CohnStriplineFormulation

class pmrf.models.components.lines.stripline.CohnStriplineFormulation

Bases: AbstractStriplineFormulation

Cohn’s stripline formulation, in the form tabulated by Pozar.

Mathematical Formulation

The filling is homogeneous, so

\[\varepsilon_e = \varepsilon_r\]
exactly, with no filling factor and no modal dispersion. With the fringing correction to the strip width,
\[\begin{split}\frac{W_e}{b} = \frac{W}{b} - \begin{cases}0, & W/b > 0.35,\\ (0.35 - W/b)^2, & W/b \leq 0.35,\end{cases}\end{split}\]
the characteristic impedance of the zero-thickness strip is
\[Z_c = \frac{30\pi}{\sqrt{\varepsilon_r}}\frac{b}{W_e + 0.441b}.\]

Conductor loss is supplied by CohnCurrentDistribution, and complex \(\varepsilon_e\) carries dielectric loss.

Validity

The impedance expression assumes zero thickness and uses a continuous fringing correction at \(W/b=0.35\). A supplied thickness must satisfy \(0<T<b\), although it does not enter the impedance expression.

References

Cohn, S. B. (1955). Problems in Strip Transmission Lines. IRE Transactions on Microwave Theory and Techniques, 3(2), 119-126.

Pozar, D. M. (2011). Microwave Engineering (4th ed.), Section 3.7. Wiley.

quasi_static(*, w, b, t, ep_r) → PlanarQuasiStaticResult

Calculate the quasi-static solution.

Parameters:

  • w (ArrayLike) – Width of the centre strip in meters.

  • b (ArrayLike) – Ground-plane separation in meters.

  • t (ArrayLike | None) – Thickness of the strip in meters, or None for a zero-thickness strip.

  • ep_r (jnp.ndarray) – Complex relative permittivity of the filling, shape (npoints,).

Returns:

The effective permittivity, impedance and effective width.

Return type:

PlanarQuasiStaticResult