Small-signal model

Fig : Small signal equivalent circuits (Photo Credit : Harvard University)

Small-signal modeling is a common analysis technique in electrical engineering which is used to approximate the behavior of nonlinear devices with linear equations. This linearization is formed about the DC bias point of the device (that is, the voltage/current levels present when no signal is applied), and can be accurate for small excursions about this point. Many electronic circuits, such as radio receivers, communications, and signal processing circuits, generally carry small time-varying signals on top of a constant bias. This suggests using a method akin to approximation by finite difference method to analyze relatively small perturbations about the bias point. Any nonlinear device which can be described quantitatively using a formula can then be 'linearized' about a bias point by taking partial derivatives of the formula with respect to all governing variables. These partial derivatives can be associated with physical quantities (such as capacitance, resistance and inductance), and a circuit diagram relating them can be formulated. Small-signal models exist for electron tubes, diodes, field-effect transistors (FET) and bipolar transistors, notably the hybrid-pi model and various two-port network.

• Large-signal DC quantities are denoted by uppercase letters with uppercase subscripts. For example, the DC input bias voltage of a transistor would be denoted V_IN.

• Small-signal quantities are denoted using lowercase letters with lowercase subscripts. For example, the input signal of a transistor would be denoted as v_in.

• Total quantities, combining both small-signal and large-signal quantities, are denoted using lower case letters and uppercase subscripts. For example, the total input voltage to the aforementioned transistor would be v_IN(t) = V_IN + v_in(t).