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The application of fiber optics to industrial information transfer is a natural extension of the current commercial uses of this technology in high-data-rate communications. While the primary advantage of fiber optics in traditional application areas has been extremely reliable communication at high rates, exceeding 1 Gbit/s over distances exceeding 100 km, other intrinsic features of the technology are more important than data rate and distance capability in industrial uses. The physical mechanism of light propagating through a glass fiber has significant advantages that enable sensors to carry data and plant communications successfully and in a timely manner a fundamental condition that must be constantly maintained in a computer-integrated manufacturing environment: The light signal is completely undisturbed by electrical noise. This means that the fiber-optic cables can be laid wherever convenient without special shielding. Fiber-optic cables and sensors are unaffected by electrical noise when placed near arc welders, rotating machinery, electrical generators, and so on, whereas in similar wired applications, even the best conventional shielding methods are often inadequate. Fiber-optic communication is devoid of any electrical arcing or sparking, and thus can be used successfully in hazardous areas without danger of causing an explosion. The use of a fiber link provides total electrical isolation between terminal points on the link. Over long plant distances, this can avoid troublesome voltage or ground differentials and ground loops. A fiber-optic system can be flexibly configured to provide additional utility in existing hardware.



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Factorial[10]/(Factorial[4] * Factorial[10 4])

2.9 A fair die has six faces, numbered 1 through 6, and each occurs with equal probability. Simulate four tosses of a fair die.

An optical fiber (Fig. 3.30) is a thin strand composed of two layers: an inner core and an outer cladding. The core is usually constructed of

(Your answers will be different from those shown here.) Random[Integer, {1, 6}] Random[Integer, {1, 6}] Random[Integer, {1, 6}]

Server data structures directly, without going through the relational engine. There is a manager to control sorting operations and one to physically manage the files and backup devices on disk.

Random[Integer, {1, 6}] 6 1 5 3





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glass, and the cladding structure composed of glass or plastic. Each layer has a different index of refraction, the core being higher. The difference between the index of refraction of the core material n1 and that of the surrounding cladding material n2 causes rays of light injected into the core to continuously reflect back into the core as they propagate down the fiber. The light-gathering capability of the fiber is expressed in terms of its numerical aperture NA, the sine of the half angle of the acceptance cone for that fiber. Simply stated, the larger the NA, the easier it is for the fiber to accept light (Fig. 3.31).

(Your answer will be different from that shown here.) Random[Real,{ , 2 }, 15] 4.13129131207734

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A fiber-optic communication system (Fig. 3.32) consists of: A light source (LED or laser diode) pulsed by interface circuitry and capable of handling data rates and voltage levels of a given magnitude. A detector (photodiode) that converts light signals to electrical signals and feeds interface circuitry to re-create the original electrical signal. Fiber-optic cables between the light source and the detector (called the transmitter and the receiver, respectively). It is usual practice for two-way communication to build a transmitter and receiver into one module and use a duplex cable to communicate to an identical module at the end of the link. The 820- to 850-nm range is the most frequent for low-data-rate communication, but other wavelengths (1300 and 1550 nm) are used in long-distance systems. Fiber selection must always take transmission wavelength into consideration.

Fibonacci[27] 196 418

Prime[37] 157 Prime[38] 163

The selection of optical fiber plays a significant part in sensor performance and information flow. Increased fiber diameter results in higher delivered power, but supports a lower bandwidth. A fiber with a 200- m core diameter (glass core, silicone plastic cladding), by virtue of its larger diameter and acceptance angle, can transmit five to seven times more light than a 100- m core fiber, or up to 30 times

Round[Sqrt[159]] 13

Floor[( 2 +1)5] 151 729 Ceiling[( 2 +1)5 ] 151 730 The number ( 2 + 1)5 lies between 151,729 and 151,730.

more light than a 40- m fiber, the historical telecommunication industry standard. Computer data communications systems commonly employ 62.5- m fiber because of its ability to support very high data rates (up to 100 Mbaud) while offering increased power and ease of handling. Factory bandwidth requirements for most links are typically one or more orders of magnitude. Therefore, fiber core size may be increased to 200 m to gain the benefits of enhanced power and handling ease, the decrease in bandwidth being of no consequence (Fig. 3.31).

x=17; Ceiling[x] Floor[x] 0 x = Pi; Ceiling[x] Floor[x] 1

GCD[5355, 40425] 105 LCM[5355, 40425] 2 061 675

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