Coplanar Waveguide (CPW) Calculator
In coplanar waveguide the signal trace and both grounds lie on the same layer with no backside ground. Grounds need no vias and shunt parts connect directly — common on single-sided boards, ceramic substrates and on-wafer probing.
What is coplanar waveguide (CPW)?
In coplanar waveguide the signal conductor (width S) and two ground planes sit on the same copper layer, separated by gaps W, with no ground plane on the back of the substrate. The field is concentrated in the gaps, so the impedance is set mainly by the ratio S/(S+2W) together with the substrate permittivity and height; a narrower gap lowers the impedance.
Because both grounds are on the surface, shunt components and coplanar (GSG) probes connect without vias, which makes CPW popular on ceramic substrates, single-sided boards and on-wafer measurements. The two side grounds must be kept at the same potential with bridges or vias at bends and junctions, otherwise an unwanted slot-line mode can be excited. If your board also has a ground plane on the bottom layer, the structure is grounded coplanar waveguide (GCPW / CPWG) and you should use the GCPW calculator; if the side grounds are far away, the line approaches microstrip. Results use conformal mapping with a copper-thickness correction; verify critical designs with an EM simulation or a test coupon.
How to use
- Enter laminate εr, substrate height h and copper thickness t (µm).
- Enter the center conductor width S and frequency f. Here S is the trace width and W the gap to the coplanar ground.
- Known gap: enter W and press Analyze to get Zo.
- Known target: enter Zo and press Synthesize to find the gap W.
Theory and formulas
Conformal mapping for CPW on a finite-thickness substrate, with an equivalent-width thickness correction (K: complete elliptic integral of the first kind):
k = S/(S+2W) kt = St/(S+2W)t k1 = sinh(πSt/4h) / sinh(π(S+2W)t/4h)
εeff = 1 + (εr − 1)/2 · [K(k1)/K(k1′)] · [K(k′)/K(k)]
εeff,t = εeff − (εeff − 1) / [ (W/0.7t) · K(k)/K(k′) + 1 ]
Zo = 30π / √εeff,t · K(kt′)/K(kt)
kv = 1/√εeff,t λ/4 = kv · c / (4f)
Design tips
- 50 Ω reference (from this tool): FR-4 (εr 4.4), h = 1.6 mm, t = 35 µm, S = 1.0 mm → W ≈ 0.23 mm.
- A 50 Ω CPW usually needs a narrow gap; on FR-4 it is more often built as GCPW with a backside ground. If your board has one, use the GCPW calculator.
- Tie the two side grounds together at discontinuities (bends, parts, tees) with bridges or vias to suppress the unbalanced slot-line mode.
- Make the coplanar ground at least S + 2W wide and keep it clear of board edges and other metal.
FAQ
- Where is CPW used?
- Single-sided or ceramic substrates, circuits with many shunt-to-ground parts, and coplanar (GSG) probe measurements.
- Does copper thickness matter for CPW?
- More so for small gaps: thicker copper adds sidewall capacitance and lowers impedance. This page corrects the width and εeff for thickness.
- Can S and W get mixed up?
- Here S is the center conductor width and W is the gap — follow the cross-section. Synthesis returns the gap W.
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 | This page |
| 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 | Open Grounded CPW calculator |
| 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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