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.