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Crystal oscillator Gain

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I was reading more about the crystal oscillators and had this question in mind.

During the initial start up, the gain of the oscillator should be large and later on, the gain should be greater or equal to 1.

I'd like to understand on how this is done? Initially gain is high and later on it decreases to a lower value. How and when does this happen?
 

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The G = 1, loop G, is minimum required to sustain oscillations. G >> 1 is to insure
osc starts up, eg. noise is amped up to get loop going. "Normally" one just seeks G >>1
and doe not modify. There are circuits, AGC, that modify loop G to force G = 1, to insure
amplitude stays constant. Usually used in low distortion sinewave type oscillators.





Regards, Dana.
 

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Typical crystal oscillators don't use AGC, nevertheless requires the oscillation condition unity loop gain in steady state. It's achieved by amplifier nonlinearity. Above a certain input level, the output voltage doesn't increase further.The higher the input voltage, the lower the effective gain.
 

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