hybridpi

Hybrid-pi is a standard small-signal model used to analyze bipolar junction transistors (BJTs) in their active region. In this model the transistor is represented by a base–emitter resistance r_pi, a dependent current source gm*v_pi from collector to emitter, and an output resistance r_o between collector and emitter. The small-signal input is the voltage v_pi, the voltage between base and emitter. The base current is approximately i_b ≈ v_pi/r_pi, and the collector current is approximately i_c ≈ gm*v_pi, with the output path impaired by r_o to account for the Early effect.

The term hybrid-pi reflects the combination of a pi-shaped input element with a controlled current source that represents transconductance. In many analyses, the model is linearized around a DC operating point, making it suitable for determining voltage gain, input and output impedances, and overall amplifier behavior in common-emitter, common-base, or common-collector configurations.

High-frequency extensions of the model incorporate parasitic capacitances, notably C_pi between base and emitter and C_mu between base and collector. These additions capture the during-high-frequency attenuation and Miller effect, improving accuracy in AC and transient simulations. In practice, the hybrid-pi model serves as a foundational tool in circuit design and teaching, and is often used as the small-signal core in larger transistor models used in SPICE and other circuit simulators. Limitations include its small-signal nature and reduced accuracy at large signals or very high frequencies where more complete transistor models are needed.