The finite-difference time-domain (FDTD) method solves the coupled Maxwell’s curl equations directly in the time domain by using finite time steps over small cells in space. The method reduces the differential equations to difference equations that can be solved by sets of simple equations. The method alternates between the electric and magnetic fields solved at locations a half-step apart because central differences are used to approximate derivatives. A 1966 paper by Yee described the basic method that many authors have improved upon, but the original method remains the approach of choice.
FDTD can solve many types of electromagnetic problems, of which antenna analyses are only one type. Computer memory and speed limit the size of problems that can be solved, but larger and larger problems can be solved as the cost of computing keeps reducing. Besides antenna problems, the method is applied to microwave circuits, biological interaction with electromagnetic waves, optics, and radar cross-section problems. The number of uses expands every day. The method allows each cell to be made of different materials, leading to the solution of volumetric complex structures. The solution of the equations is robust and the errors are well understood.
Currently, the method solves moderately small antenna problems on the order of a few wavelengths. Of course, faster and larger computers can solve larger problems, especially if the analyst has patience. FDTD handles microstrip antennas with their complex layering of dielectrics, including a finite ground plane without the use of complex Green’s functions required of frequency-domain solutions. The interaction of antennas with the near environment, such as the effect of the head on cellular telephone handsets, can be solved. In this case the complex electromagnetic properties of the head can be described as cells each with different electrical properties. In addition to giving a solution to the radiation pattern and allowing characterization of the communication system, it can provide insight into the radiation safety concerns of users. The method handles the solution of the interaction of antennas with the human body in a straightforward manner for prediction of biomedical applications, such as electromagnetic heating for cancer treatment.
Learning to apply the technique, whether formulating your own routines or using a commercial code, will yield insight for design. The method can produce time-domain animated displays of the fields that show radiation centers and where the fields propagate, but the user must learn to interpret these new displays. It will be worth your effort to learn this task. The time-domain responses using impulse signals can produce solutions over a wide band of frequencies when converted to the frequency domain using the discrete Fourier transform (DFT). The only drawback is the computer run time required. |
