How are the per unit length parameters, L, C and G calculated for MTL cables?

Question

JIF · Answer

For the calculation of the per-unit-length parameters L, C and G, the structure is meshed internally into a 2D triangular mesh. These parameters are then solved using a 2D Laplace FEM solver.

The mesh that is generated considers all boundaries, i.e. the inside and outside of the shield are 2 separate boundaries. Each conductor in this cross section is seen as if PEC, hence, the solution will compute per-unit-length parameters on a sub-circuit basis, i.e. 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 by the transfer impedance and admittance parameters, Zt and Yt.

Take for instance a coaxial cable with 2 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 will then compute C13, C12, C21 and C23 on the inside (note that C13 and C23 are the self-capacitances in the inner problem with the shield seen as the ground), using the shield inside radius. And on the outside, FEKO will compute C33, which is the self-capacitance with respect to the geometric ground. Here FEKO will consider the shield outer radius, and also the shape of the outer geometry.

For the computation of Zt the user can choose from the Schelkunoff, Kley or Vance formulas or by manually specifying the Zt and Yt parameters in a table.

FEKO makes different choices depending on the specific settings such as 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 - that is, if the shield is thicker than N times the skin depth, FEKO sets Zt = 0. This avoids numerical noise.