Common numerical approaches for determining a circuit's dc operating points usually yield no more than one solution. Even applications of homotopy methods have performed with a limited success. We propose a new method: a combination of investigating the circuit's topology and analyzing the circuit numerically. The method, named ``test for positive feedback structures,'' was previously introduced to determine which bipolar transistor, as part of a feedback structure, can cause positive feedback, and if so, what the circuit's operating points will be. We also show that the method can be extended to circuits with field effect transistors (FET's).

We investigate, analytically and via simulations, one-port circuits consisting of two bipolar junction transistors (BJT's) and a few linear resistors connected in a feedback structure. These circuits possess topologies and parameter values such that their terminal one-port i-v characteristics exhibit a negative differential resistance (NDR) region. These structures have been used in the past to model silicon controlled rectifier (SCR) devices and the latch-up phenomena in CMOS integrated circuits. We show analytically that the large voltages across transistor pn junctions predicted by SPICE are not numerical artifacts of this simulator, but are intrinsic properties of the circuits. Our analysis explicitly accounts for the influence of the Early voltage effects on the calculations of the break-over voltages and currents, and suggests that this sometimes neglected effect may indeed play a dominant role in these circuits' behavior.

Last updated Friday January 20 23:28:08 PST 2006.