  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.
