# The Barkhausen criterion for an oscillator

Electrical Engineering XYZ MCQs

The Barkhausen criterion for an oscillator:

1. The phase of a feedback signal with respect to input should be 0° or 360°
2. Loop gain should be unity
3. Both 1 and 2
4. Loop gain should be less than unity

Correct answer: 3. Both 1 and 2

Explanation: The Barkhausen criterion is a set of conditions that need to be satisfied for an oscillator to sustain oscillations. Let’s break down the options:

1. The phase of a feedback signal with respect to input should be 0° or 360°: This is a correct statement. For sustained oscillations, the feedback signal must reinforce the input signal. This means that the phase of the feedback signal should be such that it adds constructively with the input signal. Mathematically, this corresponds to a phase shift of 0° or 360°.
2. Loop gain should be unity: This is also a correct statement. The loop gain represents the gain around the feedback loop. In an oscillator, the loop gain should be exactly unity for sustained oscillations. This ensures that the output signal maintains its amplitude.

Combining both statements, we see that both conditions are necessary for the Barkhausen criterion to be satisfied. So, the correct answer is:

Option 3: Both 1 and 2

1. Loop gain should be less than unity: This statement is incorrect. In oscillators, the loop gain needs to be precisely unity, not less than unity. If the loop gain were less than unity, the output signal would decrease in amplitude over time, leading to decay rather than sustained oscillations.