DescriptionConstant-k Prototype Lowpass Image Impedance.svg	English: A graph of the image impedance of a protoype constant-k filter. Note that the impedace is purely real below ${\displaystyle \omega _{c}=1}$ and purely imaginary above this.
Date	19 April 2009
Source	Own work
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Mathematica Code

l = 1;
c = 1;

wc = 1/Sqrt[l*c];

zit[w_] := Piecewise[
  {
   {l*Sqrt[wc^2 - w], w < wc},
   {I*l*Sqrt[w - wc^2], w \[GreaterSlantEqual] wc}
   }
  ]

LogLogPlot[
 {Re[zit[w]],
  Im[zit[w]],
  100
  },
 {w, 0.01, 1000}
 ]