Magnetic Fields of Twisted - Wire Pairs

On the basis of an expression given by Buchholz for the magnetic-vector potential for an infinitely long twisted-wire pair, the expressions for the external component-flux densities in cylindrical coordinates have been developed. These expressions checked very well with data obtained in the proximity of precisionwound twisted-wire pairs. A generalized graph for various radii and pitch lengths has been developed to enable the design engineer to quickly predict the strength of the magnetic field for all three spacial components at distances in the proximity of a twisted-wire pair. INTRODUCTION ELECTRO1\IAGNETIC compatibility studies require that the fields from sources of magnetic energy be well kinown. Unfortunately, many of these sources are not defined to the desired degree of accuracy. This applies to the case of the twisted-wire pair, which, despite its widespread use, has been sparsely covered in the open literature. Two reports recently have attempted to fill this gap. One, by Alksne, is purely theoretical [1], whereas the second, by M\Ioser and Spencer [2], provides both experimeintal work as well as theoretical analysis. This paper gives the theoretical expressions for the componenits of the magnetic-field strength of a uniformly wounid twisted-wire pair in the near field expressed as an infinite series of terms. As showni later, the first term in this series is dominant; a graph of this first term is provided so that designers may quickly determine the field strenigth itear the twisted pair. This field strength is of importaince in EMIC prediction of cable-to-cable interference since, due to space limitations, the separation distance between the cables may be small. The author has not seen in the American literature an expressioni for the near field from twisted-wire pairs except in the articles previously cited. The EAIC designer at the present time must therefore rely oni rule-of-thumb approximationis for the field of twisted-wire pairs. The present article fills the gap by providilg a theoretical expressioin which gives the field of a uniform twisted-wire pair and a useful graph based oni this expression. With the magnetic-field streingth kknowni, the designer then has the means to calculate initerference geiierated in an adjacent low-level cable. A IAGNETIC-POTENTIAL I'UNCTIO-N During the course of a review of the opeii literature on this subject, an expression given by Buchholz for the magnetic-potential function for a twisted pair of infinite length was found to be useful in the determiniation of the various :Mannscript received April 28, 1969. The author is with the Navy Underwater Soutnd Laboratory, New Lonidon, Connz. 06320. components of magnetic-field strength as a function of distance [3 ]. The equation of the magnetic-potential funetioIn as given bv Buchholz in rationalized mks units is 4a 1i,3,5, 2r '(p,t9,z) = -_ E sin X (-0M'2) h xh |IX ( 27ra) K ( 27rP) P a __p K 7ra a