The Building-up of Sinusoidal Currents in Long Periodically Loaded Lines

M P O R T A N T information regarding the excellence of a signal transmission system is deducible from i knowledge of the mode in which sinusoidal currents "build-up" in response to suddenly applied sinusoidal electromotive forces, since on the character and duration of the "building-up" process depend the speed and fidelity with which the circuit transmits rapid signal fluctuations. 1 The object of this note is to disclose and discuss general formulas and curves which describe the building-up phenomena, as a function of the line characteristics and the frequency of the applied e.m.f., in the extremely important case of long periodically loaded lines. The formulas in question are approximate but give accurate engineering information and are applicable to all types of periodic loading under two restrictions: (1) the line must be fairly long, that is, comprise at least 100 loading sections, and (2) it must be approximately equalized, as regards absolute steady-state values of the received current, in the neighborhood of the applied frequency. Fortunately these conditions are usually satisfied in practice in those cases where the buildingup phenomena are of practical engineering importance. Furthermore, the formulas to be discussed supply a means for the accurate and rapid comparison of different types of loading in correctly engineered lines. The building-up process may be precisely defined and formulated as follows: Suppose that an e.m.f., E cos u>/, is suddenly applied, at reference time t = o, to a network of transfer impedance = | Z(iu) | · exp [i£(co)].