A Unified Theory of Op-amp Sinusoidal Oscillators using Reactive π and T Networks in the Feedback Path. Issue 2 (2nd July 2016) - Dutta Roy, Suhash C.
ABSTRACT: A general theory of op-amp sinusoidal oscillators using reactive π and T networks in the feedback path is presented. A total of 12 such oscillators are investigated, 6 with the π configuration and another 6 with the T configuration, of three reactive elements in the feedback network. In each case, expressions are derived for the frequency of oscillation and the gain required of the op-amp, both of which, in general, are shown to depend upon the input and output resistances of the op-amp. One or both of these resistances can generally be ignored in most op-amp applications, but not for oscillators, thus creating problems for the students when they actually try to construct an op-amp oscillator in the laboratory. It is emphasised that with the π configuration, it is essential that the op-amp has a non-zero output resistance, while with the T configuration, the input resistance has to be finite. It is also pointed out that when the gain required is negative, a single op-amp circuit has to have a finite input resistance, irrespective of the configuration of the feedback network, while if the gain required is less than unity, the output resistance automatically arises.