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Example text

This dispersion must be known before the group velocity of the waves can be found. The dispersion law is found by solving for p versus co from Maxwell's equations for the particular structure under consideration. 52) where Eq. 51 has been used. For a dispersionless line, dv±ph/du = 0, and it is seen that the group and phase velocities are in the same direc Thus the power flow is in the + z-direction for the a+-mode, tion. whereas it is in the —z-direction for the a--mode. It might be noted that it is possible to devise a transmission line in which the phase and group velocities are in opposite direction by suitable choice of the dispersion.

Assume that the two modes are continuously coupled in a linear manner. Let Oi and a2 measure the complex ampli tudes of the two normal modes before coupling. 4. a2, respectively. 4 Let coi and let dt represent the phase shift mode co2 coupling. of two coupled lossless modes of vibration. ai experiences in time dt, dt represent the phase shift of mode o2, both in the absence of * 2* refers Because of the coupling, some of the energy in mode to the a2*-mode. a2 is COUPLED MODE AND PARAMETRIC 16 ELECTRONICS transferred to mode ai and some of the energy in mode ai is transferred to mode a2.

Rep. No. 316 (April 8, 1958). Technol. H. A. Haus, "Variational Principles Derived from Power Theorems," Mass. Inst. Technol. Research Lab. Electronics, Internal Memorandum (1959). R. Whinnery, Fields and Waves in Modern Radio, John Wiley and Sons, Second Edition, New York, 1953, p. 23. R. I. Sarbacher and W. A. Edson, Hyper and Ultrahigh Frequency Engineering, John Wiley and Sons, New York, 1947, pp. 272-284, 320. S. A. Schelkunoff, "Generalized Telegraphist's Equations for Waveguides," Bell S.

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