Grounded Coplanar Waveguide (GCPW) Calculator
Grounded CPW puts ground copper on both sides of the signal trace on the same layer, plus a solid ground plane underneath, stitched together with vias. It offers good isolation and low radiation — the most common routing for RF modules, antenna feeds and dense boards.
What is grounded coplanar waveguide (GCPW / CPWG)?
Grounded coplanar waveguide, also written CPWG or conductor-backed CPW, is a coplanar waveguide with an additional ground plane under the substrate. The signal trace (width S) is flanked by top-layer ground copper at gap W, and the top grounds are stitched to the bottom ground with rows of vias. Field lines end on both the side grounds and the backside plane, so GCPW radiates less and couples less to neighbouring traces than microstrip, and its impedance can be adjusted with the gap as well as the trace width.
That is why RF modules, antenna feeds and compact wireless designs on FR-4 commonly route 50 Ω lines as GCPW. When the gap W becomes large compared with the substrate height h, the side grounds have little effect and the result approaches microstrip; without the backside ground it becomes ordinary CPW. This calculator uses conformal mapping and assumes zero-thickness copper, so leave margin for copper thickness and solder mask on small gaps, and keep via spacing well below a tenth of a wavelength.
How to use
- Enter laminate εr and substrate height h (dielectric from the signal layer to the backside ground).
- Enter the center conductor width S and frequency f. Note: here S is the trace width and W is the gap (some tools swap the symbols).
- Known gap: enter W and press Analyze to get Zo.
- Known target: enter Zo and press Synthesize to find the gap W with S and h fixed.
Theory and formulas
Conformal mapping gives the capacitance of the upper half-space and the dielectric layer. K(k) is the complete elliptic integral of the first kind, k′ = √(1 − k²):
k1 = tanh(πS / 4h) / tanh(π(S + 2W) / 4h)
q = [ K(k1)/K(k1′) ] / [ K(k)/K(k′) ]
εeff = (1 + εr · q) / (1 + q)
Zo = 60π / { √εeff · [ K(k)/K(k′) + K(k1)/K(k1′) ] }
kv = 1/√εeff λ/4 = kv · c / (4f)
K(k)/K(k′) uses Hilberg's approximation: π / ln[2(1+√k′)/(1−√k′)] for k ≤ 0.7, ln[2(1+√k)/(1−√k)] / π for k > 0.7.
Design tips
- 50 Ω reference (from this tool): FR-4 (εr 4.4), h = 0.8 mm, S = 1.0 mm → W ≈ 0.22 mm; 4-layer h = 0.2 mm, S = 0.3 mm → W ≈ 0.09 mm. Check your fabricator's minimum spacing for small gaps.
- Stitch the side grounds to the backside ground with vias spaced below λ/10 (denser at higher frequency), close to the gap edge.
- Make the coplanar ground at least 2–3 × S wide; narrow grounds shift the impedance away from the formula.
- The model ignores copper thickness and solder mask; both matter more for small gaps — use test coupons before production.
- If the side grounds are far away (W much larger than h), the result approaches ordinary microstrip.
FAQ
- GCPW or microstrip?
- GCPW gives better isolation, lower radiation and crosstalk, suiting modules and dense layouts; microstrip width depends only on the dielectric height and is easy to control. Antenna feeds and RF modules commonly use GCPW.
- Why is there no copper thickness input?
- The model assumes zero-thickness conductors. Thickness adds gap capacitance and lowers the impedance slightly; for gaps below 0.15 mm leave a few ohms of margin or simulate.
- How does it differ from CPW?
- CPW has no backside ground plane; GCPW adds it, giving lower impedance and a more confined field. Pick the calculator that matches your stack-up.
Microstrip vs CPW vs GCPW vs coplanar strips
Pick the calculator that matches your board stack-up. The structures differ mainly in where the return (ground) conductor is:
| Line type | Conductors and ground | Typical use | Calculator |
|---|---|---|---|
| Microstrip | Trace on the top layer over a solid ground plane on the other side of the dielectric | General RF routing and 50 Ω feeds on FR-4; easy to fabricate and tune | Open Microstrip calculator |
| Coplanar waveguide (CPW) | Signal trace between two ground planes on the same layer; no backside ground | Ceramic or single-sided boards, many shunt parts, GSG probe measurements | Open Coplanar waveguide calculator |
| Grounded CPW (GCPW / CPWG) | CPW plus a backside ground plane, top grounds stitched with vias | RF modules, antenna feeds and dense layouts needing low radiation and crosstalk | This page |
| Coplanar strips (CPS) | Two equal parallel strips, balanced, no ground plane | Printed dipole and folded-dipole feeds, baluns, differential lines | Open Coplanar strips calculator |
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