### LC oscillators.

LC oscillator is a type of oscillator where a LC (inductor-capacitor) tank circuit is used for giving the required positive feedback for sustaining the oscillations. The LC tank circuit is also termed as LC resonant circuit or LC tuned circuit. According to the Barkhausen criterion for sustained oscillations, a circuit will sustain stable oscillations only for frequencies at which the loop gain of the system is equal to or greater than 1 and the phase shift between input and output is 0 or an integral multiple of 2π. LC oscillators can realized using BJT, FET, MOSFET, opamp etc. Typical applications of LC oscillators include RF signal generators, frequency mixers, tuners, sine wave generators, RF modulators etc. Before going into the LC oscillators in detail let’s have a look at the LC tank circuit.

#### LC tank circuit.

Though the original tank circuit means a capacitor and inductor connected in parallel, the switch and a voltage source are included in the circuit for the ease of explanation. Initially the switch S is assumed to be in position 1. The cacpacitor will be charged to a voltage V which is the voltage source. Assume the switch is moved to position 2 as shown in the figure below.

The capacitor C will start discharging through inductor L. The voltage across capacitor will start to decrease and the current through the inductor starts increasing. The increasing current creates an electromagnetic field around the coil and when the capacitor is fully discharged the electrostatic energy stored in the capacitor will be fully transferred into the coil as electro-magnetic field. With no more energy in the capacitor to sustain the current through the coil, the field around the coil starts to fall and the current through the coil tends to decrease. Due to electromagnetic induction the inductor will generate a back emf equal to L(di/dt) in order oppose the change in current. This back emf will start to charge the capacitor again.

When the capacitor is fully charged , the energy once stored in the inductor as elecro-magnetic field will be moved to the capacitor as electrostatic field. Then the capacitor starts discharging again and the cycle is repeated. This cyclic transfer of of energy between the capacitor and inductor is the reason behind the production of oscillations in the tank circuit.

If an ideal capacitor and inductor are used, these oscillation will sustain until the end of time. But in practical case the inductor will have some ohmic resistance and the capacitor will have some amount of leakage. These imperfections will waste some amount of energy in between the cycles resulting in the loss of amplitude step by step and eventually the oscillations will die out. This gradual decay in amplitude which tends to the death of an oscillation is called damping. The oscillations produced in a damped LC tank circuit will look like what shown in the figure below.

In a practical LC oscillator, in addition to the Barkahusen criterion there must be some means to compensate for the energy lost in the tank circuit. Application of active elements like BJT, FET, opamp etc in the LC oscillator is a way for meeting all these requirements. The active element in an LC oscillator circuit has three essential jobs.

- To give necessary gain.
- Help in attaining the required positive feedback conditions.
- Compensate the energy lost in the tank circuit.

#### LC oscillators and types.

##### Tuned collector oscillator.

Tuned collector oscillator can be said to be the basic type of LC oscillators. Here a transformer and a capacitor connected in parallel across the collector circuit of the oscillator. Primary of the transformer and the capacitor forms the essential tank circuit. The secondary of the transformer feeds back a fraction of the oscillations produced in the tank circuit to the base of the transistor. The circuit diagram of a typical tuned collector oscillator is shown in the figure below.

##### Tuned base oscillator.

Tuned base oscillator is a kind of LC transistor oscillator where the tuned circuit is placed between the base and ground of the transistor. The primary coil of a transformer and a capacitor forms the tuned circuit. The secondary coil of the transformer is used for feedback. The circuit diagram of a tuned base oscillator is given in the figure below.

##### Hartley oscillator.

##### Colpitts oscilllator.

##### Clapp oscillator.

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