# how to decide the first non-dominant pole?

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#### hurongbin

##### Newbie level 4
dominant pole

The dominant pole can be easily decided using miller approximation, but there is no way to easily decide the first non-dominant pole. The first non-dominant pole is the same important as the dominant pole for stability and frequency performance.
Is there someone who kowns any method to decide the first non-dominant pole easily?

#### LvW

what is the dominant pole of an amplifier

As a first approximation you could set the second pole at (or above) the frequency where the open loop gain of the amplifier reaches 0 dB (unity gain frequency). In this case you roughly have a phase margin of at least 45 deg.

#### hurongbin

##### Newbie level 4
dominant pole of an amplifier

LvW said:
As a first approximation you could set the second pole at (or above) the frequency where the open loop gain of the amplifier reaches 0 dB (unity gain frequency). In this case you roughly have a phase margin of at least 45 deg.
Thank you LvW.
I knew that. I just do not know how to decide the second pole from the circuit.
For example, if I have a opamp, how can I decide the second pole. Usually, I can decide the dominant pole, but I can not decide the second pole.

#### LvW

non dominant pole

hurongbin said:
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Usually, I can decide the dominant pole, but I can not decide the second pole.

OK, I see. Normally, one hopes that the second pole is as far as possible. Because it will not be set intentionally, but it is determined by unwanted parasitic effects. Thus, use active parts and gain stage topologies with very high frequency capabilities - but such an approach always results in a compromize between performance and cost.
I´m afraid that´s all one can say to this point.

#### hurongbin

##### Newbie level 4
thank you very much!

#### erikl

##### Super Moderator
Staff member
hurongbin said:
... Usually, I can decide the dominant pole, but I can not decide the second pole.
May be the following paper is helpful. S. p. 40 ff.

#### hurongbin

##### Newbie level 4
As we know, we can get a formula for dominant pole using zero-value time constant method.But, It is very hard to get a formula for the first non-dominant pole.The first non-dominant pole is very important for feedback amplifier stability andfrequency performance.
What I mean is that if we get a formula for the first non-dominant pole, then we can know what factors influence the first non-dominant pole and how to improve it.
As we know, for stability, GBP must be smaller than the first non-dominat pole by a factor 4 or 3.
Normally, the GBP of the forward amplifier is the bandwidth of the feedback ampifier, so if we improve the GBP of the forward amplifier, we get wider bandwidth of the feedback amplifier.But, there is a promblem that when the GBP is bigger than the first non-dominant pole, the feedback amplifier become unstable.

#### alvays

##### Member level 4
hurongbin said:
As we know, we can get a formula for dominant pole using zero-value time constant method.But, It is very hard to get a formula for the first non-dominant pole.The first non-dominant pole is very important for feedback amplifier stability andfrequency performance.
What I mean is that if we get a formula for the first non-dominant pole, then we can know what factors influence the first non-dominant pole and how to improve it.
As we know, for stability, GBP must be smaller than the first non-dominat pole by a factor 4 or 3.
Normally, the GBP of the forward amplifier is the bandwidth of the feedback ampifier, so if we improve the GBP of the forward amplifier, we get wider bandwidth of the feedback amplifier.But, there is a promblem that when the GBP is bigger than the first non-dominant pole, the feedback amplifier become unstable.

If there are only two widely seperated poles, you can decide the location of the non-dominant poles with the short-circuit time constant method and the location of the dominant poles with the zero-value time constant method.

Sometimes, the dominant poles can be easily found. In this case, you can check carefully to find the non-dominant poles. To multistage amlifier, you can try every poles, their resitance and capacitance. If you are still not sure, then just make the dominant pole far away enough to these poles. Though this may be not so easy.

Tags: pole, non-dominant pole, dominant pole, feedback, amplifier, stability

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