Embedded Coplanar Waveguide Calculator

Calculator Inputs

Trace Width W

Gap S

Dielectric Height H

Copper Thickness

µm

Substrate Dielectric Constant

Embedded Cover Thickness

Cover Dielectric Constant

Loss Tangent

Frequency

GHz

Route Length

Copper Conductivity

MS/m

Target Impedance

Formula Used

The calculator uses a quasi-static grounded coplanar waveguide estimate. It applies complete elliptic integral ratios to model the signal trace and side gaps. The main impedance estimate is:

Z0 = (30π / √εeff) × K(k') / K(k)

Here, k = W / (W + 2S). The term W is the corrected trace width. The term S is the signal to ground gap. Copper thickness adds an effective width correction. Dielectric height adjusts the fill factor through another elliptic ratio.

Propagation velocity uses v = c / √εeff. Delay uses the inverse velocity. Capacitance is estimated with C' = 4ε0εeffK(k)/K(k'). Inductance follows from L' = Z0²C'. Loss values are engineering estimates. They include dielectric loss and conductor surface resistance.

How To Use This Calculator

Enter the trace width, side gap, and dielectric height from your stackup.
Add copper thickness after plating for a better width correction.
Enter substrate and cover dielectric constants for embedded routing.
Set frequency and route length to estimate wavelength and loss.
Press Calculate to view the result above the form.
Use CSV or PDF download buttons to save the current case.
Compare several width and gap values before layout release.
Confirm final dimensions with fabrication data and a field solver.

Example Data Table

Case	W mm	S mm	H mm	Er	Frequency GHz	Approximate Use
A	0.28	0.18	0.20	3.66	10	Digital control impedance check
B	0.20	0.12	0.15	3.48	16	Compact high speed route
C	0.35	0.25	0.30	4.10	6	Lower loss board review

Embedded Coplanar Waveguide Design Guide

An embedded coplanar waveguide places the signal trace and side grounds inside dielectric material. It is useful when a board stack needs controlled impedance, shielding, and compact routing. The calculator gives a practical first pass before field solver review. It combines width, gap, dielectric constant, copper thickness, cover material, frequency, and route length.

Why This Geometry Matters

Coplanar fields spread through the side gaps and the dielectric cover. A grounded reference plane below the trace also pulls energy downward. These paths change impedance and delay. Small changes in gap or height can move a design away from a target value. That is why the form accepts many layout inputs instead of only trace width.

Understanding The Output

The main output is estimated characteristic impedance. Effective dielectric constant follows because the wave travels partly through each region. The tool also reports velocity, delay, capacitance, inductance, wavelength, and approximate losses. These values help compare routing choices. They can also support early documentation for high speed nets.

Using Results Wisely

Use the estimate for planning, tolerance checks, and design conversations. Then confirm final dimensions with your fabricator stackup and a solver. Real boards include solder mask variation, copper roughness, plating, glass weave, and etch tolerance. Those details can shift results. Treat the recommendation line as a guide, not as a final fabrication rule.

Practical Layout Notes

Keep side grounds continuous where possible. Add stitching vias near the route when your process allows them. Avoid sudden gap changes. Keep the dielectric cover consistent above the line. Check manufacturing limits for minimum gap and copper thickness. Export the table when comparing many cases. A clear record helps review impedance goals before release.

Review Workflow

Start with the nominal stackup. Enter the actual copper thickness after plating. Run the target case first. Save the output. Next, change gap, width, and dielectric height within fabrication tolerance. Compare the exported rows. Look for combinations that stay near the target across limits. For fast digital links, also compare delay and wavelength. For RF lines, check loss at the highest operating frequency. Share the final range with fabrication notes. This keeps assumptions visible and reduces later redesign work. It also improves repeatable design handoff decisions.

FAQs

1. What is an embedded coplanar waveguide?

It is a controlled impedance line with a center trace and side grounds. The structure is surrounded or partly covered by dielectric material. A reference plane may sit below it.

2. Is this a replacement for a field solver?

No. It is an engineering estimate for planning and comparison. Use a field solver and fabricator stackup for final release dimensions.

3. Why does the cover dielectric matter?

The cover pulls more electric field into dielectric material. That changes effective dielectric constant, delay, and impedance. Embedded routes can shift compared with exposed routes.

4. What dimensions affect impedance most?

Trace width, side gap, dielectric height, and dielectric constant are usually dominant. Copper thickness and cover thickness also matter for tighter designs.

5. Why is impedance above my target?

The trace may be too narrow, the gap may be too wide, or dielectric loading may be too low. Increase width or reduce gap carefully.

6. Why is impedance below my target?

The trace may be too wide, the gap may be too small, or dielectric loading may be high. Reduce width or increase gap within fabrication limits.

7. Are the loss values exact?

No. They are approximate. Real loss depends on copper roughness, plating, solder mask, launches, vias, weave, and actual material data.

8. When should I export the result?

Export results when comparing stackups, documenting design reviews, or sharing calculations with layout and fabrication teams.