- #1

Joseph M. Zias

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You should upgrade or use an alternative browser.

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

- #1

Joseph M. Zias

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Engineering news on Phys.org

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Tom.G

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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

- #3

Joseph M. Zias

- 78

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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?

- #4

Joseph M. Zias

- 78

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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.Joseph M. Zias said:

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?

An inverted pole is a mathematical concept used in signal processing to represent a system's frequency response. It is a pole that is located in the negative complex plane, indicating an unstable system. A pole-zero diagram is a graphical representation of the inverted pole and other poles and zeros in a system's transfer function.

The pole-zero diagram is important because it provides valuable information about a system's stability, frequency response, and filtering properties. It allows scientists to analyze and understand a system's behavior and make necessary adjustments to improve its performance.

The main components of a pole-zero diagram include poles, zeros, and the unit circle. Poles are represented by an "x" symbol and indicate the frequency response's resonant frequencies. Zeros are represented by an "o" symbol and indicate the frequencies where the system's output is zero. The unit circle represents the frequencies where the system's output is 1.

A pole-zero diagram can help in designing filters by providing a visual representation of a system's frequency response. It allows scientists to identify the location of poles and zeros, which can be used to design filters that meet specific frequency response requirements.

In a pole-zero diagram, a stable system is represented by poles and zeros located within the unit circle. This indicates that the system's output is bounded and does not grow infinitely. In contrast, an unstable system is represented by poles outside the unit circle, indicating that the system's output will grow without bounds, leading to instability.

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