Oscillator conceptual basic

How oscillator will oscillate with a particular frequency if the noise voltage signal (which is the reason for the output oscillating signal) does not attain that particular frequency? (or What is the guarantee that noise voltage will be attaining that particular frequency at which the output signal will oscillate?)

The frequency of the noise voltage is irrelevant. The noise forces the output to change, and THAT'S what's needed to start oscillation.

but how I am thinking is that the input signal to the feedback network should be a particular frequency (at which Aβ = 1, here A = open loop gain of opamp and β is the feedback circuit gain) to make feedback signal = input signal to opamp in forward network.If you explain me how exactly all these things happening then that will be good .

Random noise has many frequencies.

Audioguru said:

Random noise has many frequencies.

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So can I see random noise as fourier series? Is it the right concept? Then I must see the feedback network as filter which allows only that frequency (which is not correct) ?

Timkuc - it is not true that noise starts oscillation. This is a common misconception - and it has been proved several times that it is simply the supply voltage switch-on transient which starts oscillation.

Simple (theoretical) example: What happens when an LC tank circuit (with moderate losses) is excited with a short voltage or current pulse? Answer: It reacts with a decaying sinus oscillation.
And the same happens for each circuit which is able to oscillate. As soon as you switch on the power for the active device the circuit answers with its step response which consists of a sinusoidal signal with a frequency equal to the designed oscillation frequency. If Barkhausen`s oscillation condition is fulfilled (loop gain slightly larger than unity), the circuit produces self-sustained oscillations.

All amplifers will contain contain noise in the bandwidth of the oscillator and even overtones of crystal oscillators. The harmonic with the highest gain will end up oscillating.

Both input transients on power up and random noise contribute signal that gets filtered. In the case of a balanced oscillator with exactly unity loop gain at 0 or 360 deg in noiseless system will not oscillate, so for sinusoidal ouput usually the gain is increased enough to start oscillating quickly and then limiting reduces the gain to full range sine wave output . But in any case some uV of input offset or random noise is needed for an initial condition

. Normally even with a large step input voltage on power up into a high Q oscillator , the time to full swing increases with higher stability , high Q oscillators. Thus low frequency watch crystals require a longer POR, power on reset time before a stable full logic output is reached than one > 1 MHz .

Again startup time depends on excess gain and oscillators with squarewave outputs have at least 10 dB of excess gain and usually more. Too much gain can sometimes lead to unpredictable resonance from internal buffered logic stages. E.g. 3 stage buffer logic inverter.

Timkuc - it is not true that noise starts oscillation. This is a common misconception - and it has been proved several times that it is simply the supply voltage switch-on transient which starts oscillation.

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That's true for all practical oscillators, the power density of initial transients is many times over the noise level.

But if you manage to supress initial transients perfectly, circuit noise would still stoke oscillations if the oscillation condition is fulfilled with a bit of excess gain.

FvM said:

But if you manage to supress initial transients perfectly, circuit noise would still stoke oscillations if the oscillation condition is fulfilled with a bit of excess gain.

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How could this be done?

LvW said:

How could this be done?

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One could use a circuit with adjustable gain, power it up with gain too low for oscillation, then increase the gain.

godfreyl said:

One could use a circuit with adjustable gain, power it up with gain too low for oscillation, then increase the gain.

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Ok - but I am sure that the discontinueties during the gain increase around the point where loop gain=0dB will cause a kind of inbalance - and thus start of oscillation - before any noise will be effective.
On the other hand - it`s a pure theoretical exercise only.

On the other hand - it`s a pure theoretical exercise only.

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Yes, of course. In so far it's probably not worth to discuss the point extensively. But if you manage to make the supply voltage rise very slow, then the oscillator in-band noise density can be larger than the respective spectral component of the supply transient and thus the noise command the oscillation start.

Acousical feedback howling might be a good example of noise causing the beginning of an oscillation.
We have all seen a microphone and speakers set up with a little too much gain or too much coupling between the mic and the speakers. At rest there is no oscillation. But when somebody quietly approaches the mic then some of the wideband ambient noise bounces off their face and into the mic. HOWL!

Thanks guys