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I am working on a project to model the electrical characteristics of a piezoelectric (PZT) and would like to get a sanity check to make sure I am going about it in a way that makes sense.

So I am using the Van Dyke-Butterworth model for a PZT. I have measured the absolute impedance of the PZT using an impedance analyzer and am now working to fit the impedance function for the Van Dyke-Butterworth model to my data to find the value of the model components.

Where I need a check is for the steps of calculating the magnitude of the impedance. 1 write down Z [2] multiply the numerator and denominator by the complex conjugate of the denominator [3] separate into real and imaginary parts and square them [4] take the square root

I want to make sure I am not adding any terms because the steps seem to make sense but I am ending up with values extremely different for my calculated abs(Z) than from my measured abs(Z).

Am I missing something obvious? Any thoughts would be most appreciated

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    \$\begingroup\$ I found an answer to my own question over on the math Stack Exchange \$\endgroup\$
    – prov
    Oct 21, 2017 at 16:39

1 Answer 1

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The magnitude of any complex number z can be found by taking the square root of zz*, where z* is the complex conjugate of z.

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  • \$\begingroup\$ I realize that. However if Z has a complex denominator you do have to get it to a real denominator first, correct? \$\endgroup\$
    – prov
    Oct 19, 2017 at 16:05
  • \$\begingroup\$ Not necessarily. \$\endgroup\$ Oct 19, 2017 at 16:20

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