Circuits Employing Toroidal Magnetic Cores as Analogs of Multipath Cores

Circuits which are analogous to multipath magnetic cores are described. Toroidal cores are employed to simulate the branches of the multipath core. The conservation of flux at a node is simulated by means of shorted windings connecting groups of cores. These insure that the sum of the flux changes in the cores on a given winding will vanish. Ampere´s law is simulated by proper choice of both number of turns and core dimensions. Equations are derived which determine the parameters of the analog in terms of those of the multipath core. These state that the volume of a core must be proportional to the volume of the corresponding branch, that the number of turns a shorted winding makes on a core should be proportional to the ratio of core diameter to branch length, and that the number of ampere-turns of externally supplied drive should also be proportional to this ratio. Analog circuits employing single-turn coupling loops and cores of different diameters are discussed as a special case. Another special case employs multiturn windings but identical cores. It is shown that the current flowing in a shorted winding is proportional to the magnetic potential of the corresponding node of the multipath core. The use of the core analog for the direct observation of internodal magnetic potential differences is illustrated by means of oscilloscope photographs of the magnetic potential difference between the nodes of a three-rung laddic.