On Further Discussion of Barkhausen Criterion B N Biswas 1 , S Chatterjee 2 and S Pal 1 1 Sir J. C. Bose School of Engineering, Mankundu, Hooghly, West Bengal, India 2 Kanailal Vidyamandir (Fr. Section), Chandannagore, West Bengal, India Abstract It has been pointed out that Barkhausen criterion cannot be used as a general oscillation condition, to evaluate (1) growth of oscillation, (2) steady state amplitude of oscillation in terms of circuit and active device parameters and (3) to as certain amplitude and frequency stability of oscillation, (4) to audit the nature of oscillation whether it is soft-self or hard-self excited. Here it has been shown that all these limitations can be over come through clubbing of quasi-state and quasi-linearization techniques and modified Barkhausen criterion can also be applied to four terminal as well as two terminal oscillators. 1. Introduction During the last five or six years Barkhausen criterion which he developed in 1934 during his study on a vacuum tube feedback oscillator, is being actively reinvestigated [1-7]. Before initiating any further discussion it is important to recall that a sinusoidal (nearly so) is a device / system designed conceived to start oscillating to remain in an instable state in order to generate stable periodic waves with desired distortion at the finite output. Thus there is a process of transition from the initial state to the steady state. Naturally, Barkhausen criterion that was developed for pure sinusoidal oscillation in the steady cannot be considered as a full-proof criterion for oscillation in a practical oscillator. Thus the workers felt a need for discussion on this criterion on the following aspects, viz., (1) The possibility of applying this criterion during the transition from the initial to the steady state-i.e. non- steady part of the oscillations. (2) The feasibility of applying the criterion at final part of the generation of oscillations where the growth of oscillation is restricted to a finite value - a manifestation of non-linear action producing distortion. (3) Since Barkhausen developed the criterion for four terminal oscillators, it is felt that it cannot be applied for a two-terminal oscillator (Negative Resistance Oscillator). They differ only in form – only two sides of the same coin. Basically both are oscillators and can be studied from the same view points. (4) It is sometimes felt that Barkhausen criterion can be only applied for a Lumped Parameter Localised Feedback Oscillator (like Barkhausen Oscillator). But the criterion can also be applied to the other two varieties of oscillators, viz., Distributed Parameter Localised Feedback Oscillator (Gunn oscillator) and Distributed Parameter Distributed Feedback Oscillator (Laser). (5) It is interesting that not a single report has raised a question on the modification of Barkhausen criterion for soft self and hard self excited oscillators, particularly in respect of the modes of stability. (6) Finally, physics of spectral purification of the output waveform during the growth part of the oscillation has been elaborated. (7) In this paper we briefly touch upon these points which are yet to be clarified in spite of the efforts of many workers. 2. Barkhausen Modelling of FB and NR Oscillators and Spectral Processing Referring to Appendix – I, it is seen that the following relations for the four-terminal and two-terminal oscillators can be written as [ ] Oscillator T A N s G s G i v T n 4 ) ( ) ( 1 ) ( 4 - = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ (1) 978-1-4244-6051-9/11/$26.00 ©2011 IEEE