526 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



show that ao is zero for k given approximately by 



''-V^^[i-i\^i^)] (A-1) 



For ao = 0, Ex is of course zero. We thus have a plane wave propagating 

 through the medium with a wavelength appropriate to the average dielectric 

 constant i and with a very small attenuation proportional to the square of 

 the frequency. Equation (A-1) can be obtained from equation (45) in 

 Sakurai's paper.^ 



If we wish next to observe the effect of finite thickness laminations, we 

 can require aw to be zero in equation (III-34). In this case we obtain 



Again the attenuation is proportional to the square of the frequency. The 

 attenuation given by equation (A-2) is equal to that obtained from equa- 

 tion (A-1) if 



W 



-IM^tH 



For copper, equation (A-3) requires W to be of the order of 10~^ cm. Under 

 ordinary circumstances, therefore, the attenuation given in equation (A-1) 

 is much smaller than that obtained when consideration is given to the finite 

 thickness of the laminations. 



APPENDIX B 



Transmission Line Filled with Laminations or Finite Width 



Let us consider the transmission Hne shown in Fig. 17. As before we have 

 a set of metal laminae of width W and conductivity a separated by insulat- 

 ing laminae of width / and dielectric constant e. The laminae will be num- 

 bered as shown in the figure from 1 to N. Let us define r and p by 

 the relations 



. = ^^. ; , = V^! (B-1) 



■'12 -t 12 



Then, from equations (111-19) and (111-20), we can write for the 2-com- 

 ponent of magnetic field and the rc-component of electric field, 



Hn = A^^ + B^- (B-2) 



En = r^iS" + pB^^ (B-3) 



2 Tokio Sakurai, loc. cit., page 398. 



