The Microstrip Impedance conversion calculator determines the characteristic impedance of a microstrip transmission line based on its geometry and dielectric material. By entering the substrate height, trace width, and dielectric constant, it calculates the effective dielectric constant and impedance, which are essential for designing PCB traces used in RF and high-speed circuits.
Formulas
When (W/H) < 1:
εe = (εr + 1)/2 + (εr – 1)/2 * [ 1/√(1 + 12*(H/W)) + 0.4*(1 – W/H)² ]
Zo = (60 / √εe) * ln( 8*(H/W) + 0.25*(W/H) )
When (W/H) ≥ 1:
εe = (εr + 1)/2 + (εr – 1)/2 * [ 1/√(1 + 12*(H/W)) ]
Zo = 120 * π / ( √εe * [ (W/H) + 1.393 + (2/3)*ln(W/H + 1.444) ] )
Formula Explanation
- W is the trace width in the microstrip line.
- H is the height of the dielectric substrate.
- εr is the dielectric constant of the substrate material.
- εe is the effective dielectric constant, which accounts for both the air and dielectric layers surrounding the conductor.
- Zo is the characteristic impedance, which defines how signals propagate along the trace without reflection.
- The calculator automatically applies the correct formula depending on the W/H ratio.
Uses of this calculator
- Designing PCB traces for RF and microwave circuits.
- Matching transmission line impedance to 50 ohm or other system requirements.
- Estimating dielectric effects on signal integrity in high-speed designs.
- Verifying microstrip geometry during PCB layout.
50 ohm microstrip line on FR4 substrate
Input: εr = 4.4, H = 1.6 mm, W = 3 mm
Output:
- W/H = 3 / 1.6 = 1.875 (so W/H ≥ 1)
- εe = (4.4 + 1)/2 + (4.4 – 1)/2 * [1/√(1 + 12*(1.6/3))] = 2.7 + 1.7 * [1/√(1 + 6.4)] = 2.7 + 1.7 * 0.371 = 3.33
- Zo = 120 * π / ( √3.33 * [1.875 + 1.393 + (2/3)*ln(1.875 + 1.444)] ) = 376.99 / (1.825 * 3.915) = 376.99 / 7.15 = 52.75 ohm