2D cylindrical coordinates. Create a 2D cylindrical simulation, choosing appropriate parameters ?r, ?z, and ?t to model the same wavelength as in Problem 4.6 above. Drive the simulation with the same two sources as in Problem 4.6, and compare the radiation patterns. How do the results differ from the previous problem? How does the simulation time compare?

Problem 4.6

Antenna modeling. In this problem, we will use the 3D code from the previous problem to model two types of antennas. For each of these examples, measure the radiation pattern by monitoring points at a constant radius from the center of the antenna. Make the simulation space 100 × 100 × 100 grid cells, and use 20 grid cells per wavelength; note that this implies the simulation boundaries are only 2.5 wavelengths from the antenna, so the results will be near-field radiation patterns.

(a) Model a half-wave dipole, similar to Figure 4.9, by making five grid cells perfect conductors above and below the source point. Drive the antenna with a sinusoidal source at the appropriate frequency.

(b) Model a monopole antenna above a ground plane by placing the source just above the bottom of the simulation space, and five grid cells of PEC above the source. Compare the radiation pattern to that found in (a). In both cases above, watch out for reflections from the simulation boundaries: you will need to compute the radiation pattern before reflections corrupt the solution. Why does this problem not work with a small dipole, one grid cell in length? We will revisit and solve this problem in Chapter 7.