By Ken Budnick
Booklet by means of Budnick, Ken
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The proof for the transverse electric fields is almost identical. Thus it is clear that the longitudinal components of the electric and magnetic fields and the transverse components are all separately orthogonal for any two different modes. It remains now to show that the energy flow for two modes contains no mixed terms. If two H-modes are considered. the power flow contains terms such as — / H,a o Hi dS = O, (97) as has already been shown. The argument is identical for two E-modes, Thus when several modes exist and for one H-mode and one E-mode.
I’’E’kf-wave in the medium that fills the hollow pipe. In terms of XO, the wavelength of a Z’EM-wave in free space, Eq. (41) becomes (43) lt will be noted that the cutofi wavelength defined in this way is independent of the dielectric material filling the Waveguide; the critical frequency defined in Eq. (40) is not. For frequencies below the critical value, 7 becomes real and the waves are attenuated. 3 db in a distance equal to the width of the pipe. A pair of values of n and m suffice to designate a particular mode that is called, according to the, accepted notation, a Z’E~n-mode.
If this is assumed to be true, the energy stored, W, is seen to be (78) where P is, as before, the power flow in the waveguide. Since where A and c are the wavelength and the velocity in the dielectric medium, the expression for the power flow may be written (79) The energy lost in the walls, W,, can be written 4aPl w,=—=— Ll) 2naPA. u“ (80) The energy lost in the end plates, W,, is given by where the integral is taken over the two ends. to the quantity P by This is directly related The factor 8 is a combination of two where Zw is the wave impedance.