WiFi Lab

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WiFi Lab (also known as Radio Lab) is a Division C event for the 2023 season. It was previously run as a trial event at the 2017 Ohio state tournament, the 2017 Boyceville Invitational, the 2018 Texas state tournament, the 2017 and 2018 Virginia state tournaments and the 2018 National Tournament. Competitors are asked to build an antenna that transmits a signal at 2.4 GHz and complete a written test about electromagnetic waves. Teams may bring a three ring binder and two computational calculators, and are required to provide graphs and tables showing the relationship between received power and distance for different configurations of the antenna as well as labeled design logs that detail the materials and parts used to construct the antenna.

Building an Antenna

Competitors are expected to build an antenna device that helps transmit a signal from a standard IEEE 802.11 (standard WiFi) router or access point. The antenna device is entirely passive, so it does not and should not supply any power by itself. The antenna will connect to an SMA Female connector mounted in the backplane (supplied by the event supervisor) in order to receive the 2 mW (milliwatt) signal. Thus, it must have an SMA Male connector which can connect to anything such as a loose cable or a solderable end, where the competitor's antenna begins. At this point, designs may include waveguides (such as parabolic dishes or horns) or conductive components (such as a dipole or monopole). However, the antenna must not consist of any commercial parts antenna parts like a detachable router antenna; instead, the components must be constructed by the competitor using any other materials besides magnets.

Electromagnetic Spectrum

A diagram of the electromagnetic spectrum

The electromagnetic spectrum is the range of frequencies of electromagnetic radiation, including radio waves. The frequencies of these waves are measured in hertz (Hz). The frequency range is divided into separate bands, and the waves within these bands have different names. From the largest wavelength to the shortest wavelength these bands are radio waves, microwaves, infrared and visible light, ultraviolet, x-rays, and gamma rays.

X-rays and gamma rays are known as ionizing radiation and can be dangerous if an organism is exposed to them for too long. X-rays are defined as electronic transitions and gamma rays are generated from nuclear processes such as decay. Both gamma and X-rays have many uses in medicine and occasionally gamma rays are used in the sterilization of foods and seeds. Ultraviolet (UV) rays are not ionizing, but can still break chemical bonds causing sunburn and even potentially skin cancer. Some UV rays in the middle of the range also have a strong potential to cause mutation. Most damaging UV rays emitted by the sun are absorbed by the atmosphere, being blocked by the ozone layer or being absorbed by oxygen or nitrogen in the air.

Visible light occupies a very small portion of the electromagnetic spectrum. Different visible colors are the result of differing electromagnetic wavelengths, with red having the longest wavelength and purple the shortest. Electromagnetic radiation between 400–790 terahertz (THz) is visible to the human eye, but sometimes infrared and ultraviolet rays can be referred to as light. Infrared rays are useful in thermal imaging and occasionally in data transmission. Television remotes transmit signals using infrared light, which is why if the front of the remote is blocked the signal will not be received. Some infrared light can also be detected by photograph film.

Microwaves and radio waves have the lowest frequency of the electromagnetic spectrum, and are most well known for their use in microwave ovens. They can also be used in industrial heating and radar systems, as well as transmitting information. However, at that intensity microwaves do not have the same heating effects.

Radio Waves

Radio waves are the focus of the event, as WiFi is transmitted over radio waves. Radio waves are transmitted and received by antennas and are widely used to transmit information. They are also used for GPS systems and locating distant objects with radars. To generate radio waves, a transmitter generates an AC current which is applied to the antenna and generates an electric and magnetic field.

WiFi is most commonly transmitted over the 2.4 GHz and 5.8 GHz bands which are divided into multiple channels. These channels can be shared by multiple networks, making WiFi much more vulnerable to attack than wired connections. Security protocols have been created so that WiFi access is secure as possible, including the WEP and WPA protocols.

Antennas

An antenna is an instrument that can be used for transmitting and/or receiving electromagnetic waves (usually radio waves). Transmission antennas work by emitting energy as electromagnetic radiation. Reception antennas absorb energy and use it to generate an electric current.

Radiation Patterns

An antenna's radiation pattern is a plot that represents the strength of radiation output or input in any direction.

Image of a cardioid antenna radiation pattern.

Radiation patterns like the one above are usually graphed in polar (2-dimensional) or spherical (3-dimensional) coordinates. This allows one to define the strength of the emission in terms of the direction (angle). Polar coordinates are plotted in terms of radius [math]\displaystyle{ r }[/math] (distance from the origin) and angle [math]\displaystyle{ \theta }[/math] (theta, angle from the usual [math]\displaystyle{ x }[/math]-axis, known as the polar axis). Spherical coordinates are plotted in terms of radius [math]\displaystyle{ r }[/math] (distance from the origin), azimuthal angle [math]\displaystyle{ \phi }[/math] (phi, angle from the usual [math]\displaystyle{ x }[/math]-axis), and polar angle [math]\displaystyle{ \theta }[/math] (theta, angle from the usual [math]\displaystyle{ z }[/math]-axis).

One significant property that all antennas have is that their transmission and reception radiation patterns are always the same. This fact is known as reciprocity. Reciprocity can be extended to all other properties of antennas as well, meaning there is no need to design and manufacture separate transmission and reception antennas. However, this does not necessarily mean that the same antenna should always be used for transmission and reception. Depending on the application, a transmission antenna with a certain pattern may be desired whereas a reception pattern with a different pattern may be optimal. For example, in a many-to-one network where multiple transmitters in different locations communicate to a single receiver, the transmission antennas can have their power output focused in a single direction whereas the reception antenna has to accept radiation from all directions equally.

In the radiation pattern above, the power intensity varies from 1-5 units (unspecified). However, radiation patterns are often shown with normalized power intensity, where all values are divided by the maximum power intensity. This has the effect of scaling, or normalizing, the graph from 0 to 1, where angles with the maximum power intensity have a value of 1. Normalized radiation patterns make it easier to estimate/calculate and compare the patterns and directivities of multiple antennas without having to take relative intensity into account.

Directivity

An antenna's directivity describes how concentrated the power output of the antenna is in any direction. An isotropic antenna, one that has a perfectly spherical radiation pattern, radiates equally in all directions (since the radius is the same in all directions), so it would have a directivity of 1. Although directivity is technically a function that outputs the directivity at any given angle, it is commonly defined as a constant in terms of the direction of greatest radiation (which is the definition used in this page).

Image of a cardioid antenna radiation pattern, where the arrow points to the angle of greatest radiation.

In the image above, the directivity could be given in terms of the angle [math]\displaystyle{ \theta = \frac{\pi}{2} }[/math]. However, you could also define a function [math]\displaystyle{ D\left(\theta\right) }[/math] which outputs the directivity at an angle [math]\displaystyle{ \theta }[/math].

Directivity is proportional to ratio of the maximum radiation intensity to the average radiation intensity. If these two values are not given, it is very difficult to calculate the directivity. If they are given, however, then the formula is simply [math]\displaystyle{ D = \frac{\text{Maximum radiation intensity}}{\text{Average radiation intensity}} }[/math]. For this formula, the value of the directivity is unitless. However, directivity is often represented in terms of decibels, using the formula [math]\displaystyle{ D_{\text{dB}} = 10\log{\frac{D}{D_{\text{reference antenna}}}} }[/math]. Since decibels are a relative unit, you must choose a reference antenna to compare the directivity. This is often an isotropic antenna with a unitless directivity of 1, which gives the final value of the directivity in terms of a special unit called decibels isotropic ([math]\displaystyle{ \text{dBi} }[/math]).

Gain

The gain of an antenna refers to how much power is emitted in the direction of greatest radiation. The difference between gain and directivity is that gain is calculated by multiplying the directivity of an antenna by its efficiency, meaning it takes into account power loss.

The formula for gain is [math]\displaystyle{ G = \eta D }[/math], where [math]\displaystyle{ \eta }[/math] is the efficiency. This, in turn, is calculated as [math]\displaystyle{ \eta = \frac{P_{out}}{P_{in}} }[/math], where [math]\displaystyle{ P_{out} }[/math] and [math]\displaystyle{ P_{in} }[/math] are the total power output and power input of the antenna, respectively. Efficiency essentially measures how much of the input power is actually emitted by an antenna. For an antenna that outputs all of the power put into it, the efficiency would be equal to 1 and the gain would be equal to the directivity. Such an antenna is often referred to as an isotropic antenna.

If the value of directivity used in the formula is unitless, then the gain is in decibels ([math]\displaystyle{ \text{dB} }[/math]). If the directivity is in terms of decibels isotropic ([math]\displaystyle{ \text{dBi} }[/math]), then the gain is also in decibels isotropic. Gain can also be given in comparison to a perfect dipole antenna with no loss, which has a gain of [math]\displaystyle{ 2.15\ \text{dBi} }[/math], a unit called decibels dipole ([math]\displaystyle{ \text{dBd} }[/math]). To convert to and from [math]\displaystyle{ \text{dBd} }[/math], use the formula [math]\displaystyle{ G_{\text{dBd}} = G_{\text{dBi}} - 2.15 }[/math]. An important thing to realize here is that an antenna with a gain of [math]\displaystyle{ 2.15\ \text{dBi} }[/math] would have a gain in decibels dipole of [math]\displaystyle{ 0\ \text{dBd} }[/math]. This does not mean that the antenna has no gain, but rather that its gain is the exact same as a perfect dipole antenna with no loss. This same idea applies for any values, including gain, which are represented in decibels relative to another antenna.

Impedance

Impedance is a measure of opposition against an antenna's transmission. The idea of impedance is related to that of resistance in a circuit; resistance is a measure of opposition against the flow of current. However, impedance also takes reactance into account; reactance is a measure of opposition against the change in current. Although resistance suffices for direct currents, reactance is an important measure in alternating currents, which is what antennas use.

Impedance is measured in ohms, a unit with the symbol [math]\displaystyle{ \Omega }[/math] (uppercase omega). It is written as a complex number in the form [math]\displaystyle{ Z = R + Xi }[/math], where [math]\displaystyle{ R }[/math] is the resistance and [math]\displaystyle{ X }[/math] is the reactance. The actual impedance of an antenna is difficult to determine precisely since it depends on the antenna, operating wavelength, and especially the environment. Thus, it must be either predicted through mathematical relations or recorded observationally.

Types

There are numerous types of antennas and countless ways to classify them.

Isotropic Antenna

The simplest antenna type is technically the isotropic antenna, although it is purely theoretical and cannot be constructed or even designed. Instead, the isotropic antenna is mainly used as reference for properties of real antennas, such as efficiency, directivity, and gain. However, it is possible to construct a nearly-isotropic antenna by making an antenna much smaller than the wavelength it emits. This way, the near-field radiation pattern will look nearly isotropic as the distance traveled by the waves will be too short for any losses to have occurred. This is similar to the principle applied in the design of short dipoles, which are real and can be constructed.

Monopole Antenna

Monopole antennas consist of a single radiating element, such as a rod or wire, directly linked to the transmission line. Monopoles are positioned normal to their supporting plane or structure, which has the effect of reducing the impedance in comparison to a dipole (since only half the current is being carried) while doubling the directivity in comparison to a dipole with double the length (since the entire radiation is along one direction instead of split in two directions).

Dipole Antenna

Dipole antennas are very simple and commonly-used antennas, but they also serve as the foundation for many more complex antennas. They consist of two rods, wires, or other uniform conducting material pointing out in different directions (often opposite each other but possibly at an angle). Dipole antennas can further be classified into various types, including short, half-wave, full-wave, and folded dipoles.

The short dipole is based on the principle used to mimic isotropic antennas: by having an antenna with a size much smaller than the operating wavelength (usually around 10 times smaller), the radiation pattern is nearly isotropic. In reality, the pattern is closer to that of an omnidirectional antenna.

The half-wave dipole is the most common dipole design. Half-wave dipole antennas are characterized by having a total length nearly equal to half the wavelength they operate at. The advantage of this design is that the radiation being transmitted lines up with each monopole (the wires or rods pointing out, a property known as resonance. This results in an omnidirectional antenna with optimal impedance, making it very useful for various applications such as communication and, in the past, television.

Yagi-Uda Antenna

Although dipole antennas are useful, a single dipole antenna is not very powerful. Instead, the most common antennas consist of multiple dipoles, such as the Yagi-Uda antenna. A Yagi-Uda antenna is constructed from multiple dipole elements systematically placed together at different distances. As a result of the numerous dipole elements, Yagi-Uda antennas have higher directivity and gain (shown below).

Image of a Yagi-Uda antenna radiation pattern in decibels isotropic (dBi). Note that, for a real Yagi-Uda antenna, there could be other lobes around the sides, but in this image only the main and back lobes are shown.

However, Yagi-Uda antennas can be noisy and can only operate from around 30 MHz to 3 GHz. In addition, since the design of the antenna depends on the wavelength (and thus, the frequency) at which the antenna operates, a single antenna cannot be used for multiple frequencies. Yagi-Uda antennas are most commonly used as receptors for television.

Array Antennas

In general, antennas made up of a system of multiple antennas are referred to as array antennas. The main advantage of array antennas is the ability to increase directivity by having signals interfere constructively and destructively to boost the power in certain directions and cancel it out in other directions. This is done by adding different phase shifts to the signals of each antenna. Phase shifts are essentially shifts in the position of a wave that are used to create interference. Because of their high directivity, array antennas are used for everything from broadcasting to astronomy.

Radio Wave Propagation

There are three main ways in which radio waves can be sent from a transmitter to a receiver. The simplest method is line-of-sight (LOS) propagation. LOS propagation occurs when the signal is sent straight from the transmitter to the receiver through the shortest possible straight line path. This method is primarily used for shorter distances as the signal can be affected by any obstacles in the way and can only be used when the transmitter and receiver are in view of each other. A slightly better method is ground wave propagation, where the signal travels in a curved path around the Earth, allowing it to travel farther. Sky wave propagation is the final method, which utilizes a layer of the atmosphere known as the ionosphere to bounce the signal to the receiver. The signal is sent up to the ionosphere, where it is reflected, hits the ground, and continues this cycle until it reaches the destination. Sky wave propagation is more difficult to conduct and can only be used within the frequency range from 2 to 30 MHz.

Information

Information is a very abstract concept but can be defined as any form of uncertainty or randomness in a system that allows it to store meaning. As a counterexample, a piece of paper with nothing on it contains no information at the macroscopic level. However, once one begins to write or draw on it, it now stores information, even if the writing or drawing is meaningless scribbling. As a result, the string "qwerty" contains information, as does the word "radio". This is important because, when information is stored and transmitted, it is usually not transmitted in a human-readable form. Instead, it may be represented using the binary system transmitted as voltage by computers or using the amplitudes and frequencies of radio waves transmitted by an antenna. Although neither of these forms make sense (or are even perceivable) to a person, they still store information that can be understood and decoded into something like music or text.

Information is typically measured using entropy, which measures the unexpectedness or "surprise factor" associated with an event. For example, a single fair coin with two sides carries one bit of information on average, either heads or tails (where bit refers to the fact that there are two outcomes with equal probabilities). If the coin were unfair, such that one of the outcomes is more likely than the other, then it would contain less than one bit of information on average, since one outcome would be more expected.

As another example of entropy, if you were given the letter "q" as the first letter in a word and asked what letter will come next, the letter "u" would contain very little information since, knowing the general rules of English, you can almost always assume that the letter "u" follows the letter "q". However, if the next letter turned out to be "i", this would be very surprising. As a result, the letter "i" coming after the letter "q" has higher entropy and thus contains more information. If the next letter were "u", this would not be very informative since you could easily predict it, thus the letter "u" coming after the letter "q" contains very little information.

Using entropy, engineers can determine a way to code (or translate) messages into a signal. For example, the bigram "qu" can be treated like a single letter since after a "q" is almost always a "u". This is much simpler and more cost-efficient than sending the letters "q" and "u" separately when they appear together. Message coding is a very important topic in communication theory, since sending large amounts of long and inefficient messages can cost a lot of energy. The measurement of entropy is typically made based on the use case, as entropy is a purely relative measurement and there is no way of comparing the entropies of two events without knowing the entire set of possible events and then calculating the probability of each event separately.

Resources

External Links

2018 National Tournament Trial Events
Division B: Density Lab · Solar Power | Division C: Code Busters · WiFi Lab


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