782 BELL SYSTEM TECHNICAL JOURNAL 



The filter schematics are shown on Fig. 10, the auxiliary network being 

 enclosed by broken lines. The performance of the filters was further 

 improved by choosing terminating resistances differing somewhat 

 from the nominal or mid-band, value of the filter image impedance. 

 As a result of these two modifications the reflection coefficient charac- 

 teristic shown by Curve I of Fig, 11 was obtained. Without them, 

 the reflection coefficient would have been that given by Curve II. 



The great improvement of filter impedance characteristics resulting 

 from these devices is evident from a comparison of Figs. 7, 9 and 11 

 with Fig. 2. Instead of the reflection coefficients of 50 per cent or 

 60 per cent found in the earliest filters, the technique allows us to 

 obtain reflection coefficients of the order of 10 per cent, within the 

 frequency range of interest, for filters operating alone, of about 15 per 

 cent for pairs of complementary filters in parallel, and of about 20 per 

 cent for systems of parallel band-pass filters. These results were 

 satisfactory for several years. The continued evolution of carrier sys- 

 tems toward higher and higher energy levels, however, and the constant 

 increase in the number of systems in intimate physical association with 

 one another, gradually made such standards inadequate. The reflec- 

 tion coefficient standards demanded by the severe crosstalk require- 

 ments of these systems have ranged from 2 per cent to 10 per cent in 

 recent filter designs. It became evident some years ago that if these 

 stringent reflection coefficient requirements were to be met a new ana- 

 lytical technique, more general and more powerful than its predecessors, 

 would be necessary. 



A New Technique and the Results of its Application to Impedance 



Correction 



Such a technique has been developed. The method is essentially a 

 generalization of the processes by which Zobel's "x-terminated" filters 

 were derived. It leads to a series of filter sections, the number of 

 which can be extended as far as is necessary to secure a satisfactory 

 approximation to the desired image impedance characteristic.^ The 

 generalized configurations of several sections are given on Fig. 12. 

 The a's and ^'s of this figure are design parameters, Zn, and Zik refer 

 to the filter with which the section is to be used. By choosing Zik and 

 Zih appropriately the terminations can be adapted to any type of filter 

 structure, whether low-pass, high-pass or band-pass. 



The simplest of these sections can be shown to be equivalent to an 

 "m-type" structure, and will naturally give the same results. A 



* For a detailed discussion of the theory underlying this technique see, "A Method 

 of Impedance Correction," appearing simultaneously in this journal. 



