PSICE Model for a Coaxial Cable in High Frequency Domain Submitted to a Longitudinal Temperature Gradient Using Kelvin-Bessel Asymptotic Functions

This paper investigates on the propagation in a coaxial cable with the assumption that the distributed parameters are variable with the longitudinal distance from the source due to a linear temperature variation. This work addresses the problem of propagation in borehole conditions where the temperature varies by approximately 3°C/100m. In addition to the temperature variation along the coax we have considered the high frequency domain where the skin effect is severe and leading to very high losses. Unlike the uniform temperature distribution study this case is very complex and that is the reason why we have provided a model for PSPICE simulator to represent the cascaded cells because the analytic solution is extremely tedious to solve. The idea is thus to replace the coax cable by cascaded elements whose resistance and impedance are calculated via Kelvin-Bessel functions. Because the number of cells is huge we have written a C language program to generate automatically the PSPICE .CIR file. Each cell has its own resistance and inductance according to its temperature. The capacity is assumed to be constant along the coax for each cell. Besides the PSPICE program, and for comparison, we have developed a recursive method for computing the attenuation due to the whole cascaded cells. The comparison between PSPICE and the recursive method has shown results in very good agreement. Keywords— PSPICE Model, Skin Effect, Coaxial Cable, Temperature Gradient, Asymptotic Expansions