Sage Journals: Discover world-class research

Abstract

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.

Keywords

Flux linkage method inductance per unit length telegrapher’s equations transmission line

Get full access to this article

View all access options for this article.

References

Paul

. Inductance: loop and partial, Hoboken, NJ: Wiley-IEEE Press, 2009.

Grover

. Inductance calculations, New York: Dover, 1973.

Cheng

. Field and wave electromagnetics, 2nd ed. Reading, MA: Addison-Wesley, 1989.

Sadiku

MNO

. Elements of electromagnetics, 2nd ed. New York: Oxford University Press, 1995.

Rao

. Elements of engineering electromagnetics, 5th ed. Upper Saddle River, NJ: Prentice Hall, 2000.

Johnk

CTA

. Engineering electromagnetic fields and waves, New York: John Wiley and Sons, 1975, pp. 322–326.

Boykin

. A more physical formulation of the self-inductance for spatially distributed circuits. Am J Phys 1999; 67: 320–324.

Krishna

. Teaching calculation of inductance of power transmission lines. Int J Elec Eng Educ 2011; 48: 434–443.

Demarest

. Engineering electromagnetics, Upper Saddle River, NJ: Prentice Hall, 1998, pp. 301–302.

10.

This paper only considers the telegrapher's equation involving self-inductance per unit length. In total, there are two telegrapher's equations describing wave propagation along a transmission line, which are usually presented as a pair of coupled differential equations. Because our interests lie solely in deriving the flux linkage method for inductance, we do not utilize the second telegrapher's equation involving capacitance.

11.

Ida

. Engineering electromagnetics, 2nd ed. New York: Springer, 2007.

12.

Schelkunoff

. Conversion of Maxwell’s equations into generalized telegraphist’s equations. Bell Syst Techn J 1955; 34: 995–1043.

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

Abstract

Keywords

Get full access to this article

References