ELECTRIC WAVE-FILTERS 313 



Then from (27) 



m = Vl — a, 

 and (30) 



; i - a' 



The maximum and minimum values of y (where dyjdUi: = 0) are at the 

 two values of Uk 



TT -- (^(^ - «') ± ^ ^^'' - '^y - ^^^'(^ + 2a - 2a') 



\Miere it is desired to have an especially constant value, y = 1, in 

 the neighborhood of Uk = 0, the parameters might be determined 

 from an expansion of the expression for y in powers of Uk- Equating 

 these coefficients of the first and second powers separately to zero 

 would give two independent equations from which to derive the 

 parameters.'- 



2.3 Fixed Designs 



The primary interest here is to obtain designs in which the final 

 image impedances are approximately constant resistances equal to R 

 over the entire useful parts of all transmitting bands. Such imped- 

 ances require a j'-characteristic which is close to unity from Uk = to 

 the neighborhood of t//o = — 1. With this objective a few preliminary 

 trials showed that very satisfactory results are obtained with the 

 assumed data 



yi = I at {Uk)i = - .65, 

 y.= \ at {Uk)2 = - .90. 



Then from (29) and (30) of the previous Section 



a = .4773, a' = .9107; 



and (32) 



m = .7230, m' = .4134. 



These values fix the general structures of Fig. 10, giving the specific 

 ones of Fig. 11 which are made up of definite proportions of the 

 impedances Su and Z2k of the "constant k" wave-filter of that class, 

 assumed known. The detailed ^-characteristic of Fig. 12 shows 

 that in this case there is less than a 2 per cent departure of v from the 

 constant value unity over the continuous range from Uk = to 



'2 A problem of terminal impedance is also included in the paper, "Die Sieb- 

 schaltungen der Fernmeldetechnik," W. Cauer, Zeitscliriftfiir Aiigeiiuindle Matheniatilc 

 iind Meclianik, October, 1930, p. -125—433. 



