Calculator
Example data table
| Stackup | εr | h (mm) | w (mm) | Z0 (Ω) | εeff | λg @ 1 GHz (mm) | Delay @ 50 mm (ns) |
|---|---|---|---|---|---|---|---|
| FR-4 typical | 4.4 | 1.6 | 3.0 | 50.821 | 3.324932 | 164.410 | 0.304 |
| Mid-ε laminate | 3.0 | 0.8 | 1.4 | 62.684 | 2.356753 | 195.283 | 0.256 |
| Low-ε (2.2) | 2.2 | 1.524 | 4.7 | 50.250 | 1.871300 | 219.154 | 0.228 |
Formulas used
This tool uses common quasi-static microstrip approximations with the ratio u = w/h. Effective permittivity εeff is estimated first, then characteristic impedance Z0.
εeff = (εr+1)/2 + (εr−1)/2 · ( 1/√(1+12/u) + 0.04·(1−u)² )
If u > 1:
εeff = (εr+1)/2 + (εr−1)/2 · ( 1/√(1+12/u) )
Z0 = (60/√εeff) · ln( 8/u + 0.25·u )
If u > 1:
Z0 = (120·π)/( √εeff · ( u + 1.393 + 0.667·ln(u+1.444) ) )
- v = c / √εeff and velocity factor VF = v/c.
- Delay per length: tpd = 1/v (converted to ns/m and ps/mm).
- Guided wavelength: λg = v/f, phase shift: θ = 360·length/λg.
- Per-unit-length values: C' = 1/(Z0·v) and L' = Z0/v.
How to use this calculator
- Select your preferred mode: calculate impedance or solve width.
- Enter εr and the substrate height h.
- Choose a dimension unit, then fill w and t.
- Optionally enter frequency and length for wavelength and phase.
- Press Submit. Results appear above the form.
- Use CSV or PDF exports for sharing and documentation.
FAQs
1) What does characteristic impedance mean here?
It is the transmission-line impedance seen by fast edges on a long trace. Matching this value helps reduce reflections and improves signal integrity on controlled-impedance interconnects.
2) When should I use width-solve mode?
Use it when you know the target impedance, such as 50 Ω or 90 Ω differential halves. The calculator finds a width that best matches the target for your εr and h.
3) Why is copper thickness not changing Z0 much?
For many PCB geometries, impedance is dominated by width, height, and dielectric constant. Thickness effects exist, but simple closed-form models often treat them as a small correction.
4) What is effective permittivity?
Microstrip fields live partly in the dielectric and partly in air. Effective permittivity is a weighted value that reflects this mix and determines wave velocity along the trace.
5) How accurate are these formulas?
They are widely used first-order estimates and work well for common designs. Accuracy can degrade with extreme geometries, solder mask coverage, unusual materials, or very high-frequency dispersion.
6) How do I interpret delay and wavelength outputs?
Delay tells how long a signal takes to propagate along the trace. Guided wavelength helps estimate electrical length and phase shift at a given frequency, useful for RF routing and stubs.
7) Can I use this for differential pairs?
This calculator is for a single-ended microstrip. For differential pairs, coupling depends on spacing and reference geometry. Use a differential calculator or a field solver for accurate differential impedance.
8) What inputs most affect impedance?
The ratio w/h is the biggest driver. Higher εr usually lowers impedance and slows propagation. Keeping h stable and controlling w tightly improves repeatability across fabrication lots.