Barkhausen Criterion Explained

The Barkhausen criterion is a fundamental condition that must be met for an electronic circuit to produce sustained oscillations. It is particularly important in the design and analysis of feedback oscillators, which are circuits designed to generate a repetitive, oscillating electronic signal without an external input signal.

Oscillation Conditions for Barkhausen Criterion

For a circuit to oscillate continuously and stably, two essential conditions, collectively known as the Barkhausen criterion, must be satisfied:

• Amplitude Condition: The magnitude of the loop gain (\(A\beta\)) must be equal to or greater than unity. For truly sustained oscillations that neither die out nor grow indefinitely, the ideal condition is that the magnitude of the loop gain is exactly one. This can be expressed as \(|A\beta| = 1\).
• Phase Condition: The total phase shift around the entire feedback loop must be zero degrees (\(0^\circ\)) or an integer multiple of 360 degrees (\(360^\circ\)). This ensures that the feedback signal arrives in phase with the original input signal, thus reinforcing it. Mathematically, this is written as \(\angle A\beta = 0^\circ\) or \(\angle A\beta = n \times 360^\circ\), where \(n\) is an integer.

Loop Gain in Oscillators

In the context of the Barkhausen criterion:

• \(A\) represents the gain of the amplifier stage within the feedback loop.
• \(\beta\) (beta) represents the gain (or attenuation) of the feedback network, which also typically provides the necessary phase shift.
• The product \(A\beta\) is known as the loop gain. It signifies the overall gain experienced by a signal as it travels once around the feedback loop, from the amplifier input, through the amplifier, through the feedback network, and back to the amplifier input.

The question specifically asks for the amplitude condition of the Barkhausen criterion for oscillations. For sustained oscillations, the most precise and commonly stated amplitude condition is:

\[|A\beta| = 1\]

This condition ensures that the signal strength circulating in the loop remains constant, leading to stable, continuous oscillations. If \(|A\beta| < 1\), the oscillations would eventually die out. If \(|A\beta| > 1\), the oscillations would grow until limited by the non-linear characteristics of the amplifier, leading to distortion.