## Make sense of antenna design and matching networks

#### Article By : Asem Elshimi Understanding antennas is based on empirical knowledge more than formulae and theory.

When it comes to actual antennas in the real world, much of our knowledge is empirical. We know very broadly theories that explain how a point charge radiates (Maxwell’s equations), the need for matching (microwave theory), and how dipole antennas drawn on paper radiate the way they do, but these laws are nearly useless in solving the real-world problem of antenna design. By sharing my intuition on how wireless electronics work on a physical level, I hope to be useful in shaping a broad understanding of antenna design and matching networks and underscore the value of best practices and hard-earned wisdom.

What follows is by no means a solid theoretical explanation of how antennas and matching networks work. First, we don’t have closed-form radiation equations for most antennas. Second, even when we do have the equations for some antennas, the mathematics are very involved and hard to make sense of. Antenna design is a field where empirical practice moved much faster than theoretical knowledge. That’s probably understandable given the complexity of these energy transformers.

There are also numerous physical (hardware) and non-physical (software) layers in wireless electronics. Engineers tend to only understand parts of this in silos, especially if their job is as specific as designing a matching network or a phased-array antenna. What I intend to do is to connect the dots from a radiating point charge oscillating at a non-relativistic speed to a Bluetooth communications channel conveying water meter readings to a gateway.

Figure 1 shows a few common antenna designs. The one we are mostly familiar with is the monopole antenna since it used to be the mainstream antenna for TV broadcast reception, as well as the first generation of cellular phones and even toys. Some long-time analog and wireless engineers would also recognize the Yagi-Uda antenna that occupied our rooftops until the end of the 1990s for TV receivers. For economical and mechanical reasons, the antenna that’s most common in today’s wireless electronics is the microstrip patch antenna. However, the antenna that’s easiest to explain (in my opinion) is the horn antenna. That said, the concepts I will illustrate on a horn antenna apply to the other types of antennas. It just takes a little more imagination and understanding of electromagnetism to see them in the same light. Figure 1 Antennas can take a variety of shapes, but all are energy transformers.

An antenna is an energy transformer. It takes guided electromagnetic waves from one side and radiates free-space spherical waves on the other side. Every wire does this to a certain extent; wires basically radiate part of the electromagnetic energy traversing them. That’s one of the reasons we use electrical insulation. But usually when we talk about antennas radiating electromagnetic energy, we actually are referring to a very specific type of radiation – a useful electromagnetic radiation.

In 2020, a useful electromagnetic radiation is simply an electromagnetic wave that oscillates at a frequency allowed by the standards (FCC, ETSI etc.) and has enough power to traverse across the target range for the application. For example, a Bluetooth antenna must be able to transmit/radiate an electromagnetic wave of tens of milliwatts, which can traverse a few meters of space. We will get back to this example shortly. For now, let’s focus our attention on the antenna as an energy transformer with a certain frequency and output power.

To clear up the ambiguity around the term energy transformer, let’s look at a familiar example: an electrical transformer that takes in electrical energy in one form and transmits electrical energy in a slightly different form. It changes the voltage to the current ratio of the electrical signal. In other words, it changes the wave impedance of the electrical signal (according to Ohm’s law, voltage/current = impedance). A common example of a transformer is the double-winding transformer we all studied in high school, which is still used today in the power grid (Figure 2). A power plant generates an electrical signal of very high current and low voltage. To “transmit” this signal across hundreds of miles at a minimum loss, we use the transformer to increase the wave impedance; in other words, to increase the voltage and reduce the current. A smaller current can travel across long wires with fewer losses. Figure 2 The common electrical transformer (left) provides an illustration of energy transformation (right).

In a pure electrical sense, an antenna does what the transformer just did. Looking at a rectangular waveguide with a horn antenna attached to its end, for instance, we see how the antenna prepares the electromagnetic wave to exit the waveguide toward free space (Figure 3). The gradual opening of a horn antenna is basically an energy transformer that takes a guided wave with a 50 Ω impedance from a coaxial cable and transforms it into a free space wave with 377 Ω wave impedance. Figure 3 The horn antenna transforms electromagnetic energy from one impedance to another.

Without using any mathematical formulas, we just stated something relevant and obvious about antennas: they are matching elements that match the guided wave to the free-space wave. Why does this matching matter? Because, like the electrical transformer case, a guided wave requires this energy transformation to be able to traverse the free space with minimum losses. (If an electromagnetic wave has a wave impedance that’s off from the free space impedance, it simply won’t propagate in free space.)

Wave impedance is the ratio of electrical to magnetic energy in an electromagnetic wave, so when I say that the wave impedance of free space is 377 Ω it means that, for a wave to traverse the free space, it needs to have its wave impedance to be 377 Ω. We know this number because we can solve Maxwell’s equations in free space and find out that the wave impedance is 377 Ω. Alternatively, we can conduct experiments to measure the ratio of electrical to magnetic energy in a free space wave, and get the same number to an incredible degree of accuracy. This is one of the most impressive scientific validations we have to this point in human history.

What about the 50 Ω we use for the wave impedance inside the waveguide? Historically, 50 Ω is a standard number used for microwave circuits (although some of them are 75 Ω and even higher). Yet in modern microwave technology, aka on-chip microwave circuits, nobody cares about this 50 Ω figure anymore. So, where did this standard come from? Apparently coax cable designers in the past were able to find a compromise between maximum power handling and loss across their cables. This compromise number was 50 Ω, and it became a figure of merit that every wireless engineer used since (Figure 4). Figure 4 The 50 Ω standard is a compromise between power handling and loss across coax cables.

Now, assume you are trying to build an SoC that senses and processes water meter data to be sent wirelessly to a gateway. The data held in the SoC memory is represented as ones and zeros that we can read sequentially and have all the data ready to be sent. We also have an energy transformer we call an antenna. We know that it can take electromagnetic energy from a wire and change its impedance and send it to free space. Do we just apply the ones and zeroes on the antenna? Would that even work?

In the early days of radio transmission, a developer was able to successfully apply data directly to the antenna by creating an on/off keying signal on one end of an antenna and reading the signal with another receiver at another location. In modern RF engineering, however, we can’t do this direct application for so many reasons. First, the ones and zeros are occurring at the frequency of the microcontroller unit (MCU), usually in tens of MHz. An antenna would need to be about 15 meters long to be able to efficiently transform a 10 MHz 50 Ω guided wave into 377 Ω. This dimension is huge for any of our modern-day electronics; imagine a smartphone with a 15-meter antenna.

So why does the antenna have to be that long? For an antenna to be as efficient as possible, it needs to resonate around the frequency of the wave that it is transmitting. Resonance causes the electromagnetic energy to keep oscillating between the ends of the antenna structure, thus, keeping as much energy as possible on the structure instead of reflecting it back to the source. This retention enables more radiation power. Resonance, however, requires the antenna dimension to be equivalent to half the wavelength of the propagating wave. Essentially, then, a useful antenna for this direct application would have a length in the order of magnitude of the wavelength of the propagating wave. The relationship between the speed of light, frequency, and wavelength of the propagating wave is speed of light=Wavelength*frequency, which I used to calculate the antenna’s 15-meter dimension.

[Continue reading on EDN US: Modulation]

Asem Elshimi is an RFIC Design Engineer for IoT wireless solutions at Silicon Labs.

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