128 

 Then, 



BELL SYSTEM TECHNICAL JOURNAL 



y / tanh^ {al + a^) + tan f^ + bA 



tanh {af + a^) 



+ tanh (aC + fl^) 



(5) 



ex^^') 



This expression cycles, as "(" is varied, and has its maximum or "tuned" 

 value of 



V, 



/l/1 





+ tanh {al + a^) 



(¥ + *^ 



for tan ( — - + J/ j = <» 



or 



27r^ , - (2w + l)7r ^ . ^ 



-T- + J/ = -^ TT-^ « = 0, 1, 2, • . • 



The resonant length is thus ^ = t ( 1 ~ 



(-^-^) 



for n = 0. Note that successive 



resonances differ b.v a line length of -; the reactive termination has merely- 

 shortened, by the amount of M = -—^, the first resonant element preceding 



ZTT 



it. WTien, therefore, we measure the "Q" of this line segment by line- 

 length tuning we use ^ = - in the Q process definition. 



The Q process now follows. Putting ^ = 4 =fc 5^ where 4 is the 

 actual observed resonance length, we have 



27r^ 



^. 6, = ?^- + ft, d= 



lirSC 



= ^ ± 



lirSe 



Then tan f _ + *,j = tan (2 ± "JT j = ^^ l.U ^"^ 



