTER PROGRAMS

In order to make the results widely useful, simple computer programs

have been developed in BASIC language. These have been designated as CS11,

CS21, ICS11, and ICS21 for coaxial 2 -ports, and WS11 and WS21 for rectangular

waveguide. They are reproduced in the appendix to this note and are based

on eqs (1) , (2) , and (5)

.

At the beginning of the programs the required input data and the calculated parameters are listed. Note that the computer programs WS11 and WS21

calculate the discontinuity susceptance from published formulas [7], but

one must presently determine this separately in the case of coaxial lines 1 and insert the correct value into the program. Programs CS21 and WS21 calculate group delay x r as well as both magnitudes and arguments of S~,

.

Calculation of coaxial line step capacitances is based upon the analysis of

Whinnery, Jamieson, and Robbins, 1944 [8] and is aided by the work of Somlo,

1967 [9] and Jurkus , 1972 [10]. The step capacitances vary slowly with frequency up to the highest recommended frequencies for coaxial line and this

frequency variation is presently neglected in computer programs CS11, CS21,

ICS11, and ICS21. The step ;tep capacitances c can also be determined by measuring

'ill the frequencies where | S, i ,

| is going through deep minima,
4. EXAMPLES OF CALCULATED AND MEASURED DATA

4 .

1

Reduced IDOC Coaxial 2-Port

(IDOC = 0.5135 inch, Length = 30.000 cm.)

The 2-port used in this example is shown in figure 3. Note that it

is fitted with connectors which permit it to be inserted into a standard

50 -ohm 9/16 inch (14 mm) coaxial system. Calculated values using programs

CS11 and CS21 of S, , , S

?

, and T-, for frequencies from 0.1 to 0.5 GHz are shown in figures 4 and 5. Measurements made on two automatic network

analyzers "A" and "B" of different manufacturers are plotted with calculated

data on figure 6 through 12, inclusive.

Figure 6 is a plot of S, , in polar coordinates.

Figure 7 shows return loss = -20 log,

n |S, ,| versus frequency.

Figure 8 shows ij>, , versus frequency.

Figure 9 is a polar plot of -20 l°gi(J S 21 1 an<* ^?1 at var i° us frequencies

Figure 10 shows |s„, | versus frequency.

Figure 11 shows i|j ?

, versus frequency.

Figure 12 shows t„ versus frequency.

4.2 Increased ODIC Coaxial 2-Port

(ODIC = 0.2651 inch, Length = 30.000 cm.)

The 2-port used in this example is shown in figure 13. Calculated

values using programs ICS11 and ICS21 of S, ,

, S_, , and t„ for frequencies

from 0.1 to 0.5 GHz are shown in figures 15 and 15. Calculations and

measured values are plotted in figures 16 to 22, inclusive.

4 . 3 Reduced Height Rectangular Waveguide 2 -Port

(h R

= 0.0918 inch, Length = 0.4057 inch)

The 2-port used in this example 2 is shown in figure 23. Note that it

has flanges for connection to a WR-90 (R-100) rectangular system. Calculated values using programs WS11 and WS21 of S, ,

, S~, , and x„ for frequencies from 8 to 13 GHz are shown in figures 24 and 25. Measurements

made on an automatic network analyzer are compared with calculated data

in figures 26 to 31, inclusive.

2 For the value of h

R in this example, measurements gave a value of discontinuity susceptance 4 percent higher than that calculated from [7]

.

Programs WS11 and WS21 were appropriately modified to include a factor of

1.04.
Figure 26 shows a plot of S, , and S--. in polar coordinates. Figure 27

shows return loss versus frequency. Figure 28 shows ijj,, versus frequency.

Figure 29 shows attenuation versus frequency. Figure 30 shows 4> 2 i versus frequency. Figure 31 shows i r versus frequency.

4 .4 Discussion

The examples of calculated and measured data are presented in various

forms in order to show discrepancies between measurements and calculations.

The purpose of showing the data is not to evaluate or compare automatic

network analyzers . More data would be required in order to average out

non-repeatable results due to operator errors, etc. The data shown does

demonstrate the usefulness of 2 -port standards in quickly checking all of

the parameters measured by an A.N. A. over a broad frequency range.

In the examples shown, the length of the 2-port is less than a halfwavelength so that there can be no cyclical variations due to multiple

reflections superimposed on the calculated curves. Any such variations

observed in measured data must be due to error in measurement. Also, any

sudden departures of measured data from the frequency variation of the

calculated curves must be due to error in measurement. (This can be

observed in figure 17, for example.)

In order to use 2-port standards to evaluate the accuracies of A.N. A.

measurements, all of the errors in the standards should be carefully

evaluated, and this has not been done. However, some measurements of

|S,,| have been made at fixed frequencies using tuned reflectometers with

quarter-wave short-circuit standards. These measurements indicate that

the curves of figure 33 represent the main source of error for |.S, ,|

values near the 2 -port's quarter-wavelength frequencies.

The stability of the 2-port standards is of a high order so that non- repeatable results are due to non-repeatable connectors or waveguide joints,

and to other insertion problems, operator error in calibrating the A.N. A., or A.N. A. instability. This is demonstrated in figure 7, where the results

of two runs differ by about 0.2 decibel at 0.26 GHz. Non-repeatability

effects have been observed which are much larger than this.

One should be cautious in drawing conclusions from the limited amount

of data presented here. It does appear from figure 10 that A.N. A. "B"

yields less scatter and more accurate values of | S _ -,

] over the frequency

range 0.1 to 0.5 GHz and for |S 21 | near unity. Both "A" and "B" give

accurate phase measurements of S--.. In the measurement of group delay,

neither A.N. A. has sufficient resolution to show any variation with frequency. It would appear that "B" has less scatter than "A" for this
particular 2-port over the frequency range 0.1 to 0.5 GHz. The results of

figure 31 show that for a different 2-port, measurements of group delay with

A.N. A. "A" stil] exhibit considerable scatter, but show the correct frequency dependence of group delay.

5. DISCUSSION OF ERRORS

Although a complete investigation of all sources of error in S

1 1

, S_, , and t„ of the standards is desirable, it is not included in this report in

order not to delay publication of useful information. The error in S, , due

to uncertainty in the discontinuity capacitance is very small at frequencies

for which the length of the 2-port is A„/4, but becomes large at X r /2

frequencies. Similarly, the value of S, . is insensitive to variations in

the resistivity of the metal, except at and near X^/2 frequencies. The

actual surface resistivity will vary with the fabrication process used. One

can by trial and error make the calculated data fit the measured data at

and near the A„/2 frequencies by choosing suitable values of resistivity and

step capacitance and inserting these values in the appropriate computer

programs CS11, ICS11, or WS11. The error in S

?

, due to uncertainty in the

resistivity of the metal is also greatest at X_/2 frequencies. Thus, the

best accuracy is expected to occur at and near X„/4 frequencies. It is

felt that at present, the errors in calculated results are likely to be less

than the errors in measured results at most frequencies, except near frequencies at which | S -, -,

| is going through deep minima.

Some of the sources of error are the following:

1. Dimensional tolerances in construction

a. uncertainty in reduced height or reduced IDOC

,

b. uncertainty in width or in ODIC,

c. uncertainty in length.

2. Approximations in calculation of equivalent discontinuity susceptance

a. lack of rigor in theory,

b. errors in formulas,

c. errors in computer programs.

3. Faulty construction of standard

a. poor surface finish,

b . burrs

,

c. lack of surface flatness or circularity.

4. Uncertainty in dissipative loss

a. attenuation,

b. losses at discontinuities,

c. losses at flanges or connectors.
5. Insertion errors

a. misalignment

b. system into which 2-port is inserted has non-standard dimensions and is different on one side of insertion point than

the other.

A few of the major sources of uncertainty will be discussed as follows

A given uncertainty in the reduced height or reduced IDOC produces a cor- responding uncertainty in the calculated value of | S, , | at frequencies for

which the length of the 2-port is an odd number of quarter wavelengths.

For small errors, we may use the following expressions.

For reduced height rectangular waveguide the fractional error in

11

is

d|s n

s I 2 b ll!

d h

R

(6)

1 11 ' '11' R

This is derived by differentiating the relationship

'h,

11 V

2 (7)

^R

+ 1

from [1] , which holds closely at frequencies where L is an odd number of

Ap/4. For reduced IDOC coaxial line, the corresponding fractional error in

|s n| IS

d|s n | 1 - I s lll

2 d ( Z 0R>

|s n | |s n |

> 7^OR

d|s n | 1 - I s lll

2 59.9392

or

d(IDOC

R

)

11 11 'OR

IDOC

(8)

(9)

R

Using eqs (6) and (9) , data for the curves of figures 32 and 33 were

obtained. The percent error in |S,,| corresponding to a dimensional tolerance

of 0.001 inch is shown in figure 32 for several standard sizes of rectangular

waveguide and coaxial line. Figure 33 shows the effect of a smaller tolerance

of .0001 inch.

One can easily determine the limits of uncertainty in S, , at other frequencies by perturbing the input data to computer programs CS11 and WS11, and

observing the effect on uncertainties in S, -, , S

?

, , and t„ due to uncertainties

in various input parameters with the exception of the inside width of the

rectangular waveguide.
If the inside width of the rectangular waveguide 2-port is different

than the width of the waveguide system into which the 2-port is inserted,

unwanted reflections will be produced which can cause error. Evaluation

of the uncertainty due to this error source can be accomplished using

published formulas [7], but will not be discussed further in this note.

6. DESIGN INFORMATION

A design technique which has been used is to select values of |S 11

that one would like to produce and then calculate the reduced height h D , increased ODIC, or reduced IDOC required to obtain these values of |S,,|

at frequencies for which the length L of the 2-port is an odd number of

A r /4 , neglecting the effects of discontinuity susceptance.

Table II gives values of h

R corresponding to various values of |S,,|

for WR90 (R-100) rectangular waveguide. Table III gives values of increased

ODIC and reduced IDOC for 9/16 inch (14 mm) coaxial 2-ports and table IV

gives values of increased ODIC and reduced IDOC for 7 mm coaxial 2-ports.

Table V gives approximate 3 step capacitances versus | S, ,

| for quarter

wavelength 7 mm and 9/16 inch (14 mm) coaxial 2-ports using either increased

ODIC or reduced IDOC.

The choice of length of the 2-port is arbitrary and some choices

which have proven convenient are the following: for WR90 (R-100) rec- tangular waveguide, L = 0.4052 inch, ~*

G /4 @ 9.8 GHz, L = 0.8104 inch,

~A„/2 @ 9.8 GHz. Figure 34 shows how |S,,| varies across the frequency

range for 2-ports having a length L = 0.4052 inch. A flatter frequency

response may be obtained as shown in figure 35 by choosing L = 0.3150 inch

(80 mm), ~^

G /4 @ 11.43067 GHz.

In order to facilitate design for still other standard sizes of

rectangular waveguide or coaxial line, simple computer programs may be

used. Programs IDOC and ODIC calculate the reduced IDOC and increased ODIC

for quarter wavelength coaxial line 2-ports corresponding to chosen values

of |S,,|. Program HR calculates values of reduced height hR of quarter

guide-wavelength rectangular waveguide 2-ports for chosen values of |S,,|.

These programs appear in the appendix.

3 The approximate values of step capacitance were obtained by interpolating

in the tables of Somlo, 1967 [9], for t = 2.3025 which corresponds to

Z = 50 ohms. More accurate values will be available later both from

measurements and from the computer programs of Somlo [9] and Jurkus [10].
In designing coaxial 2 -ports to have many odd numbers of quarter-wave

resonances, figure 36 is useful. At present, the calculated values of S,

are most accurate near these resonances and least accurate at frequencies

where | S, ,

| is minimum. Therefore, it might be advantageous to have a second 2-port standard for which | S, ,

| is nearly maximum at frequencies

where | S, ,| is minimum for the first 2-port standard.

7. CONCLUSION

Two-port standards in rectangular waveguide or coaxial line may be produced by reducing the height of a waveguide section, increasing the ODIC or reducing the IDOC of a coaxial line section. They may be designed to produce

desired |S,,| values at chosen frequencies. After design, the complex S,

1 and S«, and the group delay may readily be calculated over any desired frequency range. The accuracy of the calculated data at and near A„/4 frequencies is better than present measurement accuracy with many automatic

network analyzers. At and near the X r /2 frequencies, the measured data

may be assumed to be more accurate, and used to adjust the values of surface

resistivity and shunt susceptance in the calculations. The 2-port standards

are very stable and can be used for quickly checking performance and accuracy

of automatic network analyzers over broad frequency ranges.

8. ACKNOWLEDGMENTS

The assistance of a number of people made this work possible. At NBS , George H. Fentress was the principal assistant in design, measurement, and

presentation of results; Philip F. Biddle helped with mechanical design;

William E. McNaney made accurate dimensional measurements and Fred F. Jeffers

helped make measurements using an automatic network analyzer. Measurements

using a different automatic network analyzer were kindly made by

T.E. McKenzie, C.C. Gorss, and R.L. Moynihan of the General Radio Company,

Bolton, Mass. Comments and suggestions were received from William E. Little

and Clarence C. Cook of NBS, and Brent Palmer of the Hewlett-Packard Company.

9. APPENDIX

The following computer programs are given in the appendix; CS11, CS21,

ICS11, ICS21, WS11, WS21, ODIC, IDOC, and HR. The purpose of each program

is described in the REM statements, and use of the programs is intended to

be evident to those having an elementary knowledge of computer BASIC

language.
For reduced IDOC coaxial 2-port standards:

CS11 calculates return loss in decibels, magnitudes of S, , and

argument of S, -, in degrees;

CS21 calculates attenuation in decibels, magnitude of S

?1 , argument of S^-, in degrees and group delay time in nanoseconds.

For increased ODIC coaxial 2-port standards:

ICS11 calculates return loss in decibels, magnitude of S, .. , and

argument of S, , in degrees;

ICS21 calculates attenuation in decibels, magnitude of S~,

,

argument of S

?1 in degrees , and group delay time in

nanoseconds . For decreased height rectangular waveguide 2-port standards:

WS11 calculates return loss in decibels, magnitude of S, ,

, and

argument of S, , in degrees ; WS21 calculates attenuation in decibels, magnitude of S-,

,

argument of S~, in degrees, and group delay time in

nanoseconds

.

ODIC: For given values of | S _. ->

| , calculates return loss, VSWR, and

the corresponding increased ODIC of A„/4 coaxial 2-port standards

For given values of |S,,|, calculates return loss, VSWR, and

the corresponding reduced IDOC of X„/4 coaxial 2-port standards.

For given values of | S, , | , calculates return loss, VSWR, and

the corresponding reduced height of A-/4 rectangular waveguide

2-port standards.

IDOC

HR

10
10. REFERENCES

[1] Beatty, R.W., "2-Port A /4 Waveguide Standard of Voltage Standing-Wave

Ratio," Electronics Letters, 9_, no. 2, 25 January 1973, 24-26.

[2] Whinnery, J.R. and H.W. Jamieson, "Equivalent Circuits for Discontinuities

in Transmission Lines," Proc. I.R.E., 32_, no. 2, Feb. 1944, 98-114.

[3] See for example: Kerns, D.M. and R.W. Beatty, "Basic Theory of Waveguide

Junctions and Introductory Microwave Network Analysis" (Pergamon Press,

New York, New York, 1967).

[4] Pomeroy, A.F., "Waveguide Loss Charts," Electronics, Oct. 1, 1957.

[5] Moreno, T., "Microwave Transmission Design Data" (Dover Publications,

Inc., New York, New York, 1958), 63.

[6] See for example: Brady, M. Michael, "Standard Rectangular Waveguide

Constants" (Transcripta Books, London, 1972).

[7] Marcuvitz, N. (Editor), "Waveguide Handbook" (McGraw Hill Book Company,

Inc., New York, New York, 1951), 296, 307.

[8] Whinnery, J.R., H.W. Jamieson, and T.E. Robbins, "Coaxial -Line Discontinuities," Proc. I.R.E., 32., no. 11, Nov. 1944, 695-709.

[9] Somlo, P.I., "The Calculation of Coaxial Line Step Capacitances," IEEE

Trans, on MTT, 1_5, no. 1, Jan. 1967, 48-53.

[10] Jurkus , A., "Computation of Step Discontinuities in Coaxial Line,"

IEEE Trans, on MTT, 20, no. 10, Oct. 1972, 708-709.

11
TABLE I. ADDITIONAL PARAMETERS USED IN CALCULATING S n>

S^, and T Q

of RECTANGULAR

WAVEGUIDE and COAXIAL LINE 2-PORTS

.

PARAMETER RECTANGULAR WAVEGUIDE COAXIAL LINE

hN

, /

IDCV)

\ODIC /

inches m-off

Mb

ft.

5.967 ,£fi- + A_

h

R 2a

3 /

A

See [4]

-(i)

;

13.64 /iT~

X G

. £n

See [5]

r^ODIC ID0C

R /

TIdoO

\ODIC /

h

< a >•

* 1

( )

)

ODIC IDOC

t 1

nominal inside width (inches) of rectangular waveguide,

nominal inside height (inches) of rectangular waveguide system,

reduced inside height (inches) of waveguide 2-port.

outer diameter (inches) of inner conductor of coaxial line.

IDOC„ = nominal inside diameter (inches) of outer conductor of coaxial system.

ahN

hRODIC

N IDOC

c

f

V

A

P

Pi

RO

B

'RI

reduced inside diameter (inches) of inner conductor of 2-port.

2.997925 x 10

10 cm/sec.

frequency (Hz or cycles per second)

.

permittivity of air at 20°C, 760 ram pressure, 9° dewpoint temperature = 1.00064,

see [6]

.

c/2.54/e inches/sec.

K v/f inches.

resistivity of waveguide or coaxial line conductors (ohm-cm)

.

resistivity of outer conductor (ohm-cm)

.

resistivity of inner conductor (ohm-cm)

.

relative permeability of outer conductor.

relative permeability of inner conductor.

skin depth (inches) of waveguide or coaxial line conductors

.

[1/2tt(2 .54) ] /p/f inches.

skin depth (inches) of outer conductor of 2-port.

skin depth (inches) of inner conductor of 2-port.

12
TABLE II. REDUCED HEIGHT h_, VERSUS MAGNITUDE OF S.. for QUARTER-GUIDE

R XX WAVELENGTH WR-90 (R-100) RECTANGULAR WAVEGUIDE 2-PORTS

.

MAGNITUDE

OF S U

.05

.1.15

.2.25

.3.35

.4.45

.5.55

.6.65

.7.75

.8.85

.9.95

RETURN LOSS

IN DECIBELS

VSWR REDUCED HEIGHT

IN INCHES

Infinity 1 .4 26.0206 1.10526 .380476

20. 1.22222 .361814

16.4782 1.35294 .343891

13.9794 1.5 .326599

12.0412 1.66667 .309839

10.4576 1.85714 .29352

9.11864 2.07692 .277555

7.9588 2.33333 .261861

6.93575 2.63636 .246353

6.0206 3. .23094

5.19275 3.44444 .215526

4.43698 4. .2 3.74173 4.71429 .184226

3.09804 5.66667 .168034

2.49878 7. .151186

1.9382 9. .133333

1.41162 12.3333 .113899

.91515 19. 9.17663E-2

.445528 39. 6.40513E-2

13
TABLE III. INCREASED ODIC and REDUCED IDOC VERSUS |S | for 9/16 INCH (14 mm)

QUARTER-WAVELENGTH COAXIAL 2-PORTS.

MAGNITUDE RETURN CHARACTERISTIC REDUCED INCREASED

LOSS, VSWR IMPEDANCE, IDOC ODIC

OF Sn DECIBELS

1

IN OHMS IN INCHES IN INCHES

Infinity 50.0012 .5625 .24425

.05 26.0206 1.10526 47.5606 .540056 .2544

.1 20. 1.22222 45.2278 519441 .264497

.15 16.4782 1.35294 42.9874 . 500384 .27457

.2 13.9794 1.5 40.8258 .48266 .284653

.25 12.0412 1.66667 38.7308 .466081 .294778

.3 10.4576 1.85714 36.6909 .450486 .304983

.35 9.11864 2.07692 34.6953 .435735 .315308

.4 7.9588 2.33333 32.7335 .421704 .325799

.45 6.93575 2.63636 30.7948 .408283 .336508

.5 6.0206 3. 28.8682 .395368 .347501

.55 5.19275 3.44444 26.9414 .382861 .358853

.6 4.43698 4. 25.0006 .370662 .370662

.65 3.74173 4.71429 23.0289 .358668 .383058

.7 3.09804 5.66667 21.0047 .346758 .396215

.75 2.49878 7. 18.8987 .334785 .410384

.8 1.9382 9. 16.6671 .32255 .425951

.85 1.41162 12.3333 14.2377 .309738 .44357

.9 .91515 19. 11.4711 .295767 .464524

.95 .445528 39. 8.00661 .279156 .492164

14
TABLE IV. INCREASED ODIC and REDUCED IDOC VERSUS |S | for 7 mm QUARTERWAVELENGTH COAXIAL 2-PORTS.

MAGNITUDE RETURN CHARACTERISTIC REDUCED INCREASED

LOSS, VSWR IMPEDANCE IDOC ODIC

OF Sn DECIBELS IN OHMS IN INCHES IN INCHES

Infinity 1 50.0522 .2759 .1197

.05 26.0206 1.10526 47.6092 .264881 .12468

.1 20. 1.22222 45.2739 .254759 .129633

.15 16.4782 1.35294 43.0312 .245403 .134575

.2 13.9794 1.5 40.8675 .236702 .139522

.25 12.0412 1.66667 38.7703 .228564 .14449

.3 10.4576 1.85714 36.7283 .220908 .149497

.35 9.11864 2.07692 34.7307 .213667 .154564

.4 7.9588 2.33333 32.7669 .20678 .159712

.45 6.93575 2.63636 30.8263 .200193 .164967

.5 6.0206 3. 28.8977 .193854 .170361

.55 5.19275 3.44444 26.9689 .187715 .175932

.6 4.43698 4. 25.0261 .181728 .181728

.65 3.74173 4.71429 23.0524 .175842 .187812

.7 3.09804 5.66667 21.0261 .169997 .19427

.75 2.49878 7. 18.918 .164122 .201224

.8 1.9382 9. 16.6841 .158118 .208865

.85 1.41162 12.3333 14.2522 .151831 .217513

.9 .91515 19. 11.4828 .144975 .227799

.95 .445528 39. 8.01477 .136825 .241368

15
TABLE V. APPROXIMATE STEP CAPACITANCES VERSUS |S | FOR QUARTER WAVELENGTH

7 ram and 9/16 INCH (14 mm) COAXIAL 2-PORTS USING EITHER INCREASED ODIC

or DECREASED IDOC.

|s n l STEP CAPACITANCE—femtofarads

for

Quarter

7 mm 9/16 inch (14 ram)

Wavelength Decreased Increased Decreased Increased

2-Port IDOC ODIC IDOC ODIC

.05 0.62 0.40 1.3 0.82

.1 1.9 1.2 3.8 2.56

.15 3.6 2.5 7.4 5.1

.2 5.7 4.1 11.7 8.3

.25 8.2 6.0 16.8 12.2

.3 11. 8.3 22.5 16.9

.35 14. 11 28.6 22.3

.4 17.3 14 35.3 28.6

.45 20.8 17.6 42 36

.5 24.6 21.7 50 44

.55 28.8 26.3 59 54

.6 33.3 31.8 68 65

.65 38 38 78 78

.7 44 46 89 93

.75 50 55 102 112

.8 58 67 118 136

.85 67 82 137 167

.9 80 104 163 213

.95 101 144 206 294

16
a)

b)

c)

d)

COAXIAL LINE

2-PORT

D_0DI

_ c

i

-, T

QlDOC RI DOC

l

i

- t

D

IDOC

N i)

" 1

D°DJ-C

N - t

JL

T

COAXIAL LINE

, 2-PORT , J 1—L_

RECTANGULAR

WAVEGUIDE

1 2-PORT '

d:

.L

i D

I

T

°_DI_

C

N

D:°i

L

ODIC,

D

t

h N

ABC

Figure 1. Examples of 2-port standards incorporating simple 'discontinuities in

coaxial line (a-h) and rectangular waveguide (i-j)o Regions A and C denote nominal coaxial cross-sectional dimensions specified by wellknown standards, and region B denotes the 2-port sections having

modified dimensions.

17
Figure 2. Equivalent circuit for dominant mode propagation

in coaxial or rectangular waveguide 2-port standards

of the types shown in figure 1. The characteristic

admittances Yq^ and Yq^ are for the nominal standard

waveguide and the 2-port section, respectively. The

equivalent discontinuity susceptance is B, and the

real part of the propagation constant is denoted by aR

.

18
, .

'.:. . ... ^-v 1 SI; - 1 III' <r §! ! H

X.ucH

\D

r-4

-. cd

l"

Oua i

"'' . •H

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•H ''^bB 1 , ' o 5 <u

-t--_. _- rQ

".,- |

-4 CO o

f^S- ::: |;

:: |: ! '§ : 4-J l | 1

CO T3c

bfl •H

050) 1 -= T3 ; iBpl H * CO 4-1 ' 1 i \ ; . !

"i

O mm -4 i CM

ft* »; :**1 18 *~; ««t

H ; . ]£ ', ~J

cd •H 1 X

tao " : o ' • . -—

CM

"i oo ; P j E H ; ; ,v|hS£9R I _ u •a e .:.' —^SB U 4-1 3 to 1 imMm ! ' 1 0J to HI I mWW^ H I » H 4-4 Cd 1 O *H

X! cd

p., I

cd o

-9 ::i bo e I O J3

4->

O

O 1

;;;^|: j ; x o

Ph in

-9

B .

;' en V C

a) ' n ; 3

60

•H

Li

w '< i^

19
CS1 ! 08» 56 06/04/74

FOR 9/16 INCH (14 MM) COAXIAL SYSTEM:

ODIC .24425 INCHES

I DOC .5625 INCHES

TEM-MODE CHARACTERISTIC IMPEDANCE 50.0012 OHMS

FOR 2-PORT:

ODIC .24425 INCHES

I DOC .5185 INCHES

LENGTH 11.8 11 INCHES

TEM-MODE CHARACTERISTIC IMPEDANCE 45.119 1 OHMS

DISCONTINUITY CAPACITANCE 3.8E- 15 FARADS

RELATIVE PERMITTIVITY OF AIR 1 .00064

IC RESISTIVITY .000002 OHM-CM.

OC RESISTIVITY .000008 OHM- CM.

FREQUENCY RETURN LOSS ARG<S1 1) GHZ DECIBELS MAG(S1 1

)

DEGREES

.1 24.368 6.04782E-2 233.74

.11 23.6677 .065556 230. 137

.12 23.0523 7.03697E-2 226.536

.13 22.5103 7.49005E-2 222.937

.14 22.0331 7.9 131 1E-2 219.34

.15 21 .6137 8.30454E-2 215.746

.16 21 .2468 8.66287E-2 212. 153

.17 20.9279 8.98675E-2 208.563

.18 20.6537 9.27498E-2 204.974

.19 20.4213 .095265 201.387

.2 20.2285 9.74039E-2 197.802

.21 20.0734 9.91587E-2 194.219

.22 19.9547 . 100523 190.637

.23 19.8714 . 101492 187.055

.24 19.8227 . 102062 183.475

.25 19.8083 . 102231 179.894

.26 19.8281 . 101999 176.314

.27 19.8822 . 101366 172.734

.28 19.971 . 100335 1 69 . 1 54

.29 20.0953 9.89088E-2 165.573

.3 20.2562 9.70936E-2 161.991

.31 20.4551 9.48956E-2 1 58 . 409

.32 20.6938 9.23228E-2 154.825

.33 20.9747 8.938 48E-2 151.24

.34 21.3007 8.60924E-2 147.654

.35 21.6753 .082458 144.067

.36 22. 1032 .078 49 5 140.478

.37 22.58 9 7 7.42187E-2 136.889

.38 23.1422 6.96453E-2 133.299

.39 23.7695 6.47923E-2 129.709

.4 24.4836 5.96787E-2 126. 12

.41 25.3001 5.43245E-2 122.533

.42 26.2404 4.87506E-2 1 18.948

.43 27.3348 4.29793E-2 115.37

.44 28.628 1 3.70335E-2 1 1 1.802

.45 30. 1903 3.09373E-2 108.252

.46 32. 1407 2.471 52E-2 104.735

.47 34.7071 1.83926E-2 101.288

.48 38.4197 1. I9954E-2 98.0246

.49 45. 1 127 5.55092E-3 95.5923

.5 60.4747 9.468 13E-4 256.706

Figure 4. Computer printout of program CS11 for reduced IDOC

coaxial 2-port.

20
CS21 09: 18 06/04/74

FOR 9/16 INCH (14 MM) COAXIAL SYSTEM:

ODIC

I DOC

TEM-MODE CHARACTERISTIC IMPEDANCE

.24425 INCHES

.5625 INCHES

50.0012 OHMS

FOR 2-PORT:

ODIC

I DOC

LENGTH

TEM-MODE CHARACTERISTIC IMPEDANCE

DISCONTINUITY CAPACITANCE

RELATIVE PERMITTIVITY OF AIR

IC RESISTIVITY

OC RESISTIVITY

.24425 INCHES

.5185 INCHES

1 1 .8 1 1 INCHES

45. 1 191 OHMS

3.8E-15 FARADS

1 .00064

.000002 OHM- CM. .000008 OHM-CM.

DELTA F FOR CALCULATION OF GROUP DELAY 005 GHZ

FREQUENCY ATTENUATION ARG(S21> GROUP DELAY

GHZ DECIBELS MAGCS21) DEGREES NANOSECONDS

.1 2.40454E-2 .997235 -36. 1865 1.00279

.11 2.72331E-2 .99687 -39.79 54 1.00214

.12 3.04672E-2 .99 6498 -43.4019 1.00148

.13 3.37052E-2 .996127 -47.0061 1.00082

.14 .036902 .99576 -50.6078 1.00016

.15 4.00152E-2 .995404 -54.2072 .999523

.16 4.30018E-2 .995061 -57.8044 .99891

.17 4. 58 207 E2.994739 -61.399 4 .998335

.18 4.84335E-2 .994439 -64.9925 .997804

.19 5.08 046E-2 .994168 -68.5837 .997328

.2 .052903 .99 39 28 -72.1733 .996912

.21 5.46994E-2 .993722 -75.7615 .996565

.22 5.61722E-2 .993554 -79.3486 .996291

.23 5.73021E-2 .993425 -82.9349 .996093

.24 5.80768E-2 .993336 -86.5206 .995977

.25 5.84886E-2 .993289 269.894 .9959 42

.26 5.85352E-2 .993284 266.309 .99599

.27 5.82205E-2 .99332 262.723 .9961 19 .28 5.75534E-2 .993396 259. 136 .996329

.29 5.6548 2E-2 .99351 1 255.549 .996614

.3 5.52252E-2 .993662 251.961 .996973

.31 5.3608 5E-2 .99 38 47 248.371 .997399

.32 5. 17276E-2 .994062 244.779 • 997883

.33 4.96155E-2 .994304 241. 186 .998 422

.34 4.7309 4E-2 .994568 237.59 1 .999002

.35 4.48 492E-2 .99 48 5 233.993 .99962

.36 4.22769E-2 .995145 230.393 1.00026

.37 3.96372E-2 .995447 226.79 1 1.00092

.38 3.69755E-2 .995752 223. 187 1 . 00 1 58 .39 3.43365E-2 .996055 2 1 9 . 58 1.00224

.4 3. 17664E-2 .996349 215.971 1.00288

.41 2.93091E-2 .996631 212.359 1.0035

.42 .027007 .996896 208.7 46 1 .00407

.43 2.49004E-2 .997137 205. 13 1 .00461

.44 2.30264E-2 .997352 201.512 1.00508

.45 2. 14177E-2 .997537 197.893 1.0055

.46 2.01037E-2 .997688 194.273 1.0058 5 .47 .019108 .997803 190.651 1.00612

.48 1.84505E-2 .99 78 78 187.029 1.00632

.49 1.81443E-2 .997913 183.406 1 .00643

.5 1.81976E-2 .997907 179.78 3 1 .00646

Figure 5. Computer printout of program CS21 for reduced IDOC coaxial

2-port.

21
180°

270°

Figure 6. Polar plot of calculated and measured Sn of reduced IDOC coaxial 2-port for

frequencies from 0.1 to 0.5 GRz„

22
' ::

:

fr-rr --

.... i:i| j]Ti

.: !iji|-iti!

:, ,.. ill: Hi!

i

.;: ::;

!

:i:

' -- -

?* M:r. 1 -:[::;:

1 23

Measured With:

G A.N.A. "A"

+ A.N.A. "BM

:.. /- - --

.

:

:

1

r-

.

.:.:

-

\ ( v'i ii|

::':: :::

22 j 5E 0*,1 i *,\l | f in7 t) / :tv. ~f

-*** 7ft-.

~~~~

(if "

:::. 1 — :

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ill: /

.. j \, i_. /

':~.

d/

HF'' r= — 5 tf :::: /

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1

L

f

.._..

.... fc

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: ::: A

/• --

:-:;.

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y.

:::: ::.j\r\ r»/

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20

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r i t j_ yv^-;. - :- :r.fj

EL:

i

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^

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H

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::: : .. Li_J_.. : .'' illi

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:£ . . Fl DO T RiIN

•Jh^M

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1

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.

: :: " : :L .

i

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: ;| . {

::::

i - 1

•::: : : ..1 1 1 ;- • -;! i

|

: | :. 'T: -

.. :;;::/;

•

....

....

; ..„_ ._..

i

"""i""

:

i

i

i '.

::

1 ":

1:

i

1 .. ... . 19

::

..

-— — tttt --- .._ --.- — ..1: :. _-•_!::. ,.l : ......

1

':

gp \

: : ; _..

:::-

....

:::l :i:il j

;; K , rffi : M ... ....

:. If]

i.:. , .... ,, ±iii :, ; U it£j.

: :;;

.:

i

:

- :

: . - m L _— ill] •

J

mi—

i

u

o

Pip

H

w

OS

0.1 0.2 0.3 0.4

FREQUENCY, GHz

Figure 7. Calculated and measured return loss = -20 log 10 |Sn| versus frequency for

reduced IDOC coaxial 2-port.

23
w

w

u

PJQ

1

1

1 1 240 •

' "T

:

•

'

.1. :i::

! :H : .: :

! iliili

1

i

:::;

...

: . H

(

I :':::

230 ; j l\ -

[ - I

_.. - "- - \ -i. Measured Withi

0A.N.A. "A"

i

vr

\- :

| t + A.N.A. "BM zzo — i

1

«

"

.

?in

. ... . . !

. .

:

; V

V

'\-1- LT:

:

200

';:

7; Vh

_... Sd - —

190

:::i — 1—

\-\ . ::::

....

180

:

: -;- w ..' ..

i V

i

1

i P

1 « »

;

•

i 1

"

'

170 i !.

;: :f - :

. .. Vh

. ;fi:

- IfiO

.:::!. — ;

!

i

i 1 . S Hh . h

H

' . !• ---

i v

u -

150

:

1

I —

T

--

-J -J

"

....

' . .

:

'

' 1 T.

t -- ... . . .. ....

V .

14D L

i ^ : -

:

1 .. y- V

- . \'fcij ..

r _

1 3D

...

. -

• —: ... ..__ -•

.- . . .

: ;;

• —

120 1 1 _^ Ifl •: i

0.1 0.2 0.3

FREQUENCY, GHz

0.4

Figure 8, Calculated and measured arg (S n ) = \\>n in degrees versus frequency ror reduced IDOC coaxial 2-port.

24
90°

180 e

270°

Figure 9. Polar plot of calculated and measured attenuation in decibels = -20 logi j S 2 1 and arg (S21) = ^21 at frequencies from 0.1 to 0.5 GHz for reduced IDOC

coaxial 2-port.

25
1.010

1.000

en .gg

.98

.97

.... : ij '::.

•::

•

!

:

: :(;; :!

:

.

: —

fa i:- -.: n

i

: .

: ....

1

1

::.j:

fl u-.J .

r )i

.

( ) . I ..._

•I.::: u .. © C V )

j S^Ldm ai e&i

'..:. +

..-fi .

f >

r.-+- ^T ^i

p, = 2 x 10 ohm- cr11 1 s

j£<

L.

f-p-, - o X 1U

: 1 onm-cm

4. ^

+ : :.:

jr.: P j • O

•f^ ( >

• +. *++

•

• + + + J - -: 4

4*

i ^f — lit 1

1

....;.... D I •

- j:::

::!:'

:

:

:

-'.' :h o 9

j o

:::: ::.: •:- — . ..

;::; Wz

' ::

:::': :::

;

""". 53 Measured With:

OA.N.A. "A"

+ A.N.A. "B"

M

..

::: [:::: : :':'' gjj O

!'-:| ':.. ::::

'.:':': ; .:

: 4—

:

'

. . ;::.

:::: —

5

~1

::::

1

. .. — —

i

1

;:rr

- .:::

....

ji

' 1 "

....

* ::'.: .:..

i ':':

'

; ::

"

;

;;;;

.:.:

;

: : .

.

rrrrl

;*:: i:: ;

. .. ^J ;, L_ m ''-'

:

:

; ; ;.

;

....

: ';; •; •ill ilji iii; !:::

0.1 0.2 0.3 0.4 FREQUENCY--GHZ

0.5

Figure 10. Calculated and measured | S 2 1

| versus frequency for reduced IDOC coaxial

2-port.

26
320

310

300

290 g

280

270

260

250

240 =

230

220 b

•in :.'i; L

; :':• n

..: • " .... .... -; — '!".... — .. !.'

' \

• — .... $

]'

i

i "H" XT

1

1 ^...L.

• ;:;; \ .!...

j

..j....

! 1

1

! " f

.... —. .).__ [\ 1

._ -- _.. 4-

i

-- ---

-

:

i

i

|

" 1::

| i.

i - 1 ^

Measured With:

o A.N. A. "A" + A.N. A. "B"

-t--i- -;-t

..:.

i |

.

j

:: i

i

.

!

. i —

) — —

1- — 1 --.

i-

- ...

:

: 1( -

::.:: :::.

i

. ::

' -- -.-

i ||——

^:

:-. . iiiljiii: :.: 1.

|

'.'-'- 7

':'.:'- ~ 1

:..:

:'-: — ~:.

=

'

L Ci*L GUL ATFr5

..

"':'

i

-: ;

. i

j _

.;;;•

::: • :|i!l!:i ; :[ : :::

t

. :

' •

:: I .

|| j... !: \ i 1 -—V—

I

i ...

, .| :i\

, j

: -

; ;:l:x 1

1

i .

1:

: :'

I -±-

j

1 *• \

r::h :

'~:!-."~ •--

::; : : : :; -

: ••• -'- —-'-

j '-' "'

. !

•

' : "j — Mr. j:

!

1 '

: r'

1

:l V

1 j

r -I':

f

. r •;; ;

-

! r

. —: - 4-' vili!! 1

- 1-

i

!::f|;:i: ! :::l

- L... 3--

" "

1 .

' r :

:

l

.

:: -- —

H

}-\-

: li:: it 1

i

]

'

: irr%M -- ...j. ._

i'" "

| :; ; -r

... .:... vM - -

: .:.. --

i J -

.V

: .]...

iilij .

1 —

|- \

\.!:

: 4-- . I '.

1

;

:

: \

...

.: |. -i

i

--r-

! -t1

1

] .::: !_._ ...j

y.i . f-;.-t~--1

"Mi —i-

.... :. .'

! ::•.:):. i j

.

P

1

1; —|-

i

i.. -~ l ....

1

• 1

.. _]__•_ T T~

.

. i -.'

1

' :::::•:

liii -

....

;-h

..-. .... ..... L_ - K,;,

~-*

•:.:

i . ' rtiitiiii , .. ;i:j

ifi ,,.; L__ li —u ||:j 0.1 0.2 0.3 0.A FREQUENCY, GHz Figure 11. Calculated and measured arg (S21) = ^21 versus frequency for reduced IDOC

coaxial 2-port.

27
1

i

1

!

! :

1

J

1

i 1.14 Measured With:

G A.N.A. "A"

+ A.N.A. "BM

i —

a

| .1 1 10

:|

: o

u

1.06 Q n

.. ..: ._

1 4

n '

i 4 ! : :-

i, COQ

: -

.1

. .. I _G <

i o 1.02 + 4* ; +

1+ +b

, «*CA i r in A'rF

: .

i + V .i±_. :* H- T c L*

COo

*r

ft oF

, 2

-t- —f+

i -+- + - - _1_ f

Z

.08 f

rr *^ :•: r:.

L.. ... ..

!

1 >- +

C

: ?! i H ; mk , ~C l |

.

><<

.- _ +

r !

_j...-C ) : _ Q K A ,94

a,o

a;

. -i-

;

.90

( )

!

--•;-- . . .86 !

•

:

. : .. -. -i o

;

...

'.-.

. I

;

::.

'

.82 . 1 .... Milii 0.1 0.2 0.3 0.4

FREQUENCY, GHz

0.5

Figure 12. Calculated and measured group aelay time versus frequency for reduced IDOC

coaxial 2-port.

28
i^ft-tJpfeHi

J

**%

n i : <f ; rH i ffl fi I* ^-' Ik Oc

•HvO

rH -^

c^ 1

co 1

"' s

4-1 c

•H

0) *;;; ! J-l & k. u P 0) CD fi T3 COc

•H ' f; "1 2 o i co ;3

CDO 1 : 5

en

U . 1 z

CD(S60

•H

CO

.-; _i CD % •• 13

,:::: ^ Rf;b^ , ;; CO

U

g « 1 1 UO 1 fi ft1 ' 1

_—~

*<r

CMrH

CO H 1 " I COO 1 iIMB CM o ' 1

«' il'S: _£

u . 1 IwB - rHQ J E O I g3 W T3

CI) •

co e

CO CD

CD 4J H CO ; •H rH

<+-{ cfi O -H X CO i ft O

(-1 O £ u o O 1 X o

P-t

m. en

rH

a)M2

•H HBL >-» •»" Pn | .

29
T CS 1 1 0« : 3d 06/O7/74

FOR 9/16 INCH (14 MM) COAXIAL SYSTEM;

ODI C

I DOC

TEm-moDE CHARACTERISTIC IMPEDANCE

.24425 INCHES

.5625 INCHES

50.0012 OHMS

FOR 2- FORT:

ODI C TDOC

LENGTH

TEM-MODE CHARACTERISTIC IMPEDANCE

DISCONTINUITY CAPACITANCE

RELATIVE PERMITTIVITY OF AIR

IC RESISTIVITY

OC RESISTIVITY

.2651 INCHES

.5625 INCHES

11.311 INCHES

45.09 13 OHMS

2. 55531E- 15 FARADS

1 .0P064

.000003 OHM-CM.

.000008 OHM-CM.

FREQUENCY RETURN LOSS ARGCS1 1 ) OH? DECIBELS MAG( SI 1 ) DEGREES

. 1 24.3239 6.07363E-2 233.7 12

. 1 1 23.6236 6.53398E-2 230. 1 1

1

. 1? 23.0032 7.07273E-2 226. 512

. 13 22.4662 7.523 19E-2 222.9 16

. 1 4 21 .9389 7.95344E-2 219.321

. 15 21 . 569 5 3.34693E-2 215.723

. 16 21 .2025 R.707I7E-2 2 1 2 . 1 33

. 17 20.3335 9.03233E-2 203. 55

. 1« 20.6092 .093227 204.963

. 19 20.3766 9. 57 57 IE2201 .379

.2 20. 1835 9.79094E-2 197.796

.21 20.0232 .099 676 194.21 5 .22 19.9092 . 101051 190.635

.23 19.R256 . 102023 137.056

.24 19.7766 . 102606 133.477

.25 19.7613 . 10273 179.9

.26 19.73 1 1 . 102552 176.322

.27 19.8347 . 101922 172.745

.23 19.9 229 . 1 003 9 1 169. 167

.29 20.0466 9.94644E-2 165.539

.3 20.206* 9.76463E-2 162.01

1

.31 20.405 9.54443E-2 1 53 . 43

1

.32 20.6423 9.23664E-2 1 54.351

.33 20.9223 3.9921 1 E-2 151.27

.34 21 .2476 *.66199E-2 147.633

.35 21 .621

1

.03 297 5 144. 105

.36 22. 0474 7.90002E-2 140.521

.37 22.5324 7.47I03E-2 136.937

• 3R 23.03 29 7.01219E-2 133.354

.39 23. 70«? 1 6.52524E-2 129.7 7

. 4 24.4195 6.01209E-2 126. 139

.41 25.2323 5.47472E-2 122.61

1

.42 26. 169 J 4.9 1 527E-2 1 19.039

.43 27.25R3 4.33594E-2 1 15.475

. 44 23 . 5 4 43 3.73904E-2 1 11.927

.45 3P.0975 3. 12693E-2 103 .403

.46 32.0334 2.50223E-2 104.926

.47 34.5755 1 .36734E-2 101 . 543

. 4q 33.2379 1 .22492E-2 93.4103

. 49 44.7642 5.773 13E-3 96.369 1 .5 62.0733 7.37655E-4 247.325

Figure 14. Computer printout of pr ogram ICS11 for increased

coaxial 2-port.

30
ics?i 0«: 1 3 06/07/74

FDR 9/|6 INCH (14 MM) COAXIAL SYSTEM". ODIC

TDOC

TE^-MODE CHARACTER! STIC IMFEDANCE

.24425 INCHES

.5625 INCHES

50.001? OHMS

FOR ?-PORTs

ODIC

I DOC

LENGTH

TEM-MODE CHARACTERISTIC IMPEDANCE

DISCONTINUITY CAPACITANCE

RELATIVE PERMITTIVITY OF AIR

IC RESISTIVITY

OC RESISTIVITY

.2651 INCHES

•56?5 INCHES

1 1 .8 1 1 INCHES

45.0913 OHMS

?. 55531E- 1 5 FARADS

1 . 00064

.000008 OHM- CM. .000008 OHM-CM.

DELTA F FOR CALCULATION OF GROUP DELAY • P0 5, GH7

FREQUENCY ATTENUATION ARG(S21> GROUP DELAY

GH? DECIBELS MAG( S2 1 ) DEGREES NANOSECONDS

. 1 2.74383E-2 .9968 46 -36. 1859 1 .00275

. 1 1 3.08 121E-2 .996459 -39.7947 1 . 0021

. 1? 3.42262E-2 .996067 -43.401 1 .001 43

. 13 3.76386E-2 .995676 -47.005 1 .00076

. 14 4. 1 0044E-2 .99529 - 50. 6065 1 .0001

. 15 4. 4?8P7E-2 .99 49 1 5 -54.2057 .999451

. 16 4.74251E-2 .994555 -57.8026 .998832

. 17 5.03967E-2 .99421 5 -61 . 3973 .998251

• 18 5.31 57 2 E2

.99 38 9Q -64.99 .99771

4

. 19 5. 56706E-2 .99361 1 - 68 . 58 09 .997233

.? 5.79051E-2 .993356 -72. 1702 .99 68 13

.21 5.98 333E-? .9931 35 - 7 5 . 7 58 .996462

.22 6. 14317E-2 .992952 -79. 3448 .996184

.23 6.26821E-2 .99 28 09 -82.9306 .995984

.24 6.35715E-2 .992708 -8 6. 5 159 .995R66

.25 6. 409 28E-2 .992648 269.899 .99 58 3 .26 6.42432E-2 .992631 266. 31

4

. 9 9 58 7 6 .27 6.40271 E-2 .992656 262.729 .996006

.2« 6.34527E-2 .992721 259. 143 .996216

.29 6.25361E-? ,992«26 255.556 .996504

.3 6. 1 2962E-? .992968 251 .968 .996865

.31 5. 9 7 578 E-2 .9931 44 248 . 378 .997293

.32 5.79507E-2 .99335 244.787 .99778 1 .33 5.59086E-2 .993584 241 . 194 .998324

.34 5.36687E-2 . 9 9 38 4 237.599 .99891

.35 .051 271 .9941 1

5

234.002 .999532

.36 4.875«5E-2 .994402 230.403 1 .00018

.37 4.61758E-2 .994698 226.801 1 .00 08 4 .38 4.3568 2E-2 .994997 223. 197 1 .00151

.39 4.09822E-2 .995293 219. 59 1 .00218

.4 3.84636E-2 .9955* 1 215.98 1 1 .0028 2 .41 3.60566E-2 .995857 212.37 1 .00344

.4? .033805 .9961 16 208 .756 1 .00403

.43 3. 17485E-? .996351 205. 141 1 .00457

.44 2.99247E-2 .996561 201.523 1 .00505

.45 2.83672E-2 .996739 197.904 1 .00548

.46 2.71055E-2 .99 68*4 194.284 1 .00583

.47 2.61641E-2 .996992 190.662 1 .0061 1 .48 2.55623E-2 .997061 187. 04 1.00631

.49 2. 53142E-2 .99709 183.417 1 .00642

.5 .025428 .997077 1 79.794 1 . 00646

Figure 15. Computer printout of program ICS21 for increased ODIC coaxial

2-port.

31
270°

Figure 16. Polar plot of calculated and measured Sn of increased ODIC coaxial

2-port for frequencies from 0.1 to 0.5 GHz.

32
-- —

; !:•:: .... —i ~

T~~

i

!! r - TFT :.

! rr

hr ... : '!

j

1

:|::

: • ''

j

' '

rrr.

: ;;

;:l: :•.:: :.

1 r

;

•

i ... 1. .

j r -- - •l

::

1

2^ !: : }

! j --i

L.j... .._[_ —1-

i

' / --

1

1 '

1

\ 1

|

i i- :

~-\

i ..J ... .... — — —

..

.

: i ... ?? . i

.

:

H?= ::-: k c* tL QK|l FEC\ -

-/-# 1 \

: -.:. \

ii— -i-ili \

:::: .;.- .-- ~~[.. : :L--I

: : iiil — \-.TL t z 21

= . -.

:-.:1: :

- rH fc '-— =s —

—

<

V

.;-;

i

:

^irrrrf

~

;

l :

»

::::

i \

.. —". n?

~-r?:: - ':''. v

c9

: :: .::. r;£= .- --

' ::

'

tit: iTM —

: L::

:.

: :_-

-.: ' : : . . : :"

-: ! .... un -.i. . 5?0. 5=~1

20

:.;- (j SjV

';>

:•- ~ ji 1 --

riil

: .

-

:_; .-.-Jr.--. :::'

:.-. *«

4::- ::•: — }, ~::| : : :-r-": 7^7

~": :.

:

§7- ;

»

..:. ....

:..: ;:jl::;: .:rr—

' ! ; _i 19

-j-- -! "

....

: : :

:

IHilrH

. :

:

:::: : ri: :rit cbiirft

;::: L^gf

- -::rl + 1«r TTTF

-:-- \m Tfrt

: i' flr: -i

liii ::: - . S —

:::: - , tilt:

I 1 till h : ;.: :.:.

,;;. ;.;i i ;| .:. M :.;

; ! M $ ]:!: fffl m

: i;i 0.1 0.2 0.3

FREQUENCY, GHz

0.4

Figure 17. Calculated and measured return loss «= -20 log 10 |Sn| versus frequency

for increased ODIC coaxial 2-port.

33
LLl Ivl a:a

Lbo

-T

:

-T — jb _-._ rfn

1 -- 1 ii!

! '' ' *:40 '

1r

i

1 -i --

i

; |

1

- — —

i i

-- . Jill

i -

1 230

... -

,

! \ I

1 J--

:

! -^ - —

220 1 \

-

'

t>

\

1 - 1 V

•- —

V1

1 4- - 210 i • •::'

200

-

:

; \

y~ i ' \(5

i \r1-

: : 190 : \i ;: m: mM ^&1 ft lD \*i

:':

'

:: :.;;

1 80 ....

: -.: \{i

1 ::

J 1

-| - ... I 170

\c1

' ... .... \t•>

...

s= j. -

;

.

i \ly160

: :'" \c;> .: -\:\ .: :* % r4-

;f-

:

: r .-.::

' \<> --: 150 Vf> :''

: : "

E :

= . MO ; :

:u:| .::

:.-;

::::

: -..

130

•t

:•

- yi 2 .; ;;;: *

io r\ - ::::

jjjj |f,|

:

: :: ::j :... fjj ni ,,,; mil ',,,.

. :

.

;

: : ;;; ..-.

fl b .; -; !:: All :; 0.1 0.2 0.3 0.4

Figure

FREQUENCY. GHz

18. Calculated and measured arg (Sh) = ty\\ in degrees versus frequency

for increased ODIC coaxial 2-port.

34
180<

Figure 19. Polar plot of calculated and measured attenuation in

decibels = -20 log 10 |S 2 i| and arg (S 2 i) = ^21 of

increased ODIC coaxial 2-port for frequencies from

0.1 to 0.5 GHz.

35
1.01

1.000

ino

w

Q

E-U

,99 -

,98

Figure 20.

:

1

' 1 1

•--

4

i

3 - ;-- > o)

, P> oj

1

i

\

!

j o c >

\

1 o ,

• -- i— -

: o

1

i

!

i

1

• n O i

1 o 1

: ......

r ^

! r

9

j : n - r, - Q -u- in*" «!,-, ~~ k

i

1 - rs ..:._.

• La--

P

1 P

2 O A. J.W UJIIU - L.1II

• o

c \ .

1 ^f\

:

\ V

.....

i

i i- :•: ^^ '

1

: O

!

:

i

i

i :

:

-\ %,

i

i

!

i

1

! i nt

i !

:

1

:

U-i

1

o

--:-

i i A —: --"-- ! —

1

:

;

Q

...

: —

-

--

1 t ^

~

'

; < > _...u.

.._ -""

ffir ;£4 :,

...

!

: ;;;

i

:

,,i n

3J

i

;;

!

i

i O : L_ —

i

—— .... i

. Lii : :: ,i- iiii.

i iiii ffH 0.1 0.2 0.3 0.4

FREQUENCY, GHz

0.5

Calculated and measured |s 2 i| versus frequency for increased ODIC coaxial

2-port.

36
— —

- :j

1 •:

1

']': H-~ |

...

1 €:

- %.

1i- ...

;.

!

.- L 4:-

i

:...v -- I

4/

.p. -. -- - rr

;i!!l:ii=

'

1

. ,| ...

I

.-.TT

:; :

: |:

:

:

i - I -

1

... j.. . jij -r- ~r

— ...j:..

1

1 4- — - --j- rr T7-7

1;;::

..i.i

i _ - }-

i i"

*

1 i

I

.. — — — ffjf '-

320 _j. ...

i <

...... - .

-—

:

-- —

1

i \ —i

._. —

1 :l — H

;1 310 i

-

-...; y i

1 .._t _ _._ -- —-:- —

:

---

j --

300

- \

- 1 ::|::\

i

i 1

"

i h

290

:

-:. !

:•

| •:: .

; ; —:. -1

1 j

---

":

280 j

:

i

: .:(;:.: T-

; nilw ~.l 1 i \J Fn . CO - i-

;

:

Pi -- - -'-]- . ..i_'_

i' ~ — >v|._ TT

-iii: ;frj CJ ::

:

;- w 270 Q _ j, _.

.

:

' ::::

1

.

. i i- ::-

*

i

'

....,

i

: eg

1

. 4 .

i 260 — ;i:

:

:

i

""

--

:

'- —

J 1

1 — _..

: w i _--.

_.i_u.

: j !__ - j —!- —

1: —!-

: i

:

-----

1 250

...j... -j- - ---j—

y':\. r

-:' - ^

: :::: -- — _.:;_:.„

'

i

J.__

i

i Vl

240 i V" 1 \

i :: i'

i P''

I —" --

IX. 1 1

i t -": — " - __..

;-.::!:'

I''

!

i-

_ _i

i

.._!

I -j__

i

. i .' T

230 ; l- i

j ; i

!

. i

:

i —ir

i -•t— - rl .:

1:

- : - — ..:_ -..;..-

1

1

.

•

>

i "- _.^ -^: — ...

.'.' -

! : ; .*\ 220 '3m II m :... iil _1—\}; ek : . . ^j

0.1 0.2 0.3

FREQUENCY, GHz

0.4

Figure 21. Calculated and measured arg (S21) = ^21 versus frequency for increased ODIC

coaxial 2-port.

37
-:.

!

: 1 ; -i

i

.

: 1 ' iitipil p H: --:

1

1

1.16 :-- J

1 " 1 :{:::

i -C

: :. ::' ::::| 1.12 f

r .Itl c/ <u£u UAUJ;D F •OR

1

1

: ;i- -::)-:. : : | : . :

I -

yJ 3()crh A IP LJtN M : : I. .

-:: 1

I

- i.

:

to --!:: ! ^

lYIN* r~TtU jOw FHyu "HP

2

o 1 08 _ i

-.:

I

i .... •:.;::;

i

- 1- : ,

i

1 - 1

:: -! |:ii :!

» ;;;;

! J-. - Q .. !

. !

1 - 5 i \ - < A ! 2

...4- .-

1

; * i

; .,|..

' i O

r

'i- # Z 1.04

:-_- =--

1 :

1

1 /

7 i!"':

1 :.:|

>

a zkil & '

I ... "I u i 1 irk pi> 1 . t

1 ©

*n

I1

i

:..:

E- —1 .. !'•- : *E> i

i jst" Jl|:::I i

i

1 ....

.

% i 1.00

:;::!: ( J : —Jvk^

f F$R

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;„l 0.1 0.2 0.3 0.4

FREQUENCY, GHz

0.5

Figure 22. Calculated and measured group delay time versus frequency

for increased ODIC coaxial 2-port.

38
* •

"EDUCED HE,GHT WAVEGUIDE

1-0.4052". h,=0.0918"

Figure 23. Photograph of reduced height rectangular waveguide 2-port designed to be

inserted into a WR-90 (IEC-R-100) waveguide system.

39
WSI

1

13:54 06/05/74

FOR WR-9P (R-10P) WAVEGUIDE SYSTEM: INTERNAL WIDTH .9 INCHES INTERNAL HEIGHT .4 INCHES

FOR 2-PORT: INTERNAL WIDTH . 9 INCHES INTERNAL H GHT .09 1* INCHES

LENGTH .4052 INCHES

RESISTIVITY 8.SE-6 OHM-CM. RELATIVE PERMITTIVITY OF AIR 1.00064

FREf.JENCY RETURN LOSS ARGC SI 1

)

r'H7 DECIBELS MAGCSI 1

)

DEGREES

8 1 .05701 .58 542 192.856

«. 1 1 .02289 .888905 191.71

8.2 .994234 .89 1843 190.621

8.3 .970268 .894307 189. 583

8.4 .950387 .896356 188. 586

8.5 .9341 1

?

.898037 187.624

H.6 .92106 .899388 186.693

s.7 .910931 .900437 18 5.788

R.R .903484 .90121 1R4.904

8.9 .898529 .901724 18 4.038

9. .89592 .901995 183. 187

9. 1 .895548 .902033 182.347

9.2 .897331 . 9 1 8 48 18 1 .517

9.3 .901219 .901445 180.693

9.4 .907183 .9 008 26 179.873

9.5 .91522 .899993 179.055

".6 .925345 .898944 178.236

9.7 .937597 .897677 177.416

9.8 .952034 .896186 176. 591 9.9 .968736 .894465 175.759

10. .98 7805 .892503 174.919

10. I 1 .00936 .89029 1 17 4.068

10.2 1 .03356 .8878 14 173.205

10.3 1 .06058 .885056 172.327

10.4 1 .09062 .882001 17 1 .431

10.5 1 . 1239 2 .878626 170.517

10.6 1 . 16075 .8749 08 1 69 . 58 10.7 1 .20144 .8708 19 168.619

10. 8 1 .24635 .866328 167.631

10.9 1 .29 59 .861 4 166.613

1 1 . 1.35058 .855995 165.561

11.1 1 . 4 1 09 3 .850067 164.473

1 1 .2 1 .47761 .843566 163.345

11.3 1 .55136 .836434 162. 174

1 1 .4 1 .63304 .828606 160.954

11.5 1.72364 .820008 1 59 . 68 1

1 1.6 1 .82433 .8 10557 158.3 52

1 1 .7 1 .93646 .80016 156.9 59

1 1.8 2.06163 .788712 1 55.499

1 1.9 2.20171 .776094 153.964

12. 2.3589 1 .762175 152.349

12.1 2.53584 .746806 150.646

12.2 2.73562 .729826 1 48.847

12.3 2.96198 .71 1051 146.946

12.4 3.21941 .690287 1 44.934

12.5 3.51333 .667319 1 42.803

12.6 3.85036 .641922 140.544

12.7 4.23865 . 6 1 38 58 1 38 . 1 49 12.8 4.68828 .58 288 9 135.612

12.9 5.21 199 .548 78 3 132.925

13. 5.82604 .51 1326 130.083

Figure 24. Computer printout of program WS11 for rectangular

waveguide 2-port.

40
WS21 14t 00 06/05/74

FOR WR-90 CR-100) WAVEGUIDE SYSTEM: INTERNAL WIDTH INTERNAL HEIGHT

,9 INCHES

.4 INCHES

FOR 2-PORT: INTERNAL WIDTH INTERNAL HEIGHT

LENGTH RESISTIVITY

RELATIVE PERMITTIVITY OF AIR

.9 INCHES

.0918 INCHES

.4P152 INCHES 8.SE-6 OHM-CM.

1 .00064

DELTA F FOR CALCULATION OF GROUP DELAY ,05 GH7

FREQUENCY

GHT

I2

3

4

5

6

78

9 IP.

10. I 10.2

10,

10, 10,

10,

10,

10, 10,

1 1. 11.1 11.2

11.3 11.4

1 1

1 1 II,

I 1

I 1, 12. 12.1 12.2

12.3 12.4 12.5

12.6

12.7

12.8 12.9

13. NOW AT 999

SRU'St 1.1 READY

ATTENUATION

DECIBELS MAGCS21)

6.6789 1 .463505

6.80454 . 4568 49 6.91374 .451 142 7.00779 .44628 3 7.08778 .442192

7. 15464 .438801 7.209 17 .436055

7.25206 .433907

7.28 389 .43232

7.30517 .431262

7.31635 .4307 08 7.3178 .430635

7.30987 .431029

7.29 28 3 .431875

7.26693 .433165

7.23239 .434891

7 . 1 8 9 38 .43705

7 . 1 38 07 .439639

7.078 57 .442661

7.01 1 .4461 18 6.93545 .450015

6.85199 .454361

6.76066 .459 163 6.66151 .464434

6.55457 .470188

6.43986 .476439

6.31738 .483205

6. 18714 .490505

6.04913 .498 36 5.90336 .506795

5.7 498 2 .515833

5. 588 52 .525502

5.41945 .5358 3 5.24266 .546*49

5.05817 .558 588 4.86606 . 57 1 08 4.66642 .58 4358 4.45939 .598 454

4.24517 .61339 7 4.02402 .629215

3.79627 .645931

3.56238 .663561

3.3229 . 68 2 1 1 1 3.078 55 .701573

2.8302 .721922

2.57895 .743109

2.32613 .765056

2.07333 .78765

1.82246 .810731

1.57 57 5 .834089

1.33576 .857456

ARG<S2I> DEGREES

-77. 1 143 -78.2646

-79.3565

-80.3988

-8 1 .399 -82.3633

-8 3.29 7 1 -84.2051

-8 5.09 14 -8 5.9 59 6 -86.8 131 -8 7.6548

-88.4874

-89.3135

269.865

269.045

268 .224 267.402

266.574

265.741

264.899

264.046

263. 18 262.3

261.402

260.485

259.546

258.58 3 257. 59 2 256.572

255.517

254.427

253.296

2S2. 121 250.898

249.622

248.288

246.892

245.427

243.887

242.267

240.558

238.753

236.845

234.825

232.68 5 230.416

228 . 009 225.458

222.755

219.894

GROUP DELAY NANOSECONDS

3.28741E-2

3. I 108 3E-2

2.961 36E-2

2.83439E-2

2.72637E-2

.026345

2. 55655E-2

2.49077E-2

2.43571 E-2 2.39024E-2

2.35343E-2

2.32451E-2

2.30289E-2

2. 288 08 E-2 2.27972E-2

2.27743E-2

2.28 1 I9E-2

2.29067E-2

2.30588E-2

2.32676E-2

2.35337E-2

2.38577E-2

.024241

2.46857E-2

2.51937E-2

2.57683E-2

2.64126E-2

2.71308E-2

2.79275E-2

2.88077E-2

2.97774E-2

3.08432E-2

.20122E-2

,329 28 E-2 46936E-2

.62244E-2

. 78 9 58 E- 2 .97188E-2

17054E-2

4.38 68 3E-2

.04622

4.87729E-2

5. 15394E-2

5.4529 5E-2

5.77SI9E-2

6. 12109E-2

6.49053E-2

6.88268E-2

.0729 57 7.72647E-2

8. 17034E-2

Figure 25. Computer printout of program WS21 for rectangular waveguide

2-port.

41
180'

270°

Figure 26. Polar plot of calculated and measured S i i and S21 of rectangular waveguide

2-port for frequencies from 8 to 13 GHz.

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10 11 12 FREQUENCY, GHz

13

Figure 28. Calculated and measured arg (Sn) = tyu in degrees versus frequency for

rectangular waveguide 2-port.

44
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FREQUENCY, GHz

13

Figure 30. Calculated and measured arg (S21) =1^21 in degrees versus frequency

for rectangular waveguide 2-port.

46
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FREQUENCY, GHz

12 13

Figure 31. Calculated and measured group delay time versus frequency

rectangular waveguide 2-port.

for

47
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-S

1 ;:

WR- ??\ CLO ""•* i (IEC)-n

:::: -3 ) 1 — -

: :

: : : -'-

: E !

: i

....

' - m

1.0

z

<u

zwu

«w

a. 0.1

.01 .001 .01 0.1 1.0

S I = MAGNITUDE OF S n

Figure 32. Percent change in j S x l I versus ] S 1 1 | of Xq/4 2-port standards

corresponding to a change of 0.001 inch in the increased

ODIC or reduced IDOC of 9/16 inch (14 mm) coaxial 2-ports or reduced height rectangular waveguide 2-ports.

48
IV

I

I \

i \j

\ v X

\ .- Wl*-IF> \ (IF^C-R-62iO) v\ \

£ r,r A ^\VR- 9f i

,n '-°

(

b

14 m n) \N

( tEC -R

\

-IC >0)

X V V \

R

r

l HiLEh ID 00

*

\N. V

z V A > v

\

m ll\ CREAI>ED c Dl V \

z

< \k X

'v">>V \ V \

^WR- ??> 00 ^ \,

: UJo

1

Jj« O.I

(IEC;-R -3 ) >^ \

\ ss \

,N \.s

^

^

V

^

t

m

.001 .01 0.1 1.0

|Su| MAGNITUDE OF S M Figure 33. Percent change in |Su| versus |Sji| of Aq/4 2-port standards corresponding

to a change of 0.0001 inch in the increased 0DIC or reduced ID0C of

9/16 inch (14 mm) coaxial 2-ports, or reduced height rectangular waveguide

2-ports.

49
1 .Oi0.9

. :-: -

0.7

0.6

0. 5

0.4

0.3

0.2

0.1

h R

= 0.0918 INCH

0.1333

h

R

= 0.1680

h

R

- 0.2000

h

R

= 0.2309

h R

- 0.2619

H R

= 0.2935

h

R

= 0.3266

h D

= 0.3618

K

10 1

1

12 13

FREQUENCY, GHz

Figure 34. Calculated |Su| versus frequency for various reduced height

WR-90 (IEC-R-100) rectangular waveguide 2-port standards all

having a length of 0.4052 inch.

50
1 .Onto

Lio

=>

h R

= 0.0918 INCH

0.1333

0.1680

0.2000

0.2309

0.2619

0.2935

0.3266

0.3618

FREQUENCY, GHz

Figure 35. Calculated | S x x I versus frequency for various reduced height

WR-90 (IEC-R-100) rectangular waveguide 2-port standards all

having a length of 0.3150 inch (80 mm).

51
100

UJI

o

X

H

z

UJ

100

FREQUENCY, GHz

Figure 36. Plot of L = (2n-l) A G

/4 versus frequency for TEM mode propagation in

coaxial line.

52
Appendix CS11

CSII 09101 06/04/7 4

REM 2REM INPUT DATA REQUIRED!

4REM

6REM FOR COAXIAL SYSTEM INTO WHICH 2-PORT IS INSERTEDl

7REM COAXIAL SYSTEM DESIGNATOR LINE 250 8REM ODIC (INCHES) LINE 20S Al I0REM IDOC (INCHES) LINE 2IS Bl 12REM FOR REDUCED IDOC 2-PORT STANDARD!

14REM ODIC (INCHES) LINE 210 A2

I6REM IDOC (INCHES) LINE 220 B2 18REM LENGTH (INCHES) LINE 225 L 20REM IC RESISTIVITY (OHM-CM.) LINE 230 PI 22REM OC RESISTIVITY (OHM-CM.) LINE 235 P2 24REM DISCONTINUITY CAPACITANCE DIVIDED BY CIRCUMFER26REM ENCE OF IC (FARADS/CM.) LINE 240 CI 28REM (NOTE THAT CI IS ASSUMED INDEPENDENT OF 30REM FREQUENCY AND IS NOT CALCULATED BY THIS PRO- 32REM GRAM BUT MUST BE OBTAINED BY OTHER MEANS)

34REM RELATIVE PERMITTIVITY OF AIR LINE 200 E 36REM FREQUENCIES (GHZ) .' LINE 329 F 38 REM 40REM

42REM CALCULATED PARAMETERS!

44REM 46REM TEM MODE Z0 OF COAXIAL SYSTEM ( OHMS) . .LI NE305 ZI 4BREM TEM MODE Z0 OF 2-PORT (OHMS) LINE 310 Z2

50REM DISCONTINUITY CAPACITANCE ( FARADS) ... .LINE 360 C2 ^2REM DISCONTINUITY SUSCEPTANCE/Y02 LINE 370 E7 S4REM (NOTE THAT Y02=l/Z02>

56REM GUIDE WAVELENGTH (INCHES) LINE 330 W S8REM IC SKIN DEPTH (CM.) LINE 335 Kl 60REM OC SKIN DEPTH (CM.) LINE 340 K2

62REM ATTENUATION CONSTANT OF 2-P0RT( N/CM) . .L I NE 345 A 64REM (ATTEN. CONST. )«(LENGTH ) (DB> LINE 355 A7 65REM RETURN LOSS (DB) CORRESPONDING TO SI 1.. LINE 48 1 T5 66REM MAGNITUDE OF Sll LINE 480 S 68REM ARGUMENT OF Sll (DEGREES) LINE S00 T3 70REM (NOTE THAT IF Gl<0 THEN T3*180>

100P=3. 141 59265

105 C=2.997925«10M0

110N=8.68 589

1ISN1 = 2.54

125 N3=.5/P

200E=1 .00064

205AI=. 24425

210A2=. 24425 215B1=.5625

220B2=.5I8 5 225 L=30/N1

230 Pl=2/10t6

235 P2=8/I0t6

240 01=1.94969/ I0t 1

5

245V=C/(N1«SQR(E>)

246Z l = 59.9 39 2*L0G(BI/AI>

247Z2=59.9392*L0G( B2/A2)

248 C9=2. 30258 5093 250PRINT"FOR 9/16 INCH (14 MM) COAXIAL SYSTEM!"

251PRINT" ODIC ". Al» "I NCHES"

252PRINT" IDOC ". Bl J "INCHES"

253PRINT" TEM-MODE CHARACTERISTIC IMPEDANCE ", Z 1 1 "OHMS"

254PRINT 255PRINT"FOR 2-PORTl 1 ODIC

IDOC LENGTH TEM-MODE CHARACTERISTIC IMPEDANCE DISCONTINUITY CAPACITANCE " RELATIVE PERMITTIVITY OF AIR ", E IC RESISTIVITY

OC RESISTIVITY

256PRINT"

257PRINT"

258 PRINT" 259PRINT" 260PRINT"

26IPRINT" 262PRINT"

263PRINT"

264PRINT 3ISRI=Z1/Z2

320R2=R1 «2 323PRINT

324PRI NT-FREQUENCY". "RETURN LOSS"."

325PRINT" GHZ ". "DEC! BELS". "MAG( S 1 I > 326PRINT 329F0RF=.l TO.5STEP.01

330 W=V/(F*l0t9> 335KI=N3«SQR(PI/F>

340K2=N3«SQR(P2/F)

345 A=2«P«F«((K1/A2)-KK2/B2))/(N1*Z2)

3S0 A6=2»A*L»NI 355A7=A6*N/2

360C2=P*AI*N1«C1

365 B3=2*P»F«C2*10»9

370 E7=Z2«B3

375 B=4«P»L/W

38 0SS=SIN(B>

385CS=COS(B)

39 0A9=I-A6 395C6=E7«E7«R2

400R3=( l-R2+C6)»( l-A9*C5) 405R4=-2«E7*R2«A9«SS

410R5=R3+R4

4151 l = -2*E7*R2«( 1*A9»C5>

4201 2=( l-R2»C6)*A9*S5

42513=1 l + IS 430MI=SQR(R5t2*I3»2)

435R6=( I*R1 > t2-C6

440R7=(( l-Rl)t2-(E7*RI)t2)«C5

445R8 = (2«E7«R1 )»( 1-R1)«S5

450R9 = R6-A9«(R7»R8 > 455I4=(2*E7«R1>*( 1*R1> 460I5=R7«TAN(B) 465I6=-2*E7»R1«( l-RI)*CS

4701 7=1 4+( 1-A6)*(I5+I6> 475M2=SQR(R9»2*I7l2)

48 0S =MI/M2

4BIT5=(20«LOG( 1/S))/C9

48 5G1 = (R5*R9*I3*I7)/(R9«R9+I7*I7>

490GB=(I3*R9-R5*I7)/(R9*R7*I7«I7)

49 5G3=ATN(G2/G1 ) 500T3=G3*I80/P

505IF Gl<0 THEN 520 510PRINT F.T5. S. T3 515IF Gl>0 THEN 525 520PRINT F.T5.S»T3*180

525NEXT F

•.A2l"INCHES"

'. B2l "INCHES"

'.L! "INCHES"

".Z2l "OHMS" CI«P»AI*NI»"FARADS

•»P1I "OHM-CM."

- .P2( "OHM-CM."

"."ARG(SI I)' •DEGREES"

53
cs2i p°:v* 06/04/74 Appendix CS21

2REM INPUT DATA REOUI ftED: 4REM 6REM FOR COAXIAL SYSTEM INTO WW I CH 2-P0hT IS INSERTED:

7REM COAXIAL SYSTEM DESIGNATOR LINE 29 6 *RE"1 ODIC (INCHES) LINE 135 Al I0REM I DOC (INCHES) LINE 145 Bl 12REM FOR REDUCED I DOC 2-PORT STANDARD:

14REM ODIC CINCHES) LINE 140 A2

I6REM I DOC (INCHES) LINE 150 B2 18REM LENGTH (INCHES) LINE 1 55 L 20REM IC RESISTIVITY (OHM-CM.) LINE 160 PI 22REM OC RESISTIVITY (OHM-CM.) LINE 165 P2 24REM DISCONTINUITY CAPACITANCE DIVIDED BY CI RCUMFER26REM ENCE OF IC (FARADS/CM.) LINE170 C5 2RREM (NOTE TWAT CS IS ASSUMED INDEPENDENT OF FRE- 30REM OUENCY AND IS NOT CALCULATED BY THIS PRO- 32REM GRAM BUT MUST BE OBTAINED BY OTHER MEANS)

34REM RELATIVE PERMITTIVITY OF AIR LINE 130 E 36REM FREQUENCIES (GHZ) LINE 400 F 37 REM 3«REM DELTA F FOR GROUP DELAY CALCUL ATI ON. . .LI NE 205 M3

40REM

41 REM 42REM CALCULATED PARAMETERS:

44REM

46REM TEM MODE Z0 OF COAXIAL SYSTEM (OHMS). .LINE 180 Zl 48REM TEM MODE Z0 OF 2-PORT (OHMS) LINE 185 Z2

50REM DISCONTINUITY CAPACITANCE ( FARADS) ... .LI NE 190 C2 52REM DISCONTINUITY SUSCEPTANCE/Y02 LINE 480 E7 54REM (NOTE THAT Y02=l/Z02)

56REM GUIDE WAVELENGTH (INCHES) LINE 420 W 53REM IC SKIN DEPTH (CM.) LINE 435 Kl 60REM OC SKIN DEPTH (CM.) LINE 440 K2

61REM ATTENUATION OF 2-PORT ( DECI BELS) . . . .LI NE 8 I 1 T5 62REM ATTENUATION CONSTANT OF 2-PORT (N/CM) .LINE 445 A 63REM ATTENUATION CONSTANT*LENGTH (DB)....LINE 460 A7 64REM MAGNITUDE OF S2 1 LINE 810 S 66REM ARGUMENT OF S21 (DEGREES) LINE 8 60 T3 68REM (NOTE THAT IF G1<0 THEN T3+130)

70REM GROUP DELAY (NANOSECONDS) LINE 8 30 K9 72REM (NOTE THAT IF K6*K5>0 THEN LINE LINE 8 40)

7 4REM

100P=3. 14159265 105C=2.997925*10tl0

I10N=8.68 58 9

1 I5N1 = 2.54

125N3= .5/P

130E=1. 00064

135A1=. 24425

I40A2=.24425

I45B1=.5625 I50B2=.5185

155L=30/N1

160 Pl=2/10t6

165 P2=8/10t6

170 C5=l. 94969/1 0t 15 175V=C/(N1*SQR(E>>

18 0Z1=59.9 39 2*LOG(BI/A1)

185Z2=59.9392*L0G( B2/A2)

190C2=P*A1*NI«C5

195R1=Z1/Z2 200R2=Rlr2 205M3=.005

210C9=2. 30258 5093 296PRINT"F0R 9/16 INCH (14 MM) COAXIAL SYSTEM:"

300 PRINT" ODIC ".All "INCHES"

305PRINT" I DOC ". Bl» "I NCHES"

310 PRINT" TEM-MODE CHARACTERISTIC IMPEDANCE". Z 1» "OHMS"

315PRINT 318PRINT"FOR 2-PORT:

319 PRINT" ODIC "»A2» "INCHES"

320PRINT" I DOC ". B2l "INCHES"

325PRINT" LENGTH ".Ll "I NCHES"

330 PRINT" TEM-MODE CHARACTERISTIC IMPEDANCE". Z2l "OHMS"

335PRINT" DISCONTINUITY CAPACITANCE ", C5*P«A1*N1 1 "FARADS"

340PRINT" RELATIVE PERMITTIVITY OF AIR ",

E

345PRINT" I C RESISTIVITY ". P 1 J "OHM- CM. " 350PRINT" OC RESISTIVITY ", P2l "OHM-CM.

355PRINT

360 PRINT"DELTA F FOR CALCULATION OF GROUP DELAY".M3> "GHZ" 365PRINT

366PRINT

37 0PRI NT"FREOUENCY". "ATTENUATI ON", " ", "ARG( S2 1 ) ". "GROUP DELAY*

37 SPRINT" GHZ ". "DECI BELS". "MAG( S2 1 ) ". "DEGREES". "NANOSECONDS"

380PRINT

400FOR F=.l TO .5 STEP .01 410F1=F-M3 41SF2=F*M3 420W=V/(F*10t9)

425W1=W*F/F1

430W2=W*F/F2

435K1=N3*S0R(P1/F)

440K2=N3*SOR(P2/F)

445 A=2*P*F*( (K1/A2)+(K2/B2) )/(Nl*Z2) 450A6=2»A*L*N1 460A7=A6»N/2

465A8=A6*S0R(F1/F)

470A9=A6*SGR(F2/F)

47 5B5=2*P*F*C2*10t9

4S0E7 = Z2*B5

4S5E8=E7*(F1/F)

49 0E9=E7*(F2/F)

495B=4*P*L/W

500B3=B*W/W1

505B4=B*W/W2

600Q1=4»RI«( l-A6/2)*C0S(B/2)

60586= 4*R1*( l-A8/2)*C0S(B3/2)

610Q7=4*R1«( l-A9/2)*C0S(B4/2)

615H1=4*RI*( l-A6/2)*SIN(B/2)

620M1=SQR(G1 »2+Hl t2) 625D1=ATN(H1/Q1>

63002=- (( 1-R1) t2-E7»E7*R2)*( 1-A6) 63508 = - (( 1-R1 ) t2-E8*E8*R2)*( 1-A8) 64009=- (( 1-R1) t2-E9*E9*R2>*( 1-A9) 64503= (( l+RIl t2-E7*E7«R2)»C0S(B)

650D3=(( 1+R1) t2-E8*E8*R2)«C0S(B3)

655D4=(( 1+RI ) t2-E9*E9*R2)*C0S(B4)

660H6=G6*TAN(B3/2)

665H7=Q7*TAN( B4/2)

670 Q4=-2*E7*R1»( 1*R1)»SIN(B)

67 5D5=-2*E8*R1*( 1 + RI )«SIN( B3)

68 0D6*-2*E9*R1*< 1+RI )*SIN< B4>

68 5Q5=Q2+Q3*Q4

69 007= 08 +D3+D5

69 5D8 = Q9*D4*D6

700H3=(( 1+Rl)t2-E7*E7«R2)*SIN(B>

705JI=(( 1*R1) t2-E8*E8*R2)*SIN(B3)

710J2=<( l + Rl > »2-E9*E9*R2>*SIN(B4)

7I5H2=2*E7*RI«( l+Rl )+COS(B)

720H8=2*E8*RI*(1+R1)*COS<B3>

725H9=2*E9*R1*( 1+RJ )*COS( B4> 730H4=2*E7*R1*(R1-1>«( 1-A6)

735J3=2*E8*RI*(R1-1>«< 1-A8)

740J4=2«E9*R1*(R1-1)*C I-A9> 745H5=H2*H3*H4

750J5=H8+J1*J3

75SJ6=H9*J2+J4

760M2=SQR(Q5t2+H5t2)

765D2=ATN(H5/05)

770TI=D1*180/P

775J7=(Q6*D7*H6»J5)/<D7*D7*J5»J5)

78 0J8 = (Q7*D8+H7*J6)/(D8*D8*J6*J6)

78 5K3=(H6*D7-06*J5)/(D7*D7*J5*J5>

790K4=(H7*D6-O7*J6)/(D8«D8*J6*J6)

795T2=D2*180/P

800K5=ATN(K3/J7)

805K6=ATN(K4/J8)

8 10S=MI/M2

8 1 1T5=(20*LOG( 1/S))/C9 815IF (K6«K5)»2<1 TH EN 8 40 820IF K6*K5<0 THEN 830

825IF K6*K5>0 THEN 840

8 30K9=(K5+P-K6)/(4«P«M3)

835IF K6«K5<0 THEN 8 45

8 40K9=(K5-K6)/(4*P*M3)

841IF K5>K6 THEN 8 45 842K9=-K9

8 45Gl=(01»05*Hl*H5)/(05»05+H5*H5)

8 50G2=(H1*Q5-OI»H5)/(Q5*O5*H5*H5)

855G3=ATN(G2/GI

)

860T3=G3»180/P

865IF G1<0 THEN 880

870PRINT F.T5.S.T3.K9

875IF G1>0 THEN 88 5 880PRINT F.T5.S. T3+18 0.K9

88 5NEXT F 999END

54
Appendix ICS11

!CSI I 03:35 06/07/74

I REM 2REM INPUT DATA REQUIRED:

4REM 6REM FOR COAXIAL SYSTEM INTO WHICH 2-PORT IS INSERTEDl

7REM COAXIAL SYSTEM DESIGNATOR.,- LINE 250 RREM ODIC (INCHES) » LINE 205 Al I0REM IDOC (INCHES) LINE 215 HI I2REM FOR INCREASED ODIC 2-PORT STANDARD:

I4REM ODIC (INCHES) LINE 210 A£ I6REM IDOC (INCHES) LINE 220 B2 IHREM LENGTH (INCHES) i. LINE 225 L 20REM IC RESISTIVITY (OHM-CM.) LINE 230 PI 22REM OC RESISTIVI'TY (OHM-CM.) LINE 235 P2 24REM DISCONTINUITY CAPACITANCE DIVIDED BY CIRCUMFER26REM ENCE OF OC (FARADS/CM.) LINE 240 CI 28REM (NOTE THAT CI IS ASSUMED INDEPENDENT OF 30REM FREOUENCY AND IS NOT CALCULATED BY THIS PRO- 32REM GRAM BUT MUST BE OBTAINED BY OTHER MEANS)

34REM RELATIVE PERMITTIVITY OF AIR LINE 200 E 36REM FRECUENCIES (GH7) LINE 329 F 38 REM

40 REM 42REM CALCULATED PARAMETERS:

44REM

46REM TEM MODE 70 OF COAXIAL SYSTEM ( OHMS) . .L I NE305 71 «REM TEM MODE 70 OF 2-PORT (OHMS) LINE 310 72

50REM DISCONTINUITY CAPACITANCE ( FARADS )... .L I NE 360 C2 52REM DISCONTINUITY SUSCEPTANCE/Y 02 LINE 370 E7 54REM (NOTE THAT Y02=l/702>

56REM GUIDE WAVELENGTH (INCHES) LINE 330 W 53REM IC SKIN DEPTH (CM.) LINE 335 Kl 60REM OC SKIN DEPTH (CM.) LINE 310 K2

62REM ATTENUATION CONSTANT OF 2-P0RT( N/CM) . .L I NE 345 A 64REM (ATTEN. CONST .) *(LENGTH > (DB) LINE 355 A7 65REM RETURN LOSS (DB) CORRESPONDING TO SI I. .LINE 48 1 T5 66REM MAGNITUDE OF Sll LINE 430 S 6RREM ARGUMENT OF Sll (DEGREES) LINE 500 T3 70REM (NOTE THAT IF GK0 THEN T3-MS0)

I00P=3.I41 59265

105 C=2.99792S«1 0110

110N=f?.6KS«9 I1SN1=2.54

125 N3=.S/P

200E=1 .00064

205AI*. 24425

210 A2=.26S1 215PI=.S625

220B2=BI

225 L=l I. H 1 1 230PI=R/I0»6

235P2=PI

240 Cl=.569295/I0»15

245V=C/(N1«S0R(E) ) 2467 1=59.9 39 2«LOG( BI/AI)

24772= 59. 9392«L0G( B2/A2)

243 C9 = 2. 30258 5093 250PRINT"FOR 9/16 INCH (14 MM) COAXIAL SYSTEM:"

251PRINT" ODIC ".All "INCHES"

252PRINT" IDOC ", Bl I "INCHES"

253PRINT" TEM-MODE CHARACTERISTIC IMPEDANCE ",7ll"OHMS"

254PRINT 255PRINT"F0R 2-PORT:' 256PRINT" ODIC

tDOC LENGTH TEM-MODE CHARACTERISTIC IMPED DISCONTINUITY CAPACITANCE

RELATIVE PERMITTIVITY OF AIR

IC RESISTIVITY

OC RESISTIVITY

"RETURN LORS"»"

DECIBELS". "MAG( SI 1 )'

2S7PRINT"

25« PRINT" 259PRINT"

260 PRINT 261PR1NT"

262PRINT" 263PRINT"

264PRINT

31 5RI=71/72

320R2=RI t2 323PRINT 324PRINVFREQUENCY'

325PRINT" GH7 ". 326PRINT

329 FOR F=. 1TO.5STEP.0I

330 W=V/(F«l0t9)

335K1=N3*SQR(PI /F> 340K2=N3*SOR(P2/F>

34 5A=2»P*F«((KI/A2)*(K2/B?))/(NI«72>

350 A6=2»A«L*N1 35SA7=A6*N/2

360C2=P«BI«N1*CI

365 B3=2«P«F«C2» I0f9 370 E7=72«B3

375 B=4*P»L/W

3R0S5=SIN(B)

3«5C5=COS( P) 390A9 = 1-A6 39SC6=E7«E7«R2

400R3=( 1-R2»C6)*( I -A9«C5) 40SR4=-2«E7*R2«A9*S5

4I0R5=R3*R4

4151 l = -2«E7*R2«( l*A9»CS)

420I2=( l-R2*C6)«A9*S5

42513=1 1+12 430MI=SOR( R5i2*I 312) 435R6=( I »RI ) t2-C6

440R7=(( l-RI)t2-(E7»RI)t2)«C5 445R3=(2«E7*RI)«(1-R1)*SS

450R9=R6-A9«(R7-fR<?> 455I4=(2«E7*R1 )*( 1»RI ) 4601 5=R7«TAN( B) 4651 6=-2«E7*Rl«( 1-R1)*C5

4701 7= I 4*

(

l-A6>«( I 5*16)

47 5M2=SBR(R9 t2+I7tg)

4R0S =MI/M2

4R1T5=(20«LOG( l/S> )/C9

4R 5G I = ( R5* R9 I 3« I 7 > / ( R9« R9 I 7« I 7 > 49 002= ( I 3*R9-R5«I 7)/( R9«R9»I7«I7)

49SG3=ATN(G2/G1 ) 500T3=G3*I30/P

505IF Gl<0 THEN 520 510PR1NT F.TS.S.T3

5151F Gl>0 THEN 525 520PRINT F,T5,S,T3-H30

525NEXT F 999END

. A2l "INCHES'

, B2l "INCHES'

»Ll "INCHES"

.72) "OHMS"

CI«P*B1«NI) ' FARADS

,P1 1 "OHM-CM,

, P2l "OHM -CM.

"ARG(SI I 3REES"

55
Appendix ICS21

p-F* INFUT DATA RECUTRED:

fery FCR rnpXIAl iYiTE-< INTO WICH ?-POhl IS INSERTED: Sfm

ODIC COITAL

(INCHES, SYSTEM DESIGNATOR ^^A, LINE 135 Al ,n.r- rone unchesi line ,a ^ 1?HF « F«f -NCRFASF.D nr; tr p-PORT iTANDARDs

MKFm ODIC (INCHES, LINE

? I^F- rDor (INCHES, L NE 50 b? ,.MP LENGTH (INCHES, LINE 5b L

p(4m »C RESISTIVITY C0KM-CM.1 L Nt 60 P. POKFM n r RESISTIVITY (OHM-CM.) LIKE H5 Pd

P4REM DISCONTINUITY CAPACITANCE DIVIDED BY CIRCUMFEhP,cu EM FNCE OF OC (FARADS/CM., LINE I f» ~L CNOTE THAT C5 IS ASSUMED INDEPENDENT OF FRE3PKEM CUENCV AND lb NOT CALCULATED BY THIS FkO- *S ^»M TM* "UST RE OBTAINED BY «"»««««»_

3^EM RELATIVE PERMITTIVITY OF AIR LINE 130 E 36hEM FREQUENCIES (GH»> LINE 4PP

£r"e* DELTA F FOK GROUP DELAY C ALCUL AT I ON .

. .L I NE BOS M3 4PREM

41 REM 4PREM CALCULATED PARAMETERS: ""em TEM MODE 70 OF COAXIAL SYSTEM (OHMS*. .LINE JR* *l '„„ tfm MODE 'P OF P-PORT (OHMS) LINE IR5 ^

" . DISCONTINUITY CAPACITANCE ( FARADS, ... .L I NE ,9, C2 52KEM DISCONTINUITY SUSCEPT ANCE/Y 0? LINE 4« E7 S4REM (NOTE THAT Y0?=l/?P?>

l^REM GUIDE WAVELENGTH CINCHES,

^ W S9REM IC SKIN DEPTH (CM., L NE 43b

Af,REM OC SKIN DEPTH (CM., ."lU =.T tV

MfcEM ATTENUATION OF P-PORT ( DECI PELS , . • • -L I NE R 1

I T5 6PREM ATTENUATION CONSTANT OF P-PORT < N/CM , . . .L I NE 445 A 63REM (ATTEN. CONST ., .(LENGTH , —( DB, » » « "

64REM MAGNITUDE OF SP1 L ni >' 6AREM ARGUMENT OF SSI (DEGREES, LINE R 60 T3 6RREM (NOTE THAT IF GXP THEN T3+1R0)

70REM GROUP DELAY (NANOSECONDS, LINE R 30 K9 72REM (NOTE THAT IF K6*K5>0 THEN LINE LINE R40) 74REM

I00P=3. 1 41 59P65 |05C=2.997925*10Mfl

1 1 0N = « . 6R5H9

I 1SN1 = 2.54

125N3= .5/P

1 30E= I .00064 135A1=.244P5

140 A2=.2651 145B1=.5625

ISO BP=B1 I55L=30/N1

160 PI=R/I0t6

165 PP=PI

170 C5=. 569295/1 0'1S

175V = C/(N1 *SQR( E, , 1HP!7 1 = 59.9 39P«L0G( PI/AI , IR57?=59.9 39 2*L0G(FP/A2,

190 C2=P*B1*NI *C5 19SRI=7|/7?

?00R?=R1 t? 20SM3= .005 ?|0C9=2.30?SRS093

P96PRTNVF0R 9/16 INCH ( I 4 MM ) COAXIAL SYSTEM.

300 PRINT" ODIC

••; p,! "INCHES" 3lTpRINT" ^EM-MODE CHARACTERISTIC I MPEDANCE". Z 1 . "OHMS"

31 5PRINT 3|RPRINT"FOR P-PORT:"

A2. "INCHES"

3,9 PRINT" ODIC

..'feP •• NCHES"

3P0PR.NT" 1DOC

..'"f "INCHES" SS

PJKJtLE

TEM

T-MODE CHARACTERISTIC IMPEDANCE-.J8.-0HMS-,

335PRINT" DISCONTINUITY CAPACITANCE ". C5«P* E) I *N I

I FARAUS

340PRINT" RELATIVE PERMITTIVITY OF AIR '* E

„ nuM rM .. 345PRINT" IC RESISTIVITY .. 'pp Uhm CM " 350PRINT" OC RESISTIVITY "•Ml OHM-CM.

360

P PRi'nT"DELTA F FOR CALCULATION OF GROUP DELAY". M3l "GH I" 365PRINT

37CPr'inT"FRECUENCY". "ATTENUATION". " ". "ARG( S2I> ". "GROUP DELAY

375PRI NT" GH 7 ", "DEC! PELS". "MAGC SP 1 , ". "DEGREES". "NANOSECONDS"

TO .S STEP .01

(KP/PP, >/(N|*72,

3"=!0PRINT 4P0FOR F = . 1 ^1 0F 1 = F-"3 415F?=F+M3

4?(vj = V/( F* 1 0i9 , 425VM = W*F/FI

430H?=W«F/FP

435K1=N3*SCR(P1/F,

440K?=N3*SCR(PP/F,

445 A=P*P*F*( (K 1 ZAP, 45PA6=?«A«L«N1 46PA7=A6»N/P

4 ft SAR=A6.S0R(Fl/F,

47(?A9 = A6*S0R(F?/F, 475PS=P*P*F*CP* 1 0»9 4R0E7 = 7?*R5

4R5E* = E7*(F|/F>

49PE9=E7*(F?/F>

4Q5P=4*P*L/W

500B3=B*W/.V1 5P5P4=B*W/W2

6PPI01 = 4«R1*( l-A6/?,*COS(B/P,

605C6=4*R1*( i-AS/?,*COS(B3/P,

61P07=4*R1*. .-A9/P,*C0S(B4/P,

61 5H)=4*R1*( 1-A6/?,*SIN(B/P,

6P0M1=SCR(CI tP+Hl t?, 625D1=ATN(H1/C1 , 630G?=-(( 1-RI

,

»?-E7*E7*R2,*( 1-A6, 6350^ = -<< 1-Rl)t2-ER*ER*R2)*< 1 - AH

,

640Q9=-(( 1-RI, t2-E9«E9*R2,*( 1-A9, 64503= (( l*RI

,

t?-E7*E7«RP,*COS(B,

65003= (( 1+R1, »?-ER*E««RP>*COS(B3,

655D4=(( 1*R1>»2-E9*E9*R?,«C0S(B4,

660H6=Q6*TAN(B3/P,

665H7=07*TAN(B4/2,

67 fl Q4=-2*E7*R1*( 1 * R I ,*SIN(B,

67SDS=-2*ES*RI*( 1 *R 1 , SI N( B3, 6H0D6=-P*E9*R1*C 1*RI ,*SIN(B4,

6R5Q5=Q?*C3*C4

69007=0^+03+05

695DH = 09 + D4+D6 700H3=((1+RI,»?-E7*E7*RP,*S!N(B,

705ll=<< l+RI)»2-ER*ER«R2)*SINtB3)

710J2=(( 1+R1,»?-E9*E9*R?,*SIN(B4,

715H?=2«E7*RI*( l+R|,«C0S(B,

7P0K9=?*EH*R1*( 1+RI »«C0S<B3> 7P5H9=2*E9*R1*(I+R1,*C0S(B4,

730H4=2*E7*R1*(R1-1>*< I-A6, 735 J3=2*ER*R1*(R1- !,*( I-AR)

740I4=2*E9*R1*(RI-1 ,«( I-A9, 745H5=H2+H3+H4

750)5=HR+ 11+ J3 755 J6=H9+JP+ 14 760M2=SOR(O5tP+H5t2,

765D?=ATN(H5/05,

770T1=D1* 1R0/P

77 5J7 = (G6«D7 + H6* J5, /( D7«D7+ J 5* J5> 7H0 JR = <07*DR*H7*.I6)/CDR*DR + .J6*.)6) 7R5K3=(H6«D7-Q6*J5,/(D7«D7+ J 5*151

79 0K4=(H7*DH-O7* J6> /< DR«DB+.J6* J6> 795T2=D?*1R0/P

«00K5=ATN(K3/ J7, R05K6=ATN(K4/.JR,

R|0S=M1/M2

Rl 1T5=(?0*LOG( 1/S,,/C9 R15IF (K6*K5,'2<1 THEN R20IF K6*K5<0 THEN R 30 R25IF K6*K5>0 THEN R 40 R30K9=(K5+P-K6,/(4«P«M3,

R35IF K6«K5<0 THEN R45

C!40K9 = (K5-K6,/( 4*P*M3> R41IF K5>K6 THEN R45 R45G1=(Q1*Q5+HI*H5,/(Q5«Q5+H5«H5,

R50G?=(HI*O5-O1*H5,/(O5*Q5+H5«H5,

R55G3=ATN(G?/G1

,

R60T3=G3*|R0/P

R65IF Gl<0 THEN RR0

R70PRINT F.T5.S.T3.K9

R75IF G1>0 THEN RR

5

RR0PRINT F.T5.S.T3+IR0.X'' R«5NEXT F 999END

R40

56
Appendix WS11

WS1I 14157 06/04/74

2REM INPUT DATA REOUIREDt

4REM

6REM FOR WAVEGUIDE SYSTEM!

7REM WAVEGUIDE DESIGNATOR LINE

SREM INTERNAL WIDTH (INCHES) LINE

I0REM INTERNAL HEIGHT (INCHES) LINE

12REM

I4REM FOR REDUCED HEIGHT 2-PORTl

I6REM INTERNAL WIDTH (INCHES) LINE

ISREM INTERNAL HEIGHT (INCHES) LINE

20REM LENGTH (INCHES) LtNE

22REM RESISTIVITY (OHM-CM.) LINE

24REM RELATIVE PERMITTIVITY OF AIR LINE

26REM FREQUENCIES (GHZ)... LINE

2* REM 30REM

32REM CALCULATED PAhAMETERSl

34 REM 36REM GUIDE WAVELENGTH (INCHES) • LINE

3KREM NORMALIZED (TO Yd OF 2-PORT) SUSCEPTANCE

40REM OF DISCONTINUITY LINE

42REM NORMALIZED (TO Y0 OF WG SYSTEM) SUSCEPTANCE

44REM DIVIDED BY RATIO OF INTERNAL HEIGHT OF WG SYSTEM

46REM TO GUIDE WAVELENGTH LINE

4BREM SKIN DEPTH (CM.) LINE

. 50REM ATTENUATION CONSTANT OF 2-PORT ( DB/FT. > . . . .LINE

52REM ATTENUATION OF 2-PORT (DECIBELS) LINE

S3REM RETURN LOSS (DB) CORRESPONDING TO SI I LINE

54REM MAGNITUDE OF Sit LINE

56REM ARGUMENT OF Sll (DEGREES) LINE

SRREM (NOTE THAT IF Gl<0 THEN T3»I30>

60REMM

64 PO.I4IS926S

65C»2.997925«10t|0

70E*I.00064

7SAI=0.9 R0BI=0.4

R2A2«0.9

8SB2=0.09|f?

R7 L>.40S2

90 P|sR.S/|0i6

9 5N* 2*4. 342945

I00N1«2.54

I0SV»C/SOR(E)

II0V1=V/NI ll5N2n5.963

I20C9»2. 30253 S093

160 N3=.5/P

200PRINT"FOR WR-90 ( R- I 00) WAVEGUIDE SYSTEM!"

205PRINT" INTERNAL WIDTH ",AI I "INCHES"

2I0PRINT" INTERNAL HEIGHT ", Bl I "INCHES"

21 SPRINT 220PRINT"FOR 2-PORTt"

225PRINT" INTERNAL WIDTH ",A2l "INCHES"

230PRINT" INTERNAL HEIGHT "» B2) "INCHES"

235PRINT" LENGTH "»LI "INCHES"

240PRINT" RESISTIVITY ". PI I "OHM-CM.

24SPRINT" RELATIVE PERMITTIVITY OF AIR ". E 2S0V«C/(NI*SOR(E>) S55RUBI/B2

260R2iRlt2

29SPRINT

300PRINT 30SPRINT"FREGUENCY"# "RETURN LOSS"." ". "ARG( S I I )

310PRINT" GHZ ". "DEC! BELS","MAG( SI I) "."DEGREES"

200

7S Al RO Bl

R2 A2 15 B2 <n l 90 PI 70 E 320 F

5B0 W 685 E7

69 ER 325 HI 600 A5 607 A7 506 15 50S S 525 T3

315PRINT

380FOR F«B TO 13 STEP .1 32SKI=N3«SGR(PI/F>

405GOSUB 560

410

420 B«4*P*L/W

425 R3=( l-R2*(E7»2)»R2)»( l-( l-A6)»C0S( B)) 430R4«-2«E7«R2*( l-A6)*SIN(B) 43SR5=R3*R4

4401 1»-2«E7»R2*( l*C l-A6)*C0S(B>>

445 I2=( 1-R2»E7«E7«R2>*( l-A6)«SIN(B) 45013=11*12 455MI=S0R(RSt2»|3«2)

460R6i( l*RI

)

!2-(E7t2)«R2

465 R7=(( l-RI) »2-(E7«RI) »8)»C0S(B)

470RB = (2*E7«RI>«( I-R1)*SIN(B>

475R9«R6-( 1-A6)«(R7»RB)

480I4«(2*E7«RI )«( I»R1)

43 S I5=((l-RI)»2-(E7«RI)t2)»SIN(B)

490I6*-a«E7»RI*( I-R1)*C0S(B)

49 51 7= I 4* ( l-A6)»(IS*I6)

500M2=SGR( R9 «2*l 7 t2) 50SS=MI/M2

506T5=(20«LOG( 1/S) )/C9

510 Gl=(R5«R9»I3«I7)/(R9«R9*I7«I7>

515 G2»(I3«R9-RS«I7)/(R9*R9*I7«I7>

520 G3=ATN(G2/GI

)

525 T3«G3»IB0/P

530 IF Gl<0 THEN 545

S35 PRINT F.T5.S.T3

540 IF Gl>0 THEN 550

54S PRINT F»T5.S»T3*|R0

S50NEXT F S55END

560LI°SGR(E)

565L2=C/( I0t9) 570L3=(NI*F«LI/L2) t2 575L4»( 1/(2*A1>> »2 W0W=I/SQR(L3-L4)

SB 5 A2«l/L3

590 A3=SGR(SQR(A2>)

S9SA4=N2*SQR(P1 > 600 A5=((A4/A3)«(( l/B2)*A2/(2»AI t3)))/SGR( l-A2/( (2«AI ) >2>) 605 A6=(L/(6»N))»A5

607 A7=A6»N

610DI=B2/BI 6I5D2e(4»DI/( l-DI t2))t2

620D3»(( l*DI)/( l-DI)) K2/DI)

62504= ( l»SQR( l-((B2/W) t2)))/( |-SGR( l-((B2/W) »2>>> 630D5=D3«D4»(3*(D1> t2)/( |-(D1) t2) 63SD6=D3t((DI) !2> 640D73(|*SOR( l-(BI/W)»2)>/( l-SOR( l-(BI/W) »2>> 645D8»D6«D7-( I +3»( Dl «2> >/( I -( D I > t2) 65009= (( l-DI t2)/(4»DI))«(( l*DI)/( l-DI)) t(( l/2)»(DI*l/DD)

65SE1»L0G(D9) 660ES=2»(DB*D5*2«D2)/(DB*D5-D2t2)

665 E3=((B!/(4*W>) t2>»(( 1-DI)/(1*DI))»(4«DI)

670E4=((5*(Dlt2) )-!>/( l-DI t2> 67SE5=(4»(DI t2)»D2)/(3»D8) 6B0E6«E3*(E4»ES> >2 6B5E7=2»(E1*E2*E6>«(B2/W>

6X6 E7=1.04«E7

69 0E8 = E7*W/B2

695RETURN

57
WS21 I Si 16 06/04/7 4 Appendix WS21

I0REM INPUT DATAi

I2REM

I3RE* WAVEGUIDE DESIGNATOR LINE 200

I4REM FOR WAVEGUIDE SYSTEMl

I6REM INTERNAL WIDTH (INCHES) LINE 100 A| IBREM INTERNAL HEIGHT (INCHES) LINE 105 Bl 20REM

22REM FOR 2-PORTl ?«REM INTERNAL WIDTH (INCHES) LINE I I A2

26REM INTERNAL HEIGHT (INCHES) LINE IIS B2 2RREM LENGTH (INCHES) LINE I 20 L 3PREM RESISTIVITY (OHM-CM.) LINE 125 PI 32REM RELATIVE PERMITTIVITY OF AIR LINE 130 E 34REM 36REM FREQUENCIES (GHZ) LINE 300 F 38REM DELTA F FOR CALCULATION OF GROUP DELAY LINE 135 D 40REM 42REM

44REM CALCULATED PARAMETERSl

46REM «REM MAGNITUDE OF S21 LINE 39 5 S S0REM ARGUMENT OF S2 1 (DEGREES) LINE 415 T3

Sj REM ALSO LINE 475 T3*I8C

54REM GROUP DELAY (NANOSECONDS) LINE 43SK9

S6REM ALSO LINE 445 K9 c^rEm ALSO LINE 455 -K9 60REM GUIDE WAVELENGTH (INCHES) LINE 1010 W 62REM SHIN DEPTH (CENTIMETERS) LINE 43 XI 64REM ATTENUATION OF 2-PORT (DECIBELS) LINE 39 6 T5 65REM ATTENUATION CONSTANT OF 2-PORT ( DB/FT. ) . . . .L INE 1030 A5

66REM ATTENUATION CONSTANT*LENGTH (DECIBELS) LINE 1125 A7 68REM NORMALIZED (TO Y0 OF 2-PORT) SUSCEPTANCE

7PREM OF DISCONTINUITY LINE 1115 E7 72REM NORMALISED (TO Y0 0F WG SYSTEM ) SUSCEPTANCE

74REM OF DISCONTINUITY DIVIDED BY RATIO Bl/W ....LINE 1120 E8 76REM m REM 80REM

100AI=0.9 10561=0.4

I I0A2=0.9 I15B2=0.09I8 I20L=0.4052

125 Pl=8. 5/1016

I30E= I .00064 13SD=0.05

I40P=3. 14159265

I45N=B.68S89 IS0NI=2.54

I55N2=5.963 I60N3=0.S/P

I 6 SC= 2. 99 79 25* I 0t 10 170RI=BI/B2

17SR2=RI 12 l«0LI = SGR( E) I85L2=C/10»9

190C9 = 2. 30258 5093 200PRINT"FOR WR-90 (R-100) WAVEGUIDE SYSTEMl"

20SPRINT" INTERNAL WIDTH ", Al I "I NCHES"

210PRINT" INTERNAL HEIGHT ". Bl I "I NCHES"

215PRINT 220PRINT"FOR 2-PORTt"

225PRINT" INTERNAL WIDTH ", A2l "INCHES"

230PRINT" INTERNAL HEIGHT ", B2l "I NCHES"

235PRINT" LENGTH ",L« "I NCHES"

240PR1NT" RESISTIVITY ". PI I "OHM-CM.

245PRINT" RELATIVE PERMITTIVITY OF AIR ",E 2S0PRINT 25SPRINT"DELTA F FOR CALCULATION OF GROUP DELAY". D> "GHJ " 260PRI NT 265PRINT

270PRI NT"FREOUENCY"» "ATTENUATI ON". " ". "ARG( S2 I ) ". "GROUP DELAY"

?7 5PRI NT" GHZ ". "DEC I BELS". "MAG( S2 I ) ". "DEGREES". "NANOSECONDS"

280PRINT

300FOR F=8 TO 13 STEP 0.1 30IF l=F-D 302F2=F»D

305GOSUB 1000 3I0B=4»P»L/W

31 I63=4«P«L/Wl 3I2P4=4«P«L/W2

}|S0|s4*RI*< 1-A6/2)«C0S(6V2>

3I606=4»RI«( l-AR/2)«C0S(63/2>

3I707=4«KI*< I -A9/2)«C0S( 64/2)

320H1 = 4«RI (l-A6/2)«SIN(6/2)

32IH6=4»RI»(l-A8/2)»SIN(63/?>

322H7 = 4«R1 •( 1-A9/2)«SIN( B4/2) 325M1»S0R(C1 »2.HI >21 330M3 = ATN(HI/CI ) 33SG2=-((I-RI)»2-E7«E7«R2)»(1-A6>

33608 =-( (I-Rl)i2-F3«F3»R?)»(1-A">

337Q9«-(

(

I-Rl)t2-F4«F4»R2>«( I-A9) 3400 3»(< l»RI)>2-E7«E7«R2)«CnS(B) 34IR3=((I»RI)>2-F3«F3«R2>«CCS(63>

342R4=((l»RI)t2-F4«F4«R2)»C0S(F4)

34504= -2«E7«R1«( l»RI)»SIN(B)

346R5=-2«F3«R1 • ( I h I )'«S1 N( B3) 347R6=-?«F4«RI«( 1»RI)«SIN(B4> 3S0O5=C2»Q3*Q4

351 R7 = 08»R3»RS

352R« = Q9»R4.R6

3SSH3=C3»TAN( B>

356JI=R3«TAN( B3) 3S7J2"R4«TAN(E4>

360H2»-G4/TAN( B) 36IHS*-RS/TAN(B3>

362H9=-R6/TAN(B4) 365H4=2»E7«RI«(R1- !)•( 1-A6) 366J3=2«F3»RI«(RI- I >•( I-A8) 367J4.2»F4«RI«(F1-I)«( I-A9)

37 0HS*H2»H3*H4

371 J5=H8»J1«J3

372J6=H9* J2*J4

37 5M2=S0R(Q5»2»H5t2)

38 0M4=ATN(HS/C5) 3BSTI=M3«I80/P

390T2=M4«IB0/P

39SS=MI/M2

396T5=(20«LOG( 1/S) )/C9 400G1=(G1«Q5»H l«H5)/(Q5i2*H5t2>

401 J7>(G6«R7»H6«J5)/(R7f2»J5l2>

402J8 = (G7«R8»H7»J6>/( RB >2*J6»2> 405G2=(HI«Q5-QI»H5)/(Q5t2*H5t2>

406K3=(H6«R7-Q6«JS)/(R7»2»J5t2>

407K4=(H7*R8-O7«J6)/(R8»2*J6»2)

4I0G3=ATN(G2/GI ) 41 1K5=ATN(K3/J7>

4I2K6= ATN(K4/J8) 4I5T3=G3*180/P

4201 F (K6«K5)t2 <| THEN 445 425IF K6»K5<0 THEN 43S

430IF K6»KS>0 THEN 445 435K9=(K5+P-K6>/( 4«P«D>

4401 F K6«K5<0 THEN 460 445K9=(KS-K6>/( 4*P*D)

450IF KS>K6 THEN 460 455K9=-K9

460IF Gl<0 THEN 475 465PRINT F.T5.S.T3.K9

470IF G1>0 THEN 480 475PRINT F,TS»S»T3*I80.K9

48 0KI«N3*SQR(PI/F>

48 5NEXT F 999 END I000L3=(N1«F«LI/L2) 'S I00IL5=(NI«FI*LI/L2) »2 I002L6=(NI«F2«L1/L2> t2 1005L4=( I /( 2«AI > ) »2 I0I0W= l/SQR(L3-L4)

101 IW1=I/SQR(L5-L4>

10I2W2=1/SOR(L6-L4)

I0I5M5*I/L3 I016M6=I/L5

I0I7M7=1/L6

1020A3=SQR( SQR(M5»

)

1021S!=SQR(SSR<M6>>

I022S2=SGR<SQR(M7>>

I025A4*N2»SQR(PI

)

I030A5=((A4/A3>«(( l/B2)»M5/(2«AI t3)))/S0R( l-MS/( ( 2»AI ) t 2)

)

I03IS5=((A4/SI >«(( 1/B2)*M6/(2«A1 <3>>)/S0R( l-M6/( ( 2»A I ) t2)

>

1032S6=(( A4/S2)«(( l/B2)*M7/(2*AI »3)))/S0R( I -M7/( ( 2«AI ) »2>

)

1035A6=(L/(6»N))»A5

l036A8=(L/( 6«N) )»S5 1037A9=(L/(6»N))«S6

I040D1=B2/BI IB45D2=(4»DI/( 1-DI t2») t2 I050D3*(( l*DI )/( l-DI )

)

»(2/DI ) I055D4=( 1»SGR( 1-((B2/W) t2)))/( |-SOR( 1 -( ( B2/W) »2) >

)

I056S7«( 1*SQR( l-((B2/WI ) t2)))/( l-SGR( 1-((B2/WI) 12) )) I057S8=( l*SQR< l-((B2/W2) t2)))/(|-SGR( I -( ( B2/W2) 1 2) )> I060DS=D3«D4*(3*DI i2)/(l-D|i!)

I06IP3=D3»S7*(3»D| t2)/(l-D|t2>

I062P4=D3»S8*( 3»D1»2)/<1-D1»2)

I065D6 = D3K(DI )»2> 1070D7=( l»SGR( l-CBl/W) l2))/( l-SQR( l-(BI/W> »2)> 107IP7 = ( l*SOR( 1-(BI/WI ) »2))/( 1-SQR( I - ( B 1/W I ) t 2)

)

107 2PB = ( t»SQR( l-(BI/W2) l2>)/( 1-SQR( I -( Bl /W2> 1 2) ) !07 5D8=D6»D7-( I *3«< Dl t2> >/t l-DI »2>

!07 6K7=D6»P7-( l»3«(D|t2))/(|-DI»2)

107 7K8 = D6«P8-( I«3»(DU2)>/(I-D|t2>

108 0D9 = (( |-DI»2)/(4«DI>>«(<I»DI>/(I-DI>>»((1/2>«(DI*I/D1>>

108 5Et=LOG(D9)

109 0E2=2»(DS*D5»2«D2>/( D8«D5-D2t2) I09IB7=2«(K7»P3»2»D2)/(K7«P3-D2t2)

I092B8 = 2»(K8*P4»2«D2)/(K8»P4-D2»2>

109SE3=((BI/(4»W) )t2)«((l-DI)/(l*Dl))»(4«DI)

I096CI=(( BI/( 4»W1 )

)

»2>«(( l-DI >/( I *DI )) '( 4»DI

>

I 09702= ((BI/(4«W2))t2)«(( l-DI )/(l»DI))t<4«DI) H00E4=((5»(D|t2))-|)/(l-DU2>

I 105E5=(4«(DI ?2>»D2>/( 3«D8>

I I06C5=(4«(DI t2)«D2)/(3«K7>

I I07C6=( 4»(DI »2)«D2)/< 3«K8)

I I I0E6=E3»(E4»E5) t2

II I 1C7 = CI*(E4*CS) »2

I I I2C8=C2»(E4»C6) »2

I 1 I5E7 = 2«(EI*E2*E6)«(B2/W)

II I6F3=2«(EI*B7»C7)«(B2/W1 ) II I7F4=2«(EI»B8»C8)«(B2/W2)

1118 E7=I.04«E7

1 I 19 F3=I.04«F3

I I20E8 = E7«W/B2

1121 F4=I.04«F4

I 125A7=A6«N/2

I I30RETURN

58
I DOC

2REM

4REM 6REM

8 REM I0REM 12REM

14REM I6REM

18 REM

19REM 20REM

22REM 80AI=. 24425

85B1=.5625

90A2=. 24425

9 5ZI=59.9 392*L0GCB1/A| ) 100PRINT"FOR 9/16-INCH (14 MM) COAXIAL SYSTEM:"

I05PRINT" ODIC ",All"INCHES"

110PRINT" IDOC ",B1» "INCHES"

112 PRINT" TEM-MODE CHARACTERISTIC I MPEDANCE", 7 1 j "OHMS"

1 15PRINT

120PRINT"FOR 2-PORT:"

09:38 06/04/74 Appendix IDOC

INPUT DATA: MAGCSII) LINE 160 S COAXIAL LINE DESIGNATOR LINE 100 IDOC OF COAXIAL SYSTEM LINE 110 Bl CINCHES) ODIC OF COAXIAL SYSTEM LINE 105 Al CINCHES) CALCULATED PARAMETERS: RETURN LOSS LINE 200 R2 CDB) VSWR LINE 165 R TEM-MODE CHARACTERISTIC I MPEDANCE. . .LINE 175 Z2 (OHMS) REDUCED IDOC OF 2-PORT LINE 180 B2 CINCHES)

125PRINT"

130PRINT

135PRINT

140PRINT"

145 PRINT"

ODIC ",A2| "INCHES"

", "RETURN", " ", "Of ARACTERI STI C", "REDUCED"

"," LOSS "»" "."IMPEDANCE"," IDOC" 150PRINT"MAGCS1 1 ) ", "DECI BELS", "VSWR", " OHMS "."INCHES"

155PRINT

160 FOR S=0 TO 0.95 STEP 0.05

165R=( l+S)/( 1-S)

170R1=SQR(R)

175 Z2=Z1/R1

180 B2=A2*EXP(Z2/59.9392)

185C1 = 2. 30258 5093

19 0R2=0

195IF S=0 THEN 210

200R2=(20*LOG< 1/S) )/Cl

2051 F S>0 THEN 220 210PRINT S, "INFINITY", R,Z2,B2

215 IF S=0 THEN 225

220 PRINT S,R2,R,Z2, B2 225NEXT S 999END

READY

RUN IDOC 09:40 06/04/74

FOR 9/ 16- INCH (14 MM) COAXIAL SYSTEM: ODIC

IDOC TEM-MODE CHARACTERISTIC IMPEDANCE

.24425 INCHES .5625 INCHES 50.0012 OHMS

FOR 2-PORT: ODIC .24425 INCHES

RETURN CHARACTERISTIC REDUCED

LOSS IMPEDANCE IDOC MAGCS1 I) DECIBELS VSWR OHMS INCHES

INFINITY 1 50.0012 .5625

.05 26.0206 1. 10526 47.5606 .540056

. 1 20. 1.22222 45.2278 .519441

.15 16.4782 1.35294 42.9874 .50038 4 .2 13.9794 1.5 40.8258 .48266

.25 12.0412 1.66667 38.7308 .46608

1

.3 10.4576 1.85714 36.6909 .45048 6 .35 9. 1 1864 2.0769 2 34.6953 .435735

.4 7.9 588 2.33333 32.7335 .421704

.45 6.93575 2.63636 30.79 48 .408 283

.5 6.0206 3. 28.8682 .39 53 68 .55 5. 19275 3.44444 26.9414 . 38 28 6

1

.6 4.43698 4. 25.0006 .370662

.65 3.74173 4.7 1429 23.0289 .358 668

.7 3.098 04 5.66667 21.0047 .346758

.75 2.49878 7. 18.8987 .33473 5 .8 1 . 9 38 2 9. 16.6671 .32255

.35 1.41 162 12.3333 14.2377 .309 738

.9 .91515 19. 1 1.471

1

.295767

.95 .445528 39. 8.00661 .27915'

59
odic 09:44 P6/R4/74 Appendix ODIC

?REM INPUT DATA:

4REM MAGCS11) LINE 160 S 6REM COAXIAL LINE DESIGNATOR LINE 100 8REM IDOC OF COAXIAL SYSTEM LINE 110 Bl CINCHES)

1CREM ODIC OF COAXIAL SYSTEM LINE 105 Al CINCHES)

12REM

14REM CALCULATED PARAMETERS:

I6REM RETURN LOSS LINE 200 R2 COB) 1RREM VSWR LINE 165 R I9REM TEM-MODE CHARACTERISTIC IMPEDANCE. . .LI NE 17S £2 COHMS) 2PREM INCREASED ODIC OF 2-PORT LINE 180 A2 CINCHES)

22REM 80A1=.2442S

*5BI=.5625

90B2=.S625

9 5?1=59.9 39 2*L0GC Bl/Al

)

100PRINT"FOR 9/16-INCH C14 MM) COAXIAL SYSTEMt"

105PRINT" ODIC ", AU"INCHES"

1I0PRINT" IDOC ",B1J "INCHES"

112 PRINT" TEM-MODE CHARACTERISTIC IMPEDANCE", 7 ]

j "OHMS"

1 15PRINT

120PRINT"FOR 2-PORT:"

I2S PRINT" IDOC ",B2j "INCHES"

I30PRINT

135PRINT

140PRINT" ", "RETURN"," ", "CH ARACTERI STI C", "I NCREASED"

145PRINT" "," LOSS"," ", "IMPEDANCE", " ODIC"

150PRINT"MAGCS1 1)","DECI BELS", "VSWR", " OHMS "."INCHES"

15SPRINT

160 FOR S=0 TO 0.95 STEP 0.05

165R=C 1*S)/C I-S)

170R1=SQRCR)

175 Z2=Z1/R1

18 0A2=B2/CEXPCZ2/59.9 39 2)) 185C1 = 2. 30258 5093 190R2=0

195IF S=0 THEN 210 200R2=C20*LOGC 1/S) )/C1

205IF S>0 THEN 220

210 PRINT S, "INFINITY", R.Z2.A2

215 IF S=0 THEN 225

220PRINT S,R2»R,Z2,A2

225NEXT S 999END

READY

RUN

ODIC 09: 47 06/04/7 4 FOR 9/16-INCH CI4 MM) COAXIAL SYSTEM: ODIC

IDOC TEM-MODE CHARACTERISTIC IMPEDANCE

.24425 INCHES

.5625 INCHES 50.0012 OHMS

FOR 2-PORT: IDOC .5625 INCHES

RETURN CHARACTERISTIC INCREASE LOSS IMPEDANCE ODIC

MAGCS1 1) DECIBELS VSWR OHMS INCHES INFINITY 1 50.0012 .24425

.05 26.0206 1.10526 47.5606 .2544

.1 20. 1.22222 45.2278 .26449 7 .15 16.478 2 1.35294 42.9874 .27457

.2 13.9794 1.5 40.8258 .28 4653

.25 12.0412 1.66667 38.7308 .294778

.3 10.4576 1.85714 36.69 09 .30498 3 .35 9. 1 1864 2.07692 34.6953 .315308

.4 7.9 588 2.33333 32.7335 .325799

.45 6.93575 2.63636 30.7948 .336508

.5 6.0206 3. 28.8682 .347501

.55 5. 19275 3.44444 26.9414 .358853

.6 4.43698 4. 25.0006 .370662

.65 3.74173 4.71429 23.0289 .38 3058

.7 3.09804 5.66667 21 .0047 .396215

.75 2.498 78 7. 18.8987 .41038 4

.8 1.9382 9. 16.6671 .425951

.85 1.41 162 12.3333 14.2377 .44357

.9 .91515 19. 1 1 .471 1 .464524

.95 .445528 39. 8.00661 .492164

60
HR 09:32 06/04/74 Appendix HR

2REM INPUT DATA:

4REM MAGCS11) LINE 150 S 6REM WAVEGUIDE DESIGNATOR LINE 100 8REM NOMINAL HEIGHT OF WG SYSTEM LINE 95 HI (INCHES)

9REM NOMINAL WIDTH OF WG SYSTEM LINE 90 W CINCHES)

10REM

12REM CALCULATED PARAMETERS:

14REM RETURN LOSS LINE 175 R2 (DB)

16REM VSWR LINE155 R 18REM REDUCED HEIGHT OF 2-PORT LINE 165 H2 (INCHES)

20REM

9 W=.9

95 Hl = .4 100PRINT"FOR WR-90 (R-100) WAVEGUIDE SYSTEM:"

105PRINT" INTERNAL WIDTH ", WJ "I NCH ES" 110PRINT" INTERNAL HEIGHT ",H 1 I "INCHES"

115PRINT

120PRINT"FOR 2-PORT:"

125PRINT" INTERNAL WIDTH ", W; "INCHES"

130PRINT

135PRINT

140 PRINT" ", "RETURN", " ", "REDUCED"

142 PRINT" "," LOSS "," "."HEIGHT"

144 PRINT"MAG< SI 1 ) ", "DECIBELS"," VSWR", "INCHES"

145 PRINT

150 FOR S=0 TO 0.95 STEP 0.05

155R=( 1*S)/C 1-S)

160R1=SQR(R)

165 H2=H1/R1

170C1=2. 30258 5093

172 R2=0

173 IF S=0 THEN 180

175 R2=(20*LOG( l/S))/ei

176 IF S>0 THEN V8 2 180 PRINT S, "INFINITY", R,H2

181 IF S=0 THEN 185

182 PRINT S, R2, R,H2

185NEXT S 999END

READY

RUN HR 09:34 06/04/74

FOR WR-90 (R-100) WAVEGUIDE SYSTEM: INTERNAL WIDTH .9 INCHES

INTERNAL HEIGHT .4 INCHES

FOR 2-PORT: INTERNAL WIDTH .9 INCHES

RETURN REDUCED

LOSS HEIGHT

MAGtSl 1) DECIBELS VSWR INCHES INFINITY 1 .4 .05 26.0206 1. 10526 .380476

.1 20. 1.22222 .361814

.15 16.478 2 1.3529 4 .343891

.2 13.9794 1.5 .326599

.25 12.0412 1.66667 .3098 39

.3 10.4576 1.85714 .29352

.35 9. 1 1864 2.07692 .277555

.4 7.9 588 2.33333 .261861

.45 6.93575 2.63636 .246353

.5 6.0206 3. .23094

.55 5.19275 3.44444 .215526

.6 4.43698 4. .2 .65 3.74173 4.7 1429 . 184226

.7 3.098 04 5.66667 . 168034

.75 2.49878 7. .151 186

.8 1 . 9 38 2 9. . 133333

.8 5 1.41 162 12.3333 . 1 13899

.9 .91515 19. 9. 17663E-2

.95 .445528 39, 6.40513E-2

61
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS TN-657

2. Gov't Accession

No.

3. Recip 1 nt s Accessu o.

4. TITLE AND SUBTITLE

Calculated and Measured S , S__ , and Group Delay for Simple

Types of Coaxial and Rectangular Waveguide 2-fiort Standards

5. Publication Date December 1974

6. Performing Organization Code

7. AUTHOR(S)

R. W. Beatty

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF ST/^DARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2761125

11. Contract/Grant No.

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

Same as Item 9

13. Type of Report & Period

Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

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

bibliography or literature survey, mention it here.)

Formulas, simple computer programs, graphs and tables are given to aid in the

design and construction of 2-port standards for rectangular waveguide and coaxial line.

Only standards consisting of reduced height waveguide, increased ODIC (outside diameter

of inner conductor) , or reduced IDOC (inside diameter of outer conductor) coaxial line

are considered. Examples of the calculation of S^, S21 and group delay, and their

measurement with automatic network analyzers are given. Some of the important sources

of error in the standards are discussed and design data are presented for specific

standards.

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

Automatic network analyzers; coaxial; coaxial line step discontinuities; group delay;

scattering coefficients; standards; 2-ports; waveguide; waveguide discontinuities.

18. AVAILABILITY py

1 Unlimited

2 For Official Distribution. Do Not Release to NTIS

J Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C13

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67

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