Circulating currents and singing on two-wire cable circuits

One of the important factors limiting the working net losses of two-wire cable circuits is the possibility of excessive circulating currents or actual singing. A theory is developed for the computation of the distribution of singing margins on groups of two-wire circuits from the known gains and losses and known functions of the deviations of loading coils, loading coil spacing, cable capacitance and office equipment. The distribution functions of circulating current margins, of active return losses and of active singing points are also derived. The possible application of these methods to specific problems is discussed and an example of the computations involved is given. The theory herein involves certain approximations and empiricisms in determining the singing limitations but it is believed to give an answer which approaches the exact answer rather closely.