BAND WIDTH LVD TRAXS.\nsSION PERFORMANCE 573 



of X or to any number of spans when x = 20. In other words the maxi- 

 mum circuit length for x = 20 is the length of span corresponding to the 

 excess power capacity as noted above for .v = 10^. For all smaller values 

 of -v any circuit length can be achieved with any value of excess power ca- 

 pacity if a sufficient number of spans is employed. The number of spans 

 required for a given circuit length is obtained by moving the curve downward 

 until it intersects the desired length at the appropriate excess power ordinate, 

 and equating (20 — x) log n to the downward shift in decibels. 



Notwithstanding the present radio outlook in which large towers and 

 antennas seem indicated, it is of interest to imagine small repeaters powered 

 for a one-mile span, say. Using FM with limiting at every repeater, a 

 100-mile circuit could be obtained with 250 repeaters spaced 0.4 miles. 

 This result comes from Fig. 33 with excess power = zero db and x = 3.33. 

 A difficulty with such a case might be multiple paths produced by one re- 

 peater output overreaching into other spans. 



The inverse k power attenuation does not accurately describe propagation 

 over long spans; fading then occurs and is greater for long spans than short 

 spans. This introduces a term in the span loss similar to that of the metallic 

 conductor case in which the span loss is proportional to span length. 



IX. Conclusions 



We have, in this paper, examined some of the relations governing the 

 exchange of bandwidth for advantages in transmission that grow out of the 

 liberal use of bandwidth. While we have not dealt specifically with the 

 instrumentation involved in the application of the various exchange methods, 

 we have taken cognizance of certain basic obstacles in circuit design such as 

 overload distortion, phase distortion and discrimination characteristics of 

 selective networks and the limitations of microwave antennas. Not having, 

 in most cases, a wealth of experience bearing on the manner in which these 

 obstacles affect the transmission problem, we have been obliged to estimate 

 their effect in many cases. Considerable unreliability in these estimates 

 would not, however, much affect the broad purpose of the paper. The 

 economic factor that is involved in achieving reliable operation of apparatus 

 has been largely ignored, although methods that seem to lead to fantastic 

 instrumentation have not been given much attention. 



Ruggedness of the transmitted signal, which is obtained at the cost of 

 increased bandividth can, properly handled, be made to conserve frequency 

 occupancy in two ways: (a) ruggedness reduces the required "guard space" 

 between one band and neighboring bands carrying other signals; (b) rugged- 

 ness reduces the multiplication of frequency assignments necessary in 

 congested radio route situations. 



For wave guide systems, the inter-route interference problem arising from 



