320 BELL SYSTEM TECHNICAL JOURNAL 



which are exactly analogous to formulas (33) and (34) of the paper 

 cited here in footnote 2. Thus L,„,m' may be plotted so as to give an 

 additional chart for use in the method of calculating wave-tilter 

 transmission losses considered in that paper, which will apply when 

 there are these kinds of MM'-type terminations. As a convenience a 

 chart for Lm,m' is given in Appendix IV for the particular values of the 

 parameters m = .7230 and m' = .4134 already chosen in the fixed 

 terminal transducers. To take account of dissipation several curves 

 are shown for each one of which there is a different fixed relation 

 between Vk and Uk. This chart, being an extension to the former set 

 of charts, is numbered consecutively with the others as Chart 20. It 

 shows that the terminal loss at R has two maxima beyond each critical 

 frequency where Uk = — 1- Their locations correspond to one reso- 

 nant and one anti-resonant point of WikUn, m') or W^kim, m') in 

 an attenuating band. Moreover, the position of the first and lowest 

 maximum coincides with that of the maximum attenuation of the 

 terminating wave-filter, the MM'-type, while the position of the 

 second coincides with that of the maximum attenuation of the related 

 M-type. (An ilf-type termination gives only the first maximum; 

 an MM'M"-typQ gives three maxima, etc.) The transmission unit, 

 the Neper, is the same as that which was called the attenuation unit 

 on the previous charts. The corresponding number of decibels is 

 obtained by multiplying the number of Nepers by 8.686. 



When such a termination is used the interaction loss is practically 

 negligible. 



Part 3. Simulation of Wave-Filter Impedances 

 So far the two networks of Fig. 1 1 have been considered only from 

 the standpoint of their use as terminal wave-filter transducers with 

 desirable propagation and image impedance characteristics. While 

 this is their major purpose they can have a minor use to be shown 

 here, namely, as parts of two-terminal networks whose purpose is to 

 simulate wave-filter impedances where such networks may be desired. 

 This possibility is suggested by the fact that the image impedances 

 at the final terminals are approximately equal to a constant resistance 

 in all transmitting bands which can be simulated at these frequencies 

 by a simple resistance R. It follows that if each pair of final terminals 

 is terminated by a resistance R, the impedances at the two remaining 

 pairs of terminals will be approximately equal to their image imped- 

 ances, Wik and Wik, respectively, in the transmitting bands. More- 

 over, on account of the high attenuation of the transducers in the 

 attenuating bands which reduces transmission through them, the large 

 impedance irregularities at those frequencies between each network 



