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a phase shift oscillator is just basically a type of oscillator. a phase shift oscillator is a feedback oscillator. for a feedback circuit to be an oscillator it must satisfy two conditions (known as the barkhausen criterion). one is that the gain around the closed loop should be unity. and the phase shift around the closed loop should be zero.
in a phase shift oscillator a phase shift network is used which shifts the phase of the output through 180° then this shifted output is fed into the inverting input which results in a total of 0° phase shift.
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