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In an oscillator circuit, 5% of the output is fed back positively to the input. What is the minimum gain required for oscillations to occur? (Assume that proper phase-shift is achieved)

In an oscillator circuit, 5% of the output is fed back positively to the input. What is the minimum gain required for oscillations to occur? (Assume that proper phase-shift is achieved) Correct Answer 20

Concept:

  • In a transistor-based oscillator, the total loop gain required to sustain oscillation is unity.
  • To start the oscillation with the constant amplitude, positive feedback is not the only sufficient condition. Oscillator circuit must satisfy the following two conditions known as Barkhausen conditions:
  • The first condition is that the magnitude of the loop gain (Aβ) must be unity. This means the product of gain of amplifier 'A' and the gain of feedback network 'β' has to be unity. Aβ = 1
  • The second condition is that the phase shift around the loop must be 360° or 0°. This means the phase shift through the amplifier and feedback network has to be 360° or 0°.
  • Depending upon the variation in the output waveform amplitude, there are two types of oscillations. Damped and Undamped or (sustained)

 

Calculation:

Feedback gain (β) = 5% = 0.05

Gain of amplifier is A.

For oscillations, Aβ = 1

⇒ A × 0.05 = 1

⇒ A = 20

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