What is the formula for Coplanar Waveguide Impedance?

The Coplanar Waveguide Impedance formula is Z0 = (30π / √εeff) × K(k′)/K(k), k = S/(S+2W), εeff = (εr+1)/2, where Z0—Characteristic impedance (Ω); S—Centre signal-trace width (m); W—Gap to each ground (m); εr—Substrate dielectric constant; εeff—Effective permittivity ≈ (εr+1)/2.

What does Z0 mean in the Coplanar Waveguide Impedance formula?

Z0 is Characteristic impedance (Ω).

Coplanar Waveguide Impedance

Q: How do you calculate Coplanar Waveguide Impedance?

Use the formula Z0 = (30π / √εeff) × K(k′)/K(k), k = S/(S+2W), εeff = (εr+1)/2. A coplanar waveguide (CPW) carries an RF signal on a centre trace flanked by two coplanar ground planes, with the impedance set by the ratio of the signal width to the gap rather than the dielectric thickness. Enter the values you know in the calculator above and it solves for the remaining variable.

Z0 = (30π/√εeff) · K(k′)/K(k)

Calculator

Impedance

Signal Width

Gap Width

Dielectric Constant

Result

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Formula

Z0 = (30π / √εeff) × K(k′)/K(k), k = S/(S+2W), εeff = (εr+1)/2

Description

A coplanar waveguide (CPW) carries an RF signal on a centre trace flanked by two coplanar ground planes, with the impedance set by the ratio of the signal width to the gap rather than the dielectric thickness. This makes CPW easy to fabricate and tune, and it is the workhorse transmission line for microwave PCBs and MMICs. The impedance follows from a conformal mapping that uses the ratio of complete elliptic integrals.

Variables

Z0 — Characteristic impedance (Ω)
S — Centre signal-trace width (m)
W — Gap to each ground (m)
εr — Substrate dielectric constant
εeff — Effective permittivity ≈ (εr+1)/2

Practical Notes

This is the impedance for CPW on a thick substrate without a bottom ground; a grounded CPW (with a ground plane below) reads lower. Widen the gap or narrow the trace to raise Z0.

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