By Cam Nguyen
Bring together the paintings of others within the box, write a publication approximately it, improve it with a couple 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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Additional info for Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures
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 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.
A Green’s function) in that particular structure. Once Green’s function is found, the total response can easily be determined by taking a summation or integral. To illustrate this principle, we will describe and use Green’s function in obtaining the solutions of the two basic but most commonly used equations in microwave boundary-value problems: Poisson’s equation and the wave equation. 1 Solution of Poisson’s Equation Using Green’s Function We consider a medium characterized by a permittivity ε and permeability as shown in Fig.