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Design of Microwave Active Devices by Jean-Luc Gautier

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Appendix 7

Graphical Method

The scattering matrix of a two-port network with series or parallel feedback (Figures A7.1(a) and A7.1(b)), or a three-port network with a port closed by impedance (Figure A7.1(c)) can be expressed in the following general form:

images

Figure A7.1. Feedback topologies

a7-fig-001

In the above figure, z, y and T are, respectively, the impedances, admittances and normalized reflection coefficients in relation to the S matrix reference impedance, which is assumed to be identical for all the ports.

The various coefficients are given by the following relationships:

– parallel feedback:

images

– series feedback:

images

– three-port networks:

images

A7.1. Constant SijT modulus and argument circles

images

If we take the squared value of this equation, after a few calculations, the resulting expression is:

The above equation is that of a circle of center O1 and radius R1.

As changes from ο to ∞, the circles, ...

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