Barkhausen criterion

Barkhausen criterion

[′bärk‚hau̇z·ən krī‚tir·ē·ən]
(electronics)
A criterion used to determine the stability of an oscillator circuit which states that, if the circuit is seen as a loop consisting of an amplifier with gain A and a linear circuit whose gain β(j ω) depends on frequency ω, then the loop will oscillate with a perfect sine wave at some frequency ω0 if at that frequency A β(j ω0) = 1 exactly, that is, if the magnitude of A β(j ω0) is exactly 1 and its phase is 0° or 360°.
References in periodicals archive ?
4.a is based on the Barkhausen criterion which states that the looped system starts oscillating at frequency [F.sub.0] so that between the input of the LNA and the output of the resonator it has a voltage gain higher than 0 dB and a phase shift multiple of 360 [degrees].
Several novel delay cells have been demonstrated to compose the two-stage ring-VCO, but extra power is inevitably needed to provide an excess phase shift for oscillation satisfying Barkhausen criterion. On the other hand, implementation of 4 stages of RO consumes considerable amount of power due to additional stages.
Though several 2-stage ring VCO can be composed by different delay stage, extra power is certainly needed to provide an excess phase shift for oscillation fulfilling well-known Barkhausen criterion. Conversely, implementation of 4-stage ring VCO can be possible by differential topology, however, this oscillator consumes significant amount of power.
and applying the steady-state Barkhausen criterion ([I.sup.c] + j[I.sup.s])[H.sub.0] = V(1 + j2Q([omega]-[[omega].sub.0])/[[omega].sub.0]), the balance of the imaginary components leads to the following:
This relation is commonly known as the Barkhausen criterion, which states that the loop gain must be 1 and the loop phase shill multiples of 360[degrees] to obtain oscillation.
Since the oscillator has a group delay, the Barkhausen criterion changes to
The Barkhausen criterion for oscillation implies that the phaseshift in the loop must be zero and the gain equal to one.