Calculator inputs
Use the grid below. Large screens show three columns.
Plotly graph
The chart sweeps strip width while holding other values fixed.
Example data table
| Case | Model | W (mm) | S (mm) | εr | h (mm) | t (µm) | Z0 (Ω) | εeff |
|---|---|---|---|---|---|---|---|---|
| FR-4 control line | Finite substrate | 2.400 | 0.300 | 4.300 | 1.600 | 35.0 | 47.551 | 2.3888 |
| Quartz sensor trace | Finite substrate | 0.900 | 0.180 | 3.780 | 0.500 | 18.0 | 58.099 | 2.0893 |
| Grounded alumina line | Finite substrate with backside ground | 0.600 | 0.120 | 9.500 | 0.635 | 18.0 | 32.983 | 5.1397 |
Formula used
The page uses standard quasi-static CPW expressions with optional thickness correction. Geometry stays in consistent units.
k1 = W / (W + 2S)K(k) / K'(k) is evaluated with the common logarithmic approximations.
εeff = (εr + 1) / 2Z0 = (30π / √εeff) × K'(k1) / K(k1)
k2 = sinh(πW / 4h) / sinh(π(W + 2S) / 4h)εeff = 1 + ((εr - 1) / 2) × [K(k2)/K'(k2)] × [K'(k1)/K(k1)]Z0 = (30π / √εeff) × K'(k1) / K(k1)
k3 = tanh(πW / 4h) / tanh(π(W + 2S) / 4h)q = [K(k3)/K'(k3)] / ([K(k1)/K'(k1)] + [K(k3)/K'(k3)])εeff = 1 + q(εr - 1)Z0 = (60π / √εeff) / ([K(k1)/K'(k1)] + [K(k3)/K'(k3)])
Δ = (1.25t / π) × [1 + ln(4πW / t)]We = W + ΔSe = S - Δk1 is recalculated with the effective dimensions, then used for the final impedance estimate.
How to use this calculator
- Pick the CPW model that best matches your board stack.
- Enter strip width, slot width, substrate constant, and height.
- Add conductor thickness for first-order thickness correction.
- Provide frequency and line length for phase results.
- Press Calculate impedance to show results above the form.
- Review impedance, effective permittivity, delay, and guided wavelength.
- Use the graph to see width sensitivity.
- Download the summary as CSV or PDF when needed.
Frequently asked questions
1. What does this calculator estimate?
It estimates the characteristic impedance of a coplanar wave structure from geometry and dielectric properties. It also reports effective permittivity, delay, guided wavelength, and electrical length for the entered frequency and line length.
2. Which model should I choose?
Use the infinite substrate model for quick theoretical checks. Use the finite substrate model for open-backed boards. Use the backside-ground model when the lower face has a continuous ground plane.
3. Why does width strongly change impedance?
A wider strip concentrates more electric field near the conductor and usually lowers impedance. Narrow strips do the opposite. The width-to-slot ratio is one of the strongest controls in CPW design.
4. What does the thickness correction do?
The correction slightly widens the effective strip and shrinks the effective slot. That changes the elliptic modulus and shifts the impedance. It is a practical first-order estimate, not a full-wave replacement.
5. Can I use any units?
Yes, if geometry units stay consistent inside the formulas. This page uses millimeters for width, slot, height, and length, while thickness is entered in micrometers and converted internally.
6. Why is frequency included?
The core quasi-static impedance estimate is geometry driven. Frequency is used here for guided wavelength, propagation delay, phase constant, and electrical length. Those values help translate impedance into physical line behavior.
7. Are these results exact?
No. They are strong engineering estimates for early design work. Real boards also depend on copper roughness, losses, finite ground width, solder mask, dispersion, and fabrication tolerances.
8. When should I use a field solver?
Use a field solver when you need production-level accuracy, differential effects, discontinuities, loss modeling, or unusual materials. Analytical formulas are best for fast sizing, comparison, and sensitivity studies.