. The Bell System technical journal. Telecommunication; Electric engineering; Communication; Electronics; Science; Technology. 1« BELL SYSTEM TECHNICAL JOURNAL to rewrite it in terms of other parameters, and we will introduce them now. Let Kh/Wo = O () C is usually quite small and is typically often around .02. Instead of ^ we will use a quantity or a parameter b In terms of b and C, () becomes i-jY" = ( J(2^~l|â¢2)1r^l/3 () () This has three roots which will be called 5i , ^2 and 63, and these represent three forward waves. They are 8, = e-'"" = V3/2 - j/2 h =
. The Bell System technical journal. Telecommunication; Electric engineering; Communication; Electronics; Science; Technology. 1« BELL SYSTEM TECHNICAL JOURNAL to rewrite it in terms of other parameters, and we will introduce them now. Let Kh/Wo = O () C is usually quite small and is typically often around .02. Instead of ^ we will use a quantity or a parameter b In terms of b and C, () becomes i-jY" = ( J(2^~l|â¢2)1r^l/3 () () This has three roots which will be called 5i , ^2 and 63, and these represent three forward waves. They are 8, = e-'"" = V3/2 - j/2 h = -:bir/6 7V/2 = -V3/2-J/2 () 83 = e' = J Figure shows the three values of 8. Equation () was of the fourth degree, and we see that a wave is missing. The missing root was eliminated Fig. âThere are three forward waves, with fields which vary with distance as exp(âjjSe -\- 0eC5)z. The three values of 8 for the case discussed, in which the circuit is lossless and the electrons move with the phase velocity of the unperturbed circuit wave, are shown in the figure. by the approximations made above, which are valid for forward waves only. The other wave is a backward wave and its propagation constant is found to be r = j^e (â -?) () As C is a small quantity, C^ is even smaller, and indeed the backward wave given by () is practically the same as the backward wave in the absence of electrons. This is to be In the forward direction, there is a cumu- lative interaction between wave and the electrons because both are moving. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original American Telephone and Telegraph Company. [Short Hills, N. J. , etc. , American Telephone and Telegraph Co. ]
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