Analysis Methods for RF, Microwave, and Millimeter-Wave by Cam Nguyen

By Cam Nguyen

Collect 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 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

Example text

To obtain unique solutions for the fields in a particular structure, such as coplanar waveguide, we must, however, enforce the structure’s boundary conditions. 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.

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]. 36 which satisfies the boundary condition at x D a. 37 and the boundary condition at x D a, according to Properties 1 and 2 of the Green’s function, respectively.

33 SOLUTIONS OF GREEN’S FUNCTION 2. 3. 4. 5. 45 G x; x 0 satisfies appropriate boundary conditions at x D a and x D b. G x; x 0 is symmetrical with respect to x and x 0 . G x; x 0 is continuous at x D x 0 . 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.

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