**LC Oscillator Circuit – Definition, Types and Equation:**

Oscillators, which use inductance-capacitance (L-C) circuits as their tank or oscillatory circuits are called LC Oscillator. LC Oscillator are very popular for generating high-frequency outputs (e.g. 10 kHz to 100 MHz). There is a large variety of LC Oscillators such as tuned collector oscillators, tuned base oscillators, Colpitt’s oscillators, Hartley oscillators, Clapp oscillators, crystal oscillators etc.

**General form of an L-C Oscillator:**

In the general form of an oscillator depicted in Fig. 21.6 (a), any of the active devices such as vacuum tube, BJT, FET or op-amp may be used in the amplifier section, Z_{1}, Z_{2}Â and Z_{3} are the reactive elements constituting the feedback tank circuit which determines the frequency of oscillation. Here, Z_{1} and Z_{2} serve as an ac voltage divider for the output voltage and feedback signal. Thus, the voltage across Z_{2} is the feedback signal. The equivalent circuit is drawn in Fig. 21.6 (b) with the following two assumptions:

- h
_{re}of transistor is negligibly small and, therefore, the feedback source h_{re}V_{out }is negligible. - h
_{oe }of the transistor is very small i.e. the output resistance 1/h_{oe}is very large and, therefore, 1/h_{oe }is omitted from equivalent circuit.

Let us determine the load impedance between output terminals 1 and 2. Here Z_{2}Â and h_{ie}Â are in parallel and their resultant impedance is in series with impedance Z_{3}.

The equivalent impedance is in parallel with impedance Z_{1}. Thus load impedance between output terminals is given as

or

or

The voltage gain of a CE amplifier without feedback is given as

The output voltage between terminals 1 and 2 is given as

The voltage feedback to the input terminals 2 and 3 is given as

So feedback fraction,

Applying the criterion of oscillation i.e. AÎ² = 1, we have

Substituting the value of Z_{L} from Eq. (21.7). we have

or

or

or

or

This is the general equation for the LC Oscillator Circuit.