/A'./.V.SA//.V.S7().V ClI.UiACTLlilSTlCS 01- WAVE-lll.lLRS 585 



IlfNie, the two members of each pair of reflection coefficients, r„;, r„i, 

 and r^-„ r.i, differ only in si^n so that their G's are the same but their 

 lis difer by ir. 



I. Wave-Filter Structures Ilai'inii Equivalent Transmission Losses 



There are six groups of possible wave-filter networks involviriR 

 the lour terminations above, each group of wliich is made up of pairs 

 having equi\alent current ratios 2RIE and hence equivalent trans- 

 mission losses. By (5) this means that the members of such a pair 

 have products for their four factors, F,FaFbF,, which arc equal. It 

 ma\- readily be shown from preceding relations that these groups, 

 representetl symbolically by brackets enclosing the transfer constants 

 of their mid-parts and the terminations, are the following: 



(a) [T. K.Am), K,,{m')] = [r, K,,{m), KA'"')], 



(b) [T, Ku{m), A',o(m')l = tr, K^iim), A'.,,(w')l, 



(c) IT, K^iim), A',,] = [T, A.aCm). A.,], 



id) [T, Kn{m), A..) = [T, Au(m), A.^J, 

 (e) ir, A,,. A.'U =[r, A,,, AxM, 



(/) [r.A.,.A,M =ir. A.„ A/,]. 



(47) 



This symbolic representation in (c), for example, means that a 

 composite wave-filter whose mid-part has a transfer constant, T, 

 and whose terminations are those designated by AjiCw) and Kxi, 

 will gi\e the same current ratio 2RI/E as another wave-filter whose 

 mid-part has the same transfer constant, 7", but whose terminations 

 are those designated by Kn{m) and Axi where m and x are respectively 

 the same in both networks. 



III. Ch.\rts for Determining Transmission Losses 



The accompanying charts apply to the three groups of transmission 

 losses, transfer, terminal, and interaction, and are derived froiu the 

 general formulae already given. The curves represent constant 

 parameter loci for A, cB, L„, Lx, Gmi, cHmi, Gn, cHxi, and L, as 

 functions of several variables and include the most practical range; 

 where further extension is required the original formulae may be 

 consulted. The U and V variables for the ladder type of recurrent 

 network (or its equivalent) which form the basis of this chart calcu- 

 lation method are to be found as a function of frequency, in the general 

 case from formula (9), 



Zi/4zj= U+iV, 



