Calculator Inputs
This tool uses an equivalent circuit: Rs + jωLs + Rp/(1 + jωRpC).
Formula Used
Z(ω) = Rs + jωLs + Rp / (1 + jωRpC)
Z′ = Rs + Rp / [1 + (ωRpC)²]
Z″ = ωLs - [ωCRp² / (1 + (ωRpC)²)]
|Z| = √(Z′² + Z″²), phase = tan⁻¹(Z″ / Z′)
ZDC = Rs + Rp, IDC = VDC / ZDC
fc = 1 / (2πRpC)
ρ = RpA / d, σ = 1 / ρ, ASR = Rp × area
This model is useful for quick comparison between steady-state DC resistance and a frequency-dependent AC spectrum. It also highlights capacitive arcs, inductive rise, and conductivity estimates from simple geometry inputs.
How to Use This Calculator
- Enter series resistance, polarization resistance, capacitance, and optional inductance.
- Provide AC RMS voltage and DC voltage for current estimates.
- Choose one frequency for single-point evaluation.
- Set sweep start, sweep end, and total sweep points.
- Enter area and thickness if conductivity values matter.
- Press the calculate button.
- Review summary cards, sweep preview, and plots.
- Export the sweep table as CSV or PDF.
Example Data Table
Example inputs: Rs = 8 Ω, Rp = 180 Ω, C = 5 µF, L = 0.2 mH.
| Frequency (Hz) | Z′ (Ω) | Z″ (Ω) | |Z| (Ω) | Phase (°) |
|---|---|---|---|---|
| 10 | 187.426239 | -10.133748 | 187.699995 | -3.094851 |
| 100 | 144.386865 | -76.999292 | 163.635136 | -28.070313 |
| 1000 | 13.458264 | -29.609119 | 32.524218 | -65.556729 |
| 5000 | 8.224877 | -0.075059 | 8.225219 | -0.522858 |
| 10000 | 8.056272 | 9.384267 | 12.368023 | 49.354336 |
Frequently Asked Questions
1. What does this calculator compare?
It compares steady-state DC resistance with frequency-dependent AC impedance. The tool shows real impedance, imaginary impedance, magnitude, phase, admittance, conductivity, and sweep behavior from one equivalent circuit.
2. Why are AC and DC values different?
DC treats the capacitor as open at steady state. AC depends on frequency, so the capacitive and inductive terms change the measured impedance. That is why spectra reveal processes hidden in simple resistance readings.
3. What does a negative imaginary impedance mean?
A negative Z″ usually indicates capacitive behavior in this sign convention. Positive values at high frequency can appear when inductive effects dominate, such as lead inductance or contact wiring.
4. Why is series resistance important?
Series resistance captures ohmic losses from leads, electrolyte, contacts, or bulk pathways. It shifts the Nyquist plot horizontally and sets a baseline that remains even when capacitive effects are strong.
5. What does characteristic frequency show?
Characteristic frequency estimates where the Rp–C branch changes most rapidly. It is linked to the time constant RpC and helps identify the central part of a semicircle in many spectroscopy datasets.
6. Can this replace laboratory impedance spectroscopy software?
No. It is a practical calculator for estimation and education. Full fitting software can handle multiple distributed elements, diffusion models, non-ideal capacitors, weighting methods, and experimental uncertainty.
7. Why do area and thickness matter?
Geometry converts resistance into material properties. Area and thickness allow resistivity, conductivity, and area-specific resistance estimates, which are often needed when comparing samples of different sizes.
8. What do the CSV and PDF exports include?
The CSV export includes the sweep table. The PDF export includes key summary metrics and a sweep preview. These files help with reporting, quick sharing, and offline record keeping.