Calculator Inputs
Example Data Table
| Use Case | Width | Gap | Height | Dielectric | Frequency | Notes |
|---|---|---|---|---|---|---|
| FR-4 RF test trace | 1.40 mm | 0.18 mm | 0.80 mm | 4.2 | 2.4 GHz | Common wireless layout estimate. |
| Thin microwave laminate | 0.55 mm | 0.12 mm | 0.30 mm | 3.48 | 5.8 GHz | Useful for compact RF routing. |
| Wide low loss route | 2.20 mm | 0.25 mm | 1.00 mm | 3.66 | 1.0 GHz | Lower loss for longer traces. |
Formula Used
The calculator uses a quasi-static coplanar line estimate. The main geometry ratio is:
k = W_eff / (W_eff + 2S_eff)
Complete elliptic integrals are evaluated with the arithmetic-geometric mean method:
K(k) = π / [2 × AGM(1, √(1-k²))]
Characteristic impedance is estimated as:
Z0 = 30π × K(k') / [√ε_eff × K(k)]
Dielectric loading is estimated from the substrate height ratio:
ε_eff = 1 + [(εr - 1) / 2] × [K(k') / K(k)] × [K(k1) / K(k1')]
Copper thickness changes the effective width. Loss estimates include skin depth, conductor loss, dielectric loss, frequency, conductivity, temperature, and roughness. Grounded mode applies a practical backing-ground correction.
How to Use This Calculator
- Select the coplanar model that matches your board stackup.
- Choose the unit used for width, gap, height, thickness, and length.
- Enter signal trace width and gap to the coplanar ground copper.
- Enter substrate height and dielectric constant from your laminate data.
- Add frequency, loss tangent, conductivity, roughness, and temperature.
- Enter a target impedance, such as 50 Ω or 75 Ω.
- Press the calculate button to view impedance above the form.
- Use CSV or PDF export for reports, notes, or layout reviews.
Design Article
Why Coplanar Geometry Matters
A coplanar microstrip places the signal trace beside ground copper on the same layer. This shape helps control impedance. It also gives nearby return current paths. That can reduce radiation and improve high frequency behavior.
Important Board Inputs
Width and gap are the strongest layout controls. A wider trace usually lowers impedance. A larger gap usually raises impedance. Substrate height also matters. Thin dielectric layers give stronger field coupling. The dielectric constant changes phase speed. Higher dielectric values slow the wave and lower wavelength.
Copper Thickness and Frequency Effects
Real copper has thickness. Etching and plating can change the final width. This calculator applies a practical thickness correction. At high frequency, current crowds near the copper surface. This is called skin effect. The skin depth becomes smaller as frequency rises. Rough copper also increases conductor loss. Use a roughness multiplier when the copper profile is not smooth.
Loss and Target Tuning
Dielectric loss depends on frequency and loss tangent. Conductor loss depends on conductivity, skin depth, width, and surface quality. The result shows both losses separately. It also shows total loss over the entered line length.
Practical Use
Use this tool early in layout planning. Compare trace widths before routing. Keep the same unit system across all geometry inputs. Use manufacturer stackup data when possible. For antennas, filters, clocks, and fast serial lines, confirm the final result. Fabrication tolerance can move impedance several ohms. For critical work, request controlled impedance testing. A field solver or test coupon gives better confidence.
FAQs
1. What is coplanar microstrip impedance?
It is the characteristic impedance of a signal trace with nearby ground copper on the same board layer. It depends on trace width, gap, substrate height, dielectric constant, and copper details.
2. Does a wider trace increase impedance?
No. A wider signal trace usually lowers impedance because capacitance increases. A narrower trace usually raises impedance when the gap and dielectric height remain unchanged.
3. What does the coplanar gap control?
The gap controls coupling between the signal trace and side ground copper. A smaller gap usually lowers impedance. A larger gap usually raises impedance.
4. Why is effective dielectric constant important?
Effective dielectric constant shows how much of the electric field travels through dielectric material. It controls wave speed, delay, wavelength, and phase behavior.
5. Is this result exact?
No. It is a strong engineering estimate based on closed-form formulas. Critical RF layouts should be checked with a field solver, coupon measurement, or fabricator impedance report.
6. What target impedance should I use?
Use the impedance required by your circuit. RF systems often use 50 Ω. Video, antenna, sensor, or digital systems may need other values.
7. Why does frequency affect loss?
Higher frequency reduces skin depth and increases surface resistance. It also increases dielectric loss. That is why long high frequency routes need careful material and copper choices.
8. Can I export the results?
Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a compact report you can save or share.