Difference between revisions of "WiFi Lab"

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(Added reciprocity, impedance, and antenna types, as well as minor math styling.)
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[[File:Radiation Pattern.png|thumb|center|Image of a cardioid antenna radiation pattern.]]
 
[[File:Radiation Pattern.png|thumb|center|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]r[/math] (distance from the origin) and angle [math]\theta[/math] (theta, angle from the usual x-axis, known as the polar axis). Spherical coordinates are plotted in terms of radius [math]r[/math] (distance from the origin), azimuthal angle [math]\phi[/math] (phi, angle from the usual x-axis), and polar angle [math]\theta[/math] (theta, angle from the usual z-axis).
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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]r[/math] (distance from the origin) and angle [math]\theta[/math] (theta, angle from the usual [math]x[/math]-axis, known as the polar axis). Spherical coordinates are plotted in terms of radius [math]r[/math] (distance from the origin), azimuthal angle [math]\phi[/math] (phi, angle from the usual [math]x[/math]-axis), and polar angle [math]\theta[/math] (theta, angle from the usual [math]z[/math]-axis).
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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.
  
 
=== Directivity ===
 
=== Directivity ===
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In the image above, the directivity could be given in terms of the angle [math]\theta = \frac{\pi}{2}[/math]. However, you could also define a function [math]D\left(\theta\right)[/math] which outputs the directivity at an angle [math]\theta[/math].
 
In the image above, the directivity could be given in terms of the angle [math]\theta = \frac{\pi}{2}[/math]. However, you could also define a function [math]D\left(\theta\right)[/math] which outputs the directivity at an angle [math]\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]D = 4\pi \cdot \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]D_{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]dBi[/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]D = 4\pi \cdot \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]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]\text{dBi}[/math]).
  
 
=== Gain ===
 
=== 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 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]G = \epsilon D[/math], where [math]\epsilon[/math] is the efficiency. This, in turn, is calculated as [math]\epsilon = \frac{P_{out}}{P_{in}}[/math], where [math]P_{out}[/math] and [math]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.
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The formula for gain is [math]G = \eta D[/math], where [math]\eta[/math] is the efficiency. This, in turn, is calculated as [math]\eta = \frac{P_{out}}{P_{in}}[/math], where [math]P_{out}[/math] and [math]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]dB[/math]). If the directivity is in terms of decibels isotropic ([math]\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]2.15\ \text{dBi}[/math], a unit called decibels dipole ([math]\text{dBd}[/math]). To convert to and from [math]\text{dBd}[/math], use the formula [math]G_{\text{dBd}} = G_{\text{dBi}} - 2.15[/math].
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 +
=== 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. Impedance is measured in ohms, with the symbol [math]\Omega[/math] (uppercase omega). The actual impedance of an antenna is difficult to determine since it depends on the antenna, operating wavelength, and especially the environment.
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 +
=== Types ===
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There are numerous types of antennas and countless ways to classify them. Of these, the simplest type is technically the isotropic antenna, although it is purely theoretical and cannot be constructed. 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 it smaller than the wavelength it emits. This is the principle applied in half-wave dipoles, discussed below.
 +
 
 +
Dipole antennas are the simplest and most common viable antennas, and serve as the foundation for most complex antennas. They antennas consist of two wires or rods pointing out in different directions (usually opposite of each other but sometimes at an angle). Of the dipole antennas, the half-wave dipole is the most common. 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.
  
If the value of directivity used in the formula is unitless, then the gain is in decibels ([math]dB[/math]). If the directivity is in terms of decibels isotropic ([math]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]2.15 \text{dBi}[/math], a unit called decibels dipole ([math]dBd[/math]). To convert to and from [math]dBd[/math], use the formula [math]G_{dBd} = G_{dBi} - 2.15[/math].
+
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. However, they can be noisy and can only operate from around 30 MHz to 3 GHz. Yagi-Uda antennas are most commonly used as receptors for television.
  
 
== Resources ==
 
== Resources ==

Revision as of 18:38, 11 April 2021

WiFi Lab (also known as Radio Lab) is a Division C that was 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 power and distance for different configurations of the antenna.

Building an Antenna

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 uses 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]r[/math] (distance from the origin) and angle [math]\theta[/math] (theta, angle from the usual [math]x[/math]-axis, known as the polar axis). Spherical coordinates are plotted in terms of radius [math]r[/math] (distance from the origin), azimuthal angle [math]\phi[/math] (phi, angle from the usual [math]x[/math]-axis), and polar angle [math]\theta[/math] (theta, angle from the usual [math]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.

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 circular or 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]\theta = \frac{\pi}{2}[/math]. However, you could also define a function [math]D\left(\theta\right)[/math] which outputs the directivity at an angle [math]\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]D = 4\pi \cdot \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]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]\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]G = \eta D[/math], where [math]\eta[/math] is the efficiency. This, in turn, is calculated as [math]\eta = \frac{P_{out}}{P_{in}}[/math], where [math]P_{out}[/math] and [math]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]dB[/math]). If the directivity is in terms of decibels isotropic ([math]\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]2.15\ \text{dBi}[/math], a unit called decibels dipole ([math]\text{dBd}[/math]). To convert to and from [math]\text{dBd}[/math], use the formula [math]G_{\text{dBd}} = G_{\text{dBi}} - 2.15[/math].

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. Impedance is measured in ohms, with the symbol [math]\Omega[/math] (uppercase omega). The actual impedance of an antenna is difficult to determine since it depends on the antenna, operating wavelength, and especially the environment.

Types

There are numerous types of antennas and countless ways to classify them. Of these, the simplest type is technically the isotropic antenna, although it is purely theoretical and cannot be constructed. 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 it smaller than the wavelength it emits. This is the principle applied in half-wave dipoles, discussed below.

Dipole antennas are the simplest and most common viable antennas, and serve as the foundation for most complex antennas. They antennas consist of two wires or rods pointing out in different directions (usually opposite of each other but sometimes at an angle). Of the dipole antennas, the half-wave dipole is the most common. 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.

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. However, they can be noisy and can only operate from around 30 MHz to 3 GHz. Yagi-Uda antennas are most commonly used as receptors for television.

Resources

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