ELECTRIC WAVE-FILTERS 317 



both comparison transducers m = .6, this value of the parameter 

 giving results which are representative of the best constant terminal 

 impedances possible in transducers with terminal M-types. (These 

 comparison networks are identical with the general ones of Fig. 10 

 in which m = 1 and m' = .6.) Corresponding image impedance 

 ratios in a transmitting band are given in Fig. 14 where curves la 

 and lb are characteristics for the two ends of the new terminal trans- 

 ducers of Fig. 11, while curves la and 2b are those of the comparison 

 networks. The superior merits of the new transducers can be seen 

 from Figs. 13 and 14; for in addition to giving improved and prac- 

 tically ideal terminal impedances they have attenuation characteristics 

 just outside the transmitting bands which rise more rapidly than those 

 of the comparison transducers. 



By the use of such and other fixed terminal transducers at one or 

 both ends of a wave-filter network, the flexibility of the composite 

 method of designing wave-filters is still retained. The transducer 

 transfer constants and terminal losses due to reflection at given termi- 

 nating impedances are known in advance. The interior of the com- 

 posite wave-filter can then be built up of ladder, lattice or other types 

 of sections so that the desired total transmission characteristic is 

 obtained. Constant resistance phase networks can also be added at a 

 resistance termination to help improve the phase characteristic in the 

 transmitting bands, if necessary. 



2.4 Designs for Lozv Pass, High Pass, Low-and-High Pass and 

 Band Pass Wave- Filte rs 

 These fixed transducers of Fig. 1 1 may readily be translated into 

 the particular designs which they assume for any class of wave-filter 

 with Zik and Zofc known. For low pass, high pass, low-and-high pass 

 and band pass wave-filters, the four most important classes, the actual 

 physical arrangements and formulas for the inductances and capacities 

 have been worked out. As a convenience in reference these designs 

 are placed in Appendix II where all necessary formulas are given, 

 making use of Appendix II of the paper mentioned in footnote 1. 

 Little further discussion will be given here except to add the relations 

 between Uk and frequency for these different classes, with dissipation 

 neglected. By this means the characteristics which have been shown 

 as functions of Uk may be referred to the frequency scale as the 

 abscissa-axis, if desired in any particular case. 



I. — Low Pass 



TI,. = - I 



Jo 



Uk= -{() , (33) 



