By Cam Nguyen
Assemble the paintings of others within the box, write a publication approximately it, improve it with a number of mathematical appendices, ship it to the editor, and you will get two hundred pages+ of thick thought, void of useful curiosity for the layout engineer.
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Additional info for Analysis Methods for RF, Microwave, and Millimeter-Wave Planar Transmission Line Structures
24. 2. R. E. Collin, Field Theory of Guided Waves, IEEE Press, New York, 1991, pp. 329–337. 3. A. E. Taylor and W. R. Mann, Advanced Calculus, John Wiley & Sons, New York, 1983, pp. 277–279. 15) between two different media as shown in Fig. 2. 2 Using the Poynting vector, prove that the average power density of a signal propagating in a waveguide is given by Eq. 20). 3 Show that TE modes can be characterized only by the magnetic scalar potential h x, y . 4 Derive Eqs. 54). 5 Show that TM modes can be characterized only by the electric scalar potential e x, y .
Note that both e x, y, z and h x, y, z are now identical to V x, y, z . We can also write the wave equations for the field vector potentials in the plane transverse to the propagating direction. 45b yez D yet x, y eš where h and e are the corresponding propagation constants, with the š signs indicating the Ýz-directions of propagation, respectively. 47b h e 2 x, y C kc,h h 2 x, y C kc,e e where yht x, y and yet x, y are the transverse magnetic and electric vector potentials, respectively. h x, y and e x, y are the longitudinal components of the magnetic and electric vector potentials, respectively, and are referred to as the magnetic and electric scalar potentials.
44 is called the Wronskian of y1 and y2 at x D x 0 . The solutions ˛1 and ˛2 in Eqs. 43) exist and are unique when the Wronskian differs from zero, which is always valid unless y1 and y2 are linearly dependent. The closed-form solution of the Green’s function is now obtained from Eqs. 45 It is apparent that this closed-form Green’s function is only useful if the solution to the homogeneous differential Eq. 36) can be found within the interval [a, b]. As a demonstration of the procedure for finding the Green’s function in closed form, we consider a shielded microstrip line as shown in Fig.