Surge impedance of microstrip line when effective width is greater 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.

Notation:

1. \(Z_0\) (Z_0) is vacuum_impedance.

Conditions:

1. Effective width \(w_\text{eff}\) of the microstrip line should be greater than 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) / (w_eff / h + 1.393 + 0.667 * log(w_eff / h + 1.444))

Latex:

\[Z_\text{S} = \frac{Z_0}{\sqrt{\varepsilon_\text{eff}}} \frac{1}{\frac{w_\text{eff}}{h} + 1.393 + 0.667 \log \left( \frac{w_\text{eff}}{h} + 1.444 \right)}\]