364 THE BELL SYSTEM TECHNICAL JOURNAL, APRIL 1951 



except near the low-frequency end. In view of the success of the condenser 

 plate contour for producing fiat delay, it was felt that C should be chosen 

 to be nearly rectangular. An actual rectangle could have been used for C, 

 but the mapping to a circle involves unwieldy expressions containing elliptic 

 functions. The contour shown was used instead because it is nearly rectangu- 

 lar and because it has a simple mapping function 



• ^ in I 1 '7'7c 1-075 0.2 



p = t 6.10 + 1.775w — — -— 



w ixr 



(here p is expressed directly in megacycles). This contour was obtained by 

 plotting a few of the contours for different numerical values of the constants 

 in the above mapping function. The w-plane images of the singularities and 

 of the lower contour are shown in Fig. 23b. 



The charge Q as a function of d is shown in Fig. 24 together with the 

 step function approximation. Figure 25 shows the delay produced by the 

 filter and equalizer together. 



19. Acknowledgements 



The author wishes to express his indebtedness to H. W. Bode, whose 

 earlier potential analogue methods are included in this paper; to E. N. 

 Gilbert, whose suggestions regarding potential theory were most helpful in 

 simplifying the author's extension of the theory; and to S. A. Schelkunoff, 

 M. C. Gray, and E. N. Gilbert, for their cooperation in the preparation of 

 the manuscript. 



R-FERENCES 



1. H. W. Bode, Wave Transmission Network, U. S. Patent No. 2,342,638, February 29 



1944 



2. W. Cauer, Das Poissonsche Integral und seine Anwendungen auf die Theorie der 



linearen Wechselstromschaltungen (Netzwerke), Elektrische Nachrichten Technik, 

 17, pp. 17-30, 1940. 



3. R. F. Baum, Design of Broadband I.F. Amplifiers, Jour. Appl. Phys., 17, pp. 519-529 



and 721-730, 1946. 

 C. H. Dagnall and P. W. Rounds, Delay Equalization of Eight-Kilocycle Carrier 



Program Circuits, Bell Sys. Tech. Jour., 28, pp. 181-195, 1949. 

 R. M. Fano, A Note on the Solution of Certain Approximation Problems in Network 



Synthesis, Franklin Inst. Jour., 249, pp. 189-205, 1950. 

 W. W. Hansen, On Maximum Gain-Bandwidth Product in Amplifiers, Jour. Appl. 



Phys., 16, pp. 528-534, 1945. 

 W. W Hansen and O. C. Lundstrom, Experimental Determination of Impedance 



Functions by the Use of an Electrolytic Tank, I.R.E. Proc, 33, pp. 528-534, 1945. 

 W. H. Huggins, A Note on Frequency Transformations for Use with the Electrolytic 



Tank, I.R.E. Proc, 36, pp. 421-424, 1948. 

 J. F. Klinkhamer, Empirical Determination of Wave-Filter Transfer Functions with 



Specified Properties, Philips Res. Reports, 3, pp. 60-80 and 378-400, 1948. 



Note that these represent only a small fraction of the papers published in the last 

 few years, and they have been listed mainly because they consider problems closely 

 related to those in the text. A complete bibliography would be too lengthy and would 

 cover too wide a field. 



