The Bell System Technical Journal 



Devoted to the Scientific Engineering Aspects 

 of Electrical Communication 



July, 1923 



Transient Oscillations in Electric Wave-Filters 



By JOHN R. CARSON and OTTO J. ZOBEL 



I. Introduction 



' I V HE electric wave-filter has been very fully discussed with respect 

 -"■ to its remarkable steady-state properties. 1 In the present paper 

 it is proposed to give the results of a fairly extensive theoretical study 

 of its behavior in the transient state. This study is of particular 

 interest and importance in connection with the wave-filter, because, 

 as we shall find, its remarkable selective characteristics are peculiarly 

 properties of the steady state and become sharply defined only as the 

 steady state is approached. To this fact, it may be remarked in 

 passing, is to be ascribed the uniform failure of wave-filters to suppress 

 irregular and transient interference, such as "static," in anything 

 like the degree with which they discriminate against steady-state 

 currents outside" the transmission range. This limitation is common 

 to all types of selective networks and restricts the amount of protec- 

 tion it is possible to secure from transient or irregular interference. 

 In fact the general conclusions of the present study are applicable 

 to all types of selective circuits. 



In the present paper the discussion will be principally concerned 

 with the following phases of the general problem. 



1. The indicia! admittances of a representative set of wave-filters. 

 The indicial admittance, as explained below, is equal to the current, 

 expressed as a time function, in response to a uniform steady e.m.f. 

 of unit value, applied to the network at time / = 0. It has been 

 shown in previous papers that a knowledge of the indicial admittance 

 of an invariable network completely determines its behavior, both in 

 the transient and steady state, to all types of applied forces. Its 

 determination is therefore fundamental to the whole problem. 



2. The mode in which the steady-state is built up after a sinusoidal 

 voltage within the frequency transmission range is applied to the wave- 



1 Physical Theory of the Electric Wave-Filter, G. A. Campbell, B. S. T. J., 

 Nov., 1922; Theory and Design of Uniform and Composite Electric Wave-Filters, 

 O. J. Zobel, B. S. T. /., Jan., 1923. 



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