| This report presents the results of an analytic assessment of LaPlace's Equation derived using tensor calculus for a helical coordinate system. This equation was then applied to a shielded, twisted pair transmission line with the intent of calculating the capacitance. Previous work in this area has shown promise, including a numerical estimation.; A great number of assumptions and simplifying changes were made to allow for normal techniques for solving differential equations to be applied. The resultant equation is not separable which does not normally allow for a solution to be developed. However, three (3) cases are identified and presented. These are: (1) no variation in 'z', (2) 'theta' varies slowly compared to 'z' (this represents a loose twist), and (3) 'z' varies slowly compared to 'theta' (this represents a tight twist). Case #2 results are very close to observed/measured data for a standard shielded, twisted pair transmission line and support viability of using analytic methods for solving this geometry. |
