Experimental investigation of the impact of phase vs. frequency characteristic properties on steady state oscillation existence in feedback oscillators

In this contribution we present the results of computer simulations as well as real experiments which all confirm the correctness of amendments to what is known as the Barkhausen criterion, necessary for its further application in practice [1]. The Barkhausen criterion for the formation of steady state harmonic oscillations is, due to its simplicity, very often used in the design of oscillators with feedback. In the literature, however, there are examples of oscillators that, even when this condition is met, do not oscillate at the desired frequency. In this paper we show in a suitable type of oscillator that for the emergence of harmonic oscillations, additional necessary condition of negative derivative of phase vs. frequency characteristic of the open loop feedback oscillator is needed. If this condition is not met, steady state oscillations may not exist, even if one may expect their existence from the Barkhausen criterion. Moreover, in some types of feedback oscillators, relaxation oscillations may occur at different frequencies as well. For verification of the additional condition, we proposed a proper RLC band pass filter, by means of which it is possible to easily change the sign of the derivative of the phase vs. frequency characteristic.