Definitions

# Small-signal model

Small-signal modeling is a common analysis method used in electrical engineering to describe nonlinear devices in terms of linear equations. This linearization is done by first calculating (possibly by an iterative process if the circuit is complex) the DC bias point (that is, the voltage/current levels present when no signal is applied), and then forming linear approximations about this point.

## Motivation

Electronic circuits generally involve small time-varying signals carried over a constant bias. This suggests using a method akin to approximation by differentials 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 diodes, field-effect transistors (FET) and bipolar transistors, notably the hybrid-pi model and various two-port networks.

## Notation

• 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 $V_\left\{IN\right\}$.
• Small-signal quantities are denoted using lowercase letters with lowercase subscripts. For example, the input signal of a transistor would be denoted as $v_\left\{in\right\}$.
• 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 $v_\left\{IN\right\}\left(t\right)=V_\left\{IN\right\}\left(t\right)+v_\left\{in\right\}\left(t\right)$.

## Example: PN junction diodes

The (large-signal) Shockley equation for a diode can be linearized about the bias point or quiescent point (sometimes called Q-point) to find the small-signal conductance, capacitance and resistance of the diode. This procedure is described in more detail under diode modeling, which provides an example of the linearization procedure followed in all small-signal models of semiconductor devices.