IRAS'SMISSIOX CII.IR.ICTERISriCS OF ll.llT.tll.rfRS 573 

 AiiiitluT form nliiaiiuil l)\- suitable transformaliori is 



( IV, Wi+ZM) sinh r+ ( WM + WiZa) cosh T 



(4) 



Formula (3), derivfii in the Apponciix with several general trans- 

 ducer formulae ant! relations, is especially useful when applied to 

 n)mptisite wave-filter networks, since, as w'e shall see, it contains 

 the natural parameters for such structures. Upon comparing Fig. 2, 

 which represents such a general network, with Fig. 3 we find that the 

 two can he made to correspond exactly if the mid-part of the wave- 

 hlter, iK'twcen terminals a and b in Fig. 2, is considered to be the trans- 

 ducer of Fig. 3, and if the wave-filter terminations combined with the 

 resistances R are considered to be the terminal impedances Za and Zt, 

 of Fig. 3. The relation between the electromotive force, E, applie<J in 

 R and that, £«. acting through Za depends upon the particular wave- 

 filter termination at terminals a. Similarly, the relation between the 

 currents, / and h, transmitted to R and Zi,, respectively, depends 

 uf)on the termination at terminals b. 



As already stated, the mid-part of the composite wave-filter consists 

 in general of mid-series, mid-shunt, and mid-half sections, properly 

 combined as to their impedance relations at the junction points. 

 The method of combination employed in a composite wave-filter consists 

 in connecting two sections whose image impedances at their junction 

 are equal. (An analogy which might be given is the matching of 

 (lominoes in a line by the corresponding ends, numbers referring to 

 image impedances.) 



Let us assume for the moment that the mid-part, as thus made u[), 

 is lerminatetl by impedances respectively equal to its image im{x;- 

 dances. There is then an "image condition" for the impedances 

 measured in the two directions not only at each of these terminal 

 points but also at each junction point throughout the network; and 

 in this case each section transmits under the "image condition" of 

 its terminating impedances. As a result we obviously obtain the 

 following properties for the mid-part. 



1. The transfer constant of the mid-part of a composite wave-filter, 

 consisting of mid-series, mid-shunt, and mid-half sections, is the sum 

 of the transfer constants of all the individual sections. 



2. The image impedances of the mid-part of a composite wave-filter 

 are the external image impedances of the two end sections. 



In addition we have the following important relations between the 



