572 BELL SYSTEM TECHNICAL JOURNAL 



by its distributed capacity and the input impedance approaches that 

 for the resistance termination. 



Conclusion 



Theory indicates that the exponential line may be used as an imped- 

 ance transformer over a wide frequency range. The results of experi- 

 ment show that the desired characteristic can be realized in practice. 

 Among the applications of the exponential line may be mentioned its 

 use in transforming the impedance level back to its original value after 

 the paralleling of two transmission lines feeding two antennas. It 

 could be used to transform the input impedance of a rhombic antenna 

 down to the usual 600-ohm level of open wire transmission lines. If 

 twin coaxial lines are used inside the transmitter building to eliminate 

 undesired feedback, coupling, etc., the exponential line could be used to 

 transform from the highest practical impedance level of such lines to a 

 practical level of the more economical open wire lines for use outside 

 the building. 



Appendix 



The exponential line is a non-uniform line so that the terms "charac- 

 teristic impedance" and "surge impedance" of an exponential line are 

 not synonymous. The terms "surge impedance" ' and "nominal 

 characteristic impedance" ^ may be used synonymously for the charac- 

 teristic impedance of the uniform line that has the same distributed 

 constants as the non-uniform line at the point in question. Expressed 

 as functions of the distributed "constants" of the line they are the 

 square root of the ratio of the distributed series impedance to the 

 distributed shunt admittance at the point along the line in question. 

 It will be expedient to refer to the nominal characteristic impedance 

 as the impedance level at the point in question. Schelkunoff ^ has 

 defined the characteristic impedances as the ratio of voltage to current 

 at the point in question for each of the two traveling waves of which 



1 The term "surge impedance" is defined by A. E. Kennelly on page 73 of "The 

 Applications of Hyperbolic Functions to Electrical Engineering Problems " (McGraw- 

 Hill 1916) as follows: "The surge impedance of the line is not only the natural imped- 

 ance which it offers everywhere to surges of the frequency considered, but it is also the 

 initial impedance of the line at the sending end." Hence the "surge impedance" 

 should be independent of the configuration of the line except at the point in question 

 and in particular it should be equal to that for a uniform line constructed so as to have 

 the same dimensions everywhere as the non-uniform line has at the point in question. 



2 The word nominal as used here has the same meaning as in "nominal iterative 

 impedance" as used by K. S. Johnson in "transmission circuits for telephone com- 

 munication" (Van Nostrand 1925). 



* S. A. Schelkunoff, "The Impedance Concept and its Application to Problems of 

 Reflection, Refraction, Shielding and Power Absorption," Bell System Technical 

 Journal, 17, 17-48, January, 1938. 



