{E'/^'P) 



W = 

 W = 



1/3 



APPENDIX III 

 ireiya)' \ lo — hh 



■weya 



L n 



+ 



i^Tn iTo — K. 



2-1 



T^2 



K 







E- 



{c/vY'^ivM 



1/3 



120 



ni/3 





249 



(8) 



(9) 



A3. 2 Pill-Box Resonators 



Schelkunoff gives on page 268 of Electromagnetic Waves an expression 

 for the peak electric energy stored in a pill-box resonator, which may be 

 written as 



.135 7r€a2/;£2 



Here a is the radius of the resonator and h is the axial length. For a series 

 of such resonators, the peak stored electric energy per unit length, which is 

 also the average electric plus magnetic energy per unit length, is 



For resonance 



Whence 



W = .135 7rea2£2 



a = 1.2Xo/7r 

 W = .0618 €Xo2£2 



And 



(EP/^'-Pyi^ = 5.36 (v/vgY'^ {v/cy' 

 The case of square resonators is easily worked out. 

 A3.3 Parallel Wires 



(10) 



(11) 

 (12) 

 (13) 



Let us consider very fine very closely spaced half-wave parallel wires with 

 perpendicular end plates. 



If z is measured along the wires, and y perpendicular to z and to the 

 direction of propagation, the field is assumed to be 



Ej: — E cos 8xe cos — z 



Ao 



Ey = E sin I3xe cos — z 

 Xo 



(14) 



Here the + sign applies for y < and the — sign for y > 0. We will then 

 find that 



