Fig 1.
Equivalents to capactive and inductive CPEs.
Equivalent circuit for a capacitive Constant Phase Element (a) and an inductive Constant Phase Element (b). Inductance and capacitance respectively increase linearly with time.
Fig 2.
Micro-Cap 12 simulation of current response to a voltage impulse for the circuit of (11) shown in Fig 1a) with R = 1, L = 1 + t/0.9, i.e. τ = α = 0.9 (red, open squares), R = 1, L = t/0.9, i.e. α = 0.9 (green, solid) compared to an ordinary RL-circuit with response e−t/τ/R, τ = L/R, L = 1, R = 1 (blue, filled squares). Pulse length is ts = 1 ms.
Fig 3.
Plot of analytically found response.
Current response to a voltage impulse for the circuit of Fig 1a) for α = 0.9 computed in Matlab from (15) (green, solid line), (16) (red, dotted line), and (17) (black, dash-dot line) compared to a standard RL-circuit (blue, dashed line).
Fig 4.
Plot of analytically found response.
Current response to a voltage impulse for the circuit of Fig 1a) for α = 0.5 (Warburg element) computed in Matlab from (15) (green, solid line), (16) (red, dotted line), and (17) (black, dash-dot line) compared to a standard RL-circuit (blue, dashed line).