Wave impedance of coplanar line when length to distance ratio squared is between \(\frac{1}{2}\) and \(1\)¶

Under the conditions described below, the wave impedance of a coplanar line depends on its effective permittivity and physical dimensions.

Conditions:

\(h < \frac{d}{4}\)
\(\frac{1}{2} < \left( \frac{l}{d} \right)^2 \le 1\)

Here, \(h\) is the thickness of the substrate, and \(d\) is the distance between the first and last electrodes.

wave_impedance¶: wave_impedance of the coplanar line.

Symbol:: eta
Latex:: \(\eta\)
Dimension:: impedance

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

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

electrode_distance¶: euclidean_distance between the first and last electrodes.

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

central_electrode_width¶: Width (see length) of the central electrode of the coplanar line.

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

resistance_constant¶: Constant equal to \(30 \pi^2 \, \Omega\) (30 * pi^2 Ohm).

Symbol:: R_0
Latex:: \(R_0\)
Dimension:: impedance

law¶

eta = R_0 / sqrt(epsilon_eff) / log(2 * (1 + sqrt(l / d)) / (1 - sqrt(l / d)))

Latex:: \[\eta = \frac{R_0}{\sqrt{\varepsilon_\text{eff}}} \frac{1}{\log \left( \frac{2 \left(1 + \sqrt{\frac{l}{d}}\right)}{1 - \sqrt{\frac{l}{d}}} \right)}\]