This expository manuscript presents generalized expressions for the low-frequency voltage gain and terminal impedances of each of the three fundamental bipolar-amplifier topologies (i.e., common emitter, common base, and common collector). Unlike the formulas that students typically learn and designers typically use, the equations presented in this tutorial assume the most general set of conditions: finite output resistance and base-collector current gain, a load resistor at each non-input terminal of the transistor, and a "feedback" resistor between the base and collector terminals. Although perhaps algebraically complex at first glance, emphasis is placed on mathematical elegance and ease of use -- expressions are formulated in terms of sub-terms that capture important aspects of the circuit's behavior. Similarities in the mathematical structure of the results reveal a deeper conceptual connection between different amplifier topologies and, ultimately, a reciprocity relationship between the base and emitter terminals. Familiar approximate expressions are subsumed as special cases. Tables consolidating the expressions in an organized fashion are provided. Companion results for metal-oxide-semiconductor (MOS) single-transistor amplifiers are also included.

翻译：本综述性文稿提出了三种基本双极型放大器拓扑（即共射极、共基极和共集电极）的低频电压增益和端口阻抗的广义表达式。与学生们通常学习的及设计者通常使用的公式不同，本教程中呈现的方程假设了最一般的条件集：有限输出电阻和基极-集电极电流增益、晶体管每个非输入端口上的负载电阻，以及基极与集电极之间的“反馈”电阻。虽然初看可能代数结构复杂，但本文强调数学优雅性与易用性——表达式以子项形式构建，这些子项捕捉了电路行为的重要方面。结果在数学结构上的相似性揭示了不同放大器拓扑之间更深层的概念联系，并最终体现了基极与发射极端口之间的互易关系。常见的近似表达式作为特例被涵盖其中。文中以组织有序的表格形式汇总了这些表达式，并补充了金属-氧化物-半导体（MOS）单晶体管放大器的对应结果。