When Are Transitors Passive?

When Are Transistors Passive?* By B. GOPINATHt and D. M I T R A t (Manuscript received December 8, 1970) The paper presents results on the stability and dynamic behavior under large signal conditions of networks consisting of transistors and sources connected to a linear, passive, memoryless subnetwork. The transistors' model incorporates various nonlinearities. A characteristic common to the main results of the paper is that they relate to properties of the transistors alone and, hence, are independent of the passive part of the network. Sufficient conditions are obtained for asymptotic and bounded inputbounded output stability. The conditions impose restrictions on some of the physical constants of the transistors' model. These conditions have an interesting physical interpretation in terms of temperature differentials in the transistor junctions. In particular, any transistor with the exponential type of static diode characteristic is passive only if the ratio of the junction temperatures lies inside an interval determined by the a's. In the state space of the network there exists a well-defined region R specified by the transistors' model with the property that constant terminal states in R are independent of initial conditions. The region R is in a certain sense maximal. I . INTRODUCTION AND DERIVATION OF THE DIFFERENTIAL EQUATION The network considered is shown in Fig. 1 and it consists of a number of transistors connected to a subnetwork composed of voltage sources, current sources, and linear, passive, memoryless devices such as resistors and transformers.