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By Cam Nguyen

Bring together 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 thought, void of sensible curiosity for the layout engineer.

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Extra resources for Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures

Example text

The medium is characterized by a dielectric constant ε and permeability . Taking the curl of Maxwell’s Eq. 5a) and making use of Maxwell’s Eq. 24 is the wave number. 25 where A is an arbitrary vector, we can then rewrite Eq. 26 where r2 denotes the Laplacian operator. This equation is called the wave equation for the electric field. 27 W2 H C k 2 H D 0 Both of these wave equations are also known as Helmholtz equations. Other commonly used wave equations are those in the plane transverse to the direction of wave propagation.

Collin, Field Theory of Guided Waves, IEEE Press, New York, 1991, pp. 329–337. 3. A. E. Taylor and W. R. Mann, Advanced Calculus, John Wiley & Sons, New York, 1983, pp. 277–279. 15) between two different media as shown in Fig. 2. 2 Using the Poynting vector, prove that the average power density of a signal propagating in a waveguide is given by Eq. 20). 3 Show that TE modes can be characterized only by the magnetic scalar potential h x, y . 4 Derive Eqs. 54). 5 Show that TM modes can be characterized only by the electric scalar potential e x, y .

69 n. 70 and the same boundary conditions for G x; x 0 in Eqs. 69). 72 is the Kronecker delta function. 73 nD1 where an is the amplitude coefficient. Multiplying both sides of Eq. 74 a Now multiplying Eq. 32) by ˚n x and Eq. 75 SOLUTIONS OF GREEN’S FUNCTION 51 whose left-hand side vanishes upon using Eqs. 70). 76 a Substituting Eq. 78 a The series-form Green’s function of Eq. 73) now becomes, upon substitution of Eq. 79 n nD1 The Green’s function in series form is useful for bounded microwave structures, in which the orthogonal functions ˚n x used to describe the Green’s function represent standing waves, and when the eigenvalue spectrum formed by n is discrete.

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