REGENERATION THEORY 



139 



This converges to as / increases regardless of how great B may be 

 taken. If the admittance diagram is drawn tliis is again found to check 

 the rule. 



3. Let the network be as in 1 except that there are two separated 

 condensers bridged across resistance circuits. Then 



AJ(ioj) 



B^ 



(a + iu))^ 



(48) 



The solution for s(t) is obtained most simply by taking every other 

 term in the series obtained in 1. 



s(t) = Be-"'(Bt + BHySl + • • •) 

 = Be-"' sinh Bt. 



(49) 



4. Let the network be as in 3 except that there is a reversal. Then 



- 52 



AJ(iw) = 



{a -\- ioi'f 



(50) 



The solution is obtained most directly by reversing the sign of every 

 other term in the series obtained in 3. 



s{t) = - Be-"'{Bt - BH'131 + • • •) 

 = - Be-"' sin Bt. 



(51) 



This is a most instructive example. An approximate diagram has 

 been made in Fig. 5, which shows that as the gain is increased the 



B = IO 



W - PLANE 



Fig. 5 — Illustrating Example 4, with three values for B. 



