Computing Impedance Values


		Computing Impedance Values

RESOURCES > EIS > COMPLEX NUMBERS > COMPUTING IMPEDANCES

I recently wanted to calculate some impedance values using some of the equations given in this web site. I was embarrassed to find out how long it took me to figure it out!. Since you might have the same problems, here are the tricks I finally remembered. If you need a refresher on complex numbers, see "Simple Stuff about Complex Numbers"

The one equation that is key to translating the equations given on this web site and elsewhere is

$e^jx = cos(x) + j sin(x)$

Not only does this allow us to exponentiate an imaginary number, but it is also the clue to other arithmetic operations. For example, if we substitute x= $pi / 2$ (or 90°), we get

$exp(j*pi/2)=j$

Although this looks like the hard way to write j, taking the square root of both sides gives

$sqrt(j)=exp(j pi/4)$

We need the square root of j to calculate the values of diffusional impedances, W, O, and T.

A similar trick helps us to calculate the impedance of a Constant Phase Element.

$j^n$

Some other relationships may be needed as well. I found the identities involving tanh( jx ) and coth( jx ) in the CRC Handbook. More tips are in Numerical Recipes, along with techniques to make things more "computable," i.e., how to compute values without crashing your program! See Sec 5.4.

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