Wave impedance of coplanar line when hyperbolic sine ratio squared is between \(0\) and \(\frac{1}{2}\)¶

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

Conditions:

\(h < \frac{d}{4}\)
\(0 < \left( \frac{\sinh{ \left((\pi l) / (4 h)\right) }}{\sinh{ \left((\pi d) / (4 h)\right) }} \right)^2 \le \frac{1}{2}\)

See below for symbol descriptions.

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 \(30 \, \Omega\) (30 Ohm).

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

law¶

eta = R_0 / sqrt(epsilon_eff) * log(2 * (1 + (1 - (l / d)^2)^(1 / 4)) / (1 - (1 - (l / d)^2)^(1 / 4)))

Latex:: \[\eta = \frac{R_0}{\sqrt{\varepsilon_\text{eff}}} \log \left( \frac{2 \left(1 + \left(1 - \left(\frac{l}{d}\right)^{2}\right)^{\frac{1}{4}}\right)}{1 - \left(1 - \left(\frac{l}{d}\right)^{2}\right)^{\frac{1}{4}}} \right)\]