936 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



A" = P(0)a;„5 

 = P(0)a;o5 

 = P(0)coo6 



'^IjyzMf.,: 



1 



_47rT/32 

 / 1 \^'^- 



/3(tan 'a)/j8) 



1/2 



1/2 



(44) 



.4Ti3, 



P(0) ,/qY'^ 



(45) 



Let the output of the first resonant circuit be appUed to a second 

 resonant circuit, and in turn to n successive resonant circuits, with an 

 ampHtude amphfication ^ between successive resonant circuits. At the 

 output of the 71* resonant circuit, the rms amplitude of the response 

 is then obtained from 



Aa,/' = P(0)coo5 



r /j2(n - 1) /•« 



47rT 



f [z\ico)T 



V — 00 



d 



CO 



1/2 



= P(0)coo5 

 P(0) 



1 r 



■TB'~ i-oc (1 



du 



1/2 



coo5 I — 



_47rr/32 J-oc (1 + wV/32)"J 



(46) 



where 



r ^ = 1 ["^ _ 



f/, 



CO 



9 l02\r,.^ 



^ j_=c (1 + CoViS^) 



(47) 



1, 



2n - 3 



2(w - 1) 



n 



In-\, 



n >2, 



(48) 



1 



2{n - 1)/' 



// = (1 - i), /a"^ = (1 - l)h\ li = (1 - D/sl 



Thus (46) can be written: 



As^n = As^a-yQiz ' ' ' «« , (49) 



where 



1 



a> 



1 - 



2(i- D' 



(50) 



