By Cam Nguyen
Collect the paintings of others within the box, write a e-book approximately it, improve it with a number of mathematical appendices, ship it to the editor, and you will get 2 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
29 which, after substituting into Eq. 30 It is now apparent that the Green’s function for a microwave structure can be obtained as the solution of the Sturm–Liouville equation when the source has unit amplitude, subject to appropriate boundary conditions. 3 SOLUTIONS OF GREEN’S FUNCTION In general, Green’s function can be described in three forms: closed form, series form, and integral form . The formulation of these functions is given as follows. 31 [L C P3 x ]y D f x where a Ä x Ä b; L is again the Sturm–Liouville operator; and is a constant.
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. As an illustration for the formulation of the series-form Green’s function, we consider a rectangular-waveguide resonator whose dimensions along the x, y, and z axes are a, b, and d, respectively. We assume that a current source, represented by the current density J x, y, z , exists in the resonator and TE modes are excited.
5 Show that TM modes can be characterized only by the electric scalar potential e x, y . 6 Prove that, in any waveguides, both Ez and Hz cannot be even or odd simultaneously. 7 Consider a general waveguide with perfectly conducting walls as shown in Fig. 3. 8 Verify the power orthogonality relationship for nondegenerate modes in a lossless circular waveguide. 9 Verify the power orthogonality relationship for nondegenerate modes in a lossless rectangular waveguide. 10 The electric and magnetic fields of the eigenmodes existing in planar transmission lines are normally determined approximately.
Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures by Cam Nguyen