WheelerMicrostripSolver
- class pmrf.models.components.lines.physical.WheelerMicrostripSolver
Bases:
AbstractMicrostripSolverAnalytical solver for microstrip line RLGC parameters using the standard Wheeler approximations.
Mathematical Formulation
With ratio \(u = \frac{W}{H}\), the effective relative permittivity (\(\varepsilon_e\)) and ideal impedance terms (\(Z_a, Z_e\)) are:
\[\varepsilon_e = \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r - 1}{2} \frac{1}{\sqrt{1 + 12/u}}\]\[Z_a = \frac{120\pi}{u + 1.393 + 0.667 \ln(u + 1.444)}\]\[Z_e = \frac{Z_a}{\sqrt{\varepsilon_e}}\]Which provide the per-unit-length components:
\[L = \frac{Z_e \sqrt{\varepsilon_e}}{c}\]\[C = \frac{\sqrt{\varepsilon_e}}{Z_e c}\]\[R = \frac{1}{W} \sqrt{2 \mu_0 \rho \omega}\]\[G = \frac{1}{Z_a c} \frac{\varepsilon_r (\varepsilon_e - 1)}{\varepsilon_r - 1} \tan\delta \cdot \omega\]References
Wheeler, H. A. (1977). Transmission-Line Properties of a Strip on a Dielectric Sheet on a Plane. IEEE Transactions on Microwave Theory and Techniques.
- run(freq: Frequency, w, h, epr, tand, rho, t) RLGCResult