By Cam Nguyen
Collect the paintings of others within the box, write a booklet approximately it, improve it with a couple of mathematical appendices, ship it to the editor, and you will get two hundred pages+ of thick idea, void of functional curiosity for the layout engineer.
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Extra info for Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures
All the orthogonality relationships are given as follows. 86b S S Hybrid Modes S S Note that Eq. 86) is valid even when m D k and n D l. 87b e h where Cemn , Chmn , Dmn , and Dmn are the orthogonal coefficients. As for the case of the scalar potentials, when the modes are degenerate and nonorthogonal, we can construct a new set of transverse fields, each of which is a linear combination of certain fields of the nonorthogonal degenerate modes, such that the new fields are mutually orthogonal. 3 Orthogonality Relations Between Electric and Magnetic Fields Let’s consider again two different TMmn and TMkl modes.
9 WAVE EQUATIONS Electromagnetic fields may be determined by using Maxwell’s equations and constitutive relations directly. However, the most convenient way of obtaining these fields is solving a special class of equations known as the wave equations. We shall derive these equations as follows. We consider a medium that is source free ( D J D 0) and simple (homogeneous, isotropic, and linear) and assume that the fields are time harmonic. The medium is characterized by a dielectric constant ε and permeability .
It should also be noted that the boundary conditions for the normal and tangential components of the fields between any two media are not independent of each other. 6 SKIN DEPTH One of the most important parameters of a medium is its skin depth or depth of penetration. The skin depth is defined as the distance from the medium surface, over which the magnitudes of the fields of a wave traveling in the medium are reduced to 1/e, or approximately 37%, of those at the medium’s surface. 17 The skin depths of good conductors are very small, especially at high frequencies, causing currents to reside near the conductors’ surfaces.
Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures by Cam Nguyen