Small-Signal Models of Bipolar Transistors

Analog circuits often operate with signal levels that are small compared to the bias currents and voltages in the circuit. In these circumstances, incremental or small-signal models can be derived that allow calculation of circuit gain and terminal impedances without the necessity of including the bias quantities. A hierarchy of models with increasing complexity can be derived, and the more complex ones are generally reserved for computer analysis. Part of the designers' skill is knowing which elements of the model can be omitted when performing hand calculations on a particular circuit, and this point is taken up again later.
Consider the bipolar transistor with bias voltages VBE and VCC applied as shown in the Figure. These produce a quiescent collector current, IC, and a quiescent base current, IB, and the device is in the forward-active mode. A "small-signal" input voltage, vi, is applied in series with VBE and produces a small variation in base current ib and a small variation in collector current ic. Total values of base and collector currents are Ib and Ic, respectively, and thus Ib=(IB + ib) and Ic=(IC + ic). The carrier concentrations in the base of the transistor corresponding to the situation in Figure a are shown in Figure b. With bias voltages only applied, the carrier concentrations are given by the solid lines. Application of the small-signal voltage, vi, causes np(0) at the emitter edge of the base to increase, and produces the concentrations shown by the dotted lines. These pictures can now be used to derive the various elements in the small-signal equivalent circuit of the bipolar transistor.