TRANSMISSION LINES FOR RADIO SYSTEMS 



419 



and // was reduced by a factor of approximately 1 .X which corresponds 

 to a dielectric constant of about 3.2. Line / which was made with 

 insulators spaced at 9-inch intervals was the only other line which 

 showed a pronounced reduction in the velocity of propagation, the 

 factor in this case being 1.18. 



It is of interest to observe that if for economic reasons the diameter 

 of the outer conductor is fixed there is an optimum inner conductor 

 size for minimum attenuation. Employing (la), (2d), and (3) the real 

 part of the propagation constant may be written as: 



^PfJ^f 



276 



a b 



logio- 



X 10- 



(4) 



20 40 60 80 100 



RATIO OF RADII-^ 



400 600 8001000 



Fig. 4. — The most desirable ratio (36) of outer to inner conductor and the penalty 

 incurred in departing from this value. 



This neglects leakage loss and assumes that both conductors are made 

 of the same material. Upon minimizing with respect to a, the optimum 

 ratio : ^ 



- = 3.6 (4a) 



is readily obtained. This ratio corresponds to a characteristic imped- 

 ance of 77 ohms. Fig. 4 gives the manner in which the attenuation 



^ An experimental figure for the optimum ratio was given by C. S. Franklin in a 

 British Patent, No. 284005. The above derivation for the optimum ratio was 

 disclosed to the writers by E. I. Green and F. A. Leibe, American Telephone and 

 Telegraph Company, New York City. 



