Antenna design traditionally involves a trial-and-error process consisting of building a series of prototypes and testing their performance while iterating to an optimized design. More recently, antenna designers have begun to simulate antennas as software prototypes, making it possible to analyze alternative designs in a fraction of the time required by physical prototyping. But normally this approach still follows the iterative process that was previously used in physical prototyping: model the design, simulate its performance, make changes to the model in an effort to improve the design, then start the process over again by simulating the new design. A few companies have adopted a new approach, in which a wide range of design parameters are evaluated in a single analysis run with the goal of exploring the entire design space and selecting the optimized design without need for the normal iterative process. As will be shown, this method was used to design the feed network of a WiMAX array and helped achieve full frequency coverage over the band of interest.

The past decade has witnessed the introduction of many new wireless technologies, including Bluetooth, WLAN, 2.5G and 3G cellular telephony, radiofrequency identification (RFID), ultrawideband (UWB) communications, and more. Each new technology requires innovations in antenna design to achieve their full potential; often multiple wireless technologies are combined within a single system, creating further complications. A modern personal computer (PC) may have one or more WiFi, Bluetooth, and cellular antennas in close proximity. In addition to normal antenna design issues, this creates a new range of complex concerns caused by coupling between the antennas.

The traditional approach to designing the antenna involves a trial-and-error process consisting of building a series of prototypes and testing their performance levels while iterating to an optimized design. The biggest problem with this approach is that it typically takes about a month to design, build, and test each prototype. A considerable number of iterations may be required to meet design requirements and more are generally needed to optimize the design. Another problem with this approach is that it is usually impossible to achieve the final installed environment on the bench. It usually becomes necessary to perform additional rounds of design iterations late in the design cycle. This sometimes means that the product launch may have be held up for antenna development, with the potential for losing a substantial amount of revenues or even, in a worst-case scenario, missing the market window that the product was intended to address.

What follows is an example of a newer antenna design approach in which the initial concept design is modeled and simulated and then key design parameters are replaced by variables. The user defines ranges for each variable and the simulation engine creates models and performance predictions for every possible combination of variables. The time required to optimize the design is substantially reduced because rather than individually creating each design the user need only define the design space of interest and pick the best design from the alternatives created by the parametric simulation process.

The purpose of this project was to design a WiMAX antenna array to cover the band from 3.4 to 3.65 GHz. The wavelength is (2.998 x 108)/(3.4 109) = 8.818 mm. The design strategy-is to have a central feed with equal length distribution to each patch so that the elements radiate in phase. The network is fed at its center with a 50-Ω coaxial probe, connected to the center of a 100-Ω line. Each end of the line ends in a quarter-wave transformer that transforms the 100-Ω impedance to a segment that splits into two lines, each feeding a patch antenna element.

The first basic step in the design process is to calculate the edge impedance of the patch and match it back through the transformer to the 50-Ω line through the feed network. This will be done using a formula-based transmission-line calculator, but could also be performed with trace impedance formulas from basic microwave theory. Another constraint is that the four radiating patches must be sufficiently separated to avoid interfering with each other.

The thickness of the substrate is 1.6 mm and the substrate material is selected for a relative dielectric constant (εt) of 3.58. The next step is calculating the edge impedance of the patches using approximation formulas. A thin halfwavelength patch has a corrected side length of:

L = 0.49t)0.5> = 22.18 mm

All trace impedances must be matched to the coaxial probe feed so there is no need to do an insert feed at the element. By selecting a 25-mm-wide patch, the approximate edge impedance can be calculated from the length (L) and width (W) as:

Zedge = 90t/(εt - 1)>(L/W)2 = 100 Ω

A simple RF calculator was used to calculate the width of a 100-Ω feed on the desired substrate:

W100 = 0.852 mm

With the edge impedance known, the other impedances and microstrip widths can now be calculated. Two 100-Ω patches will be connected to the feed point from above and the other two patches connected to the feed point from below. Each connection trace segment must have the impedance (Z):

Z=100/2 = 50 Ω

The 50-Ω microstrip width is:

W50=3.497 mm

In addition, a quarter-wave transformer will be used to connect the 50Ω segments at each point of the 100-Ω line:

Zt = (100 x 50)0.5= 70.07Ω

W70 = 1.96 mm

Lt = 11.9 mm

Figure 1 shows the resulting feed network.

The next step is to evaluate the performance of this initial design. Rather than taking the time that would be required to build a prototype, the antenna will be simulated as a software prototype using MicroStripes software from Flomerics (www.microstripes.com). This software package uses the Transmission Line Matrix (TLM) method for solving Maxwell's equations in the time domain. MicroStripes solves for all frequencies of interest in a single calculation and therefore captures the full broadband response of the system in one simulation cycle. The TLM method creates a matrix of equivalent transmission lines and solves for voltage and current on these lines directly. This approach uses less memory and central-processing-unit (CPU) time than solving for electric (E) and magnetic (H) fields on a conventional computational grid.

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The initial antenna design was evaluated by using the simulation program's ACIS-based modeler to construct the WiMAX antenna geometry from primitive shapes. In addition to the feed network described above, this involved creating patches at the end of each trace and a substrate and a ground plane with a size of about 110 x 100 mm, chosen for clearance to the edge of the patches, in order to reduce sidelobes. The complete design is shown in Fig. 2. The computational domain was expanded by 30 percent of the model's largest dimension to place the external absorbing boundaries in the far-field region. The simulation is then equal to a measurement of E and H fields in an anechoic chamber. The software then automatically generated the mesh, snapped it to the geometry, and refined it around edges in curved areas and dielectric regions.

A common problem with time-domain simulation is that the fine cells bleed out to the boundary of the computational domain. This greatly increases the number of cells in the mesh and leads to large memory consumption and long computational times. The TLM software, however, has an octree subgrid meshing algorithm that progressively and automatically lumps together computational cells in regions remote from the geometric detail. The software's multigrid meshing capabilities enabled fine cells to be localized to the space occupied by the antenna while the surrounding free-space region was modeled using a coarser mesh. The ultimate size of the lumped cells is limited only by the local permittivity, permeability, and the highest frequency of interest. This enables critical but electrically small detail to be captured with an exceedingly high-resolution mesh, without having a significant impact on the global cell count. The initial design had 801600 cells reduced to 71313 by the octree algorithm. The lumped cells are visualized as yellow regions in Fig. 3.

The simulation was excited with a broadband Gaussian pulse injected into the coaxial antenna port; the time signature was captured by stepping through time. Fast Fourier Transform (FFT) processing of this response was used to generate frequency-domain results across the full frequency band of the antenna (Fig. 4). The plot in the upper left-hand corner of Fig. 4 shows gain on a threedimensional (3D) diagram while the graph in the upper right-hand corner shows the gain over a single cross section of the 3D plot. The plot in the lower left-hand corner shows the surface current plotted on the conducting bodies and the electric field on a plane near one edge of the patches. Finally, the chart on the lower right-hand side shows the return loss of the antenna plotted against frequency. The return-loss plot illustrates that that rather than meeting the goal of operating over the entire WiMAX frequency range, the design is actually effective only over a small segment of the band. The return loss is lower than 6 dB only over the range from 3.38 to 3.48 GHz.

The first attempt to improve the frequency response of the antenna was simply to round off the sharp corners of the lines leading to the patches to reduce unwanted reflections. This provided a minor improvement but not nearly enough to meet the design objective. The next step was adding another section to the transformers to reduce the mismatch that each transformer corrects and thus provides broader frequency coverage. A formula-based calculator for multisection transformer design was used to provide the initial dimensions for a new transformer. In the initial broadband design when the complete antenna was simulated, the simulation results showed the antenna provided two separate frequency bands at opposite ends of the WiMAX band as plotted in Fig. 5.

Clearly the design of the new feed network needed to be better matched to the input impedance and resonance frequency of the current patch element design or opposite. Using conventional simulation methods, this would involve a trial-and-error process that might involve changing the lengths, widths, and angles of the transformer sections and patch elements until satisfied with the results. This approach is considerably more efficient than building and testing prototypes but it still takes a considerable amount of time to construct each model and wait for the simulation results. With multiple design parameters to consider, the number of simulations required to fully interrogate the design space grows geometrically. For example, investigating four different widths, four different lengths, and four different angles of all segments in this feed network would require a total of 4096 different simulation runs.

In this application example, the design process was streamlined by taking advantage of a software feature that allows users to substitute variables for design parameters. Users model their concept design, identify geometric entities as variables, pick upper and lower limits for each variable, and select a step size. The software then generates as many simulationiterations as are required to completely explore the design space defined by the user. The results of each simulation are plotted on a single graph so users can quickly determine which design parameter values provide optimal performance. In this case, the lengths of the two different transformer sections were varied with three different values for each variable. The software generated a design for each combination of variables and produced the frequencydomain results for each design.

When the simulation runs were concluded, it was easy to evaluate the results to compare the performance of the different designs. The best case feed network design (Fig. 6) provided excellent gain and returnloss values (Fig. 7) when combined with patch antennas that were tuned to the desired center frequency by also using the software's variable sweep functionality. At this stage, the return-loss values for the entire WiMAX band were safely beyond the 6-dB minimum requirements. The simulation results also indicated the potential that additional parametric design iterations of the lines connected to the patches might provide further improvements. The results in Fig. 8 show that considerable sidelobes exist in the latest design iteration but not in the initial narrowband antenna design. A reasonable approach to eliminate these sidelobes would consist of setting up another series of parametric simulations that involve changing variables such as the size of the ground plane and the distance between the upper and lower pair of patches.

This example demonstrates how computer simulation can help engineers improve antenna performance by evaluating many more potential designs than would be possible using traditional bench methods. Simulation has the potential to improve the reliability of antennas by making it possible to evaluate a wide range of potential configurations prior to installation in order to evaluate and optimize system performance inexpensively without disrupting operations. The latest advance enables a series of simulations to be run automatically while varying one or more design parameters over a user-specified range. This feature speeds up the design process by making it possible to, for example, quickly consider a wide range of locations and determine the ideal feed network dimensions.