Precision Inductance Modelling Is The Basis For Accurate PFN Simulation

Abstract

The results reported here form the basis of powerful new design tools for the modulator engineering community that enable rapid computation of the full inductance matrix of solenoidal structures with any form factor to absolute accuracy. Coaxial, single layer solenoids are modelled from the physical parameters of mean winding diameter, bare wire diameter, coil length, pitch and number of turns using the Round Wire Model (RWM). The RWM is based on Maxwell’s quasi-stationary equation for mutual inductance in elliptic integrals of the first and second kind, and Rayleigh-Niven’s formula for self-inductance. The RWM is assembled in the form of a Toeplitz matrix. This structure permits ready determination of the boundaries required to compute the mutual inductances for tapped and digitated coil sections. The RWM is a fast computing absolute formula supplanting the need for Rosa’s correction as well as the idealised Current Sheet Model (CSM) of Lorenz. The algorithms analytically define all elements of the inductance matrix. The Current Sheet Model The CSM assumes that, the solenoid is wound from an infinitely thin strip of conductor, the breadth of the conducting strip is equal to the winding pitch, the tums have infinitesimal separation between them, the diameter of the conducting strip equals the mean diameter of a similar winding made with real wire. S e e figure 1. Although the CSM seems to be somewhat idealized, it is sufficiently accurate in most practical applications. Lorenz’s Eauation in Elliptic Integrals The CSM inductance is evaluated using Lorenz’s formula: where r(k; I) and E(k; 3) are the complete elliptic integrals of the fiist and second‘ kind.’ variables are illustrated in figure 1. The parameter k and the other