TescheCoaxialSolver

class pmrf.models.components.lines.physical.TescheCoaxialSolver

Bases: AbstractCoaxialSolver

Analytical solver for coaxial line RLGC parameters using the Tesche high-frequency approximation.

Mathematical Formulation

Ideal non-dispersive components (\(L'\) and \(C'\)) and dielectric loss (\(G\)) are given by:

\[L' = \frac{\mu_0 \mu_r}{2\pi} \ln\left(\frac{b}{a}\right)\]

\[C' = \frac{2\pi \varepsilon_0 \varepsilon_r}{\ln(b/a)}\]

\[G_{diel} = \frac{2\pi \omega \varepsilon_0 \varepsilon_r \tan\delta}{\ln(b/a)}\]

The internal surface impedance defining frequency-dependent skin resistance (\(R_{skin}\)) and skin inductance (\(L_{skin}\)) is governed by:

\[R_{skin} = \frac{1}{2\pi a} \sqrt{\frac{\omega\mu}{2\sigma_a}} + \frac{1}{2\pi b} \sqrt{\frac{\omega\mu}{2\sigma_b}}\]

\[L_{skin} = \frac{1}{2\pi a} \sqrt{\frac{\mu}{2\omega\sigma_a}} + \frac{1}{2\pi b} \sqrt{\frac{\mu}{2\omega\sigma_b}}\]

Where \(a\) is the inner radius, \(b\) is the outer radius, and \(\sigma\) is the conductor conductivity (\(1/\rho\)). The total per-unit-length inductance is \(L = L' + L_{skin}\).

References

Tesche, F. M. (2007). A Simple Model for the Line Parameters of a Lossy Coaxial Cable Filled With a Nondispersive Dielectric. IEEE Transactions on Electromagnetic Compatibility, 49(1), 12-17.

Schelkunoff, S. A. (1934). The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields. Bell System Technical Journal, 13(4), 532-579.

run(freq: Frequency, din, dout, epr, mur, tand, rho) → RLGCResult