Resistor-capacitor ladder network

Cable theory Representation of a cylindrical fiber as two parallel rows of resistors (one each for the intracellular and extracellular spaces) connected in a ladder network by a parallel combination of resistors and capacitors (the cell membrane). 

Figure 1.82 shows the model circuit which takes the form of a diagonally connected discrete ladder network or in simple terms, a dual-rail transmission line of finite dimension. The essential problem is to replace the general impedance elements x, y, and z by suitably arranging such passive circuit elements as resistors and capacitors that adequately represent the microscopic physics occurring within an electronically conducting polymer. 

We extend the analysis and consider the entire ladder network in terms of distinct R and C circuit elements. The impedance x can be represented by a resistance Ri, which defined the resistance of counterions in the pore electrolyte. Furthermore the impedance element z, which is that of the solid polymer, is replaced by a Randles equivalent circuit (see Fig. 1.84), where there is a parallel arrangement of a resistor Rj. and a capacitor Q in series with a resistor Ra- Hence we see that the pore solution is modeled in terms of a simple resistor, whereas the solid polymer is a binary composite medium. TTie latter assumption can be justified as follows. From a macroscopic viewpoint (and this has been demonstrated experimentally), the electronic resistance of the polymer is due to two contributions the first, Ra, from regions of high structural order the second, R, from regions of low structural order. Hence Ra is smaller than R. From a microscopic point of view, the polymer may exhibit two fundamentally different types of conduction. As noted in... 

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