In this example, FDTD is used to simulate a coaxial-fed rectangular patch antenna mounted over an infinite PEC ground plane, in which the antenna’s return loss, directivity, and far-field patterns are found with the help of the Directivity analysis group. More details on setting up the simulation and helpful tips can be found in the Quarter-Wave Monopole example.
The rectangular patch antenna is a low-profile antenna composed of a patch of metal mounted onto a substrate that is backed by a metallic ground plane. It is used in applications from MHz to THz frequencies when size, weight, cost, reliability, and aerodynamic performance are constraints. When mounted on electrically large objects, such as the hull of an aircraft, the ground plane is considered as infinitely large, and, at low enough frequencies, a perfect electric conductor (PEC). In these situations, the patch antenna is excited from the bottom using a coaxial pin extending out of the ground plane and terminating on the top patch. This can be seen in the above figure.
Details on how to design the patch antenna and its coaxial feed can be found in Balanis . Here, the patch antenna is designed according to Examples 14.1, 14.2, and 14.3 in Balanis . The theory relies on a transmission-line and cavity model to represent the patch antenna as an array of two radiating apertures of width (slots) separated by a transmission line of length L. When the patch’s dominant TMx010 is excited, the radiation from each slot along the patch’s width add constructively in-phase (hence termed radiating slots) while the radiation from each slot along the length add destructively out of phase (hence termed non-radiating slots). The total directivity pattern is found by relating the fields on the slots to an equivalent current density, in which the radiation equation is used to find the far-fields with the assumption that the ground plane is infinite and the substrate is truncated at the edge of the patch.
The patch antenna is constructed from a 2D rectangular sheet of width (y span) 11.86 mm and length x span) 9.06 mm that is mounted onto a rectangular substrate of 11.06X13.86X1.588 mm possessing a refractive index of 1.48. The substrate is backed underneath by a ground plane constructed from a 2D rectangular sheet, which extends out of the simulations domain’s X-Y plane, rendering infinite.
Note: Mesh order between 2D and 3D objects
A pair of concentric rings form the coaxial waveguide’s interior vacuum region and outer PEC conductor. These rings surround the inner PEC conductor which is modeled using a circle. The coaxial waveguide extends out of the bottom (z min) FDTD boundary. To have a characteristic impedance of 50Ω at the desired frequency, the x position of the feed must be optimized and the inner and outer conductor radius of a=0.29107 m and b=1 mm are chosen.
Since the coaxial waveguide’s model intersects the ground plane at z=0 and its inner conductor passes through the substrate, we need to manually specify the mesh override for these objects. This allows us to ensure the correct structure is being simulated and that the inner conductor is not shorted to the ground plane. The mesh order is assigned as follows: inner conductor = 1, outer conductor =2, ground=3,substrate=4 (and coax dielectric). The above index monitor shows the surface conductivity in the X-Z plane at y=0 and verifies the patch is being properly fed by the coaxial waveguide
A port is placed near the bottom edge of the simulation region which is used inject and measure the coaxial TEM mode over a frequency range of 8 GHz to 12 GHz.
Mesh override region is placed to the patch. This ensures that the near fields are sampled to a high enough resolution to give accurate far field results. The mesh accuracy of 4 is used for the rest of the simulation region. Note that this override mesh has exceptionally high accuracy which is not usually necessary for other applications.
PML boundaries are specified on all boundaries to be at least λ0/4 thick such that no reflections will occur outside of the Directivity analysis group’s monitors which would skew the far-field results. To speed up the simulation, symmetry boundaries are specified on the y min boundaries.
The Directivity analysis group is used to setup the monitors and find the directivity of the patch antenna. In the analysis group’s Setup Variable tab, the x, y, and z span are chosen such that the monitors are at least λ/4 away from the edge of the patch antenna. It should not be too close to PML. Since an infinite ground plane is used here, the inf gp variable is set to 1. Also, since the coaxial feed does not pass through any monitors, we set the source window variable to 0. The down sample variable is set to 1, so that no down sampling occurs on the monitors.
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 for RF application this option be turned on in antenna applications so as to improve the calculation of radiation efficiency.
Results and Analysis
The mesh settings have exceptionally high accuracy and thus the simulation will take longer simulation time. To have a fast simulation, users can increase the override mesh size.
After opening the rectangular_patch.fsp file and running the simulation, the rectangular_patch.lsf script is used to generate the patch antenna’s performance and radiation properties. This script is similar to the one found in the Quarter-wave Monopole example and first finds the reflection seen from Port 1 (S11) of the coaxial line (return loss=-20log10|S11|).
The simulated patch antenna’s resonant frequency of 10.08 GHz is within 0.8% of the theoretical resonance of 10 GHz. This level of match is quite excellent, since the theory does not account for the reactive input impedance. In fact, we see that the input resistance reaches its peak neat 10.08 GHz. The antenna’s input impedance (Zin) is shown in the figures above, which has a 50.19 Ω characteristic impedance at the resonance frequency, very close to the theoretical value of 50 Ω.
Note : Simulation results and mesh size
These results were obtained with a finer mesh size setting in the Patch Mesh. If mesh size increases (mesh accuracy decreases), the resonance frequency will change.
The directivity analysis group is used to calculate the farfields at the resonant frequency. The farfield θ and ϕ resolutions are set to 1 deg and 10 deg, respectively, which accurately captures the directivity’s variation the θ and ϕ planes. The analysis can be sped up further by lowing the ϕ resolution without sacrificing accuracy. The directivity components Dθ and Dϕ and the radiated power are then returned in the analysis group’s result view.
The script then generates plots of the antenna’s directivity in the E-plane (X-Z cut) and H-plane (Y-Z cut) and compares them to theory . In the E-plane, the Dθ polarization between theory and FDTD general match but exhibits differences due to a number of assumptions in the theory. Nevertheless, it is encouraging that the Dϕ polarization is well below -80 dB in the E-plane, matching the theory. The asymmetry in the FDTD directivity is due to the feed which is positioned asymmetrically along the E-plane. This asymmetry is not accounted in the theory. Furthermore, the presence of the substrate over the ground plane in FDTD alters the magnitude and phase of the image and breaking down the assumptions in the theory’s use of image theory to derive the directivity. This has the largest effect near grazing (θ=90deg) in the E-plane.
In the H-plane, the Dθ polarization obtained from FDTD and theory are extremely close and within 0.2dB of one another. This result is expected since the H-plane is unaltered by the presence of the substrate. Furthermore, the asymmetry of the feed does not affect Dϕ. However, it does introduce a significant Dθ polarization in the H-plane.
Simulation results generated in the script prompt using the script file rectangular_patch.lsf.
============Radiation Performance============== Resonant Frequency: 10.08 GHz Input Power: 1.44 nW Accepted Power: 1.44 nW Radiated Power: 1.44 nW Radiation Efficiency from Input Power: 100 % Radiation Efficiency from Accepted Power: 100 % Maximum Directivity: 7.95 dB Total Realized Gain: 7.95 dB
The radiation performance of the patch is displayed in the script prompt. 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.The input power and accepted power are equal due to the extremely small value of S11 at the resonant frequency. As a result, both definitions of radiation efficiencies are roughly the same value. Comparing the radiation efficiency to the radiation efficiency versus substrate height curves in Fig. 14.27 of Balanis  reveal the efficiency obtained from simulation is comparable and within a few percent to theory.
- C. A. Balanis, Antenna Theory and Design, 4th Edition. John Wiley & Sons (2016).