126 



BELL SYSTEM TECHNICAL JOURNAL 



of this series. We can, therefore, express the current i at the time 

 / by the integral 



[f 



i = E\ a{t)e-^'"^dt + a^ 



\ 



(42) 



where the value of a{i) for any interval of time {n — \)2D to n(2D) 

 is the constant of the above series an-i divided by 2D. The value 

 of this integral for an infinite time must reduce to the steady state 

 value of i = E/Z, hence 



= E 



u: 



a{t)e-i'-'^dt + ao 



0.1 0.2 0.3 0/4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 

 VALUE OF TIME X CRITICAL FREQUENCY = tfc 



Fig. 8 — Current resulting from the application of an alternating voltage, 

 £ = £o cos uct, on several sections of lattice network. The current plotted is the 

 current in the termination of the network. The frequency of the applied voltage 

 is the resonant frequency, /«, of the network. 



Cancelling out the common factor E, we have the infinite integral 

 equation 



^ = [£a(0.-..W/ + a,]. (43) 



The physical interpretation of the quantity a{t) is readily obtained 

 by reference to equation (42). If we set co = and E = 1 m this 

 equation we have 



i = r a{t)dt + ao = r a{t)dt + h{0), 

 Jo Jo 



