On the uniqueness of a circuit's DC operating point when its transistors have variable current gains

The theory regarding the uniqueness of the DC operating point of bipolar transistor circuits is extended to the more general situation where each transistor model's controlled-source current gains are allowed to vary. It is then shown that, in certain cases, a transistor with variable current gain can be modeled at two of its operating points as a transistor with fixed gain combined with nonpassive elements. The topological criteria for unique DC operating points is examined.<>