THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1952 



ponents corresponding to any particular H^ are easily obtained from 

 equations (2). 



A concept important in what follows is that of wave impedances^ at 

 a point. For a wave whose field components are Hx , Ey , E^ , the wave 

 impedances looking in the positive and negative y- and ^-directions at a 

 typical point are defined to be, respectively, 



Zy = EJHx , Zt = — Ey/Hx , 



(7) 

 Z^ = —EJHx , Z^ = Ey/Hx . 



For waves of the type that we consider, Zy and Z~ are functions of 

 y only, so that if two media ha\'ing different electrical properties are 

 separated by the plane y = yo , the continuity of the tangential compo- 



z {^) .^ , 



f^y 



^0'7c 



-^E-, 



W//: \/.////^/y//////////////////^^^^ 





Fig. 1 — Transmission line bounded by parallel impedance sheets. 



nents of E and H across the boundary can be assured by merely re- 

 quiring the continuity of Z^ (say) at t/ = yo . This is equivalent to the 

 requirement that the sum of the impedances Z^ and Z^ looking into the 

 media on opposite sides of the boundary be zero. A similar condition 

 holds for the impedances Zt and Z7 at a boundary z — z^ . 



As an example of the use of the wave impedance concept, we shall 

 consider the propagation of a transverse magnetic wave between parallel 

 impedance sheets which are separated by a distance 6. For the moment 

 nothing is specified about the structure of the sheets except that the 

 normal surface impedance looking into each is ^(7), for a wave whose 

 propagation constant in the ^-direction is 7. The fact that in general Z 

 will depend upon 7 should be noted, since in some cases this dependence 



^ S. A. Schelkunoff, Electroniagnetic Waves, D. van Nostrand Co., Inc., New 

 York, 1943, pp. 249-251. Since in our problem three field components vanish identi- 

 cally, we need only two of the six impedances which are defined in the general case. 



^ Reference 3, pp. 484-489. 



