Design Optimization of Miniaturized Antennas
Overview
The growth of wireless communications networks and navigation systems requires the design of innovative miniaturized antennas that can be implemented at low cost. Designing small integrated antennas requires a deep understanding of the trade-offs between the demanding specifications, the restrictions on the available space where the antenna is to be placed, and the cost of the implementation.
PCB antennas can provide the optimal solution, but this often comes at the cost of higher design complexity. The design space of printed antennas is very large in terms of geometric properties and variety of the available materials. An almost infinite number of different choices are possible, often leading to conservative strategies based on previous designs.
In this webinar, we will show how Antenna Toolbox can help you with the design of innovative antennas. Using different examples, we will demonstrate how fast analysis techniques enable design space exploration and antenna optimization for different applications. By including the estimation of losses in dielectric and metal materials, you will see how to improve the antenna efficiency and examine implementation trade-offs. We will show how to explore the design space manually and through optimization using surrogate techniques. At last, we will rapidly prototype the antenna for testing its performance.
Highlights
- Metal catalog
- Efficiency estimation
- Optimization
About the Presenter
Dr. Giorgia Zucchelli is the product marketing manager for RF and mixed-signal at MathWorks. Before joining MathWorks in 2009 as an application engineer focusing on signal processing and communications systems with specialization in analog simulation, Giorgia worked for two years at NXP Semiconductors on mixed-signal verification methodologies. Before then, she worked for Philips Research, where she contributed to the development of system-level models for innovative telecommunication systems. Giorgia has a master’s degree in electronic engineering and a doctorate in electronic engineering for telecommunications from the University of Bologna. Her thesis dealt with modeling high-frequency RF devices.
Recorded: 27 May 2021
Welcome to this MathWorks presentation on design and optimization of miniaturized antennas with MATLAB.
My name is Giorgia Zucchelli, and I've been with MathWorks since 2009, when I started as an Application Engineer here in the Eindhoven office in The Netherlands. Since 2013, I am the Technical Marketing Manager for MathWorks RF and mixed-signal product areas.
If you have any questions concerning this presentation or related topics, such as RF and mixed-signal space, please feel free to directly contact me via email. You can see my email address here on the slides
In the next half hour, using MATLAB examples, we will describe how you can use MATLAB for antenna design.
And we will start by choosing the antenna geometry, then we will discuss how you can shrink the size of your antenna. We will use, for example, a high permitivity dielectric materials. And we will also increase the fidelity of the antenna model by including conductor losses.
We will also see how optimization techniques can be applied to improve the antenna performance. And when the finalized geometry has been determined, we will discuss how to generate Gerber files to fabricate printed antennas.
And finally, we will conclude this presentation, and share some additional information for you to get started.
Miniaturized antennas are a requirement for wireless portable devices, such as communication, localization, or power transfer systems.
There are a number of techniques that allow you to reduce the size of an antenna. This might include a structural modification, or using lumped component loading, or make use, for example, of high permitivity materials.
For example, you can reduce the size of an antenna using slots, slits, meanders, and other geometries-like factors.
However, often, decreasing the size of an antenna results in a direct reduction of the bandwidth and efficiency. So as an antenna designer, we need to evaluate the trade offs between the antenna size and its performance.
In this presentation, we will introduce MATLAB for the design of miniaturized antennas and optimization. Before we go through the specific workflow details, however, let's start with a simple example.
The MATLAB Antenna Toolbox helps you with the design of antennas using electromagnetic analysis techniques. If you are not an EM expert, or if you are an EM expert but have not used Antenna Toolbox, you can start from the Antenna Designer app.
The Antenna Designer app provides an intuitive interface that guides you through a typical antenna design and analysis workflow.
Let's start with a new design. You can select an antenna configuration from the control elements, each parameterized in geometry. For example, we can choose a horn, different patch microstrip configurations, or a fractal antenna.
In this case, we choose a fractal Koch antenna and design it to be resonant at 2 gigahertz. On the left, we see the geometric properties of the antenna. In this case, the shape is constructed with two fractal iterations.
We set the frequency range of the analysis to be between 1 and 3 gigahertz, and computed the antenna impedance to verify the resonance frequency. The Antenna Toolbox uses the method of moments technique to analyze the antenna.
As you can see, the EM analysis is executed very rapidly. We can verify that the internet is resonant around 2 gigahertz where the reactants is zero.
Additionally, we computed the S-parameters of the intent to verify the matching bandwidth. We can zoom in the region where S11 is smaller than 10dB, and we can estimate that the bandwidth is approximately 100 megahertz.
We can also plot the far-field radiation pattern at 2 gigahertz, and see that the antenna directivity is 1.93 dBi. To this point, the antenna metallization used in the analysis has been a perfect electrical conductor, or PEC. As such, conductor losses have been neglected.
We tile our figures so that we can view all of the antenna analysis plots simultaneously. Let's now evaluate what happens when we change the number of iterations for the creation of the fractal shape.
We start from one. Notice that the antenna length does not change. However, with the lower number of iterations, the geometry simplified, while the resonant frequency and the bandwidth increase.
As we increase the number of iterations to two, and then to three, we see that the geometry becomes more complex, the resonant frequency and bandwidth are both reduced, while the far-field pattern and peak directivity remain almost unchanged.
We can increase the number of iterations up to four, which results in a meandering structure. The analysis time for this more complicated structure is increased. However, you can still get the result in a matter of seconds.
You can now intuitively understand how increasing the number of fractal iterations is a technique to miniaturize antennas, as it reduces the resonance frequency at the cost of a narrower bandwidth.
For this example, we evaluate the performance of a fractal Koch antenna that makes use of three iterations. The resonance frequency is 1.8 gigahertz, and the resulting antenna directivity is approximately 1.89 dBi.
We can now determine the impact of a metal material with finite conductivity. There is a readily available catalog of metals that include the most common conductive materials such as copper, aluminum, gold, silver, and others to choose from.
Let's see what happens when we change the electrical conductor to copper. The analysis is still very fast, thanks to the method of moments. We noticed that the resonance does not significantly change. However, as a result of the conductor losses, the bandwidth has increased slightly.
Let's repeat the analysis in case you missed the change in the S-parameter plot. Also note that when finite conductivity is specified, the peak value of the far-field pattern is reported as gain, rather than directivity.
The gain value includes the finite conductivity losses. As expected the peak gain is reduced, and is now approximately 1.68 dBi and 1.8 gigahertz.
If we zoom in to the antenna impedance plot, we see that the antenna is resonant at 1.8 gigahertz, but it's not perfectly matched to 50 ohms. This can be improved with a machine network, or by adding a lumped component on the antenna surface.
To demonstrate what happens when we add a lumped component on the antenna surface we added 20 ohm resistors at the antenna feed point. The real part of the impedance is now 50 ohms, as desired, and the bandwidth has also increased and exceeds 100 megahertz.
Let's pause here for a second, and let's recap how you can use MATLAB and Antenna Toolbox for antenna design.
Antenna Toolbox is your one stop shop for antenna and the array design in MATLAB. It provides a catalog of elements to rapidly get started, select, and analyze different antenna configurations.
It also includes the method of moments, along with other EM solvers, to analyze antennas.
You can also analyze the impact of installing an antenna on a large platform, such as a plane or a car. The same approach can also be used to compute the radar cross section of a target.
You can optimize the antenna performance using surrogate optimization methods based on machine learning techniques. We will see this. And you can also fabricate printed circuit board antennas by generating Gerber files.
And you can also integrate your antenna into system simulations. An example of this is where you want to include the behavior of the [INAUDIBLE] transceiver, so as to model and evaluate hybrid performing systems.
And finally, you can position the antenna on a 3D terrain, determine coverage, and link performance.
We have seen how the Antenna Designer app can be used for rapidly get started. You define the specifications, choose the type of antenna, and you get an initial design with the correct geometric properties.
You can view the results for both near- and far-field analysis, and then you can iterate on the design. From the app you can also generate MATLAB scripts for a programmatic approach towards design.
The app provides access to a comprehensive catalog of antennas, each with parameterize geometry. In addition to the catalog of antennas, you can also include the impact of reflectors or backing structures with different shapes.
And with each new release of the Antenna Toolbox new antennas are added to the catalog. You can now see here in this slide some of the latest antennas, such as one based on dielectric resonators or Vivaldi architectures.
If you want to design an array of antennas and compute the effect of coupling in between elements using EM analysis, you can make use of the Array Designer app.
The Array Designer app is very similar to the Antenna Designer app. The major difference is that you will find the array catalog next to the antenna catalog.
You can design linear, rectangular, circular arrays. Along with a uniform array configuration you can also analyze conformal structure, even with different antennas. And you can also analyze very large structures using the infinite array approach.
In this snapshot here you see some of the typical array analysis that can be performed with the Array Designer app.
For example, to understand the coupling in between antenna elements, you can compute the far-field radiation pattern either using the method of moments, or by using pattern multiplication of the isolated element.
And you can also compute the pattern for each of the respective elements while embedded in array, and see how ideation elements impact each other.
With the Array Designer app you can also compute the array impedance, the S-parameters, and the correlation matrix. And these are all useful matrixes to investigate coupling effects.
But what can you do if the antenna that you want to design is not part of the catalog? If your antenna is not planar, you can import an STL file-- a CAD format-- to define its 3D geometric shape.
Once you define the feed point you can then analyze the antenna. And this approach can also be used for installation platforms.
If your antenna is planar, you can use geometric shapes to define the metal they are representing, the radiating element. You can specify shapes, such as a rectangle, circle, ellipsis, along with Boolean operations to sum intersect, or subtract.
There is also a unique workflow that makes use of the Image Processing Toolbox, where you can define the boundary of a shape using the photo of an antenna.
Once you define the shape of the antenna you can add a backing structure and specify the properties of the dielectric material that the antenna is mounted on.
Once you've specified the antenna feed point you can then analyze your antenna. In this example, you see an antenna with a rectangular and a circular slot designed using basic shapes.
Again, if your antenna is planar and it has multiple dielectric and metallization layers, or if it makes uses of vias, you can use the pcbStack object. You can either start from a planar antenna in the catalog, imported in a pcbStack object, and further manipulated.
Or you can start with basic geometric shapes, as described before. Or you can import Gerber files that define the properties of each layer of the printed circuit board.
Once in pcbStack, you can define an arbitrary number of dielectric and metallization layers, add vias, and define feed points-- one or more.
Let's now go through a simple example on how you can create a PCB antenna. Instead of designing an antenna in the Antenna Designer app, I'm now going to design an antenna from the command line.
Let's start with designing a circular patch antenna resonating at 2.4 gigahertz. The diameter of a patch is approximately three centimeters. Let's now analyze the antenna impedance between two and three gigahertz, taking steps of 50 megahertz.
We want to modify the antenna by inserting a circular slot in the middle of the patch. The first step consists in importing the antenna element into the pcbStack object.
This operation does not change the physical or electrical properties of the element. But it allows us to modify different properties of the antenna.
The first step consists in designing a circle that represents the notch in the antenna. The circle is smaller than the patch antenna, with a radius of one centimeter.
The second thing that we need to do is to perform a Boolean subtraction of the shape from the top layer of the pcbStack. We can build the resulting antenna element layout, and verify that this is still resonating at 2.4 gigahertz.
We can also view the resulting pattern and antenna directivity. We can now add a dielectric layer to the Stack. For example, we can mount the antenna on Teflon.
By mounting the patch on a dielectric material, we can reduce the antenna height to just one millimeter, and once again view the resulting structure. We can use the same approach also to add additional dielectric and metallization layers.
We can now see that with the addition of a dielectric layer, the resonant frequencies has decreased, which effectively allows us to reduce the size of the antenna.
This brings us to the second part of our presentation. How do we deal with material properties, namely the metallization and dielectric substrates.
As we saw in this last example, Antenna Toolbox provides a dielectric catalog with common dielectric board materials. As the catalog is editable, you can define your own board material by simply providing its relative permitivity and loss tangent.
Increased permitivity of dielectric materials affect the antenna performance. Actually, it reduces the propagation velocity, and therefore it enables the possibility to reduce the size of the resonator element.
With a similar approach, you can also specify the metal material, choosing from the catalog, or by providing your own material specifications, in terms of conductivity and thickness.
You may also want to know that this can be used not only to estimate the efficiency of printed antennas, but also large antennas, such as horns, that are often fabricated with heavy metals, such as brass or steel.
This brings us to the next topic, optimizing the antenna performance. Before we dive into this, let's see an example on how it can be done with the Antenna Toolbox.
From the Antenna Designer app, I start with the design of a fractal island antenna with three iterations, and resonant at 2.4 gigahertz. From the initial analysis, we can see that the antenna directivity is 4.6 dBi.
The impedance match, along with the boundaries of the antenna, is not very good. And the area of the antenna is approximately 30 square centimeters.
The goal of the optimization is to minimize the surface of the antenna, while improving its gain and bandwidth performance. This is not an easy task to achieve via conventional means, as the design space is very large.
We first select our objective function. In this case, we want to minimize the area of the antenna. Then we select the optimization variables that we want to sweep. For each optimization variable we need to provide an upper and lower limit. We can optimize geometric properties, as well as material specifications, along with element values. But in this case, we just choose to optimize the shape of the antenna.
For the length and width, we provide a minimum bound of 10 and max of 50 millimeters, which is slightly smaller than the current value. For the slot length and width, we provide a smaller range-- so one and five millimeters, respectively.
We also enabled the ground plane length and width optimization. We set the bounce to 50 and 100 millimeters, respectively. The ground plane, in this way, will always be larger than the patch antenna.
We apply these changes, and we now specify the optimization constraints. To improve the current gain, which is 4.6 dBi, we set a constraint for the gain to exceed eight dBi.
We add one additional constraint to improve the input match, and set the S11 to be smaller than minus 10 dB. We now apply these constraints.
We also changed the frequency range to fewer points, so in this way the optimization will be faster.
The final parameters that we need to set is the number of iterations for the optimizer. We increase the number of iterations to 300 and enable parallel computing to achieve an additional speed-up. Even if my laptop only has two cores, this is already beneficial.
Let's start the optimization, and as it takes a few minutes, while we wait for the results let's discuss the underlying technology of the optimizer. In the meantime, we can also see the progress of the convergence.
We have seen how to rapidly get started with antenna optimization for the most common use cases. The same optimization capability is also available, by the way, with the Array Designer app.
From the app you just open the Optimization tab. And for the Array Designer app case, actually you will find additional objective functions and constraints that are specifically for array.
Both the Antenna Designer and the Array Designer apps supported the SADEA, or S, A, D, E, A, optimization method. Other global optimization methods could also be used.
The steps to set up the optimization are straightforward. You first choose the objective function. You select the optimization variable, and define their upper and lower bounds. You provide constraints and then let the optimization algorithm do its job.
SADEA is a surrogate optimization method that uses machine learning. Surrogate optimization methods are often used to solve problems that are computationally expensive to evaluate, such as EM analysis. Especially when many design variables are involved, even just a single iteration can be very time consuming.
The other advantage of surrogate optimization methods is that they are not based on gradients, and therefore the probability of finding a local minimum is reduced. Additionally, these methods also work on problems that are non-smooth.
The main idea behind the surrogate optimization methods is that they use a surrogate model for the objective function, and the surrogate model is faster to evaluate.
This surrogate model also gets regularly updated during the optimization. And as a result, fewer EM analysis are required for the optimization of antenna performance.
If your optimisation problem requires a configuration more complex than the one allowed by the app, or if you are an expert in setting up optimization, you can customize the objective function.
And you can use any of the methods provided by optimization or Global Optimization Toolbox. And you will find several examples showing this custom workflow.
We can see now that the antenna optimization is completed. Let's go back to our demo. We see that the progression towards convergence and the results achieved with 300 iterations. We can accept the results and verify the antenna performance.
As you can see, the antenna stayed resonant at 2.4 gigahertz, and the S11 behavior is significantly improved. The directivity of the antenna is also significantly improved. The gain now exceeds eight dBi.
We can change the metal to copper and determine the antenna efficiency. As you can see from the results, the antenna's electrical performance has significantly improved on all fronts. And the antenna size is now smaller than eight square centimeters.
This brings us to the final part of this presentation and Antenna Design workflow. That is to say, antenna fabrication. We have already seen how the pcbStack object can be used for the design of multilayer antennas.
We will now see how it can be used to generate Gerber files for PCB fabrication. The steps are straightforward once you have designed a planar antenna with pcbStack.
First, you select the online PCB service. This is very convenient for inspecting the generated files before sending them to the manufacturer.
Second, you choose the connector, and how it gets connected to the board, whether it gets soldered on top of the board, or on the side of the PCB.
Third, you can generate Gerber files. You'll get all of them in the working directory, and then you can share them directly with the manufacturer. And by the way, this is the same process that we used the MathWorks app to verify many of the designs done with the Antenna Toolbox.
I would like to conclude this presentation by summarizing what we have seen today. We saw how MATLAB can be used for antenna design.
And we examined the drivers behind miniaturization, such as using fractals, slots, and mounting antennas on dielectric materials.
We were able to estimate the impact of conductor losses by using metals with finite conductivity and thickness. We were also able to evaluate how the antenna performance is impacted by the use of dielectric substrates.
We also used surrogate optimization methods to improve the antenna performance, and at the same time, reduce the size.
And as a final step, we discussed how Antenna Toolbox facilitated the antenna fabrication workflow via the Gerber file generation.
With that, I thank you very much for your attention, and I encourage you to try Antenna Toolbox, and MATLAB, and other MathWorks products in your next wireless system design.
I would also like to recommend you to explore the numerous examples that come along with the Antenna Toolbox.
These examples cover many of the topics that we discussed today, but you will also find lots of interesting things that for sure you would like to see. If you have any questions, please don't hesitate to reach out. Thank you again.