How are the Per-Unit-Length Parameters Calculated for MTL Cables?

Question: How are the per-unit-length parameters, L, C and G calculated for MTL cables (including thick shields)?

Answer: For the per-unit-length parameters calculation, the structure is meshed into a 2D triangular mesh. The parameters (L, C and G) are then solved using a 2D Laplace FEM solver.

The generated mesh considers all boundaries. The inside and outside of the shield are two separate boundaries. Each conductor in this cross-section is considered as if it is a perfect electric conductor (PEC). The solution computes the per-unit-length parameters on a sub-circuit basis (there are no capacitance / inductances between conductors on either side of the shield). The parameters G and R are introduced to model the metallic and dielectric losses respectively. The cable coupling is modelled using the transfer impedance and admittance parameters, Zt and Yt.

Take for instance a coaxial cable with two cores inside and a very thick shield. If the cores are numbered 1 and 2, and the shield 3 forming an outer geometric boundary, Feko computes C13, C12, C21 and C23 on the inside, using the shield inside radius.
Note: C13 and C23 are the self-capacitances in the inner problem with the shield seen as the ground.
On the outside, Feko computes C33, which is the self-capacitance with respect to the geometric ground. Here Feko considers the outer shield radius, and also the shape of the outer geometry.

For the computation of Zt, you can choose from the Schelkunoff, Kley or Vance formulas or specify the Zt and Yt parameters.

Feko selects one of the following: (the option selected depends on the specified shield thickness and frequency):
  • Low-frequency approximation
  • Exact description
  • High-frequency approximation
  • Practical shields where the wall thickness is small compared to the radius of the tube

If the shield is PEC, then it is known that Zt = 0.

Furthermore, Feko uses a dynamic range of -120 dB to calculate a cutoff distance of N * delta, after which Zt = 0 is set. If the shield is thicker than N times the skin depth, Feko sets Zt = 0 to avoiding numerical noise.