Davis W.A.Radio frequency circuit design.2001

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 C

Double-Tuned Matching Circuit

Example

Assume that an impedance transformation is required between a 50 source and a 15 load. The matching is to be done using the double-tuned matching circuit described in Chapter 3 for the program DBLTUNE. The center frequency is at 4 MHz, the bandwidth is 100 kHz, and the pass band ripple is 0.5 dB. The capacitances and transformer parameters are to be determined. In the following computer output, the bold characters are the responses the program expects from the user. Furthermore, in this example, the verbose mode is chosen by choosing to display the intermediate results. An analysis of this circuit using SPICE is shown in Fig. C.1.

Display intermediate results? < Y/N > Y Center Freq, Bandwidth (Hz) = ? 4.E6, 100.E3 Fm1 = 0.396480E+07 Fm2 = 0.403551E+07

GTMIN = 0.99992E+00

Passband ripple in dB = ? 0.5 Resistance Ratio r = 0.19841E+01

Q2 m1 = 0.97432E+00 Q2 m2 = 0.10097E+01

Generator and Load resistances values = 50., 15. L2’ = 0.56259E+02 H C2’ = 0.28140E+02pF

RL’ = 0.79332E+05 Bm1 = 0.19480E-01 Bm2 = -0.20193E-01 Given terminal resistances: RG = 0.500E+02 RL

= 0.150E+02

Input Circuit: C1 = 0.446554E+05pF L11 = 0.354637E-01 H Output Circuit: C2 = 0.148828E+06pF L22

= 0.106441E-01 H

Transformer coupling coefficient k = 0.250991E-01

290

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.

292

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.

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 E

Termination of a Transistor Port

With a Load

In the three-port circuit in Fig. E.1, one of the three ports is terminated with an impedance that has a reflection coefficient relative to the reference impedance

Zref:

In this expression the subscript i represents s, g, or d depending on whether the device connection is common source, gate, or drain terminated with Zs, Zg, or Zd. The incident and scattered waves from the three-port is

When one of the ports is terminated with ri, then the circuit really is a two-port. The scattering parameters for the common source, gate, and drain connection is shown below:

Common source

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