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Finite Length Warburg - Open Circuit Terminus Z = R*ctnh(^P) / (I*T*w)^P Parameters: Wo-R, Wo-T, Wo-P This element is also known as a Generalized Finite Warburg element (GFW). It is an extension of another more common element, the Finite-Length Warburg (FLW). To use the FLW equation, set Wo-P = 0.5 and set its freedom to 'fixed'. The FLW is the solution of the one-dimensional diffusion equation of a particle, which is completely analogous to wave transmission in a finite-length RC transmission line. In the diffusion interpretation Wo-T = L2 / D. (L is the effective diffusion thickness, and D is the effective diffusion coefficient of the particle). The GFW is similar to this, but for it the square root becomes a continuously varying exponent Ws-P such that 0 < Ws-P < 1. This version of the Warburg element is terminates in a open circuit. At very low frequencies, the Z' approaches Wo-R and Z'¡® continues to increase - similar to the behavior of a capacitor. If the data exhibits only the high frequency (45 degree slope) behavior and not the transition to low frequency behavior, either Wo-R or Wo-T must be set as Fixed(X). Alternately, a CPE can be used in this situation. |
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