Appendix D.Two-port parameter conversion

Radio Frequency Circuit Design. W. Alan Davis, Krishna Agarwal

Copyright 2001 John Wiley & Sons, Inc.

Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9

APPENDIX D

Two-Port Parameter Conversion

D.1 TWO-PORT VOLTAGE AND WAVE PARAMETERS

Conversion between the z, y, h, and g two-port voltage-current parameters is simply rearrangement of two linear equations relating voltages and currents at the two ports. Converting between these and the S parameters requires relating the voltage waves to voltages and currents. This latter relationship always includes the characteristic impedance, Z0, by which the S parameters are defined. Typically this value is 50 . Table D.1 shows this conversion. The program PARCONV is basically a code of many of the conversions in Table D.1.

The definitions of the various two-port parameters are described below. In each case it is assumed that the current is flowing into the port terminal.

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294 TWO-PORT PARAMETER CONVERSION

For conversion to and from S parameters for circuits with more than two ports, the following formulas may be used [1]. Each variable is understood to be a matrix representing the S, z, or y parameters. The conversion formulas are

The I in Eqs. (D.8) through (D.10) is the square identity matrix, and the Z0i, i D 1, . . . , n, are the characteristic impedances associated with each of the ports. An example of the usage of PARCONV is shown below. In using the program make sure to include the decimals with the input data. The bold values represent user inputs to the program. To exit the program, use Ctrl. C.

TYPE SOURCE AND LOAD REFERENCE IMPEDANCE Z01,Z02 =

50.,50.

Y --> S = YS OR S --> Y = SY

Z --> S = ZS OR S --> Z = SZ

ABCD --> S = AS OR S --> ABCD = SA H --> S = HS OR S --> H = SH

H --> Z = HZ OR Z --> H =ZH

SY

INPUT S11, MAG. AND PHASE (deg)

.9,-80.

INPUT S21, MAG. AND PHASE (deg)

1.9,112.

INPUT S12, MAG. AND PHASE (deg)

.043,48.