What is the Barkhausen criterion, and how does it relate to oscillator stability?
1 Answer
The Barkhausen criterion is a principle used in the analysis and design of electronic oscillators, which are circuits that produce periodic waveforms such as sine waves or square waves. It was first formulated by German physicist Heinrich Georg Barkhausen in the early 20th century.
The criterion states that for sustained oscillations to occur in an electronic oscillator circuit, the total phase shift around the feedback loop must be exactly 360 degrees (or 0 degrees, which is equivalent). In other words, the loop gain of the oscillator at the frequency of oscillation must be equal to unity, and the phase shift around the loop must be an integral multiple of 360 degrees.
Mathematically, if Aβ is the loop gain (the product of the gain around the loop, A, and the feedback factor, β), and θ is the total phase shift around the loop, then the Barkhausen criterion can be expressed as:
Aβ = 1
θ = 2πn, where n is an integer (0, 1, 2, 3, ...)
When the Barkhausen criterion is met, the output signal of the oscillator will maintain a constant amplitude and frequency, leading to a stable and sustained oscillation.
In practice, oscillator stability is a critical consideration in electronic circuit design. If the phase shift around the feedback loop is not exactly 360 degrees, the oscillator's output frequency may drift, leading to instability. In some cases, the oscillator may not start oscillating at all.
Achieving the Barkhausen criterion for oscillator stability typically involves careful design of the feedback network and control of the loop gain. Factors such as component values, parasitic capacitance, and inductance can influence the phase shift and affect oscillator performance. Proper compensation and feedback control are necessary to maintain stability and ensure the oscillator operates at the desired frequency without excessive frequency drift or unwanted behavior.
The criterion states that for sustained oscillations to occur in an electronic oscillator circuit, the total phase shift around the feedback loop must be exactly 360 degrees (or 0 degrees, which is equivalent). In other words, the loop gain of the oscillator at the frequency of oscillation must be equal to unity, and the phase shift around the loop must be an integral multiple of 360 degrees.
Mathematically, if Aβ is the loop gain (the product of the gain around the loop, A, and the feedback factor, β), and θ is the total phase shift around the loop, then the Barkhausen criterion can be expressed as:
Aβ = 1
θ = 2πn, where n is an integer (0, 1, 2, 3, ...)
When the Barkhausen criterion is met, the output signal of the oscillator will maintain a constant amplitude and frequency, leading to a stable and sustained oscillation.
In practice, oscillator stability is a critical consideration in electronic circuit design. If the phase shift around the feedback loop is not exactly 360 degrees, the oscillator's output frequency may drift, leading to instability. In some cases, the oscillator may not start oscillating at all.
Achieving the Barkhausen criterion for oscillator stability typically involves careful design of the feedback network and control of the loop gain. Factors such as component values, parasitic capacitance, and inductance can influence the phase shift and affect oscillator performance. Proper compensation and feedback control are necessary to maintain stability and ensure the oscillator operates at the desired frequency without excessive frequency drift or unwanted behavior.