What is the voltage gain condition for oscillator start-up?*

The voltage gain condition for oscillator start-up is that the overall gain of the oscillator circuit must be greater than or equal to one (Av ≥ 1). This is necessary to sustain oscillations because any loss in the signal during one cycle of oscillation must be compensated by the gain of the oscillator.

Here are the steps to understand this:

1. An oscillator is a circuit that produces a repetitive waveform on its output with only the input DC signal. It basically converts DC from a power supply to an AC signal.

2. The oscillator uses a positive feedback loop, meaning that some of the output signal is fed back into the input. This feedback signal aids the input signal and helps the oscillator maintain a continuous oscillation.

3. For the oscillator to start up, the total loop gain (product of gain and feedback) must be equal to or greater than one. This is because any loss in the signal during one cycle of oscillation must be compensated by the gain of the oscillator.

4. If the loop gain is less than one, the oscillations decay to zero. If the loop gain is more than one, the oscillations increase in amplitude. Therefore, to maintain a stable oscillation, the loop gain must be exactly one.

5. In terms of voltage, this means that the voltage gain of the oscillator must be greater than or equal to one for the oscillator to start up and maintain its oscillations.