ELECTROMAGNETIC THEORY OF LINES AND SHIELDS 565 



impedances themselves have to be computed by means of equations 

 (94) and (95). 



If the return path is inside the laminated conductor, instead of 

 outside, formulae (92) and (93) still hold, provided we interchange 

 a and h, and count layers from the outside instead of the inside, so 

 that w = 1 is the outermost, rather than the innermost, layer. 



The basic rule for determining the surface impedances of laminated 

 conductors can be put into the following verbal form: 



Theorem 3: Let two conductors, both of zvhich may be made up of coaxial 

 layers, fit tightly one inside the other. Any surface self-impedance 

 of the compound conductor equals the individual impedance of the 

 conductor nearest to the return path diminished by the fraction 

 whose numerator is the square of the transfer impedance across this 

 conductor and ivhose denominator is the sum of the surface impedances 

 of the two component conductors if each is regarded as the return 

 path for the other. The transfer impedance of the compound con- 

 ductor is the fraction whose numerator is the product of the transfer 

 impedances of the individual conductors and whose denominator is 

 that of the self -impedance. 



If two coaxial conductors are short-circuited at intervals, short 

 compared to the wave-length, the above theorem holds even if the 

 conductors do not fit tightly one over the other, provided we add in 

 the denominators a third term representing the inductive reactance of 

 the space between the conductors. 



Disks as Terminal Impedances for Coaxial Pairs 



So far we have been concerned only with infinitely long pairs. We 

 now take up a problem of a different sort; namely, the design of a 

 disk which, when clapped on the end of such a pair, will not give rise 

 to a reflected wave. 



The line of argument will be as follows: To begin with, we shall 

 assume a disk of arbitrary thickness h, compute the field which will 

 be set up in it, and then adjust the thickness so as to make this field 

 match that which would exist in the dielectric of an infinite line. 



The field in the disk has to satisfy equation (2) where iwe can be 

 disregarded by comparison with g. Thus, we have 



dH, _ 1 {pH,) _ 



"' ' '" (96) 



dE^ _ dEp 

 dp dz 



icofiH^. 



