The high-frequency resistance of multiply-stranded insulated wire

Abstract

Conductors which have to carry high-frequency currents are often made up of a large number of separately insulated fine wires stranded together, with the object of compelling the current to distribute itself over the whole cross-section of the conductor. This may be done for two different reasons: firstly, to decrease the variation of inductance and resistance with change of frequency; and, secondly, to decrease the effective resistance of the conductor at high frequencies. To be effective, it is necessary that every wire should occupy in turn the same relative position in the conductor, so that the electromotive force induced in each wire by the magnetic flux should have the same average value over the whole length of the wire. If every separate wire has the same resistance, the same applied P. D. and the same induced E. M. F., both in amplitude and phase, they will all necessarily carry the same current, and the total current will therefore be uniformly distributed between all the wires. The usual method of obtaining this similarity in the path of every strand is to make a conductor of three, four, or five wires twisted together, and then to twist three such conductors together, and so on until the resulting conductor contains the required number of wires. A large number of such multiple conductors are sometimes plaited or braided into a tubular con­ductor. Two of the individual wires of such a conductor may be in contact, except for the insulation, at a certain point, and then again further on at another point, one wire having followed an internal and the other an external path between the two points. From a knowledge of the current, frequency, and projected area of the loop formed by the two wires, measured normal to the magnetic flux, the E. M. F. induced in the loop can be calcu­lated; thus, if the multiple conductor has a diameter of 1 cm. and is wound into a coil with one turn per centimetre, and if the current is 100 amperes at a frequency of 10 6 , the E. M. F. induced in a loop of 5 sq. cm. is about 20 volts, giving 10 volts between the wires at each point of contact. In circuits containing spark-gaps the rate of change of the current may reach very high values and thus cause much greater potential differences between the separate strands, which must therefore be efficiently insulated to prevent sparking between them.