Far-field radiation pattern. In this problem we will use the code from Problem 4.7, modeling a half-wave dipole antenna. Modify this code to include a PML as in Problem 9.11. Now, include a near-to-far field transformation boundary around the antenna using the time domain implementation of Luebbers et al. presented in this
(a) Measure the far-field pattern ∼100 wavelengths from the antenna, at 100 locations equally spaced in θ. Since the antenna is symmetric in φ, there is no reason to measure the radiation pattern in more than one φ direction. Compare this far-field pattern to the near-field pattern measured in Problem 9.11.
(b) Repeat (a), but include the thin-wire approximation around the antenna. Does this affect the far-field pattern? Why or why not?
Problem 9.11
Radiation pattern of a monopole. Modify your code from Problem 7.4, the monopole above a ground plane, to include a PML on five of the six boundaries. The lower boundary should still be PEC, and the monopole antenna should be modeled using the thin-wire approximation. Measure the radiation pattern of the antenna about ∼3 wavelengths from the source.
Problem 7.4
Thin-wire antenna in 3D. Repeat Problem 4.6, exciting a half-wave dipole and monopole in a 3D Cartesian grid; however, this time, model the antenna using the thin-wire approximation for the conductive parts of the antenna. Compare the radiation patterns in the near field; how do they compare to the method in Chapter 4?
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.
