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 for the input reflection coefficients
S

₁₁

^'
and
S

₂₂

^'
at ports 1 and 2 of a three-port network having port 3 terminated with ¿
₃
. |
S

₁₁

^'
| = 1 and |
S

₂₂

^'
| = 1 then give two stability circles in the ¿
₃
-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. The explicit expressions of the boundary for port 3 are then acquired. This procedure may be followed for the other two ports in order to fully characterize the unconditional stability boundaries of a three-port network. In addition, issues pertaining to uniqueness and continuity in the plotting of unconditional stability boundaries are addressed. Using the agilent advanced design system software tool, the derived expressions of the unconditional stability boundary for the terminating port and related extreme phase values of reflection coefficients of the other two ports are implemented. These derived expressions can then enhance the computer-aided capability on the stability analysis of a three-port network and provide useful information for the microwave circuit designer.