Calculator Inputs
Example Data Table
| Board Type | W mm | S mm | H mm | Er | Frequency GHz | Use Case |
|---|---|---|---|---|---|---|
| FR laminate prototype | 0.50 | 0.20 | 0.80 | 4.20 | 2.45 | Wireless test coupon |
| Low loss microwave board | 0.38 | 0.16 | 0.50 | 3.48 | 5.80 | Antenna feed line |
| Thin RF module | 0.22 | 0.10 | 0.25 | 3.66 | 10.00 | Compact transition |
Formula Used
The calculator uses a quasi-static conformal mapping model for grounded coplanar waveguide geometry. It estimates impedance from elliptic integral ratios for the top coplanar field and the lower ground plane field.
Basic variables are signal width W, side gap S, substrate height H, relative permittivity Er, frequency f, and length L.
For the top field, k = W / (W + 2S). For the grounded field, k1 = sinh(πW / 4H) / sinh(π(W + 2S) / 4H).
Effective permittivity is estimated with dielectric filling. Characteristic impedance is then found from the combined elliptic ratios. Guided wavelength equals c / (f √Eeff). Phase delay equals 360 × L / wavelength.
Loss is estimated from conductor skin resistance and dielectric loss tangent. These loss values are practical estimates, not a replacement for field solver validation.
How to Use This Calculator
- Enter the signal trace width in millimeters.
- Enter the gap from the signal trace to each ground pour.
- Enter the dielectric height from top copper to bottom ground.
- Add copper thickness, dielectric constant, frequency, and length.
- Enter loss tangent, conductivity, and roughness for loss estimates.
- Press Calculate to show results above the form.
- Use CSV or PDF export for reports and layout notes.
Grounded Coplanar Waveguide Design Guide
Purpose
A grounded coplanar waveguide is a controlled impedance structure. It has a center trace, two top ground pours, and a solid lower ground plane. It is common in RF modules, filters, launch transitions, antennas, and measurement coupons. The layout keeps return current close to the signal. That can reduce radiation and improve shielding.
Geometry Matters
The three strongest inputs are trace width, gap, and dielectric height. A wider trace usually lowers impedance. A narrower gap also lowers impedance. A thicker substrate usually raises impedance for many practical layouts. The bottom ground plane changes field distribution, so grounded waveguide results differ from simple coplanar waveguide results.
Material Inputs
Dielectric constant controls wave speed and impedance. Higher permittivity slows the wave and shortens wavelength. Loss tangent affects dielectric loss. Copper conductivity, thickness, and roughness affect conductor loss. These values become more important as frequency increases. Use real laminate data when possible. Nominal catalog values can shift with frequency, resin content, and fabrication tolerance.
Advanced Review
This tool estimates effective permittivity, guided wavelength, phase delay, capacitance, inductance, and loss. These outputs help compare design choices before a layout is finalized. They also help when checking line length, phase matching, or feed network balance. The exported files make it easier to record assumptions during design review.
Practical Limits
The model is best for early engineering checks. It assumes clean geometry and approximate field behavior. Real boards include solder mask, plating variation, etching tolerance, copper profile, via fences, connectors, and nearby parts. These details can change impedance. For critical microwave work, compare this estimate with a two dimensional field solver, test coupons, and vector network analyzer measurements.
Layout Tips
Keep ground pours continuous near the line. Add via stitching beside the waveguide when needed. Avoid sudden gap changes. Use tapered transitions at connectors and packages. Keep discontinuities short. Document the exact stackup. Small geometry changes can matter greatly at high frequency.
FAQs
What is a grounded coplanar waveguide?
It is a transmission line with a signal trace, side grounds, and a bottom ground plane. It supports controlled impedance routing on RF circuit boards.
Why does the gap affect impedance?
The gap controls electric field coupling between the signal trace and top grounds. A smaller gap usually increases capacitance and lowers impedance.
Does copper thickness matter?
Yes. Thickness changes effective conductor geometry. It can slightly change impedance and affects conductor loss, especially at higher frequencies.
Can this replace a field solver?
No. It is a practical estimate for early checks. Use a field solver and measured coupons for critical RF designs.
Why is effective permittivity lower than Er?
Some field energy travels in air, and some travels through dielectric. Effective permittivity combines both regions into one useful value.
What frequency should I enter?
Use the operating frequency of the signal. For broadband designs, test several frequencies and compare wavelength, loss, and phase delay.
What is guided wavelength?
Guided wavelength is the wavelength along the board trace. It is shorter than free-space wavelength because the dielectric slows propagation.
Why include roughness?
Copper roughness increases current path length near the surface. That can raise conductor loss at microwave frequencies.