Discussion on Barkhausen and Nyquist stability criteria

Abstract

Most textbooks on analog circuits and signal processing describe the Barkhausen criterion pertaining to the determination of sinusoidal oscillations in a closed-loop system. On the other hand, the Nyquist stability criterion is well known, as discussed in most textbooks on control systems. Recently, some examples in which the Barkhausen criterion fails to produce the correct condition for startup of oscillations have been reported. In the present paper, an explanation of oscillation startup based on the Nyquist stability criterion is given and the close relationship between the Barkhausen and the Nyquist criteria highlighted. It is shown that the Nyquist criterion (which is a rigorous technique) is a more robust approach than the Barkhausen criterion concerning the determination of sinusoidal oscillations in a closed-loop system and that the Barkhausen criterion (whenever it yields the correct result) is subsumed by the Nyquist criterion as a special case. The textbooks usually describe the Barkhausen criterion as a separate topic, i.e., do not discuss the relationship of this criterion with the Nyquist criterion. It is, therefore, felt that the present discussion will go a long way to put the subject in a broader perspective.

Identification of a class of two CFOA-based sinusoidal RC oscillators

“…It appears, therefore, that the conditions of oscillation startup stated as e 0 = 0, and obtained using the Barkhausen criterion, are not sufficient to startup and maintain oscillation. In fact the validity of the Barkhausen criterion in determining the startup condition of oscillation has been recently challenged [13][14][15][16][17] and its failure to determine the startup and building of oscillation has been reported. Thus, it is essential to revisit Eq.…”

“…On the other hand, the condition of startup and the frequency of oscillation of the circuits proposed in [1][2][3][4][5][6][7][8][9][10][11] are obtained by applying the Barkhausen criterion. Recently the use of this criterion for determination of the startup condition of oscillation has been challenged [13][14][15][16][17] and its failure has been reported. In fact in [10,11] the author noted that the startup of oscillation is achieved only when the values of the passive components deviate from the condition imposed by this criterion.…”

Comment on “Identification of a class of two CFOA-based sinusoidal RC oscillators”

“…Recently, some contributions have been published in this magazine dealing with the start-up condition for sinusoidal RC oscillators [1][2][3][4][5][6][7]. In this context, the applicability and limitations of the well known oscillation criterion from Barkhausen [8] have been discussed-in particular, the relation to the more general Nyquist stability criterion.…”

New two CFOA-based sinusoidal RC oscillators with buffered outlet

“…It appears, therefore, that the conditions of oscillation startup stated as e 0 ¼ 0; and obtained using the Barkhausen criterion, are not sufficient to startup and maintain oscillation. In fact the validity of the Barkhausen criterion in determining the startup condition of oscillation has been recently challenged [7][8][9][10][11][12] and its failure to determine the startup and building of oscillation has been reported. Thus, it is essential to use Eqs.…”

“…In practice oscillation can start up only if the condition of oscillation obtained by applying the Barkhausen criterion is violated. Recently the use of this criterion for determination of the startup condition of oscillation has been challenged [7][8][9][10][11][12] and its failure has been reported. Thus, similar to the circuits presented in [6], the startup condition and the frequency of oscillation of the circuits presented in this paper will be obtained first by applying the Barkhausen criterion and then by finding the roots of the characteristic equation.…”