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Question in Poles in miller Capacitor

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diego.fan

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About the yellow part in attached, could you please tell how to explain this from theoretical aspect?

Can I always deleted the highest order to get dominant pole?
Delete 1 to get fnd?
 

If you assume that the poles are -p1 and -p2 then p1+p2 = -a/b and p1 * p2 = 1/b. Since a Miller capacitor splits the poles, we can assume that one of the poles happens at a much higher frequency than the other one. Assume that p1 << p2, then, p1 + p2 will be approximately p2 and we can find the dominant pole p2= -a/b. Having p2, we can use p1 * p2 =1/b to find p1.
 

mahdi3999 said:
If you assume that the poles are -p1 and -p2 then p1+p2 = -a/b and p1 * p2 = 1/b. Since a Miller capacitor splits the poles, we can assume that one of the poles happens at a much higher frequency than the other one. Assume that p1 << p2, then, p1 + p2 will be approximately p2 and we can find the dominant pole p2= -a/b. Having p2, we can use p1 * p2 =1/b to find p1.
Click to expand...

Thanks. I don't know why we can get p1+p2=-a/b and p1*p2=-1/a
 

Assume that p1 and p2 are the roots of the denominator.
(s+p1)*(s+p2) = s^2 + (p1 + p2)*s + p1*p2

Multiply the above by b ( you can because the roots will not change) and equate with the denominator of the fraction.
 
Since you know the Miller Theorem, one pole is closer to operating frequency/band, other pole is too far from the other.That's why one is dominant ( you can say that "effective") other one is nonfunctional.
 

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