Effect of nonlinear collector capacitance on collector current rise time

The collector capacity, C, of a junction transistor is known to vary as a nonlinear function of the voltage, V, across it. A calculation is made of the collector current rise time of a grounded emitter alloy junction transistor for which C = kV^-1/2. A comparison is then made with linear analyses in which C is assumed to have one of the following constant values. 1) C = Ccc, where Cccis the small signal capacity measured at the collector supply voltage, Vcc. 2) C = 1.52Ccc. This capacity is one which displaces the same charge as the nonlinear capacity as the voltage across it changes from 0-90 per cent of its final value. 3) C - 2Ccc. This capacity is one which displaces the same charge as the nonlinear capacity as the voltage across it changes from 0-100 per cent of its final value. The linear analysis using the latter two capacity values gives 0-90 per cent and 0-100 per cent rise times which are very close to those given by a numerical solution of the nonlinear circuit equation. The usual linear analysis using C = Ccc, on the other hand, is very much in error for predicting rise time. Experimental results show that the 2Cccvalue, in a linear analysis, predicts the 0-100 per cent rise time almost exactly. In addition, analog computer solutions of the nonlinear circuit equation give results almost identical with the shape of the experimental curves.