The circuits we have encountered so far are passive and dissipate power. Even a transformer that is capable of giving a voltage gain to a circuit is not an active element. Active elements in a circuit increase the power by controlling or modulating the flow of energy or power from an additional power supply into the circuit.
Transistors are active circuit elements and are typically made from silicon or germanium and come in two types. The bipolar transistor controls the current by varying the number of charge carriers. The field effect transistor (FET) varies the current by varying the shape of the conducting volume.
Before starting we will define some notation. The voltages that are with respect to ground are indicated by a single subscript. Voltages with repeated letters are power supply voltages. And voltages between two terminals are indicated by a double subscript.