Grounded Coplanar Waveguide (CPWG) Calculator
A surface trace with ground pour either side and a reference plane underneath - the usual choice for RF on a thick board, because the gap sets the impedance rather than the substrate height. Most free calculators skip this geometry or fold it into microstrip; this one solves the conformal mapping properly.
Choosing something to solve for makes Characteristic impedance an editable target and computes the chosen input from it.
Formula
| w | signal trace width (m) |
| s | gap from trace edge to coplanar ground (m) |
| h | substrate height to the lower plane (m) |
| k1, k3 | conformal moduli for the coplanar and backed problems |
| K | complete elliptic integral of the first kind |
What this model assumes, and where it stops
Assumptions
- Quasi-TEM propagation: the cross-section is small against a wavelength.
- Static (low-frequency) solution - no dispersion, so Dk and Z0 do not change with frequency.
- Perfect conductors and a lossless, homogeneous, isotropic dielectric.
- Infinitely wide reference plane with no splits, voids or stitching gaps under the trace.
- A uniform, straight, infinitely long line - no bends, vias, stubs or terminations.
- Zero conductor thickness.
- Coplanar grounds extend far enough either side to be treated as semi-infinite.
- The coplanar grounds and the lower plane are at the same potential everywhere, which in practice means dense stitching vias.
Limitations
- The model assumes the upper and lower grounds are perfectly tied. Without enough stitching vias a parallel-plate mode propagates between them and the real behaviour departs sharply from this result - this is the single most common CPWG design mistake.
- Semi-infinite coplanar grounds. If the pour is only a gap-width or two wide, the real impedance is higher than this.
- Zero thickness: 35 um copper in a 0.2 mm gap changes the gap capacitance noticeably.
- No dispersion or loss.
- Solder mask over the gap lowers Z0, and the gap is exactly where the field is strongest, so the effect is larger than on microstrip.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Reference-plane splits, voids or antipads under the trace, which the infinite-plane assumption cannot see.
- Vias, layer transitions and connector launches, where the discontinuity dominates the impedance budget.
- Tight bends, taper transitions and length-matching serpentines.
- Anything above roughly 5 GHz, where dispersion, surface roughness and dielectric loss stop being negligible.
- Trace-to-trace coupling beyond a single adjacent pair, and coupling between layers.
- Etch-factor trapezoidal cross-sections, where the top and bottom widths differ enough to shift Z0 by several percent.
- Deciding stitching via pitch and pattern, which is a 3D resonance question this 2D model cannot answer.
- Narrow ground pours, or pours interrupted by other routing.
- The launch from connector to CPWG, where the geometry changes over a few millimetres.
Common questions
When should I use CPWG instead of microstrip?
Mainly when the substrate is too thick for a sensible microstrip width. CPWG impedance is set largely by the gap to the coplanar ground rather than by the substrate height, so you can hit 50 ohm on a 1.6 mm board with a reasonable trace width. It also gives better isolation between adjacent traces.
How close together do the stitching vias need to be?
Close enough to short the coplanar grounds to the lower plane across the whole frequency range of interest. A common rule is a twentieth of a guided wavelength at the highest frequency. Without adequate stitching a parallel-plate mode propagates between the grounds and the line stops behaving as this model predicts - it is the most common CPWG mistake.
Does the width of the ground pour matter?
Yes. The conformal-mapping solution assumes the coplanar grounds are effectively semi-infinite. If the pour is only a gap-width or two wide, the real impedance is higher than calculated.
References
- Ghione & Naldi - Coplanar Waveguides for MMIC Applications, IEEE MTT 1987
- Wadell - Transmission Line Design Handbook, Artech House 1991, ch. 3
- Simons - Coplanar Waveguide Circuits, Components and Systems, Wiley 2001