I have learned that there is two basic conditons for sustain oscillation

1. A(w)b(w)=1 (loop gain=1)
2.phase shift of 0 or multiple of 360

but to start A(w)b(w)>1

why those conditions? how to understand that?

 

For an oscillation to start an amplifier has positive feedback .

 

@athulascc

Because all other conditions will either dampen the oscillation or cause a stable saturation condition at the positive or negative rail.

 

Hello,

Have a look at the following PDF:
sloa087_sinewave_oscillators.pdf

Bertus

 

yes @Dodgydave , but if A(w)b(w)>1 at the start then how it becomes =1 when oscillation?
when we design we can't make actually A(w)b(w)=1 , but how it oscillate?

@GopherT I am trying to find theory behind these two conditions?

 

@bertus thanks.that contains what I am looking for.

 

yes @Dodgydave , but if A(w)b(w)>1 at the start then how it becomes =1 when oscillation??

You don't really need to worry about that. The amplifier's gain will, at some point, decrease to the point where loop gain will = 1. At that point, you have sustained oscillation.

 

yes @Dodgydave , but if A(w)b(w)>1 at the start then how it becomes =1 when oscillation?
when we design we can't make actually A(w)b(w)=1 , but how it oscillate?

@GopherT I am trying to find theory behind these two conditions?

I thought it was obvious.
Any phase shift not = 360 degrees (or multiples) will cause the gain of 1 condition to not be true at various times in the oscillation period.
Any gain below 1 will cause the signal to dampen each oscillation.
Any gain over 1 will cause signal to saturate after some number of oscillations.

 

A gain of 1 will sustain an oscillation, but that is of little use at start up when there is no oscillation. So a gain >1 is required to start.

Once an oscillation begins a gain >1 will indeed produce saturation; saturation is a non-linear condition with a side effect of limiting gain, so the now distorted (or clipped) signal will be running about with a gain of precisely 1.

 

great. that means gain depends on frequency. and when w comes to A(w)b(w)=1 it sustains.
I am getting more and more knowledge.