Electronic amplifiers are designed to magnify small input signals. While DC biasing establishes the operating point (Q-point) of the transistor, it's the AC signal that carries the information we want to amplify. Small-signal analysis is a powerful technique that allows us to simplify the complex non-linear behavior of transistors into a linear model, valid for small variations around the DC operating point. This linearity is crucial because it allows us to use superposition and other linear circuit analysis techniques.

The core idea behind small-signal analysis is linearization. A transistor, whether BJT or FET, is a non-linear device. Its output current is not directly proportional to its input voltage or current over a wide range. However, if the AC input signal is small enough, the transistor's operating point effectively 'moves' within a very small, approximately linear region of its characteristic curves. Within this small region, the transistor can be modeled as a linear circuit element.

1. Determine the DC Operating Point (Q-point): First, the DC bias voltages and currents for the transistor must be found. This defines the quiescent state around which the AC signals will vary. This step involves setting all AC sources to zero (shorting AC voltage sources and opening AC current sources) and analyzing the DC equivalent circuit.
2. Replace DC Voltage Sources with Shorts and DC Current Sources with Opens: For AC analysis, all DC voltage sources are considered ideal shorts because they present zero impedance to AC signals. Similarly, ideal DC current sources are considered open circuits. This is a critical simplification for creating the AC equivalent circuit.
3. Replace Capacitors with Shorts: At the low frequencies we are considering in this module, coupling and bypass capacitors are assumed to have negligible impedance. Therefore, they are treated as short circuits for AC signals. This allows AC signals to pass through while blocking DC.
4. Replace Transistors with Their Small-Signal Models: This is the most crucial step. The non-linear transistor is replaced by a linear equivalent circuit model (e.g., π-model or T-model for BJTs, or small-signal models for FETs). These models consist of resistors, dependent sources, and sometimes capacitors.
5. Analyze the Resulting AC Equivalent Circuit: Once the circuit is transformed into its AC equivalent, standard linear circuit analysis techniques can be applied to determine AC voltage gain, current gain, input resistance, and output resistance.

The term "small" refers to the amplitude of the AC signal. If the AC signal is too large, the transistor's operation will swing beyond the linear region, and the small-signal model will no longer accurately represent its behavior, leading to distortion. Generally, an AC voltage is considered "small" if it causes variations in terminal voltages and currents that are significantly less than the DC bias values, ensuring the linear approximation holds. For example, for a BJT, the AC base-emitter voltage v_be should be much less than the thermal voltage V_T (approximately 25 mV at room temperature).