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Coplanar Waveguide (CPW) Characteristic Impedance Calculator

Coplanar Waveguides (CPW) and Grounded Coplanar Waveguides (GCPW) are planar RF transmission lines where signal trace and ground returns reside on the exact same surface layer.

Width of center conductor strip.

Spacing gap between center trace and coplanar ground planes.

Thickness of dielectric board core (e.g. 1.6 mm standard FR-4).

Relative dielectric constant (4.4 for standard FR-4, 3.55 for Rogers 4003C).

Finished copper weight (35 µm for 1 oz copper).

Presence of continuous bottom ground shield plane.

Calculated Result
60.2 Ω

Characteristic Impedance (Z₀)

Characteristic Impedance (Z₀)

60.2 Ω

Effective Dielectric (ε_eff)

2.81

Propagation Delay

5.59 ps/mm

Waveguide Modulus (k)

0.6

Configuration

GCPW (Grounded Coplanar Waveguide)

Calculation Breakdown

  1. Conformal Mapping Aspect Ratiok = W / (W + 2S) = 1.2 / (1.2 + 2 × 0.4) = 0.6
  2. Complete Elliptic Integral EvaluationZ₀ = (60π / √ε_eff) / [K(k)/K'(k) + K(k₃)/K'(k₃)] = 60.2 Ω

CPW Electrical Parameters

Interactive visualization based on your current inputs

Value
0.015304560Impedance (Ω)Dielectric (ε_eff)Delay (ps/mm)Modulus k (x 100)ParameterValue

What Is the Coplanar Waveguide (CPW) Characteristic Impedance Calculator?

The Coplanar Waveguide (CPW) Characteristic Impedance Calculator designs controlled-impedance RF printed circuit board traces.

How Does the Coplanar Waveguide (CPW) Characteristic Impedance Calculator Work?

It utilizes conformal mapping elliptic integral approximations to calculate capacitance per unit length and electromagnetic propagation velocities.

Coplanar Waveguide (CPW) Characteristic Impedance Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Z_0 = \frac{60\pi}{\sqrt{\varepsilon_{eff}}} \frac{1}{\frac{K(k)}{K'(k)} + \frac{K(k_3)}{K'(k_3)}}, \quad k = \frac{W}{W + 2S}

Conformal mapping transformation of coplanar geometries into parallel plate capacitors.

How to Use the Coplanar Waveguide (CPW) Characteristic Impedance Calculator

  1. Enter center trace width and ground gap spacing in mm.
  2. Specify substrate core thickness and dielectric constant.
  3. Select between standard CPW and Grounded GCPW topology.

Step-by-Step Example Calculation

50-Ohm Grounded Coplanar Waveguide on FR-4

Input Values:

centerTraceWidthWMm:1.2
gapWidthSMm:0.4
substrateThicknessHMm:1.6
dielectricConstantEr:4.4
conductorThicknessUm:35
groundPlaneType:conductor-backed-gcpw
Worked Steps: Aspect ratio k = 0.60, delivering 50.8 Ω characteristic impedance, ε_eff of 2.76, and 5.54 ps/mm propagation delay.

Understanding Your Result

Characteristic Impedance (Z0): Target transmission line impedance (typically 50 Ω).

Effective Dielectric Constant: Mixed dielectric constant between air and substrate.

Propagation Delay: Signal transit time in picoseconds per millimeter.

Factors That Affect the Result

  • Widening the gap spacing S increases impedance, while widening the trace W decreases impedance.

When Should You Use This Calculator?

  • 5G RF front-ends, Wi-Fi 6/7 antenna feedlines, high-speed serializer/deserializer routing, and radar transceivers.

Assumptions & Limitations

  • Assumes continuous ground stitching vias spaced ≤ λ/10 along the ground gaps for GCPW.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard microwave engineering conformal mapping formulation per Ghione & Naldi.

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