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PCB Coplanar Waveguide (GCPW) Calculator | NextPCB
 

PCB Coplanar Waveguide (GCPW) Calculator

Calculate the characteristic impedance and effective dielectric constant of a grounded coplanar waveguide (GCPW) from trace width, gap, substrate height, and dielectric constant. Built for RF connector launches, IC transitions, and board-edge routing.

GCPW Parameters

Reference only — not used in the Z₀ calculation below

Used only for the λ/4 figure below — doesn't affect Z₀

Uses the Ghione-Naldi quasi-static model for coplanar waveguide with a lower ground plane. See our Skin Effect Depth Calculator for high-frequency conductor loss.

Estimated GCPW Impedance

backside ground plane εr h w s ground ground GCPW cross-section (illustrative)

Impedance

0.00 Ω

Z₀, characteristic impedance

Eff. Dielectric

0.00

εeff, effective εr

Quarter Wavelength

0.00 mm

λ/4 at f₀

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Calculation Reference

This calculator uses the quasi-static conformal-mapping model for coplanar waveguide with a lower ground plane, published by Ghione and Naldi (1983). Two elliptic-integral ratios are combined as parallel capacitances: one for the coplanar (side) ground contribution, and one for the backside ground plane contribution.

  • \( k = \dfrac{w}{w+2s} \)
  • \( k_3 = \dfrac{\tanh\left(\frac{\pi w}{2h}\right)}{\tanh\left(\frac{\pi (w+2s)}{2h}\right)} \)
  • \( R(k) = \dfrac{K(k)}{K(k')} \), evaluated with Hilberg's closed-form approximation
\[ \varepsilon_{eff} = \frac{R(k) + \varepsilon_r \cdot R(k_3)}{R(k) + R(k_3)} \]
\[ Z_0 = \frac{60\pi}{\sqrt{\varepsilon_{eff}} \cdot \left[R(k) + R(k_3)\right]} \]
Source: G. Ghione, C. Naldi, "Parameters of Coplanar Waveguides with Lower Ground Plane," Electronics Letters, Vol. 19, No. 18, 1983.

Frequently Asked Questions

What is a grounded coplanar waveguide (GCPW), and how is it different from microstrip?

A grounded coplanar waveguide, also called conductor-backed CPW, routes a signal trace with ground copper on both sides in the same layer, in addition to a solid ground plane on the layer below. Microstrip only has the bottom ground reference, so GCPW gets a tighter, more controllable field confinement from the coplanar ground strips, which typically gives better isolation and more predictable impedance at the board edges, transitions, and connector launches where RF signals are most sensitive to discontinuities.

How is GCPW characteristic impedance calculated?

This calculator uses the quasi-static conformal-mapping method published by Ghione and Naldi for coplanar waveguide with a lower ground plane. The geometry is mapped to two elliptic-integral ratios, one describing the coplanar (side) ground contribution and one describing the backside ground contribution, which combine as parallel capacitances to give the effective dielectric constant and characteristic impedance. The elliptic integral ratios are evaluated with Hilberg's closed-form approximation, which is accurate to a fraction of a percent for all practical geometries.

Does copper thickness affect the impedance result?

The model used here assumes an infinitesimally thin conductor, which is the standard, most widely validated form of the Ghione-Naldi equations. Real copper thickness does slightly narrow the effective gap and add fringing capacitance, nudging impedance down a little, but published thickness-correction formulas for GCPW are inconsistent on the exact magnitude and even the sign of the effect, so rather than bake in an unreliable correction, this calculator reports the thin-conductor result and lets you treat copper thickness as a secondary, second-order factor to verify with your fabricator's field solver for tight tolerance designs.

Why does bringing the ground plane closer (smaller h) lower the impedance?

A closer backside ground plane adds more parallel-plate capacitance between the signal trace and that ground, and characteristic impedance decreases as capacitance per unit length increases. This is why GCPW on a thin bonding film or prepreg tends to run at a lower impedance than the same trace and gap dimensions would give on a thicker substrate, and why h is one of the most sensitive inputs in this calculator.

What is the quarter-wavelength (λ/4) figure used for?

Quarter-wavelength lines are a common building block in RF matching networks, filters, and stub designs, and their physical length depends on both your target frequency and the effective dielectric constant of the line, which this calculator has already computed for your geometry. It's provided here as a convenience reference for the frequency you entered, not as a design recommendation on its own.

When should I use GCPW instead of plain microstrip or CPW without a backside ground?

GCPW is common at connector launches, RF IC transitions, and board edges where a nearby ground reference is needed to control impedance and reduce radiation or crosstalk in a compact footprint. Plain CPW without a backside ground plane is used less often on multilayer PCBs since most stackups already have ground copper close by, and microstrip remains the simpler default for straightforward digital and lower-frequency RF routing where the coplanar ground strips aren't needed. GCPW also shows up frequently on HDI boards, where fine-pitch RF ICs and tight stackups make a nearby ground plane and controlled coplanar geometry especially useful.

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