Oscillation in a circuit is undesirable if the circuit is an amplifier or part of a control system which needs to be stable without oscillation. However, oscillation is desirable in many applications such as sinusoidal signal generator, carrier signal generation is broadcast transmission (radio and TV), clock signal in digital systems, etc.
An oscillator is a feedback system composed of a forward path with gain and a feedback path with gain :
For the system to oscillate at a certain frequency, the feedback needs to be positive for the frequency to be positively reinforced while passing through the forward path in order to sustain the output with zero input . Specifically, the output and the input of a feedback system are related by
There exist many different configurations of oscillators based on a single transistor. Shown below are three typical Colpitts oscillators: common-base (CB, left), common emitter (CE, middle), and common collector (CC, right). All such circuits contain a “tank” LC circuit composed of an inductor in parallel with and in series, with a resonant frequency
Here are the requirements for these circuits to oscillate:
More specifically, we consider the common-collector circuit as an example. To find out why the circuit oscillates and the resonant frequency, we disconnect the base path of the circuit and consider the open-loop gain of of the feedback loop. We further model the transistor by a Thevenin voltage source in series with an internal , as shown in the figure:
As the load of the Thevenin source, the tank circuit receives an input at the tap point, and produces an output across the parallel combination of and in series with . Applying KCL at the tap point we get:
We see that when , the open-loop gain is real but greater than 1. However, the non-linearity of the transistor as the feedback path (from to ) will force the open-loop to be 1. The circuit is an oscillator with frequency at .