Microstrip Calculator
Synthesis (Z₀ → W) and Analysis (W → Z₀) for microstrip transmission lines. Computes trace width, impedance, effective permittivity, wavelength, λ/4 length, phase velocity and attenuation. Uses the Hammerstad–Jensen model with trace-thickness correction.
We = W + (t/π)·(1 + ln(2h/t)) [thickness correction]
εeff = (εr+1)/2 + (εr−1)/2·(1+12h/We)^−½
Z₀ = (60/√εeff)·ln(8h/We + We/4h) [We/h < 1]
Z₀ = 120π / (√εeff·(We/h + 1.393 + 0.667·ln(We/h+1.444))) [We/h ≥ 1]
αd = (π·f·εr·(εeff−1)·tan δ) / (c·√εeff·(εr−1)) dB/m → dB/cm
αc = Rs / (Z₀·We) (Wheeler incremental inductance rule)
λ = c / (f · √εeff) mm
About the Microstrip Calculator
Microstrip is the most widely used transmission line topology in RF and microwave PCB design. It consists of a conducting trace on top of a dielectric substrate with a ground plane on the bottom. The characteristic impedance depends on the trace width, substrate height, dielectric constant and trace thickness.
Synthesis vs Analysis
Synthesis mode takes a target impedance (typically 50 Ω) and computes the required trace width for your substrate. Analysis mode takes an existing trace width and computes the resulting impedance — useful for checking legacy designs.
Key Parameters
Substrate height (h) is the distance from the trace to the ground plane. Common values are 0.8 mm, 1.0 mm and 1.6 mm for standard FR4. Relative permittivity (εr) — FR4 is typically 4.2–4.6 at 1 GHz. Loss tangent (tan δ) — FR4 is around 0.02, Rogers 4350B is 0.0037.
50 Ω Microstrip on FR4
For a standard 1.6 mm FR4 board (εr = 4.4), a 50 Ω microstrip trace is approximately 3.0 mm wide. The effective permittivity is around 3.1, giving a wavelength of about 170 mm at 1 GHz.
Hammerstad-Jensen Model
This calculator uses the Hammerstad-Jensen closed-form model with trace thickness correction. Accurate to within 1–2% of full-wave EM simulation for most PCB work.