186 



BELL SYSTEM TECHNICAL JOURNAL 



angle subtended by the plates at the frequency co. From this figure it may 

 be seen that the field intensity in the region between the plates will have a 

 fairly uniform value which falls off sharply as the edges are reached and 

 becomes vanishingly small at frequencies remote from the plates. 



Along with this simple determination of the average delay characteristic, 

 D. F. Tuttle in an unpublished memorandum has derived expressions for 

 the magnitude of the delay ripple. As shown in the appendix, the field 



W - PLANE 



DELAY 



+ P 



Fig. 6 — Delay-frequency characteristic of the network of Fig. 5. 



intensity or delay for an infinitely long set of charged filaments may be 

 expressed in the form 



27r lirkn 



1 = — tanh 



a a 



cos 



Iwo} 



cos 



liro) 



cosh 



2irkn 



+ 



cosh 



2irkn 



(4) 



For reasonably large values of 2irkn/a, this relation may be replaced by the 

 approximate expression 



r = ro[l - 5 cos Toco] (5) 



where Tq = l-w/a is the average delay and 5 = 2^"^" " is the percentage 

 ripple about the average value. The ratio ^„/a may thus be determined 

 from the percentage delay ripple in accordance with the formula 



a Zir 



(6) 



