Uncompensated transmission lines

Application of series capacitors and analysis of an uncompensated transmission line and the capability of power transfer and system regulation with and without series compensation are also presented. 

Figure 15 shows a set of complex plane impedance plots for polypyr-rolein NaC104(aq).170 These data sets are all relatively simple because the electronic resistance of the film and the charge-transfer resistance are both negligible relative to the uncompensated solution resistance (Rs) and the film s ionic resistance (Rj). They can be approximated quite well by the transmission line circuit shown in Fig. 16, which can represent a variety of physical/chemical/morphological cases from redox polymers171 to porous electrodes.172... 

Figure 16. General transmission-line model for a conducting polymer-coated electrode. CF is the faradaic pseudo-capacitance of the polymer film, while Rt and Rt are its electronic and ionic resistance, respectively. R, is the uncompensated solution resistance.

For the sake of analysis, we consider the behavior of an oxidized organic pol5mier material to be represented as a single pore that is either of infinite or finite length. This type of system can be treated from a mathematical viewpoint as a transmission line in series with the uncompensated solution resistance Ru (see Fig. 1.54). The electrode is characterized by the electronic resistance Re oi its solid phase, the ionic... 

FIGURE 1.54. Schematic representation of dual-rail transmission line for electroactive polymer films. The / is resistance for electron hopping, Rj is resistance for counterion transport Cp is the distributed Faradaic capacitance, and denotes the uncompensated solution resistance. 

The shape of the chronoamperometric current response depends to a large extent on the value of the uncompensated solution resistance R . We note from Fig. 1.54 that is in series with the finite transmission line element. The presence of uncompensated solution resistance effects can be clearly identified by examining the current/time data when the latter is plotted in i(t) versus format. In many cases (see Fig. 1.56) such plots are nonlinear, so we observe deviation from the expected linear response at both short and long time periods. At short time... 

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