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Barkhausen criterion and oscillation

The usual explanation of a feedback oscillator goes like this. ""We have an Amplifier 'A(w)', a feedback circuit 'B(w)'. An initial input v=Ke(jwt) produses an output A(w)*B(w)*Ke(jwt) which in turn produces an output (AB)^2 * Ke(jwt) ...... => If the signal is to be sustained |AB|=1 and arg(A)+arg(B)=2*pi then each delayed echo or cycle of fluctuation will ?tack itself onto the tail? of the previous fluctuation with the same sinusoidal phase leading to oscillation."" I really don't get it . An Amplifier produces the output based on instantaneous value of input signal and there is no mechanism which stores an AC signal. Then how is the oscillation sustained if the initial disturbance is removed ? Please correct me if I am wrong.

Reply to
Manu Varkey
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Any real amplifier has time lags of various forms, the simplest being the limits of the speed of light through the amplifier and whatever path closes the feedback loop. Very high-frequency oscillators are dominated by this lag. Slower amplifiers have internal capacitive and inductive elements that slow them down, add phase shift, and effectively store information within the amp.

The A(w) transfer function would be dimensionless (like '3' or some such) for an ideal, zero-delay, infinite bandwidth amp, but it never really is, except maybe in Spice.

You can still build an oscillator from an ideal zero-delay amp, so long as the B(w) transfer function keeps things happy. If you connect the input of a very fast amplifier to its own output through a long hank of coaxial cable (the cable providing a nice time delay), that will oscillate too. The information storage is then inside the length of the cable.

John

Reply to
John Larkin

Capacitence and inductanace store charge and delay the signal. Amplifiers are not perfect... there are also transient behaviors that you are not taking into account.

Try this,

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Reply to
Jon Slaughter

It is impossible to remove the initial disturbance. All electronic components, including resistors, exhibit some noise. At frequencies where Barkhausen's criteria are met, any signal at those frequencies will grow until limited. Limiting occurs when amplitude reaches a point where gain is reduced, often due to saturation of some component.

Reply to
Don Foreman

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