Consider an op-amp with negative feedback which uses a feedback resistor network which may be used as an inverting amplifier for V­­2 = 0 and non-inverting amplifier V1 = 0

The closed loop transfer function is given by ACL = A/1+Aβ

Where; A : open loop voltage gain
               B : Feedback ratio

If (1+Aβ) = 0 the circuit will become unstable and gives sustained oscillations.

Re-writing 1+Aβ = 0 as 1-(-Aβ) = 0 leads to –Aβ = 1

Aβ is a complex quality

 

Therefore, │Aβ│ = 1 and phase condition Lle– Aβ =0 or (multiple of 2π)
                                                                          Lle– Aβ =1 or (multiple of π)  

Since, resistor is the present in feedback network it does’t provide any phase shift.

When op-amp is used in inverting mode it provides phase shift 

Of 180o and at low frequencies.

However at high frequencies due to each corner frequency an additional phase shift of maximum -90o can take place in open loop gain phase. So, for two corner frequencies maximum phase shift is added

Hence at high frequencies magnitude Aβ becomes unity when A has an addition phase shift of 180o whic make total phase shift is ‘0’.

 

This causes the amplifier to begin to oscillates and oscillations are the starting point for in stability.

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