A Theoretical Analysis of Telephone Dial Pulse Signaling

This paper presents a theoretical analysis of the distortion of the dial pulse waveform and its effects on the response characteristics of the pulse-receiving circuit in the telephone office. To derive expressions for the waveform for dial speeds of 10 and 20 pulses per second (pps) Laplace transformation and matrix algebra are applied to the system, represented by two complementary linear lumped-constant time-invariant networks responsible for the generation of the leading and trailing edges of a dial pulse. Based on the known waveform and the operational requirements of the pulse-receiving circuit, a function is derived showing the percent break value of a pulse train as it arrives at the central office, and the dependence of the percent break on the number of extension (branch) telephones connected and the subscribers´ loop parameters. Its inverse, shown in graphical form, presents the upper limits for the number of extensions to be associated with a transmission line of given electrical parameters. The conditions under which abrupt changes of the percent break value and quasi-pulses occur are analyzed.