Tuned Oscillator

Tuned Oscillator:

A variety of oscillator circuits can be built using LC tuned circuits. A general form of tuned oscillator circuit is shown in fig. 1. It is assumed that the active device used in the oscillator has very high input resistance such as FET, or an operational amplifier.

Fig. 1	Fig. 2

Fig. 2 shows linear equivalent circuit of fig. 1 using an amplifier with an open circuit gain –A_v and output resistance R_O. It is clear from the topology of the circuit that it is voltage series feedback type circuit.

The loop gain of the circuit –Aβ can be obtained by considering the circuit to be a feedback amplifier with output taken from terminals 2 and 3 and with input terminals 1 and 3. The load impedance Z_L consists of Z₂ in parallel with the series combination of Z₁ and Z₃. The gain of the the amplifier without feedback will be given by

The feedback circuit gain is given by

Therefore, the loop gain is given by

If the impedances are pure reactances (either inductive or capacitive), then Z₁ = jX₁, Z₂= jX₂ and Z₃= jX₃. Then

For the loop gain to be real (zero phase shift around the loop),

X₁ + X₂ + X₃ = 0

and     

Therefore, the circuit will oscillate at the resonant frequency of the series combination of X₁, X₂ and X₃. Since –A β must be positive and at leat unity in magnitude, then X₁ and X₂ must have the same sign (A_v is positive).In other words, they must be the same kind of reactance, either both inductive or both capacitive.