24 BELL SYSTEM TECHNICAL JOURNAL 



stop band or the phase constant in a pass band) ; this fixes 

 the value of the constant G and thus completely determines 

 formula (8) on which the propagation constant depends. 



(d) Assign to the lower or upper end of each stop band the iterative 

 impedance zero; this fixes the corresponding optional sign in 

 formula (9) as + or — , respectively. 



(e) Assign the iterative impedance at any one non-critical fre- 

 quency (subject to the condition that it must be a positive 

 resistance in a pass band and a reactance in a stop band) ; 

 this fixes the constant H and thereby the entire expression (9) 

 upon which the iterative impedance depends. 



The quotient and product of the impedances Zi and Z2 are now 

 fully determined; the values of Zi and Zi are easily deduced and also 

 the propagation constant and iterative impedance by formulas (11) 

 and (12); Zi and Zi are physically realizable except for the necessary 

 resistance in all networks. 



These important results may be summarized as follows: 



A lattice wave-filter having any assigned pass bands is physically 

 realizable; the location of the pass bands fully determines the propagation 

 constant and iterative impedance at all frequencies when their values 

 are assigned at one non-critical frequency, and zero phase constant and 

 zero iterative impedance are assigned to the lower or upper end gf each 

 pass band and stop band, respectively. 



Lattice Artificial Line Equivalent to the Generalized 

 Artificial Line of Fig. 1 



Since any number of arbitrarily preassigned pass bands may be 

 realized by means of the lattice network, it is natural to inquire 

 whether this network does not present a generality which is essen- 

 tially as comprehensive as that obtainable by means of any network 

 N in Fig. 1, provided the generalized line is so terminated as to equalize 

 its iterative impedances in the two directions. This proves to be 

 the case. 



If network A^ has identical iterative impedances in both directions, 

 the lattice network equivalent to two sections of N is shown by Fig. 

 17; each lattice impedance is secured by using an N network; the N's 

 placed in the two series branches of the lattice have their far terminals 

 short-circuited so that they each give the impedance denoted by 

 Zo; the N's in the two diagonal branches have their far ends open 

 and they each give the impedance denoted by Zoo. 



