48 BELL SYSTEM TECHNICAL JOURNAL 



film. This picture is suggested by the analogy of a transmission line ter- 

 minated, at the receiving end, in its characteristic impedance, so that there 

 is no reflected wave. The difficulty with the analogy is that free space 

 exists beyond the film and cannot be cut off". This idealized picture may 

 serve, however, to indicate the simplification made possible by the intro- 

 duction of characteristic impedances in practical problems involving reflec- 

 tion, refraction and absorption. 



The characteristic impedance of free space may be usefully introduced 

 into formulas for the characteristic impedances of transmission lines. Thus, 

 assuming perfect conductors, we have: 



For flat strips, width w, separation d, if wjd is large or the guard-ring 

 method is employed in measurements, 



Kf = 376.54-; 



w 



For concentric cylinders, with radii b and c, 



376.54, b 

 Ac = -^ log-. 



These characteristic impedances will each agree with the characteristic 

 impedance of free space \i w = d and b = 535.49 a. Since these strips are 

 not wide compared with the separation, it would be necessary to employ 

 the guard-ring method to maintain the plane wave assumed in the square 

 shaft between the two strips. These two characteristic impedances would 

 each become one ohm if w = 376.54 d, and b = 1.0168 a. 



Practically, the finite conductivity of copper would add a reactance com- 

 ponent and change the resistance component. It would be interesting to 

 investigate simple cases numerically and include mutual characteristic 

 impedances between two metallic circuits. 



My own interest in the applications of the impedance concept to 

 the electromagnetic field theory dates back to the last quarter of 1931. 



