Discussion on the general oscillation startup condition and the Barkhausen criterion

Abstract

The Barkhausen criterion has been widely used to determine the oscillation startup condition. However, we propose it is only partially correct. The general oscillation condition and the relation between the general oscillation condition and the Barkhausen criterion are reviewed in this paper. The oscillation frequency related to the general oscillation startup condition is also presented.

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.…”

“…Combining inequalities (16) and (18), the condition for startup and maintaining sinusoidal oscillation is…”

“…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.…”

On the Barkhausen and Nyquist stability criteria

“…Unfortunately, in many textbooks this fact is not explicitely mentioned which can lead to severe misinterpretations of this criterion. Therefore, it is very useful that some theoretical investigations have been published recently dealing with ''oscillation startup conditions'' [1][2][3][4][5][6]. Together with the classical Barkhausen criterion such a condition would constitute a condition for oscillation which is necessary as well as sufficient.…”

Discussion on Barkhausen and Nyquist stability criteria

“…Given an oscillator circuit, one needs to determine the condition of oscillation and the frequency of oscillation therein. This paper specifically refers to the Barkhausen criterion for the determination of oscillations, which is described in most textbooks [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and which has been the subjet of recent discussions [20][21][22][23]. In [20,21], some examples in which the Barkhausen criterion fails to produce the correct condition for startup of oscillations have been reported.…”