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:
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:
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, ...