When we looked at RC networks in Chapter 1, we saw that a single RC network was asymptotic to 90 of phase shift. To make an oscillator, we need 180 of phase shift, so a single stage amplifier with one RC network causing an LF or HF cut-off cannot oscillate. If we cascade two such stages, we can approach 180 of phase shift, and if we feed this back into the input, it will ring, but not oscillate. If we have three such stages, it is a racing certainty that we can make the cascade oscillate when we apply feedback, and this is the basis of the phase shift oscillator.

To achieve oscillation, we need more than phase shift. Just because our feedback signal s phase has been shifted by 180 , it will not necessarily generate oscillation. We also need sufficient loop gain. The basis of oscillation is that it is self-sustaining; the gain of the amplifier must be sufficiently high to overcome the losses in the feedback loop before oscillation can occur. Loop gain is thus defined as the gain of the amplifier multiplied by the loss of the feedback loop.

If we have a phase shift of 180 , and loop gain ?1, the circuit will oscillate.

Now that we have this definition, we can see how to avoid designing oscillators. We have two weapons at our disposal:

• We can reduce the number of stages, such that phase shift never reaches 180 .