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In summary, when analyzing a Bode plot or its transfer function the technique of "inverted poles" is sometimes used.f

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https://web.archive.org/web/20160331135833if_/http://ardem.com/downloads/GFTManual.pdf

A Google search for Dr. R. David Middlebrook turned up over 400 000 hits. The above link is reference [8] in the first hit (https://en.wikipedia.org/wiki/R._D._Middlebrook)

Cheers,

Tom

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Erickson gives an example of this technique: http://ecee.colorado.edu/~ecen2270/materials/Bodenotes.pdf

Basically having a transfer function such as Erickson uses for example: A = A0 (1 + s/w1)/(1 + s/w2) ; A0 being the DC gain we can re-write with a little algebra

A = Ahf (1 + w1/s)/(1 + w2/s); here Ahf is A high frequency or A infinity. The numerator is an inverted zero and the denominator is a inverted pole, inversion being w1/s instead of the non-inverted s/w1. Well, all this makes good sense and bode plots and math are relatively easy to follow. You are referencing gain to the high frequency gain instead of the low frequency gain. Sometimes you will have mixed poles and inverted poles and mixed zeros and inverted zeros.

So I muse - how do you put both poles and inverted poles on the same pole-zero diagram?

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Well, I guess I will answer my own question. There is no special symbol that I know off for an inverted pole on a pole-zero diagram. However, an inverted pole is equivalent to a real pole and a real zero at the origin. Apparently no one goes to that detail but instead just use the method with transfer functions and bode plots to simplify the analysis. So I think this thread can be closed.

Erickson gives an example of this technique: http://ecee.colorado.edu/~ecen2270/materials/Bodenotes.pdf

Basically having a transfer function such as Erickson uses for example: A = A0 (1 + s/w1)/(1 + s/w2) ; A0 being the DC gain we can re-write with a little algebra

A = Ahf (1 + w1/s)/(1 + w2/s); here Ahf is A high frequency or A infinity. The numerator is an inverted zero and the denominator is a inverted pole, inversion being w1/s instead of the non-inverted s/w1. Well, all this makes good sense and bode plots and math are relatively easy to follow. You are referencing gain to the high frequency gain instead of the low frequency gain. Sometimes you will have mixed poles and inverted poles and mixed zeros and inverted zeros.

So I muse - how do you put both poles and inverted poles on the same pole-zero diagram?

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