Probable singing points on loaded cable circuits

The amplification which can be obtained from any 2-way repeater depends on the accuracy with which the impedance-frequency characteristic of the line on each side can be simulated by that of the balancing network, or in the case of a 1-element repeater by that of the line on the other side. If the gain of such a repeater exceeds the limits fixed by the irregularity of the line-impedance, then it will sing, provided that the phase relationships are suitable. The author describes a method of predicting singing points, which is based on the theory of normal probabilities, where the singing point is due to a number of small irregularities distributed at random. Particulars of data required and a method of making the calculations are explained, and several curves are given to assist in making the matter clear. Practical examples have shown that the method is capable, if used with caution and judgment, of giving a useful indication of the performance to be expected in any normal case, provided that the deviations of inductances and capacities of individual circuits from the average of all the circuits can be estimated sufficiently accurately.