The Electromagnetic Spectrum
Electromagnetic waves span a wide range of frequencies (and, accordingly, wavelengths). This range of frequencies and wavelengths is called the electromagnetic spectrum. The part of the spectrum most familiar to humans is probably light, the visible portion of the electromagnetic spectrum. Light lies roughly between the frequencies of 7.5*1014 Hz and 3.8*1014 Hz, corresponding to wavelengths from circa 400 nm (violet/blue) to 800 nm (red).
We are also regularly exposed to other regions of the electromagnetic spectrum, including Alternating Current (AC) or grid electricity at 50/60 Hz, Ultraviolet (on the higher frequencies side of visible light), Infrared (on the lower frequencies side of visible light), X-Rays / Roentgen radiation, and many others. Radio is the term used for the portion of the electromagnetic spectrum in which waves can be generated by applying alternating current to an antenna. This is true for the range from 3 Hz to 300 GHz, but in the more narrow sense of the term, the upper frequency limit would be 1 GHz.
When talking about radio, many people think of FM radio, which uses a frequency around 100 MHz. In between radio and infrared we find the region of microwaves - with frequencies from about 1 GHz to 300 GHz, and wavelengths from 30 cm to 1 mm.
The most popular use of microwaves might be the microwave oven, which in fact works in exactly the same region as the wireless standards we are dealing with. These regions lie within the bands that are being kept open for general unlicensed use. This region is called the ISM band, which stands for Industrial, Scientific, and Medical. Most other parts of the electromagnetic spectrum are tightly controlled by licensing legislation, with license values being a huge economic factor. This goes especially for those parts of the spectrum that are suitable for broadcast (TV, radio) as well as voice and data communication. In most countries, the ISM bands have been reserved for unlicensed use.
The frequencies most interesting to us are 2.400 - 2.495 GHz, which is used by the 802.11b and 802.llg radio standards (corresponding to wavelengths of about 12.5 cm). Other commonly available equipment uses the 802.11a standard, which operates at 5.150 - 5.850 GHz (corresponding to wavelengths of about 5 to 6 cm).
Bandwidth
A term you will meet often in radio physics is bandwidth. Bandwidth is simply a measure of frequency range. If a range of 2.40 GHz to 2.48 GHz is used by a device, then the bandwidth would be 0.08 GHz (or more commonly stated as 80MHz).
It is easy to see that the bandwidth we define here is closely related to the amount of data you can transmit within it - the more room in frequency space, the more data you can fit in at a given moment. The term bandwidth is often used for something we should rather call a data rate, as in "my Internet connection has 1 Mbps of bandwidth", meaning it can transmit data at 1 megabit per second.
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Mass spectrometers
Everyone loves a rainbow and most people understand, at least roughly, how they work: raindrops split a beam of white sunlight into rays of colored light, bending the bluish ones more than the reddish ones to make the well-known arc in the sky. Rain, then, is a brilliant method for separating sunlight. Chemists and physicists use a similar method for separating mixtures of substances into their components, turning them into beams of particles and then bending them with electricity and magnetism to make a kind of spectrum of different atoms that are easier to identify. This technique is called mass spectrometry and it was pioneered by British physicist Francis Aston in 1919. Let's take a closer look at how it works!
What is a mass spectrometer?
Mass spectrometers are much simpler than they look-or sound. Suppose someone gives you a bucketful of atoms of different chemical elements and asks you what's inside. You need to separate out the atoms quickly and efficiently, but how do you do it? Simple! Tip your bucket into a mass spectrometer. It turns the atoms into ions (electrically charged atoms with either too few or too many electrons). Then it separates the ions by passing them first through an electric field, then through a magnetic field, so they fan out into a spectrum. A computerized detector tallies the ions in different parts of the spectrum and you can use this information to figure out what kinds of atoms were originally in your bucket. That's the basic idea, anyway. In reality, it's a bit more complex than this-there's no bucket, for a
start!
How does a mass spectrometer work?
There are numerous different kinds of mass spectrometers, all working in slightly different ways, but the basic process involves broadly the same stages.
1. You place the substance you want to study in a vacuum chamber inside the machine.
2. The substance is bombarded with a beam of electrons so the atoms or molecules it contains are turned into ions. This process is called ionization.
3. The ions shoot out from the vacuum chamber into a powerful electric field (the region that develops between two metal plates charged to high voltages), which makes them accelerate. Ions of different atoms have different amounts of electric charge, and the more highly charged ones are accelerated most, so the ions separate out according to the amount of charge they have. (This stage is a bit like the way electrons are accelerated inside an old-style, cathode-ray television.)
4. The ion beam shoots into a magnetic field (the invisible, magnetically active region between the poles of a magnet). When moving particles with an electric charge enter a magnetic field, they bend into an arc, with lighter particles (and more positively charged ones) bending more than heavier ones (and more negatively charged ones). The ions split into a spectrum, with each different type of ion bent a different amount according to its mass and its electrical charge.
5. A computerized, electrical detector records a spectrum pattern showing how many ions arrive for each mass/charge. This can be used to identify the atoms or molecules in the original sample. In early spectrometers, photographic detectors were used instead, producing a chart of peaked lines called a mass spectrograph. In modern spectrometers, you slowly vary the magnetic field so each separate ion beam hits the detector in turn.
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Sieve of Eratosthenes
In mathematics, the Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer. It works efficiently for the smaller primes (below 10 million). It was created by Eratosthenes, an ancient Greek mathematician.
Algorithm
A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. To find all the prime numbers less than or equal to a given integer n by Eratosthenes' method:
1.Create a list of consecutive integers from two to n: (2, 3, 4,..., n).
2.Initially, let p equal 2, the first prime number.
3.Starting from p, count up by p and cross out thus found numbers in the list (which will be 2p, 3p, 4p, etc.).
4.Find the first number not yet crossed out after p; let p now equal this number (which is the next prime).
5.Repeat steps 3 and 4 until p[1] is greater than n.
6.All the numbers in the list which are not crossed out are prime.
As a refinement, it is sufficient to cross out the numbers in step 3 starting from p (because all the lesser ones will be already crossed out at that point), and so also stop when p2 is greater than n, in step 5. A common improvement is to work with odds only (3, 5,..., n), and count up using 2p as a step (thus excluding all the multiples of two in advance).
Example
To find all the prime numbers less than or equal to 30, proceed as follows. First generate a list of integers from 2 to 30:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Starting from 4, count up by 2 and cross out these numbers in the list:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
The first number in the list after 2 is 3; count up by 3 from 9 and cross out these numbers too:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
The first number not yet crossed out in the list after 3 is 5; proceed by counting up by 5 from 25:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Next number in the list after 5 that is not crossed out is 7, but 7 squared is 49 which is greater than 30 so the process is finished. The numbers left not crossed out in the list are all the prime numbers less than or equal to 30:
2 3 5 7 13 17 19 23 29
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Integral
Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. Given a function / of a real variable x and an interval [a, b] of the real line, the definite integral
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is defined informally to be the net signed area of the region in the xy-plane bounded by the graph of /, the x-axis, and the vertical lines x = a and x = b.
The term integral may also refer to the notion of antiderivative, a function F whose derivative is the given function /. In this case, it is called an indefinite integral, while the integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between antiderivatives and indefinite integrals.
The principles of integration were formulated independently by Isaac Newton and Gottfried Leibniz in the late 17th century. Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if / is a continuous real- valued function defined on a closed interval [a, b], then, once an antiderivative F of / is known, the definite integral of / over that interval is given by
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Integrals and derivatives became the basic tools of calculus, with numerous applications in science and engineering. A rigorous mathematical definition of the integral was given by Bernhard Riemann. It is based on a limiting procedure which approximates the area of a curvilinear region by breaking the region into thin vertical slabs. Beginning in the nineteenth century, more sophisticated notions of integrals began to appear, where the type of the function as well as the domain over which the integration is performed has been generalised. A line integral is defined for functions of two or three variables, and the interval of integration [a, b] is replaced by a certain curve connecting two points on the plane or in the space. In a surface integral, the curve is replaced by a piece of a surface in the three-dimensional space. Integrals of differential forms play a fundamental role in modern differential geometry. These generalizations of integral first arose from the needs of physics, and they play an important role in the formulation of many physical laws, notably those of electrodynamics. There are many modern concepts of integration, among these, the most common is based on the abstract mathematical theory known as Lebesgue integration, developed by Henri Lebesgue.
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Types of networks
There are many types of networks that provide us with different kinds of services. In the course of a day, a person might make a phone call, watch a television show, listen to the radio, look up something on the Internet, or even play a video game with someone in another country. All of these activities depend on robust, reliable networks. Networks provide the ability to connect people and equipment no matter where they are in the world. People use networks without ever thinking about how they work or what it would be like if the networks did not exist.
Communication technology in the 1990s, and before, required separate, dedicated networks for voice, video and computer data communications. Each of these networks required a different type of device in order to access the network. Telephones, televisions, and computers used specific technologies and different dedicated network structures, to communicate. But what if people want to access all of these network services at the same time, possibly using a single device?
New technologies create a new kind of network that delivers more than a single type of service. Unlike dedicated networks, these new converged networks are capable of delivering voice, video and data services over the same communication channel or network structure.
New products are coming to market that take advantage of the capabilities of converged information networks. People can now watch live video broadcasts on their computers, make a telephone call over the Internet, or search the Internet using a television. Converged networks make this possible. In this course, the term network refers to these new multi-purpose, converged information networks.
Networks come in all sizes. They can range from simple networks consisting of two computers, to networks connecting millions of devices. Networks installed in small offices, or homes and home offices, are referred to as SOHO networks. SOHO networks enable sharing of resources, such as printers, documents, pictures and music between a few local computers. In business, large networks can be used to advertise and sell products, order supplies, and communicate with customers.
Purpose
The primary purpose of any network is to provide a method to communicate information. From the very earliest primitive humans to the most advanced scientists of today, sharing information with others is crucial for human advancement.
All communication methods have three elements in common. The first of these elements is the message source, or sender. Message sources are people, or electronic devices, that need to communicate a message to other individuals or devices. The second element of communication is the destination, or receiver, of the message. The destination receives the message and interprets it. A third element, called a channel, provides the pathway over which the message can travel from source to destination.
In any conversation between two people, there are many rules, or protocols, that the two must follow in order for the message to be successfully delivered and understood. Among the protocols for successful human communication are:
• Identification of sender and receiver
• Agreed-upon medium or channel (face-to-face, telephone, letter, photograph)
• Appropriate communication mode (spoken, written, illustrated, interactive or one-way)
• Common language
• Grammar and sentence structure
• Speed and timing of delivery
Imagine what would happen if no protocols or rules existed to govern how people communicate with each other. Would you be able to understand them? Are you able to read the paragraph that does not follow commonly accepted protocols?
Protocols are specific to the characteristics of the source, channel and destination of the message. The rules used to communicate over one medium, like a telephone call, are not necessarily the same as communication using another medium, such as a letter. Protocols define the details of how the message is transmitted, and delivered. This includes issues of:
• Message format
• Message size
• Timing
• Encapsulation
• Encoding
• Standard message pattern
One of the first steps to sending a message is encoding it. Encoding is the process of converting thoughts into the language, symbols, or sounds, for transmission. Decoding reverses this process in order to interpret the thought. Imagine a person watching a sunset and then calling someone else to talk about how beautiful the sunset looks. To communicate the message, the sender must first convert, or encode, their thoughts and perceptions about the sunset into words. The words are spoken into the telephone using the sounds and inflections of spoken language that convey the message. On the other end of the telephone line, the person listening to the description, receives and decodes the sounds in order to visualize the image of the sunset described by the sender.
Encoding also occurs in computer communication. Messages sent across the network are first converted into bits by the sending host. Each bit encoded into a pattern of sounds, light waves, or electrical impulses depending on the network media over which the bits are transmitted. The destination host receives and decodes the signals in order to interpret the message.
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