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

By Cam Nguyen

Assemble the paintings of others within the box, write a e-book approximately it, increase it with a couple of mathematical appendices, ship it to the editor, and you will get two hundred pages+ of thick concept, void of useful curiosity for the layout engineer.

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

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54), derived earlier can therefore be used directly to determine the fields of the hybrid modes. TEM Modes Solution for the TEM mode can be viewed as a special solution of either the TE or TM mode when Hz or Ez is set to zero, respectively. For instance, we consider the TE mode and let Hz in Eq. 55c) equal zero. This leads to kc,h D 0 and, consequently, Eq. 65 28 FUNDAMENTALS OF ELECTROMAGNETIC THEORY which is basically Laplace’s equation in the transverse plane. The transverse fields can be obtained from Eqs.

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 [2]. 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.

4 Derive Eqs. 54). 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.

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