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# dominant pole and stability

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#### Junus2012

dear friends

I would like to ask you why when the second pole of the OPAMP become before the GBW, the amplifier will be unstable ???

the second question which I am sorry to ask it, What is the meaning of dominant and non dominant poles? do we have more than one dominant pole ?

thank you very much

Hi Junus,

at first, stability of an amplifier can be discussed only in conjunction with feedback.
That means: An opamp without feedback is always stable - independent on pole location.
In case the second pole of an opamp is still in the active region (open-loop gain>0 dB) the stability properties depend on the feedback factor.
Thus, each opamp with a second pole below the transit frequency (GBW) is stable if the closed-loop gain is large enough (feedback small enough).
Regarding stability the gain of the open loop (loop gain) is the characteristic which matters only.

Junus2012

### Junus2012

Points: 2
thank you LvW for replying me
if we consider the buffer connection which represent the worst stability case, still the concept of puttong the second pole beyond GBW is the same which still I dint know how this assure the stability ? why when it come before the GBW the closed loop Opamp become not stable ?

You'll determine stability by analyzing the loop gain magnitude and phase characteristic. For the simple case of monotone magnitude characteristic, a positive phase margin implies stability. A considerably larger phase margin will be required for acceptable time domain behaviour, however.

Strictly speaking, an OP with only two poles and real feedback factor has still a positive phase margin, independent of the second pole frequency. But that's somewhat theoretical, most OPs have more than two poles, and the feedback path often involves additional poles created by OP input capacitance.

Points: 2

### Junus2012

Points: 2
why when it come before the GBW the closed loop Opamp become not stable ?

As mentioned above by FvM, the closed-loop will always be stable - even if there is a 2nd pole before the open-loop gain crosses the 0 dB line.
However, for certain applications the stability margin may be too small (step response with severe overshoot, ringing).
In addition, unwanted parasitic phase shifts within the loop may bring the circuit close to instability. Thus, a certain phase margin (in practice: 50...60 deg) is required.

Junus2012

### Junus2012

Points: 2
Regarding stability the gain of the open loop (loop gain) is the characteristic which matters only.

I'm rather sure you thought of closed loop, isn't it?

I'm rather sure you thought of closed loop, isn't it?

No, indeed I thought of the gain for the open loop, which is known as the "loop gain".
But - I agree, perhaps my wording was not clear enough.
Of course, it is the closed loop that matters primarily - stable yes/no.
However, as you certainly know quantitative stability properties (how much margin?) are checked using the open-loop characteristic.
And because the questioner (Junus) spoke about the amplifier gain only, it was my intention to point to the fact that the whole (open) loop has to be considered - that is the PRODUCT "gain*feedback".
The loop phase at the cross-over frequency of the loop gain must be "far away" from the stability limit (0 deg).

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I'm used to distinguish three gain terms related to OPs:

- amplifier open loop gain A(ωt)
- circuit loop gain A(ωt)*β(ωt)
- circuit closed loop gain ≈ α(ωt)/β(ωt)

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