This calculator makes it possible to determine the characteristic impedance of a microstrip transmission line based on the physical dimensions of the conductor and the dielectric properties of the substrate. It is widely used in RF and microwave circuit board design.
Formulas
When (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) )
When (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
The equations distinguish two cases according to the width/height ratio (W/H). They take into account the relative permittivity (εr) of the substrate and the effect of the partially confined electromagnetic field. The impedance value (Z0) depends on the geometry of the track and the material used.
Uses of the calculator
- Sizing of microstrip tracks on RF printed circuits.
- Optimization of impedance matching for antennas and filters.
- Used for the design of high frequency transmission lines.
- Essential tool for microwave design engineers and technicians.