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An Intro to Antenna Arrays

Written by Robert Lacoste

Elements, Interference and More

As an expert in RF technology, Robert has deep knowledge about antennas. And, in this era of IoT, his expertise is more relevant than ever. That’s because every wireless device has some kind of antenna, and these antennas can often be the cause of engineering problems. With that in mind, in this article Robert discusses the math, technology and design issues that are basic to antenna arrays.

Welcome to “The Darker Side.” Twenty years ago, I used to describe my area of expertise as “radio frequencies” (RF for short). Then that term became a little dated, and I found I was working in the “wireless” industry for a while. A couple of years later, my wife convinced me that we could attract more customers if we presented ourselves as “connected-objects experts”—and she was right. And more recently we changed once again, and now we’re in the Internet of Things (IoT) business. Of course, over all those years, nothing changed—we still do RF, but the buzzwords of the day can’t be ignored. Another thing that hasn’t changed is that every wireless device has some antennas, and these antennas are the root cause of many headaches. Why? Simply because antennas are not well understood by many electronics engineers.

With the main focus of Circuit Cellar being embedded electronics, antennas as components aren’t a primary focus of this magazine. But I simply can’t leave this subject in the dark. Moreover, the design of embedded systems that have antennas is very much in Circuit Cellar’s wheelhouse.

If you’re a regular reader, you know that I’ve already devoted some articles to antennas. These include “The Darker Side – Antenna Basics” (Circuit Cellar 211, February 2008) [1] and “The Darker Side – Antenna Measurement Made Easy” (Circuit Cellar 327, October 2017) [2]. This month, my goal is to introduce you to an interesting class of antennas: antenna arrays. You will see that these antennas are based on very simple principles, and can have more than interesting applications—even for relatively simple projects. Even if you don’t need such an antenna, I hope you will enjoy learning about this topic. And, as usual, I promise I will not use any complex math—just words and illustrations.

Some basics first: A radio frequency (RF) signal is an electromagnetic wave of a given frequency (F). This frequency can range from kilohertz to hundreds of gigahertz. For example, F is 2.4 GHz for Bluetooth. I’m sure you know that such a wave propagates at the speed of light. Therefore, a Bluetooth transmitter generates a signal oscillating 2,400,000,000 times per second, and this signal travels in the air at the speed of c = 300,000,000 m/s. That means the wavelength in the air—which is the distance between two maximums or minimums of the electric field—is, in this case, λ = c/F = 0.125 m. Very simple math, as I promised. (Don’t be afraid of the Greek letter lambda, “λ” This is just the usual way to name a wavelength.)

Now it’s time to introduce a very basic but fundamental concept: Interference (Figure 1). Imagine you have two antennas radiating an RF signal at the same frequency and at the same power (P). If they are at the same distance from the receiver, then the waves will be in phase and will add. The result will be an electromagnetic wave twice as powerful (2 × P). However, if the two signal sources are not at the same distance, then the waves will not be in phase, and the resulting signal may not be as strong. The worst case is when the signals are exactly out of phase (a 180-degree phase shift). They will cancel out, and the result will be zero. If you look again at Figure 1, you will see that this situation occurs when the distance between the two sources is half the wavelength, or 12.5 cm/2 = 6.25 cm for a 2.4 GHz system, then 3λ/2 and so on.

FIGURE 1 – Two waves cancel out if they have the same power, but are half a wavelength apart

I have presented enough theoretical background to now explain what an antenna array is. This is simply a set of simple antennas—called “elements”—working together as a single antenna and using interferences to improve the performances. All elements are interconnected through a so-called “feed network,” which sets precise phases and amplitudes between the antenna elements. This means the designer tunes these parameters to enhance the radiated power in some directions—thanks to constructive interferences—or to nullify it in other directions. These gain and phase parameters can be either fixed or dynamically modified. More on that later.

So, an antenna array is a kind of directive antenna, in which the antenna pattern is built by an association of several small antennas interconnected by a properly designed feed network. Also keep in mind that a directive antenna focuses the energy in some direction, which means it provides a higher gain in that direction, and so a longer range. I’m talking about transmitters, but keep in mind that nearly all antennas work exactly the same way in transmission and reception. That means that such an antenna array will have exactly the same beam shape in both directions.

An example will be welcome, won’t it? Look at Figure 2 where two identical antenna elements are connected through a feed network, which is nothing more than a power splitter—50% of the input power is sent to each antenna, with the same phase. What is the behavior of the resulting antenna? In the plane perpendicular to the line connecting the two antennas, the waves will be in phase, and the power will be twice the power of a single antenna. This direction is called the “main lobe.” However, in other directions, the interference will not be so powerful, and will eventually cancel out completely.

FIGURE 2 – If the same signal is sent by two antennas, then radiated power will not be the same in all directions due to interferences.

In some other directions there could be local maximums (side lobes). If you are not averse to trigonometry have a look at Figure 3 which provides a little more detail on what’s going on in the case of two antennas. As Figure 3 shows, the phase shift in a given direction is proportional to the distance between the two elements, inversely proportional to the wavelength of the signal and proportional to the sine of the angle.

FIGURE 3 – Some trigonometry, if you like …

Ok, now you know the basics. But how can an antenna array be designed? Such arrays exist in zillions of variants, but in this article, I will limit the discussion to the most basic kind. Let’s assume that all antenna elements are identical. Let’s also assume that these elements are aligned and regularly spaced. Now what are the remaining design parameters?

First, the distance between each pair of elements can be tweaked, and of course the number of elements can be freely set. An antenna array can have 2, 3, 4 … or thousands of elements. The feed network can also split the input power equally among all elements, or can implement more complex sharing methods. Signal phase between elements can be adjusted too. And finally, each element can be any kind of antenna, not necessarily the simplest one—which is the so-called “dipole.”


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Rather than a theoretical presentation, I propose in this article to illustrate the effect of each of these parameters one by one. For that, I coded a small antenna array simulation software using Scilab—an open source, numeric programming language. I will not go through the details of the code here, but don’t hesitate to download it. The code is available for download on Circuit Cellar’s article code & files download webpage. The code is straightforward—no more than 200 lines and annotated—and should be easy to read.

Basically, each antenna element can be a dipole or a “patch” (radiating only in one half of the space), and all other parameters can be freely set—number of elements, distance between elements, input power and phase to each element and so on. The software then simply calculates the array factor—which is the effect of interferences—multiplies it by the theoretical pattern of a single element and generates some nice plots (Figure 4). No electromagnetic simulation is involved, and just the effect of the array is simulated. You can use this software freely—and Scilab is free too—but no warranty is provided, because my only goal was for illustration’s sake in this article.

FIGURE 4 – These twleve graphs were generated by my Scilab antenna array simulation software. By columns, from left to right: design parameters, gain in dB, gain in volt on polar plot and gain in dB on polar plot. By rows, from top to bottom: single element, array factor and resulting antenna array.

With this software, we can now play and see the effect of each antenna array design parameter. You probably figured out already that the distance between elements is directly linked to the wavelength. This means that a given antenna array—used at a frequency of say 1 GHz—will have exactly the same characteristics as an antenna array used at 100 MHz (10 times less), if all lengths are multiplied by 10. That means that each element will have to be 10 times larger, and that the distance between elements also will have to be multiplied to 10.

Two photos will be better than a long explanation of which antenna array uses the highest frequency. Figure 5 is a picture of the SCR-270 antenna installed in Hawaii during World War II to detect Japanese attacks. It worked at 110 MHz, so the elements were large and far from each other. Now look at Figure 6, which is a reference design proposed by Texas Instruments (TI) for a 77 GHz antenna array for automotive radar applications. Do you see that higher frequencies means smaller elements and shorter distances between elements?

FIGURE 5 – The SCR270 WWII antenna array (photo taken by R. Haupt at the National Electronics Museum [3]).

FIGURE 6 – A 77 GHz antenna array on a printed circuit board (Source: Texas Instruments)

Now, how to fix the distance between elements more precisely? It can be set freely, but some distances are usually better than others. As explained above, waves cancel out if one wave is half a wavelength late compared to the other. That means that if the distance between two antenna elements is λ/2, and if both are fed by the same signal, then no power will be radiated in the lateral direction. The beam will be highly focused in one direction only. If the distance between elements is smaller than λ/2, then the main lobe will be wider. And finally, if the distance between elements is larger, for example λ or more, then several main lobes will appear.


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A simulation will be helpful to explain this phenomenon. Look at Figure 7. Here the array is only a two-dipole antenna array, separated respectively by λ/2.5, λ/2 and λ. Based on this simulation, you will understand that λ/2 is usually a nice choice.

FIGURE 7 – Effect of the distance between elements (from top to bottom, respectively, λ/2.5, λ/2, λ)

Now, how many elements are needed? Simple—a greater number of elements gives a narrower main lobe and a higher gain. As an order of magnitude, an antenna built with 10 elements can provide a gain of about 20 dB, whereas a 1,000-element array can provide 30 dB, which means a main lobe 10 times narrower in surface.

Another example will be welcome, won’t it? Look at Figure 8. Here the antenna elements are still dipoles spaced by λ/2, but the number of elements are, respectively, 2, 6 and 20. If you check the simulated antenna pattern carefully, you will see that the main beam is narrower, and the gain is higher, when the number of elements is increased. The amplitude of the side lobes is reduced too. The downside is that the antenna size is larger. This is unfortunately a rule applicable to all antennas—usually a larger antenna is better than a miniature one.

FIGURE 8 – Effect of the number of elements (from top to bottom, respectively, 2, 6, 20)

Up until now, all my simulations used a so-called “equipower weighting.” This means that the same power was applied to each antenna element. The input power P is split by N, and each of the N elements gets an input power of P/N. This approach is simple and provides a very narrow main beam, but at the expense of rather strong side lobes. Other power-splitting techniques allow us to reduce the side lobes, but at the expense of a slightly wider main lobe.


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I illustrated two of the simplest methods in Figure 9: triangle power sharing and cosine power sharing. The principle is very simple. For triangle sharing, the power is linearly decreased from the center to the edge elements, whereas it follows a cosine shape in the last example. The difference is obvious in the figures, because side lobes are greatly reduced in particular with a triangular weighting.

FIGURE 9 – Effect of the power weighting method
(a) isopower

FIGURE 9 – Effect of the power weighting method
(b) triangle

FIGURE 9 – Effect of the power weighting method
(c) cosine

Dipoles—the most basic kind of antenna—radiate the same power in any direction on the horizontal plane. But what is the change in the beam shape of an antenna array if the antenna element is changed to another type? In fact, the resulting antenna pattern is simply the pattern of the element alone, multiplied by the pattern of an array of dipoles (which is called “antenna array factor”).

Once again let’s consider an example, shown in Figure 10. The first is the antenna pattern of a 20-dipole array, whereas the second is the pattern of a 20-patch array. You can see that the main lobe and side lobe are identical, but the overall envelope is different, and they closely map the antenna pattern of a single patch.

FIGURE 10 – Effect of the antenna element design (respectively, dipole (top) and patch)

Last but not least, let’s talk about the phase of the feed network. Up until now, all antenna elements received a signal with exactly the same phase. What happens if this is not the case? The interferences will not be the same, and the antenna pattern will be distorted. Could it be useful? You bet it could! The first practical example is achieved when the same phase shift is applied between antennas—for example, a 10-degree phase shift between elements 1 and 2, 10 degrees more phase shift between element 2 and 3, and so on. In that case, the phase shift simply rotates the main beam. If you don’t trust me, look at Figure 11. That shows a simulation of a 20-element patch array with triangle power weighting, and with a phase shift between elements of 0, 40 and 140 degrees, respectively. Impressive isn’t it?

FIGURE 11 – Effect of the phase shift between elements (respectively from top to bottom 0, 40, 140 degrees)

Now the last and most interesting aspect is that all these parameters, and in particular the phases, can be either fixed or dynamically modified if the feed network includes electronically controllable gain and phase adjustments. Such an antenna array with computer-controlled phases and amplitudes is called a “phased array,” and allows you to electronically steer the main beam direction anywhere—just by changing amplitudes and phases of the signals injected into each element.

This results in an orientable antenna, without any movement of the antenna structure by itself, and it allows steering the main beam in tens of nanoseconds. Moreover, providing several lobes simultaneously is as easy as a single lobe. Think about it. Such an antenna is a linear system, so you simply have to add the injected signals for each of the lobes you want.

Phased arrays were invented for military radar systems, because they can quickly be targeted anywhere. According to Wikipedia, the largest phased array radar on earth is the so called “SBX-1,” a US defense 1,800 metric ton radar, built on a movable sea-based platform and including no less than 45,000 elements.

Antenna arrays and phased arrays also have plenty of non-defense applications. Radio astronomy is an example. Look, for example, at the Very Long Baseline Array (VLBA) in Hawaii, a set of 10 antennas built on an 8,000 km base. Ham radio guys are also fans of short-wave antenna arrays to increase the overall directivity and gain of their transceivers. Last but not least, look at your Wi-Fi router. Do you see that it has at least two identical antennas? Those aren’t exactly an antenna array but rather a multiple input, multiple output (MIMO) system—and they are in fact closely linked. However, I’m afraid that will would have to be the subject of another article.

Now, what can you do with all this information? First, I encourage you to download and play with my small array simulation software. Tweak the parameters, run the simulations—which are very fast—and discover by yourself all the details. Then, why not try using an antenna array in your next project? For example, if you are working on a robot, why not try finding its base with a phased array? Just fix a transmitter on the base, and “scan” the phased array to locate the direction. Or try using the same technique with lower frequencies—sound, for example. Take ten loudspeakers, drive then with computer-controlled phase and amplitudes, and you will be able to focus a sound in any direction. It may not be the simplest project, but for sure you will learn a lot! And you will have fun! 


[1] “The Darker Side – Antenna Basics” (Circuit Cellar 211, February 2008)
[2].”The Darker Side – Antenna Measurement” (Circuit Cellar 327, October 2017 free sample issue )
[3] (photo taken by R. Haupt at the National Electronics Museum), source :

Antenna Array Developments: A Perspective on the Past, Present and Future
Randy L. Haupt and Yahya Rahmat-Samii
Department of Electrical Engineering and Computer Science, Colorado School of Mines

TI Designs: TIDA-01570
Automotive 77-GHz Radar Module Reference Design
Texas Instruments

Antenna arrays
Prof. Sean Victor Hum, university of Toronto

Phased Array Antenna, Radiation Pattern and Array Configuration
Vardan Semerjyan

Electromagnetic Waves and Antennas, Chapter 22 (Antenna Arrays)
Sophocles J. Orfanidis
ECE Department, Rutgers University

Scilab Manual for Antenna
Prof Rajiv Tawde
Pratishthan’s College of Engineering,Mumbai

Scilab |
Texas Instruments |


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Robert Lacoste lives in France, between Paris and Versailles. He has more than 30 years of experience in RF systems, analog designs and high-speed electronics. Robert has won prizes in more than 15 international design contests. In 2003 he started a consulting company, ALCIOM, to share his passion for innovative mixed-signal designs. Robert is now an R&D consultant, mentor and trainer. Robert’s bimonthly Darker Side column has been published in Circuit Cellar since 2007. You can reach him at

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An Intro to Antenna Arrays

by Robert Lacoste time to read: 13 min