# Don't oscillator work when phase shift is 180 degrees or 0 degree?

#### skatefast08

##### Full Member level 3
Don't oscillator work when phase shift is 180 degrees or 0 degree? Because in the oscillator design guide on the keysight webpage as shown in a screenshot below, says the widespread belief is when the phase of the transfer function is 0 and magnitude greater than 1 then the system is unstable. (therefore oscillations will occur, my words). So is the statement correct that a system is unstable when the phase difference is 0 and mag is greater than 1 which would create an oscillation or is it when the difference is 180 degrees? Thanks There are two required conditions to make a feedback system oscillate: the open loop gain must be greater than unity, and total phase shift must be 0° or 360° at the frequency of oscillation.
The oscillation starts when the loop gain |Aβ|>1, and returns to unity |Aβ|=1 once oscillation stabilize.

Although the stated conditions are true for most oscillator circuits, there are circuits with a loop gain point Aβ>1 that don't oscillate. This can happen if the loop gain crosses |Aβ|=1 multiple times. You need to evaluate the Nyquist stability criterion in this case.

There are two required conditions to make a feedback system oscillate: the open loop gain must be greater than unity, and total phase shift must be 0° or 360° at the frequency of oscillation.
The oscillation starts when the loop gain |Aβ|>1, and returns to unity |Aβ|=1 once oscillation stabilize.
Then can you explain why many papers and Google say that you need at least a 180 degree phase shift to create an oscillator? Not 0 or 360 degrees. See example paper here on page 4: Design and Simulation of RF CMOS Oscillators in Advanced Design System ... https://www.eleceng.adelaide.edu.au/personal/dabbott/wiki/images/b/b4/OscillatorsADS.pdf

There's no derivation of oscillation condition in the paper at all. It just states that the circuit oscillates if the frequency dependent phase shift is 180°, without clearly explaining that it uses an inverting amplifier, resulting in a total open loop phase of 0°.

### skatefast08

Points: 2

The above might help.....

Regards, Dana.

• skatefast08

### skatefast08

Points: 2
There's no derivation of oscillation condition in the paper at all. It just states that the circuit oscillates if the frequency dependent phase shift is 180°, without clearly explaining that it uses an inverting amplifier, resulting in a total open loop phase of 0°.
So the paper is incorrect?

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