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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)

Why Parallel Matters ​

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

Code ​

ts
import { createEditor } from 'velo-circuit'

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 ​

ts
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:

ts
editor.setValue('R0-p(R1,C1)-Wo2')
Randles + Warburg open (Wo)

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:

ts
editor.setValue('R0-p(R1,Q1)-Wo2')
Randles with CPE and Warburg open

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

API ​

Next ​

Explore Warburg elements