Surge impedance of microstrip line when effective width is less than substrate thickness¶

The microstrip line is a dielectric substrate on which a metal strip is applied. When a wave propagates along a microstrip line, part of the field goes out, since the microstrip line does not have metal borders on all sides, unlike, for example, rectangular waveguides.

Conditions:

Effective width \(w_\text{eff}\) of the microstrip line should be less than or equal to thickness \(h\) of the substrate.

surge_impedance¶: surge_impedance of the microstrip line.

Symbol:: Z_S
Latex:: \(Z_\text{S}\)
Dimension:: impedance

effective_permittivity¶: Effective relative_permittivity of the microstrip line. See Effective permittivity of microstrip line.

Symbol:: epsilon_eff
Latex:: \(\varepsilon_\text{eff}\)
Dimension:: dimensionless

substrate_thickness¶: thickness of the substrate.

Symbol:: h
Latex:: \(h\)
Dimension:: length

effective_width¶: Effective width (see length) of the microstrip line. See Effective width of microstrip line.

Symbol:: w_eff
Latex:: \(w_\text{eff}\)
Dimension:: length

law¶

Z_S = Z_0 / sqrt(epsilon_eff) * log(8 * h / w_eff + w_eff / (4 * h))

Latex:: \[Z_\text{S} = \frac{Z_0}{\sqrt{\varepsilon_\text{eff}}} \log \left( \frac{8 h}{w_\text{eff}} + \frac{w_\text{eff}}{4 h} \right)\]