Bipolar junction transistor amplifiers-state-space modeling across frequencies

Abstract

This study presents a unified time-domain analysis of three fundamental bipolar-junction-transistor amplifier topologies-common-emitter (CEA), common-collector (CCA), and common-base (CBA)-under both low- and high-frequency transient conditions. Unlike traditional small-signal or SPICE-based approaches, this work employs a state-space modeling framework implemented in MATLAB-Simulink to derive and simulate the dynamic behavior of each topology. The models capture both steady-state and transient responses, offering deeper insight into system dynamics, including the effects of Miller capacitance at high frequencies. The CEA demonstrates high voltage gain, while the CCA and CBA exhibit lower but topology-consistent gains, with simulation results closely matching analytical predictions. Although experimental validation is not included, the simulation parameters are carefully selected to reflect realistic operating conditions. The novelty of this work lies in its application of state-space methods to analog amplifier modeling, providing a transparent and extendable foundation for analyzing more complex circuits such as operational amplifiers. This approach enhances theoretical understanding and supports practical design decisions across a wide range of analog applications.