hi, our electronics tutor was talking to us about phase-shift oscillators using op amps. one thing he has never been able to under stand is. If you have 3 capictors and 3 resistors it 60 degrees out of phase across each capictor but if you increase this to 4 capictors and 4 resistor then its 45 degrees out of phase. how can the circuit work out what the phase angle is?

 

The circuit oscillates at the frequency where the phase shift around the loop is exactly 360 degrees. The amplifier provides 180 degrees. The other 180 comes from the RC network.

 

how can the circuit work out what the phase angle is?

Asking a question like that is to implicitly subscribe to the anthropocentric method of circuit analysis.

The circuit doesn't "work out" anything. To say it like that suggests that the circuit is a living being that has to "work out" what it's going to do.

The answer is that in order for the oscillations to be continuous, which is what we want oscillators to do, some of the output must be fed back to the input of the amplifier to make up for losses in the circuit.

The fed back signal must be in the right phase with respect to the oscillations that are already going in order to sustain them. The phase shift network is there to make sure that there is only one frequency that will have the required 180° phase shift when it is fed back.

If any other frequency tries to get through the network (there's that anthropocentric point of view again), its phase shift through the network won't be 180°, and it will eventually die out because it won't reinforce the correct frequency.

So, when you first turn the power on, the inevitable noise present in electronic circuitry (or the turn-on transient) will contain many frequencies which will be applied to the phase shift network. Only one frequency will reinforce itself in the amplifier, the one with exactly 180° of phase shift through the network, and its amplitude will gradually build up until it is limited by some mechanism, such as clipping, or perhaps some deliberate regulation by a specific part of the circuit. Other frequencies will not be reinforced, and their amplitude will remain at the noise level.

 

At any other angle than optimal it won't oscillate, can't oscillate. If its feedback is 200° phase shift then you don't get oscillation, only when the conditions are met exactly does oscillation happen. It is very math based, which is't that surprising.