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BELL SYSTEM TECHNICAL JOURNAL 



(3) The input standing- wave ratio passes through zero on either side of 

 mid-band, and although it has a 0.6 db dip at mid-band for the case of 

 k = 0.5, it is under one db over a larger frequency range than in the transi- 

 tionally coupled case. 



(4) The bandwidth between points one db down on the loss curve is very 

 nearly equal to the bandwidth between the cut-off frequencies. This 

 bandwidth is simply related to the tune frequency /o and the geometric 

 midband frequency /« as shown below. 



A/ = /o/vr^=rfe-/o/' 



(15) 



Thus, given required values of/^, A/, Ci (or i?i), and C2 (or R2), the matched 

 transformer can be designed by the use of formulas (3), (8) and (15). These 

 formulas are summarized at the end of this paper. 



A transformer of different phase and loss characteristics results if the 

 loading resistance is removed from one side of a matched transformer. 

 Equation (5), if i?2 = °o , becomes, 



El 



Vi - k'' 



\\&)o/ Wo « / J 



(16) 



At w = coo, 



I E./E'^' 1 2 = C2/C. (17) 



while from (10) the corresponding ratio for the matched transformer is, 



|£./£2|2 = 4C2/C. (18) 



Thus this mis-matched transformer has 6 db more gain at the tune fre- 

 quency than the corresponding matched transformer, whether used as an 

 interstage, an output or an input transformer. 



The transmission loss referred to the loss at co = coo is, 







■-p[' -©'"-'■'] 



** Lw 



(1 - k') 



COo CO J 



(19) 



