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:

${\epsilon }_{\text{eff}}$

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:

$$Z_{\text{S}}=\frac{Z_0}{\sqrt{{\epsilon }_{\text{eff}}}}\frac{1}{\frac{w_{\text{eff}}}{h}+1.393+0.667\log (\frac{w_{\text{eff}}}{h}+1.444)}$$