Coplanar Waveguide Impedance Calculator

Calculator Inputs

Center trace width

Gap width to each ground

Substrate height

Relative dielectric constant

Frequency in GHz

Line length

Geometry unit

Effective permittivity model

Design notes

Example Data Table

Material	Trace width	Gap width	Height	Dielectric constant	Approximate impedance
General FR laminate	3.00 mm	0.30 mm	1.60 mm	4.40	49.78 Ω
Low loss laminate	1.20 mm	0.20 mm	0.80 mm	3.48	62.34 Ω
High dielectric substrate	0.50 mm	0.15 mm	0.635 mm	10.20	45.43 Ω
Thin RF substrate	0.25 mm	0.12 mm	0.30 mm	2.94	87.84 Ω

Formula Used

The calculator uses a quasi static coplanar waveguide model for a thin center conductor.

Geometry ratio: k = W / (W + 2S)

Complement: k′ = √(1 − k²)

Characteristic impedance: Z0 = 30π × K(k′) / [√εeff × K(k)]

Simple effective permittivity: εeff = (εr + 1) / 2

Finite substrate estimate: εeff uses width, gap, substrate height, and dielectric constant. It is best when h / S is at least 1.

K is the complete elliptic integral of the first kind. This file evaluates it with the arithmetic geometric mean method.

How to Use This Calculator

Enter the center trace width.
Enter the equal gap between the trace and each ground plane.
Enter substrate height and relative dielectric constant.
Choose a shared unit for all geometry fields.
Enter frequency and physical line length.
Select the effective permittivity model.
Press calculate to show results below the header.
Download CSV or PDF for documentation.

Coplanar Waveguide Impedance Guide

A coplanar waveguide places the signal trace and both ground planes on the same board side. This layout is popular in RF modules, microwave fixtures, probes, antennas, and test coupons. It gives easy shunt component mounting. It also keeps fields near the surface.

Why Geometry Matters

Impedance depends mainly on trace width, gap width, substrate height, and dielectric constant. A wider trace lowers impedance. A wider slot usually raises impedance. A higher dielectric constant slows the wave and lowers impedance. Substrate thickness affects how much field travels in air or dielectric material.

The calculator uses a quasi static conformal mapping method. It treats metal as thin and assumes the line is uniform. That is useful for early layout work. It is not a substitute for field simulation when tolerances, plating, solder mask, or launch transitions are critical.

Useful Design Checks

Start with the board stackup. Enter the dielectric constant supplied by the laminate vendor. Use the same units for width, gap, height, and length. Then compare the impedance with your target, such as 50 ohms. Adjust the trace and gap in small steps. Keep manufacturing limits in mind. Very narrow slots can raise cost and reduce yield.

Frequency entries help estimate guided wavelength, phase, and delay. These values matter for stubs, filters, phase matched paths, and time domain checks. They also reveal when a short physical trace becomes electrically long.

Interpreting Results

The effective permittivity sits between air and substrate values. A lower value means more field in air. A higher value means more field in dielectric material. The capacitance and inductance estimates describe the distributed line. They help compare different geometries with the same impedance.

Good CPW practice includes solid side grounds, frequent via stitching when a rear ground exists, smooth transitions, and controlled gaps near components. Keep copper roughness and solder mask effects in mind at high frequency. Final validation should include fabrication notes, connector launches, and measurement with suitable calibration standards.

Use this tool for planning, comparison, and documentation. Recalculate after every stackup or geometry change. Small changes can move the impedance enough to affect return loss, matching, and repeatability. Document the chosen target and save exports for later fabrication reviews and approvals.

FAQs

What is coplanar waveguide impedance?

It is the characteristic impedance seen by a wave traveling along the center trace between two nearby ground planes.

Which dimensions matter most?

Trace width and gap width are usually the strongest controls. Substrate height and dielectric constant also shift the result.

Can this calculator target 50 ohms?

Yes. Change trace width or gap width until the calculated impedance is near 50 ohms or your chosen target.

Does metal thickness affect the answer?

This model treats conductors as thin. Thick copper, plating, roughness, and solder mask can change real board impedance.

What does effective permittivity mean?

It is the dielectric value experienced by fields traveling partly in air and partly through substrate material.

Why enter frequency?

Frequency is used for guided wavelength, phase, and delay estimates. The main impedance estimate is quasi static.

Should I use field simulation too?

Use simulation or measurement for final high frequency work, launches, solder mask, tight tolerance designs, and unusual stackups.

Can I use inches or mils?

Yes. Choose the geometry unit before calculating. Use the same unit for trace width, gap, height, and length.