Reference no: EM132407695

ELG 5104/EACJ 5401 Electromagnetic Waves Theory and Applications Assignment

School of Electrical Engineering and Computer Science - University of Ottawa, Canada

Question 1 - Consider the case of a lossless distributed circuit (TL) that has series capacitance and shunt inductance, as depicted by an infinitesimal section of such a circuit in Fig.1(b). This is the usual case, as discussed in Chapter 3 of the course notes, specifically a lossless version of the latter. By carefully considering γ, determine (show details) the phase and group velocities of such a TL. Then consider a TL whose infinitesimal section is depicted in Fig.1(a). Determine (show details) the phase and group velocities of such a TL. Compare, and comment on, the phase and group velocities in the two cases.

Question 2 - We wish to excite only the 2^nd natural mode of a homogeneous 1D resonator at some frequency ω. Determine what distribution of impressed current density could be used to do this. You need not worry about the practical aspects of actually setting up such a current density.

Question 3 - Does loss in a medium change the velocity of a plane wave that is propagating through the medium? Discuss in depth, and demonstrate quantitatively.

Question 4 - Consider the uniform rectilinear parallel plate wave-guiding structure in Fig.2. The top and bottom walls are PEC, on which the boundary condition is of course n^{^} x E^- = 0. It does not have sidewalls, but the boundary condition n^{^} x H^- = 0 must be assumed on the sides. In other words

n^{^} x H^- = 0 over (x = 0, 0 ≤ y ≤ d)

and

n^{^} x H^- = 0 over (x = w, 0 ≤ y ≤ d)

The medium between the top and bottom walls has properties ε and μ.

Solve Laplace's equation to find φ(x, y), e_t^-(x, y) and h_t^-(x, y) of the TEM mode of this waveguide structure. Also write down E^-(x, y, z) and H^-(x, y, z).

You must work out what the boundary condition is for φ(x, y) on the magnetic walls before finding your solution, and then use this in finding the above-mentioned solution.

You must use the notation of Section 10.4.