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sci.electrochemical-impedance-Warburg Calculator
Calculates electrochemical impedance spectra (Nyquist and Bode plots) from a Randles circuit model with Warburg diffusion element. Warburg impedance Z_W = σω^(−0.5)(1−j) appears as a 45° line on the Nyquist plot — it represents semi-infinite planar diffusion to the electrode surface.
Inputs
R Ohm
Opposition to current flow (Ω). V = IR. Resistors in series add; in parallel their reciprocals add.
R Ct Ohm
Opposition to current flow (Ω). V = IR. Resistors in series add; in parallel their reciprocals add.
Cdl F
Ability to store electric charge (F). Capacitors charge quickly and release energy fast. Common values: pF to μF.
Sigma Warburg
Reference formula or conversion factor shown for context.
F Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Results
impedance magnitude |Z| (Ω)
Total opposition to AC current (Ω), combining resistance and reactance. Z = √(R² + X²). Maximum power transfer occurs when source and load impedances match.
real part Z\
Reference formula or conversion factor shown for context.
imaginary part Z\
Sample size or count used in the calculation.
Warburg impedance Zw (Ω)
Total opposition to AC current (Ω), combining resistance and reactance. Z = √(R² + X²). Maximum power transfer occurs when source and load impedances match.
Randles circuit: Z = RΩ + Rct/(1+jωRctCdl) + Zw
Sample size or count used in the calculation.
frequency regime
The operating regime — the mode or zone in which the system is currently operating.