. The Bell System technical journal . ltimately have a lower attenuation constantthan the former; but we shall not take space to investigate it here. LAMINATED TRANSMISSION LINES. II 1 1 SO ^- 0 ^ t < i^„, w(^) = A sin [A + iCmon, w(^) = B cos [A - iC/2(l - $n)]-(| - ^), ko 0 we have Re Ai > tt^ and Im Ai > 0. For large C the asymi)-totio expression for Ai turns out to be. C = 100 C = 100 (a) (b) Fig. 23—Real and iniaginary parts of the first two eigenfunctions, wi = wi +iviand wi = U2 + ivi , for the nonuniform stack of Fig. 22. 1190 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 &
. The Bell System technical journal . ltimately have a lower attenuation constantthan the former; but we shall not take space to investigate it here. LAMINATED TRANSMISSION LINES. II 1 1 SO ^- 0 ^ t < i^„, w(^) = A sin [A + iCmon, w(^) = B cos [A - iC/2(l - $n)]-(| - ^), ko 0 we have Re Ai > tt^ and Im Ai > 0. For large C the asymi)-totio expression for Ai turns out to be. C = 100 C = 100 (a) (b) Fig. 23—Real and iniaginary parts of the first two eigenfunctions, wi = wi +iviand wi = U2 + ivi , for the nonuniform stack of Fig. 22. 1190 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 < <v -. f( +1 0 -1 K) p — ^ f~ ./■ X s ^^ 2/^ — f- ,^ ReAi/TT • X y .^^ ^^ • ^ ,^^ ^^^ X-^^ :^® t* 20 50C 70 Fig. 24—Real and imaginarj parts of Aj/tt^ and Aj/tt^ for a nonuniform stack\vhose average properties are constant except at a single, unsymmetric discon-tinuity. (1 - y^ L T (1 - ^o)Cj + *■ C 47r- L2(i - ^0) (1 - k^Y /o^ ^o)Cj (550) Numerical values of Ai were found for the case ^o = I on the analogcomputer and refined afterward by desk computation. The real andimaginary parts of Ai/x are plotted over the range 0 ^ C ^ 100 inFig. 25, and the corresponding eigenfunction Wi{^) = Wi(^) + ivi{^) isshoAvn in Fig. 26 for C = 0, 20, and 100. b m ^x 0 -1 < a, _ 1/2 —(^ .x .4 ^ .- Re A /rr^ _,-<• ^ 0 ^^- --^ e^ 0 10 20 30 40 50 60 70 80 90
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
