2.8 Series and shunt resistances

Figure 2.4 shows the equivalent circuit that \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} SimSS}}\) and \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} ZimT}}\) use. 1 However, the way this circuit is used differs for the two codes.

\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} SimSS}}\) treats the applied voltages (as specified by parameters \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Vmin}}\), \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Vmax}}\), etc.) as the voltage across the simulation volume, i.e. as \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Vint}}\), the internal voltage. When using finite shunt and/or series resistances, it calculates the corresponding external voltage and current density as measured by an experimenter. Both the internal (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Vint}}\), \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Jint}}\)) as well as the external voltages and currents (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Vext}}\) and \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Jext}}\)) are stored. 2 Any current (\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Jshunt}}\)) flowing through the shunt resistance is also stored. The \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} varFile}}\) stores how the internal variables depend on position within the device. As these are internal to the simulation volume they do not contain any contributions from the series or shunt resistances.

\(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} ZimT}}\) is a little bit more sophisticated in that it treats the applied voltage (as specified by the input \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} tVGFile}}\), see section 3.5) as the external voltage \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Vext}}\). Thus, if there is a (finite) series resistance, \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} ZimT}}\) will solve for the voltage that is applied to the electrodes (i.e. \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Vint}}\)) by using another iteration loop. This arrangement makes it possible, for example, to use \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} ZimT}}\) to simulate an \(RC\)-circuit, or transient measurements where one needs to consider the internal series resistance of the source. 3

\includegraphics[width=0.4\linewidth ]{figs/Equivalent_circuit.svg}
Figure 2.4 Equivalent circuit illustrating the meaning of the internal voltage and current versus the external ones.
  1. I realise that these hand-drawn images may look a bit primative. I hope, however, that they add a personal touch. Besides, I do not want to spend too much time on stuff like this.
  2. Any comparison done with an experimental, user-supplied current-voltage characteristic is based on the external voltage and current.
  3. \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} ZimT}}\) can also be used in steady-state, see section 3.5. Thus, it is possible to specify the external voltage \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} Vext}}\) while still incorporating a finite series resistance by using \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} ZimT}}\) instead of \(\mathtt{\require{color}{\color[rgb]{0.000000000000000,0.500000000000000,0.500000000000000} SimSS}}\).