By Cam Nguyen
Assemble the paintings of others within the box, write a ebook approximately it, improve it with a number of mathematical appendices, ship it to the editor, and you will get 2 hundred pages+ of thick conception, 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
The derivative of G x; x 0 has a discontinuity of magnitude 1/P1 x 0 at x D x 0 . 34 Properties 1 and 2 are readily seen, while Properties 3, 4, and 5 can easily be proved. We assume that the function P1 x is continuous and nonzero at any point within the interval [a, b]. The discontinuity of the derivative of G x; x 0 in Property 5 thus has a finite value. We also assume that P1 x and P2 x are continuous in the interval [a, b]. Once G x; x 0 is found, the solution to Eq. 35 a We now find the Green’s function by dividing the interval [a, b] into two separate regions: [a, x 0 ] and [x 0 , b].
53) as 2 m x 0 sinh m,1 h sinh[ m,0 b sin a a Qm gm y; x 0 , h D 0 2 sin m x sinh[ m,0 b h ] sinh a a Qm y] m,1 y , 0ÄyÄh , hÄyÄb The Green’s function is then derived, from Eqs. , at y D 0 and b). 2 Series-Form Green’s Function We consider again the Sturm–Liouville Eq. 67 where ˛i and ˇi (i D 1, 2) are constants. Accordingly, the Green’s function G x; x 0 must satisfy Eq. 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.
This is in fact similar to using Kirchhoff’s voltage and current laws in a lumpedelement circuit to obtain unique solutions for the voltages and currents in that circuit. For time-harmonic fields, the boundary conditions between two different media, shown in Fig. 15d where the subscripts 1 and 2 indicate media 1 and 2, respectively. n is the unit vector normal to the surface and pointing into medium 1. Js and s are the (linear) surface current density (in A/m) and surface charge density (in C/m2 ) existing at the boundary, respectively.