THEORY AND DESIGN OE WAVE-FILTERS 19 



constant resistance terminal impedances without introducing appreci- 

 able reflection losses at the important frequencies to be transmitted. 

 It may also be added that where a number of wave-filters trans- 

 mitting in different bands are to be joined in series or in parallel the 

 usual terminations correspond to iCi 2 (m) and -K" 2 i(m), respectively 

 (where m is about .6), with the omission of the terminal half-series 

 impedance in the first case and terminal double-shunt impedance 

 in the second. In the transmitting band of any one of these wave- 

 filters the role of the omitted impedance is approximately fulfilled 



1 7' 



AMA/Y 



1 



Fig. 6 — Lattice Type Recurrent Network 



by the resultant impedance of the other wave-filters. The ap- 

 proximation is very close when such connections are made with two 

 complementary wave-filters having the same critical frequencies. 



4. Equivalent Lattice Type Wave-Filters. 



The lattice type of recurrent network shown in Fig. 6 offers a 

 simple example of a uniform type which can physically be made to 

 have properties equivalent to those of the ladder type. Its formulae 

 for propagation constant and characteristic impedance in terms of 

 the series and lattice impedances, \z\ and 222', are known to be 



2s i 

 cosh r" = 1 -f- -—. 7, 



4z2 — z\ 



(23) 

 and K'^Vz'iZ',. 



A comparison of these formulae with those of the ladder type in (1) 

 shows that when r' = r, and K' = K U 



Zi=Zi, 



(24) 

 and 22 = 421 + 22; 



