In this example, FDTD is used to simulate a leaky-wave antenna (LWA) implemented as a longitudinal slit in the side-wall of a metallic rectangular waveguide. The radiation pattern and radiation efficiency are investigated using the Directivity Analysis group. This example demonstrates how to modify the Directivity Analysis group to account for the power carried in the input and output ports of the rectangular waveguide which passes through the directivity group's monitors. This allows for an accurate calculation of the total radiated power.
The LWAs consists of a guiding structure that is properly terminated with a matched impedance to minimize reflections. The LWA supports a fast traveling wave that continuously radiates power as it propagates on the guiding structure. The angle of the main beam is determined from phase matching of the guided wave to free space and scans with frequency. The earliest forms of leaky-wave antennas was constructed from a closed rectangular waveguide containing a long uniform slot along its longitudinal axis such as shown in the above figure. The slot is introduced into the narrow waveguide wall to allow for continuous leakage of its fundamental TE10 mode which radiates a conical beam about the z-axis at an angle given approximately by cos(θo)=β/k0. Using image theory and the equivalence principle, the radiation can be approximated as that of a z-directed magnetic line current (Balanis ).
This example utilizes a modified directivity analysis group to find the radiation features of a uniform LWA. The frequency scanning of the LWAs radiation pattern is presented.
The simulation file leaky_wave.fsp contains the simulation model for this example. It consists of a vacuum filled rectangular waveguide of width b=15mm and a=8mm with a wall thickness of 2mm. These are constructed using the Rectangle structure. A longitudinal air gap of length l=150mm is placed on the side wall using a rectangular structure with a higher mesh override region than the metal walls, and the rest simulation region has a mesh accuracy of 2.
To excite the rectangular OEWG probe’s fundamental TE10 mode and measure its scattering parameters, two ports are placed inside the waveguide’s PEC walls and are spaced a distance L=165mm apart. The TE10 mode is injected over a frequency span from 11 to 15GHz, which is above the TE10 mode's cutoff frequency of 9.93GHz.
PML boundaries are specified on all boundaries with the Custom profile for RF applications that was specified in the methodology page. These ensure no reflections will occur outside of the Directivity analysis group’s monitors. To speed up the simulation, an antisymmetry boundary is specified on the z min boundaries.
Note : Advanced Option - Snap PEC to yee cell boundary
When the "snap pec to yee cell boundary" option is enabled in the FDTD object's advanced option tab, the interface of any PEC is forced to align with the Yee cell boundary (more details can be found in Simulation - FDTD). It is recommended that this option be always turned on in antenna applications so as to improve the calculation of radiation efficiency.
The directivity analysis group is used to setup the monitors and find the far fields of the LWA. In the analysis group’s Setup Variable tab, the x, y and z spans are chosen such that the monitors are close to the waveguide's metal walls. The source window is turned on and is set to be the same size as the antenna's feeding port. The directivity analysis group in this example is modified to account for the waveguide's output passing through the x2 monitor. This is achieved by using an output window which overlaps the x2 monitor. Details on how to setup the window can be found in the Directivity page. Users need to check that the power going through the directivity monitor box is the same as the power going through feed to the desired accuracy to make sure that the computed radiation results are accurate.
Results and Analysis
After opening up the FDTD file leaky_wave.fsp and running the simulation, the leaky_wave.lsf script is used to generate the results. With the current mesh settings, the simulations take a few minutes to run.
The script first generates the LWA's scattering parameters, which are shown in the above figure. Due to the presence of the gap, the transmission decreases in some frequency spans. As will be shown shortly, these bands will correspond to increases in the LWA's radiation efficiency.
The above radiation pattern of the LWA is generated by the script at three frequencies in the band at θ=90deg (please refer this page for the definitions of theta and phi). It is clear that as the frequency increases, the angle of the main beam scans towards 0deg because now it is excited from Port1. As typical with uniform LWAs, the beam cannot be scanned near broadside because this corresponds to the waveguide's TE10 cutoff frequency. Also, the beam cannot be scanned to close to endfire due to the excitation of higher order modes at the significantly greater frequencies.
Simulation results generated in the script prompt using the script file leaky_wave.lsf:
|Frequency (GHz)||Directivity (dB)||Radiation Efficiency (%)||Total Realized Gain (dB)|
After the script ends, the radiation performance of the LWA is generated in the script prompt. It is observed that the LWA has a directivity of approximately 14dB and a radiation efficiency of around 50% which can be further improved by increasing the length of the gap. In calculating the radiation efficiency, the power carried into and out of the waveguide is included accounted for in the radiated power quantity. As such, we see that an increase in transmission through the waveguide (S21) corresponds to a decrease in radiation efficiency. Please refer the script file for details for those quantities, which is at the end of the script. Definitions and explanations of those quantities can be found in the Methodology page.
 C. A. Balanis, Modern Antenna Handbook, 4th Edition. John Wiley & Sons (2011).