Principle of working of an oscillator:
a. A simple oscillator consists of an amplifier and feedback network with frequency determining components.
b. A frequency-determining network, (resonant tank circuit) which also works as feedback network and transistor amplifier acts as element.
c. With enough feedback, the oscillations start as soon as the circuit is switched on.
d. With positive feedback, the output current of the amplifier will be in the right phase to increase the alternating current in the resonant circuit.
e. The oscillations then built up in amplitude until the power losses in the circuit are equal to the power that the amplifier can develop.
f. The natural frequency of the oscillator is close to the resonant frequency of the resonant circuit.
g. Suppose the voltage gain without feedback of the amplifier is A = \(\frac{V_o}{V_i}\)
h. The feedback factor β is the fraction of the output voltage fed back to the input,
Vi = Vf = βVo
∴ A = \(\frac{V_o}{V_i}\) = \(\frac{1}{β}\)
∴ Aβ = 1
i. The condition Aβ = 1, is called Berkhausen’s criterion. It states that the phase shift of the feedback voltage will be zero or integral multiple of 2π rad, i.e., there will be positive feedback.
j. The voltage gain of complete system is given by, Af =\(\frac{A}{1 - Aβ}\)
Thus, for the frequency for which Aβ = 1, Af will be infinite, i.e., the circuit will operate without any external signal voltage, which means the circuit will oscillate at that frequency.
