By G. Mourier
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Extra info for Crossed-field Microwave Device. Principal Types of Crossed-Field Devices Analysis of Oscillator system Performances Regional Progress and Trends
Sample text
VI. Group Velocity and Energy Velocity T h e group velocity in a medium can b e considered as t h e velocity of a pulse shaped signal; in general, such a signal becomes distorted and spreads in space. A velocity can be defined b y considering a signal covering a very narrow b a n d of frequencies, or consisting of t w o waves of slightly different frequencies, ω/2π a n d (ω + Δω)/2π. I n t h e case of a uniperiodic medium, t h e y have equal phases if ω< - βζ = (ω + Δω)ί - (β + Αβ)ζ (33) T h e group velocity is defined as Ζ Δω οω * = ϊ = ϊ-β^Τβ ν , .
On t h e contrary, if we p u t a ground plate near t h e bars of a ladder, covering only p a r t of the length of t h e bars, t h e discontinuities a t t h e edges of t h e plate permits propagation (9). We shall now consider t h e symmetric structure of Fig. 3. W e can h a v e ground Π FIG. 3. Ladder line with a grounded plate; only the symmetric wave is considered. The origin of the coordinates is at the discontinuity brought by the grounded plate. symmetrical modes for which t h e structure can be cut in its middle with out a n y i m p o r t a n t changes, a n d antisymmetrical modes for which t h e middle of t h e bars can be grounded without a n y i m p o r t a n t changes.
Let us consider a n a r r a y of infinite cylindrical conductors called " b a r s ' ' directed along Ox. If t h e y a r e immersed in a m e d i u m of constants €o a n d μο over all space, transverse electric a n d magnetic waves c a n propagate along t h e bars (1). F o r these modes of propagation t o which we limit ourselves Maxwell's equations a n d t h e b o u n d a r y conditions a r e satisfied b y t h e fields Ε and Η if E y = Ε,= - ψ dy ^ - ψ e-*> dz " Η,-^βψβ-** \μ0 dz Η , ^ - ^ ψ e-** \μο dy 35 (1) 36 J.