Randles Circuit

The Randles circuit is one of the most common equivalent circuit models in EIS. It models the interface between an electrode and an electrolyte.

DSL

R0-p(R1,C1)

Structure

        ┌──[ C1 ]──┐
[ R0 ]──┤          ├──
        └──[ R1 ]──┘

Why Parallel Matters

The parallel branch p(R1,C1) represents the charge-transfer resistance (R1) in parallel with the double-layer capacitance (C1).

Code

import { createEditor } from 'velo-circuit-editor'

const editor = createEditor()

editor.mount(document.getElementById('canvas'), {
  initialDsl: 'R0-p(R1,C1)',
  width: 700,
  height: 400,
})

editor.on('ast-changed', () => {
  const dsl = editor.getValue()
  document.getElementById('dsl-display').textContent = dsl
})

Validation

const result = editor.getValidation()
if (result.hasErrors) {
  for (const issue of result.issues) {
    console.error(issue.message)
  }
}

Adding Warburg

Extend the Randles model with a Warburg element to model diffusion:

editor.setValue('R0-p(R1,C1)-Wo2')

This adds a finite-length Warburg open element in series with the Randles branch, modeling semi-infinite diffusion.

Using CPE Instead of Capacitor

Replace the ideal capacitor with a CPE for more realistic modeling:

editor.setValue('R0-p(R1,Q1)-Wo2')

The CPE element Q models non-ideal capacitive behavior with a fractional exponent n.

Next

Explore Warburg elements