750 BELL SYSTEM TECHNICAL JOURNAL 



and the step-up turns ratio, a, of the ideal transformer is 



1.98. 



These values then represent the input coupling network which theoreti- 

 cally equalizes to the specified degree of precision one-quarter of the power 

 loss between coaxial repeaters over a frequency band from 2.5 to 8.0 mc. 

 The computed gain characteristic of this network is plotted in Fig. 25, 

 Curve I. The presence of the ideal transformer represents an added constant 



gain. Curve II, given by db = 10 log ~ = 5.96. The total gain inserted by 



-ft/, 



7? 7? 



the network, the sum of Curves I and II, is db = 10 log^- = 10log-=-+ 5.96. 



Rl Ri) 



Since Curve III represents one-quarter of the power loss between repeaters, 

 Curve IV is the overall transmission gain of the line and equalizer.-^ The 

 deviation of Curve IV from a constant transmission over the useful band 

 is less than ±0.08 db. It may be concluded, then, that a satisfactory non- 

 dissipative design has been obtained. 



References 



1. H. W. Bode, "Network Analysis and Feedback Amplifier Design," Chap. 16, Van 



Nostrand, New York, 1945. 



2. S. Darlington, "Synthesis of Reactance 4-Poles," Journal of Mathematics and Physics, 



Vol. XVIII, pp. 275-353, September, 1939, Also Bell System Monograph B-1186. 



3. R. M. Fano, "Theoretical Limitations on the Broadband Matching of Arbitrary 



Impedances," Report No. 41, M. I. T. Research Laboratory of Electronics, Janu- 

 ary, 1948. 



4. E. A. Guillemin, "Classroom Notes on Network Synthesis" (Notes dictated at M. I. T., 



course 6.561 and 6.562 — as yet unpubUshed). 



5. E. L. Norton, "Constant Resistance Networks with Applications to Filter Groups," 



B. S. T. J., Vol. XVI, pp. 178-193, April, 1937. Also Bell System Monograph B-991. 



6. R. M. Redheffer, "Design of a Circuit to Approximate a Prescribed Amplitude and 



Phase," Report No. 54, M. L T. Research Laboratory of Electronics, November, 1947. 



^ Criticism may well be directed at the gain peak above the useful band. However, 

 this condition is somewhat exceptional and probably would not occur with an in-band 

 approximating function of order n rather than (« — 2). 



