By Cam Nguyen
Assemble the paintings of others within the box, write a e-book approximately it, improve it with a couple of mathematical appendices, ship it to the editor, and you will get 2 hundred pages+ of thick thought, void of sensible curiosity for the layout engineer.
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Additional info for Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures
This leads to kc,h D 0 and, consequently, Eq. 65 28 FUNDAMENTALS OF ELECTROMAGNETIC THEORY which is basically Laplace’s equation in the transverse plane. The transverse fields can be obtained from Eqs. 66b where is the TEM mode’s propagation constant. Proceeding with the TM mode also gives identical results. It should be noted that for the TEM case, both e x, y and h x, y are equal to the two-dimensional voltage or potential V x, y . 12 ORTHOGONALITY RELATIONS Consider a general waveguide as shown in Fig.
For degenerate modes not satisfying Eq. 101). 109d D Hkl PROBLEMS 37 where the constant C is chosen to satisfy the power orthogonality. It should be noted that the power orthogonality is only approximately held for low-loss waveguides propagating nondegenerate modes. For degenerate modes, strong couplings between these modes occur. One remark needs to be made at this point. All the derived orthogonality relations are completely satisfied only if the modes were calculated exactly. Normally, the eigenmodes in planar transmission lines can only be determined approximately.
Substituting Eq. 33 kc and ωc are referred to as the cutoff wave number and cutoff frequency, respectively, due to the fact that they reduce to the corresponding parameters at the cutoff ( D 0). 32) is known as the wave or Helmholtz equation in the transverse plane, with z as the direction of propagation. 10 ELECTRIC AND MAGNETIC POTENTIALS The fields in a microwave structure, in general, and in a transmission line, in particular, may be determined by directly solving the wave equations subject to appropriate boundary conditions.
Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures by Cam Nguyen