550 BELL SYSTEM TECHNICAL JOURNAL 



produces an inverse change in the possible rate of transmission will 

 be used later. 



Steady State and Transient Viewpoints 



So far very little has been said about frequencies, and in fact nothing 

 in the sense of the term in which our results are to be stated. By 

 this I mean the use of the word "frequency" as applied to an alter- 

 nating current or other sinusoidal disturbance in the so-called "steady 

 state." The steady state viewpoint has proven very useful in certain 

 branches of communication, notably telephony. During the past few 

 years much progress has been made in establishing relations between 

 steady state phenomena and what might be called transient phenomena 

 of the sort which we have just been discussing. Before proceeding 

 with the main argument I shall attempt to review in non-mathematical 

 language the relationship of these two points of view to each other. 



As its name implies, steady state analysis deals with continuing 

 conditions. If a sustained sinusoidal electromotive force be applied 

 at the sending end of a system, a sinusoidal current of the same 

 frequency flows at the receiving end. The vector ratio of the received 

 current to the sending electromotive force is known as the transfer 

 admittance of the system at that frequency. It is assumed ideally 

 that the driving electromotive force has been acting from the beginning 

 of time, and practically that it has been acting so long that the results 

 are indistinguishable from what would be obtained in the ideal case. 

 The absolute magnitude of the transfer admittance gives the amplitude 

 of the received current which results from a driving electromotive 

 force of unit amplitude, and its phase angle gives the phase of the 

 current relative to that of the driving electromotive force. The 

 curves which represent this amplitude and phase as functions of the 

 frequency constitute a steady state description of the transmission 

 properties of the system. For a system which is free from energy 

 storage such as a circuit containing resistances only, the transfer 

 admittance is the same for all frequencies. The amplitude-frequency 

 curve is a horizontal line whose position depends on the magnitude 

 and arrangement of the resistances while the phase-frequency curve 

 coincides with the frequency axis. The storage of energy in the 

 system and its subsequent release cause the admittance-frequency 

 curves to take other forms. If the only storage is that which occurs 

 in a dissipationless medium, a condition which is approximated when 

 a sound wave traverses the open air, the only effect is to make the 

 phase-frequency curve a straight line passing through the origin and 

 having a slope proportional to the time of transmission through the 



