Collector Output Resistance (Early Voltage)

Up until now in this course we have assumed that the collector of a BJT acts like an ideal current source when the transistor is operating in forward active mode. (Recall that the output resistance of a current source is taken in parallel with the source. When a current source is ideal, its output resistance is infinity.) In other words, we have taken the small signal output resistance associated with the collector to be infinite. This is usually a very good approximation, especially when we have passive loads. When active loads are involved, we often have to consider the finite output resistance that is in parallel with the collector. (This resistance is usually on the order of 100K or greater.) When we have to consider small signal output resistance associated with the collector current it is given as follows:

Detailed analysis of the small signal equivalent circuits shows that when r_o must be included to calculate the voltage gain of difference amp, it is taken to be in parallel with R_L. Therefore, the more precise expression for voltage gain of the circuit in Fig. 6.2, is given by