## Construction of tuned collector oscillator

It consists of a tank circuit or LC tuned circuit connected to the Collector of the transistor. Hence, the name of this oscillator is tuned collector oscillator. The stabilized self bias to the amplifier is provided by the arrangement consisting of R_{1} , R_{2} , R_{3} and C_{e}.

The coil L_{2} is coupled to the coil L_{1 }of the tank circuit. In fact, L_{1} is the primary and L_{2} secondary coil of a transformer. The low resistance path to the oscillation is provided by the capacitor C.

We know, a transformer introduces a phase shift of 180^{o} between its primary coil and secondary coil. Hence a phase shift of 180^{o} is introduced between the voltages of L_{1} and L_{2}.

When a transistor is in common emitter configuration, a phase shift of 180^{o} is introduced between the input circuit (i.e. base-emitter circuit) and the output circuit (i.e. collector-emitter circuit).

A phase shift of 180^{o} is also introduced in the circuit by the transistor. Therefore, a total phase shift of 360^{o} or 0^{o} exists between the input and output voltages, leading to positive feedback which is essential for sustaining the oscillation in the circuit.

## Working of tuned collector oscillator

When key K is closed, collector current begins to flow. As the collector current increases, the capacitor C_{1} stars getting charged. After the capacitor is fully charged, it begins to discharge through the coil L_{1 }, giving rise to the damped oscillations of a definite frequency.

The voltage in coil L_{2} is induced by these oscillations. This voltage is applied between the base and emitter and appears in the collector circuit in the amplifier form.

Feedback of energy from the collector circuit to the based circuit is achieved losses taking place in the tank by means of mutual inductance M between L_{1} and L_{2}. Thus circuit are compensated. Hence undamped oscillations are obtained at the output.

## Analysis of tuned collector oscillator

The equivalent circuit of a tuned collector oscillator is shown in the figure 3. Let R be the resistance of the secondary side reflected to the primary.

The voltage across the tank circuit ( L_{1}-C_{1} ) is given by

and feedback voltage

where M is the mutual inductance between primary and secondary coils of the transformer.

Now, feedback ratio is given by

Base current

Current

The impedance of transformer is given by

Using eqns. (1) and (2), we get

Putting this value in eqn. (6) and using eqn. (5) also, we get

Using eqn. (7), we get

According to Barkhausen criterion for sustained oscillations,

Using eqns. (4) and (8), we get

Multiplying both sides by (h_{oe} / jwC_{1}), we get

Comparing real parts of eqn. (9), we get

Which is the required condition for sustained oscillations.

Comparing imaginary parts of eqn. (9), we get

which is the angular frequency of oscillations.

Eqn. (12) tells us that the frequency of oscillations is more than the frequency of resonance of the tuned circuit.

If the resistance R is negligible, then eqn. (12) becomes

Which is the frequency of oscillations in a **tuned collector oscillator**.