This calculator determines the characteristic impedance of a microstrip line according to the width of the track, the thickness of the substrate and the dielectric constant. It helps design RF circuit boards with precise impedance matching to avoid signal reflections.
Useful for RF engineers, PCB designers and students working on high frequency circuits where impedance matching is critical to signal performance.
Formulas
For (W/H) < 1:
ε e = (ε r + 1)/2 + (ε r – 1)/2 × [1/√(1 + 12 × (H/W)) + 0.4 × (1 – W/H)²]
Z 0 = (60 / √ε e ) × ln(8 × (H/W) + 0.25 × (W/H))
For (W/H) ≥ 1:
ε e = (ε r + 1)/2 + (ε r – 1)/2 × [1 / √(1 + 12 × (H/W))]
Z 0 = 120 × π / [√ε e × ((W/H) + 1.393 + (2/3) × ln(W/H + 1.444))]
Explanation of formulas
- ε r is the dielectric constant of the material.
- W is the width of the track and H is the thickness of the substrate.
- ε e represents the effective permittivity of the electromagnetic field in the dielectric and air.
- Z 0 is the characteristic impedance of the line, determined by geometry and material properties.
Calculation of a 50 ohm microstrip line on FR4
Input : ε r = 4.4, H = 1.6 mm, W = 3 mm
Output : Z 0 ≈ 50.3 Ω
Benefits and uses
- Allows you to adjust the track width to achieve a specific impedance.
- Avoids mismatches and losses in RF circuits.
- Essential tool for designing microstrip filters, amplifiers and transmission lines.
- Facilitates modeling and simulation in PCB design software.