The Present Status of Wire Transmission Theory and 

 Some of its Outstanding Problems 



By JOHN R. CARSON 



Synopsis: The rapid development in the technique of wire transmission 

 and the increasing complexity of the problems involved calls for a more 

 adequate theoretical guide and a more rigorous transmission theory. This 

 paper gives an account, practically without mathematics, of classical 

 transmission theory and its limitations; of the several ways the problem 

 may be attacked more fundamentally and rigorously, and the lines along 

 which transmission theory must be extended, as the writer has come to 

 view the problem in the light of his own experience. 



IN the present paper the term wire transmission theory will be under- 

 stood to mean the mathematical theory of guided wave propaga- 

 tion along a system of parallel conductors; which is supposed to be 

 geometrically and electrically uniform throughout its length. The 

 theory of wave propagation along such a system is of fundamental 

 theoretical and practical importance to the communication engineer 

 and presents some extremely interesting and difficult problems to the 

 mathematician. The development of the elementary or classical 

 theory will first be briefly sketched, after which the rigorous mathe- 

 matical theory will be discussed together with some of the important 

 unsolved problems. 



Historically wire transmission theory goes back to the early work of 

 Kelvin and Heaviside. It is based on the simple idea that a trans- 

 mission line (say consisting of two similar and equal wires in which 

 equal and opposite currents flow) can be represented as consisting of 

 uniformly distributed series inductance and resistance and shunt 

 capacitance and leakance, these concepts deriving from electrostatics 

 and elementary circuit theory. In accordance with this idea, if X 

 denote the axis of propagation, the current / and voltage V are related 

 by the familiar equations 



4 + ^)^ = -^^' (^^) 



4t + <')''= -I'- ('"> 



(2) 



268 



