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Input stability circle

The input reflection coefficient of a loaded two-port network is given by


displaymath3033
One of the criteria for the loaded two-port network to be unconditionally stable is that text_wrap_inline3035. We are going to find out what kind of load text_wrap_inline2885 will give the network to the boundary of stability represented by text_wrap_inline3039.
eqnarray711
The condition can be rearranged as
equation719
which is an equation of a circle on text_wrap_inline2885 complex plane with
equation728

equation734

equation741