HYPER-FREQUENCY TRANSMISSION 323 



where 



(|C„|2+ \D,^'){J,.{rnJ)Y = n^\ (30) 



Thus 



where, as given alnne, r„„/ is the mth root of 7„'(Xa) and, by (10) 

 . c 1 



Thus the mean transmitted energy and the characteristic impedance of 

 all components of the il-wave increase as the square of the frequency 

 whereas these characteristics of the £-wave are constant with respect 

 to frequency. To appreciate the bearing of this difference upon the 

 comparative attenuations consider the following argument. 



Since the wave varies along the s-axis of the transmission system as 

 exp. ((— a — i^)z), a and jS denoting the attenuation and phase con- 

 stants per unit length, respectively, 



^-^^^-laW. (32) 



dz 



But, denoting by Q the dissipation loss per unit length of the trans- 

 mission system, we have also 



^-^=-Q. (33) 



dz 



Hence, 



a = Q/2W (34) 



= (47r^/c?5[£-/^*].)Rea,Parf (35) 



Thus, w^e see that, if the mean dissipation loss^ Q, is known or readily 

 obtainable, the Complex Poynting Vector, W, leads immediately to 

 the attenuation. 



To obtain Q we have the formula 



Q= -(^fdSlE-H*2r) • (36) 



\ OTTJ / Real Part 



Thus a may also be written 



- fdSlE-H* J\ .37. 



2/rf5[£-//*]. /Real Part 



