Inductance of transmission lines: Deriving the flux linkage method from the generalized telegrapher’s equations

This paper presents a clear derivation of the flux linkage method for calculating inductance of transmission lines with spatially disturbed (non-filamentary) current. The flux linkage method is a common tool for teaching and calculating inductance of distributed circuits, yet rarely derived from first principles in textbooks. This may confuse students into thinking the method is obvious. This paper proves the flux linkage method by generalizing the ordinary telegrapher’s equations to the case of transmission lines with spatially distributed current. Furthermore, we demonstrate the advantages of a systematic approach for calculating inductance by comparing it with the traditional approach for a coaxial cable.