FDFD method in 2D. Repeat Problem 9.9, the system of scatterers with a PML boundary, in the FDFD method using the wave equation for z. Derive the simulation with a sinusoidal source with a wavelength of 0.5 m. Measure the field distribution throughout the space; evaluate the reciprocity of the simulation by alternating points A and B as source and receiver.
Problem 9.9
Problem 7.9
Horn antenna. Modify your 2D TE simulation code to excite a horn antenna, as illustrated in Figure 7.8c. Excite the antenna with an y source at the left end of the antenna, with a given voltage across the antenna plates (note that this 2D horn is really the opening of a 2D waveguide).
(a) Measure the antenna radiation pattern some distance from the antenna at a range of frequencies. (You can do this either by exciting a Gaussian pulse, or by running the simulation multiple times with a sinusoidal source at different frequencies.) Vary the length l2 and the angle θ of the horn antenna and compare the results.
(b) Measure the characteristic driving-point impedance of this horn / waveguide combination, and compare to the impedance of the waveguide alone in the previous problem. Comment on the effect of the horn in this context. You will need to take special care when handling the boundary conditions on the angled section of the horn, since the "normal" and "tangential" fields are no longer along grid edges; this will result in a stair-stepped horn aperture.
