Calculating Impedance

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Complex impedance is computed using time histories of voltage and charge therefore the following code must be included in the input file to enable impedance to be extracted in Review:

pout
      histname electrode vq all      /* Volt/charge time histories 1 & 2
      end

Once the input file is run, it creates a history file which is read into Review using code such as the following:

text filename = InsertNameHere      /* Change filename as required
read f1 '$filename.flxhst'          /* Read time history

Windowing/Padding

In some cases, the impedance plot is poorly discretized (or fractured). This is because the number of data points in the time history is insufficient to produce a suitably small frequency step size when the FFT was calculated. 

The solution is to pad out the time history with extra zeros. Although this may sound like a cheat, it simply adds extra data points after the charge on the electrode in the model has already rung down to zero. This does not change the data; it merely extends the data set. The addition of the zero data points in the time set increases the number of points in the frequency set, thereby decreasing the frequency time step.

freq
     file f2                          /* Local file to store results
     time pad 4                       /* Zero padding for better resolution
     end    

Another common problem with impedance plots is the addition of ringing resonances in the operational impedance, when the simulation has not run for long enough and the charge has not dissipated from the electrode. This truncation of the charge signal introduces spurious signals into the impedance characteristics. Windowing the new local file prevents generation of these frequencies.

freq
      file f2                          /* Local file to store results
      wndo hann righ 0.15              /* Windowing to ensure signals terminate at zero
      end

 Calculation

The voltage and charge time history on an electrode where the drive function was applied are stored in records 2 and 3 which is what is used to calculate impedance.

freq
     file f2                             /* Local file to store results
     type amp                            /* Results in Amplitude and Phase
     impd f1 2 f1 3                      /* Calculate Impedance Magnitude
     end

By default, impedance data is output in magnitude and phase format; use of the type command can change this to real and imaginary. The impd command calculates the operational impedance based on arrays 2 and 3 in local file f1 and outputs the amplitude and phase to arrays 1 and 2, respectively, in local file f2.

Plotting 

Impedance curves can be plot using the grph command. The number of viewports is set using the nvew command and then plot is used to specify which curves to plot in the ports. Limits can be set on the X and Y axis using the pset command. 

grph
       type stnd                          /* Use standard graphics for Logarithmic plots
       nvew 2
       pset wndo 0 10.e6                  /* Set up X Scale
       plot f2 1                          /* Plot Amplitude
       set log y on
       plot f2 2                           /* Plot Phase
       end

  • Download our Review template to calculate impedance here
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