Example Data Table
| Use Case |
W mm |
G mm |
H mm |
Er |
Target |
| RF module feed | 1.20 | 0.20 | 0.80 | 4.20 | Near 50 Ω |
| Thin laminate line | 0.45 | 0.12 | 0.30 | 3.48 | Compact routing |
| Low loss board | 0.80 | 0.18 | 0.50 | 3.00 | Fast signal path |
Formula Used
The calculator uses quasi-static conformal mapping for grounded coplanar waveguide estimation. It starts with k = W / (W + 2G). It also estimates a substrate correction using hyperbolic sine terms from W, G, and H. Complete elliptic integral ratios are approximated through an arithmetic geometric mean method.
The main impedance relation is Z0 = 30π / sqrt(Eeff) / ratio. Effective permittivity is estimated from the substrate permittivity and elliptic ratio comparison. Thickness correction slightly lowers impedance when copper thickness is meaningful compared with trace width.
How to Use This Calculator
Enter the center conductor width, side gap, substrate height, and relative permittivity. Add copper thickness, line length, operating frequency, loss tangent, and conductor conductivity. Press Calculate. The result appears below the header and above the form. Use CSV for spreadsheet records. Use PDF for quick reports.
Grounded Coplanar Waveguide Design Guide
A coplanar waveguide with ground is common in RF boards. It places a signal strip between ground pours. A bottom ground plane also supports the field. This structure is useful for antennas, filters, mixers, sensors, and high speed interconnects. The geometry gives practical control over impedance while keeping the return path close.
Why Geometry Matters
Width and gap are the strongest inputs. A wider signal trace usually lowers impedance. A wider gap usually raises impedance. Substrate height changes how much field reaches the lower ground plane. A thin board can pull more field into the dielectric. That often changes effective permittivity and phase velocity.
Material Effects
Dielectric constant is another key factor. Higher values slow the wave and reduce impedance. The effective value is lower than the raw material value because some field remains in air. Loss tangent estimates dielectric loss. Copper conductivity and frequency estimate skin depth and conductor loss. These values are useful for early comparisons.
Advanced Output Meaning
Characteristic impedance helps match sources, loads, and connectors. Effective permittivity helps predict delay and wavelength. Capacitance and inductance per meter describe the distributed line model. Electrical length shows how long the trace appears at the entered frequency. This is important when a trace becomes a meaningful fraction of a wavelength.
Practical Layout Notes
Keep ground pours continuous near the line. Add via fences when the board process allows them. Avoid sharp corners and sudden gap changes. Confirm final values with a field solver before fabrication. Manufacturing tolerance can shift impedance. Solder mask, plating, roughness, and nearby copper can also change results. Use this tool for planning, comparison, and documentation. Use measurements or solver data for final signoff.
FAQs
What is grounded coplanar waveguide?
It is an RF transmission line with a center trace, side grounds, and a lower ground plane. It supports controlled impedance routing.
What raises CPWG impedance?
A larger gap, narrower trace, lower dielectric constant, or thicker substrate can raise impedance. The exact shift depends on the full geometry.
What lowers CPWG impedance?
A wider signal trace, smaller side gap, higher dielectric constant, or stronger ground coupling can lower impedance.
Is this result exact?
No. It is an analytical estimate. Final designs should be checked with a field solver, board stackup data, and fabrication tolerances.
Why is effective permittivity important?
It controls wave speed, delay, and electrical length. It is usually between air permittivity and substrate permittivity.
Does copper thickness affect impedance?
Yes. Thicker copper can slightly reduce impedance. The effect is stronger when trace width is small.
Why include loss tangent?
Loss tangent estimates dielectric energy loss. It becomes more important at higher frequencies and longer line lengths.
Can I use this for microwave layout?
Yes, for early estimates. For production microwave layouts, compare results with simulation, measured coupons, and supplier stackup data.