Is there any shortcut to calculate zeros?

[sk1105]

I'm focus on the frequency response of a amplifier, but I find no sense of calculating the zeros. Is there any handy methord to estimate the zeros?
The ampifier circuit is in the attachment. If I add a ac signal to the Vdd, how to estimate the zeros of the frequency response of the ac gain from vout to vdd?
Thanks very much.

 

[arebee]

Hi. Do you want to find the zero's numerically or symbolically? If you mean numerically then you can use SPICE. If you need a symbolic expression then there's no way around doing some circuit analysis (rather tedious), although there are some techniques that can speed up this process if you just need the zero's and not the whole transfer function.

Why do you need the zeroes in the first place? If you want the frequency response then usually finding the poles is sufficient as the zeroes are usually larger. You can find the dominant pole using the open circuit time constants method in that case.

 

[sk1105]

Thanks. i want to find the zero's symbolically. i've done some circuit analysis. i wonder if there is some techniques that can simplify the analysis.

 

[arebee]

You could try the symbolic SPICE simulator SAPWIN (use google). It'll give you an expression, albeit a very complicated one (not easy to interpret).

There's a relatively new book that explains how to use Middlebrooks Exra Element Theorem to more easily derive transfer function and thus get the poles and zeros: https://www.amazon.com/gp/reader/05...7479105?_encoding=UTF8&p=S00A&j=0#reader-page

Its in ebook form, but I havent been able to find a copy.