HybridpiModell

HybridpiModell, also called the hybrid-pi model in English, is a small-signal equivalent circuit used to analyze bipolar junction transistors (BJT) in the active region. It represents the transistor by three key elements: a base-emitter resistance r_pi between base and emitter, a dependent current source g_m v_pi from collector to emitter, and an output resistance r_o between collector and emitter that models the Early effect. The controlling voltage v_pi is the small-signal voltage between base and emitter, and g_m is the transconductance (approximately g_m = I_C / V_T). In common-emitter configurations with the emitter at AC ground, the input impedance is roughly r_pi and the small-signal current gain is β ≈ g_m r_pi.

For high-frequency analysis, capacitive elements are added, typically C_pi between base and emitter and C_mu between base and collector. These capacitances account for diffusion and depletion effects and produce the Miller multiplication of C_mu, influencing the input capacitance and bandwidth.

Hybrid-pi modelling is widely used for hand analysis and circuit simulation to determine voltage gain, input and output resistances, and bandwidth of BJT amplifiers. It forms the basis of many SPICE transistor models and serves as a bridge to more comprehensive models such as the Gummel-Poon model. It is also common to compare the hybrid-pi with the T-model as an alternative small-signal representation.

Limitations include its validity only for small-signal conditions around a bias point and its neglect of some nonlinear effects and higher-order capacitances. For more accurate results at low to medium frequencies, the hybrid-pi model is often extended with ro and frequency-dependent capacitances; for large-signal or high-frequency behavior, more advanced models are used.