Language: EN
Coplanar waveguide calculator
A grounded coplanar waveguide is a track with ground on both sides and a ground plane underneath. It is common for RF traces, like antenna feeds. Change any value and the results update at once.
Results
- Characteristic impedance
- – Ω
- Effective dielectric constant
- –
- Wavelength on the line
- – mm
- Quarter wavelength
- – mm
PCB materials
Typical dielectric constants (Dk) and loss tangents (Df). For Rogers laminates, use the design Dk for impedance. For FR-4, the value depends on the glass weave, the resin and the frequency, so use the one from your PCB maker’s stackup when you have it.
| Material | Type | Dk | Df | At | Use this Dk in the calculator |
|---|---|---|---|---|---|
| FR-4 (generic) | Standard | 4.2–4.7 | 0.015–0.020 | 1 GHz | |
| Rogers RO4003C | RF | 3.38 (design 3.55) | 0.0027 | 10 GHz | |
| Rogers RO4350B | RF | 3.48 (design 3.66) | 0.0037 | 10 GHz | |
| Rogers RO3003 | RF | 3.00 | 0.0010 | 10 GHz | |
| Rogers RO3006 | RF | 6.15 (design 6.5) | 0.0020 | 10 GHz | |
| Rogers RO3010 | RF | 10.2 (design 11.2) | 0.0022 | 10 GHz | |
| Rogers RT/duroid 5880 | RF | 2.20 | 0.0009 | 10 GHz | |
| PTFE (generic) | RF | 2.1 | 0.0002–0.0005 | 1–10 GHz | |
| Polyimide (flex) | Flex | 3.2–3.5 | 0.002–0.005 | 1 kHz–1 GHz | |
| Alumina 96% | Ceramic | 9.0–9.6 | 0.0002–0.0005 | 1 MHz–10 GHz | |
| Alumina 99.6% | Ceramic | 9.7–9.9 | 0.0001–0.0002 | 1 MHz–10 GHz |
How it’s calculated
The calculator uses the quasi-static formulas by conformal mapping from B. C. Wadell, Transmission Line Design Handbook (Artech House, 1991), page 79. K is the complete elliptic integral of the first kind.
k = W / (W + 2S)
k1 = tanh(πW / 4H) / tanh(π(W + 2S) / 4H)
k' = √(1 − k²) k1' = √(1 − k1²)
q = K(k')/K(k) · K(k1)/K(k1')
εeff = (1 + εr · q) / (1 + q)
Z0 = 60π / √εeff · 1 / (K(k)/K(k') + K(k1)/K(k1'))Keep its limits in mind.
- The copper thickness is taken as zero. Real copper lowers the impedance a little, more when the gap is small.
- The side grounds are taken as infinitely wide, and the vias that tie them to the ground plane aren’t modelled.
- It’s quasi-static, so it doesn’t change with frequency. It doesn’t include losses, solder mask or the roughness of the copper.
- Expect a few percent of difference from a field solver or a measurement. For a final design, ask your PCB maker to check the impedance.