CPE and Complex Elements

The Constant Phase Element (CPE) models non-ideal behavior at electrode interfaces.

CPE vs Capacitor

A pure capacitor assumes ideal behavior. Real electrodes show non-ideal (depressed semi-circles) due to surface heterogeneity.

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

// CPE (non-ideal) — use Q instead of C
editor.setValue('R0-p(R1,Q1)-Wo2')

CPE Parameters

CPE has two parameters:

• Q₀ — pseudo-capacitance (S·sⁿ)
• n — ideality factor (0 < n ≤ 1)

// n=1 → pure capacitor
// n=0.8 → typical depressed semi-circle
// n=0.5 → Warburg-like behavior

Element Code

Important: CPE uses the code Q, not CPE. The Boukamp DSL uses single-character codes where possible.

// Correct ✓
editor.setValue('R0-p(R1,Q1)')

// Incorrect ✗ — "CPE" is not a valid element code
// editor.setValue('R0-p(R1,CPE1)')

Full Complex Circuit

// Multi-element model with CPE and Warburg
editor.setValue('R0-p(R1,Q1)-p(R2,C2)-Wo3')

Validation Rules

const result = editor.getValidation()
result.issues.forEach(issue => {
  if (issue.type === 'error') {
    // blocking: duplicate IDs, syntax errors, empty parallel groups
  } else {
    // warning: no DC path, conflicting reactive elements
  }
})

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API Reference