. The Bell System technical journal . s usable as transmission devices tlie following approximationshold: y/DZ = ^ =21/1 + 14/1 /3 = a,VZC = ^ = ^ = a/ ^, C = -^r^ , L = -^, V = 3 X 10^ cm/sec. for air. For the case of near-end input and output the second of equations (1) canbe rewritten as , Zf , cosh yjDZ t + —y= sinh \/DZ t /o= ° i/^ —^ cosh ^DZ i + sinh \/DZ I (3) \ T) + —j^ /cosh \/dZ C + —k sinh \/dZ t If now we assume a quarter-wave line, the condition of resonance implies 1 /zl 1 /zl that Rfy>\ A/ —\ and RaZ I + ^) We now make the assumption that Zo is a pure resistance (which
. The Bell System technical journal . s usable as transmission devices tlie following approximationshold: y/DZ = ^ =21/1 + 14/1 /3 = a,VZC = ^ = ^ = a/ ^, C = -^r^ , L = -^, V = 3 X 10^ cm/sec. for air. For the case of near-end input and output the second of equations (1) canbe rewritten as , Zf , cosh yjDZ t + —y= sinh \/DZ t /o= ° i/^ —^ cosh ^DZ i + sinh \/DZ I (3) \ T) + —j^ /cosh \/dZ C + —k sinh \/dZ t If now we assume a quarter-wave line, the condition of resonance implies 1 /zl 1 /zl that Rfy>\ A/ —\ and RaZ I + ^) We now make the assumption that Zo is a pure resistance (which is nolimitation on the measurement to be discussed) and put ^ = a^ + ihi. 128Then, 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 tunedvalue 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 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 theactual observed resonance length, we have 27r^ ^. 6, = ?^- + ft, d= lirSC = ^ ± lirSe Then tan f _ + *,j = tan (2 ± JT j = ^^ ^^ DIELECTRIC CONSTANTS AND POWER FACTORS 129 /o V. 1 + tanh {a€ + af) • tan IttSC V I / r ^0 ,1 rj + tanh {aC + flf) Ye 2 + Forming the current values | /m | = | /021 = 1 + —-Tj tan
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
