By William R. Smythe
This ebook has hardback covers.Ex-library,With ordinary stamps and markings,In reasonable situation, appropriate as a research reproduction.
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The wave impedance Zx can be written in a more useful form when the dielectric is not lossy. Since ~ = j(27r/A,) ,where X, is the wavelength in the waveguide, where A is the wavelength in the dielectric medium for a TEM-wave. The equations that H. must satisfy are identical in form with those which apply to the velocity potential governing the propagation of sound waves. Sound waves are essentially simpler in nature than electromagnetic waves, since they can always be derived from a scalar field.
9. FIG. 13. The Normal Modes in Round Pipes. 11,,-modr. 213] THE NORMAL MODES to choose the axis as the direction of propagation. L)E. = O. +(7’ the (50) If the variables are separated by taking E, = R(r)@(@), the equation for @ is ~2@ W+ XW=O, where xz is the separation constant. The solution is @ = ~ixo, (51) and hence x must be an integer or zero. The complex form of the function @ is interpreted to mean that two solutions are possible: One is @ = cos xO; the other is @ = sin x6. Thus the modes are degenerate in pairs.
32), H. and Hu are determined; and from these values and Eqs. (29), E, and E, are obtained. Thus all the components of the field are determined from a single scalar quantity H.. It should be noted that Eq. (33) is just the wave equation for H. derived in Sec. 3. To apply this to a waveguide of a particular shape, it is necessary to find an Hz that satisfies the proper boundary conditions at the walls of the guide. If the \valls are perfect conductors, E, must vanish over the surface. These boundary conditions ~vill give rise to a relation connectThe form of this ing y and o and the dimensions of the waveguide.