LAMINATED TFL^NSMISSION LINES. II 1205 



arc given by oqiiatinns (33) of Soctioii IT, wliicli read 

 H^ = Ahia^p) + BIu(<r,p), 



E, = 1 [Ah(a,p) + Blu(a^p)], (A20) 



E, = vUIo(arp) - BIu(<Tip)], 



proxidcd that we i\vo\) the i)i()i)aj>;ati()ii factor e~^^ and make the usual 

 approximations 



gi/o)ei » 1, Ki --^ 0-1 , Ki/gi ^ 771 , (A21) 



for a good conductor. Tlic constants A and B are determined by the 

 boundary conditions 



H^(pr) = /i/27rpi , H^(p.2) = /2/27rp2 , (A22) 



\\hicli follow directly from Ampere's circuital law. We find without diffi- 

 culty 



^ ^ {h/2Trp2)Ki{aipi) — {Ii/2irpi)Ki(aip2) 



Kl{(Tipi)Ii{(TiP2) — Ki{cip2)h{(TlPi) 



^ _ (/i/27rpi)/i((rip2) — (/2/27rp2)/i(q-ipi) 

 -K^i(o-ipi)/i(crip2) — Ki{crip2)Ii{(Tipi) 



(A23) 



The average power dissipated in the conducting cylinder is equal to one- 

 half the real part of the inward normal flux of the complex Poynting vector 

 E X H*. For the average power P dissipated per unit length we have 



P = Re h[2rp2EMHt(p2) - 2ir p^EMKip,)] 



= Re \[EMlt - EMI*x] 



= Re ^''^ 



(i^n/12 - i^i2/n) I2irp 



(Kn/02 + Ko2/n) (A24) 



(/1/2 + /r/2) , IJl 



2ir(X\p\p2 27rpj 



+ ^-^ (Koi/12 + A'12/ 



01 



where 



/„ = /r(o-lp.s), Krs = Kr{(J\P,). (A25) 



The combinations of Bessel functions appearing in (A24) are just those 

 for which we gave approximate expressions in etiuations (A8) of AppcMidix 

 I, assuming the thickness h (= p2 — p\) of the conducting cylindei' to be 

 small compared to pi . Substituting these approximations into (A24) and 



