Explicit expressions of the unconditional stability boundaries of a three-port network

An analytical approach for acquiring the explicit expressions of the boundaries concerning the unconditional stability regions of a three-port network is presented. This approach begins with the expressions of the input reflection coefficients at the ports 1 and 2 with a terminating port 3 to give two stability circles in the terminating plane. One can graphically determine that the tangent point of these two stability circles is on the boundary of the unconditional stability region for the terminating port. Then, the explicit boundary expression for the port 3 is derived. This procedure may be followed for the other two ports in order to fully characterize the unconditional stability boundaries of a three-port network. Using the Agilent ADS software tool, the derived expressions are implemented. These expressions can not only enhance the computer-aided capability on the stability analysis of a three-port network but also provide useful information for the microwave circuit designers.