Barkhausen Criteria Explained: Loop Gain and Phase Shift

This document explains the basics of the Barkhausen criteria and outlines the difference between the first and second Barkhausen criteria. If a negative feedback circuit satisfies the following two conditions, the circuit may oscillate at a specific frequency, denoted as W₀.

Barkhausen Criteria

Based on the principles illustrated above, we can define the Barkhausen criteria as follows:

• Loop Gain: A * Β >= 1
• Phase Shift: The phase shift around the entire circuit loop must be 2π (360 degrees) or a multiple of 2π.

First Barkhausen Criterion

The first Barkhausen criterion focuses on ensuring reliable oscillation. In practice, we typically design the loop gain (A*B) to be at least two or three times greater than the minimum required value (1). This safety margin compensates for variations in temperature, component tolerances, and other process-related fluctuations that could otherwise prevent sustained oscillations.

Second Barkhausen Criterion

The second Barkhausen criterion addresses the phase shift requirement for oscillation. This criterion can be stated as follows:

• A 180-degree phase shift criterion is equivalent to a complete 360-degree loop phase shift.

Second Barkhausen Criterion

• Figure-2a illustrates a scenario where a 180-degree phase shift is introduced by the negative feedback network, while the amplifier contributes the remaining 180 degrees.
• Figure-2b depicts a situation where the amplifier alone provides the entire 360-degree phase shift.
• Figure-2c shows that a phase shift of 2nπ (where ‘n’ is an integer) functions identically to the scenario in Figure-2b, as it represents a complete rotation around the phase circle.