Phase Shift Oscillator

[stitch]

I can understand the source of oscillations in a Colpitts oscillator (the tapped tank circuit).  But I am having difficulty understanding the source of oscillations in a phase shift oscillator.  I do see a feedback path in a phase shift oscillator, but where do the oscillations come from?  Thank you.

[IanB]

To have oscillations you need positive feedback.

Supposing your oscillator output is going to be a sine wave, then if you shift a sine wave by 180 degrees it will look like an inverted form of the original wave. So  take that wave, shift it by 180 degrees and then feed it to the inverting input of an amplifier and you will have positive feedback. Voila! You have oscillation.

[stitch]

Thank you IanB.  But what is the source of the sine wave that you mention?  Where did the sine wave come from in the first place?

[ejeffrey]

Noise.  There is always a small amount of broadband noise present due to the amplifier input noise or the resistor johnson noise.  The noise at the selected frequency is amplified each time it goes through the feedback loop until it gets to be full-scale.

Some types of oscillators actually do have trouble starting up in a reasonable amount of time.  In that case, injecting some signal from an external source may help things get going.

[stitch]

Thank you, ejeffrey. That is the missing link I was looking for. 

[w2aew]

Noise.  There is always a small amount of broadband noise present due to the amplifier input noise or the resistor johnson noise.  The noise at the selected frequency is amplified each time it goes through the feedback loop until it gets to be full-scale.

Some types of oscillators actually do have trouble starting up in a reasonable amount of time.  In that case, injecting some signal from an external source may help things get going.

This is precisely why is sometimes is difficult to simulate these types of oscillators - because there might not be enough numerical rounding (noise) to get the oscillation started.  For these circuits, one often has to apply a transient or use some other initial conditions to get "things moving"...

[Zero999]

This is precisely why is sometimes is difficult to simulate these types of oscillators - because there might not be enough numerical rounding (noise) to get the oscillation started.  For these circuits, one often has to apply a transient or use some other initial conditions to get "things moving"...

Yes, that's true for many circuit. In LTSpice the easiest way to do this is to skip the initial operating point calculation which means the power supply voltage is suddenly applied, charging up all the capacitors, rather than the simulator figuring out the DC voltages around the circuit before starting the simulation.