THE L3 SYSTEM AMPLIFIERS 899 



. _ (2r - 1) X . 



^'•- (2r+ 1) 2- «r = gamat</». 



2. The coefficients of a related power series are determined: 



e'« = 1 + A^Z' + A4Z' + • • • A.nZ'"' ^ i^(Z') (4) 



where A2 + S2 = and 1^2* = kC2k 



2A4 + ^2*5^2 + >S4 = 

 nA2n + A2n-2 + " ' ' = 



3. F(Z ) is expressed as a rational fraction containing both natural 

 modes and infinite loss points. 



where the coefficients of N and D may be found from the continued 

 fraction expansion of F(Z^). The degree of N and D fixed by the allow- 

 able approximation error and the complexity of the network. 



4. The roots of N and D (in terms of Z^) are found and then trans- 

 formed to the p-plane using the transformation 



These fours steps result in a polynomial F{p) satisfying the require- 

 ments on the change in gain. In this specific case 



F{v) = 

 1.06(p + 0.0960) (p -f 0.0280) (p + 0.9890) (p + 0.2890) ^ „+y^ 



(p + 0.1058)(p + 1.803)(p + 0.0300)(p + 0.3492) 

 Solving (1) and (2) obtain 



e"-'^^ (7) 



' n, z.= ^f- ']['! - II (8) 



kF - I ' ^ {kF - l)(fc - F) 



where F{p) ^ F 



Since the design must absorb the interstage capacities, (and also the 

 stray capacities of some of the elements in the physical network) Zi 

 must include a shunt condenser. It can be shown that the desired result 

 is obtained when 



F — > 1 + gr - as p ^ c» (9) 



P 



