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An engineering-level course for an engineering technology school Djafar K. Mynbaev New York City Technical College of the City University of New York Department of Electrical Engineering Technology and Telecommunications
Abstract This paper discussed the major features of engineering technology program and the possible way of teaching engineering-level course for such program. Examples are taken from fiber-optic communications course taught at the last year of baccalaureate program. The students of engineering technology schools are trained to work as technologists, which means their major responsibilities lie mostly in maintenance rather than in design, development, or research. This peculiarity implies that engineering-technology graduates must be able to understand technical documentations, mostly specifications sheets, describing devices and systems that they will be working with. Such academic training has to rely on deep knowledge of technology based, in turn, on general education. Typically, mathematical education in such schools doesn’t include courses higher than Calculus II and education in the physical science doesn’t exceed two courses in non-calculus physics. On the other hand, the scientific description of processes, devices, and systems that have to be learned requires deep discussions, involving fundamental knowledge of mathematics, physics, and other disciplines. Thus, some compromise should be reached between the need to deliver the full scale of required knowledge and certain restrictions in tools that could be used for this delivering. A fiber-optic communications course is particular challenging because it heavily relies on deep understanding of physical processes that control behavior of components and subsystems of this technology. Optical fiber itself, light sources (LEDs and laser diodes), photodiodes, all passive and active components of fiber-optic networks demand deep knowledge of classical optics, processes in semiconductor materials, micro-mechanical and micro-optical processes, and many aspects of the modern sciences. Detailed discussion of the above problems and examples of teaching of the specific course at New York City Technical College (NYCTC) constitutes the content of the proposed paper.
Major features of engineering technology programs When teaching for an engineering technology program, two issues should be addressed. First is the nature of the future work of the graduates. They are trained to work as technologists, which means their major responsibilities lie mostly in maintenance rather than in design, development, or research. This peculiarity implies that engineering-technology graduates must be able to understand technical documentations, mostly specifications sheets, describing devices and systems that they will be working with. Such academic training has to rely on deep knowledge of technology based, in turn, on general education. Second feature is the background of students of engineering technology programs in basic sciences. Typically, their mathematical education doesn’t include courses higher than Calculus II and education in the physical science doesn’t exceed two courses in non-calculus physics. On the other hand, the scientific description of processes, devices, and systems that have to be learned requires deep discussions, involving fundamental knowledge of mathematics, physics, and other disciplines. Thus, some compromise should be reached between the need to deliver the full scale of required knowledge and certain restrictions in tools that could be used for this delivering. A fiber-optic communications course is particular challenging because it heavily relies on deep understanding of physical processes that control behavior of components and subsystems of this technology. Optical fiber itself, light sources (LEDs and laser diodes), photodiodes, all passive and active components of fiber-optic networks demand deep knowledge of classical optics, processes in semiconductor materials, micro-mechanical and micro-optical processes, and many aspects of the modern sciences. Let us consider several examples of how we are trying to resolve the discussed problems at New York City Technical College (NYCTC).
Example 1: Reading the data sheet of an optical fiber Fiber-optic communications course at NYCTC usually starts with the brief introduction to the role of fiber optics in telecommunications and review of basics of optics. The first actual topic is, naturally, optical fiber itself. Several sessions are devoted to discussion of processes that cause attenuation and restriction in bandwidth of multimode and singlemode fibers. Consideration of physical mechanisms leading to absorption, scattering, and bending losses leads to discussion of manufacturing processes where all these flaws stem from. Intermodal and chromatic dispersions are discussed based on the physical processes of light propagation within an optical fiber. This discussion is followed by consideration on how these dispersions affect bandwidth (bit rate) of an optical fiber. All these sessions along with laboratory exercises are concluded by discussion of the data sheet of an optical fiber. For class discussion the specifications sheet from Plasma Optical Fibre Company given in the textbook [1] is used; as homework, students are assigned to discuss the data sheets from different manufacturers (Corning, Lucent Technologies, SpecTran, and others). The format and examples of such discussion can be found in [1]. The following is an example of discussion of a specific optical characteristic of a multimode optical fiber – bandwidth – given in a manufacturer’s data sheet. First, students are asked to discover what phenomenon stands behind this specification. Since they already know that bandwidth is restricted by intermodal and chromatic dispersions and that an intermodal dispersion puts much severe limitations on bandwidth, they have to make a conclusion that this specification is determined by the intermodal dispersion. Here we need to recall that intermodal dispersion is the phenomenon leading to spread of the output pulse. This widening is caused by the fact that light inside a fiber breaks down into separate discrete beams called modes. These beams travel at different angles with respect to a fiber centerline; therefore they arrive at the receiver end at different time. The output pulse is composed from the small pulses delivered by individual modes. Thus, the front edge of the output pulse is determined by the fastest mode, while its rear edge is determined by the slowest mode. This is why output pulse is spread as compared to the input. Secondly, bandwidth is usually specified in this data sheet as a set of numbers, such as 200/400 at 850/1300 nm, even without mentioning its units. This fact arises discussion how manufacturers measure the fiber bandwidth and why they use MHz-km rather than sheer MHz. Thus, students arrive to the conclusion that manufacturers specify bandwidth-length product rather than pure bandwidth. Third, students encourage questioning why the manufacturer needs to specify bandwidth as two numbers. This discussion turns to the question what essentially changes in optical fiber with changing of operating wavelength. Students have to recall that number of modes, N, depends on wavelength through the following formulas:
where
Here d is the core diameter, NA is the numerical aperture, and l is the operating wavelength [1]. From calculations using these formulas and made in the preceding sessions, students already know how number of modes depends on a wavelength; therefore, they come to the conclusion that the shorter the wavelength the more number of modes exist within a fiber and the more pulse spreading caused by intermodal dispersion. The discussion of other specifications is going in a similar way.
Example 2: Derivation of formula for a chromatic-dispersion parameter Another phenomenon restricting a bandwidth of optical fiber is chromatic dispersion. Students find a formula for chromatic-dispersion parameter in a data sheet, but they don’t know where this formula comes from. This is how we discuss this topic. Recall the basics of chromatic dispersion in an optical fiber: Output light pulse spreads while traveling down an optical fiber that restricts fiber bandwidth. Physics behind this result is as follows. A light pulse carrying information along an optical fiber is composed of light having several wavelengths. This is simply because there is no source in nature that can radiate a single wavelength. The key point is that the core refractive index depends on wavelength; thus, n = n (l ). In other words, for every specific wavelength there is a specific refractive index. Since the velocity of light, v, within a material is given by v = c/n, where c is the speed of light in a vacuum, then light of different wavelengths travels along the fiber at different velocities. Even if all of these beams propagate along the same path, they will arrive at the receiver end at different times. This results in the spreading of the output light pulse. This phenomenon is referred to as chromatic dispersion. Chromatic dispersion plays a major role in limiting the bandwidth of a singlemode fiber; this type of dispersion is important, too, for multimode fibers even though modal dispersion is the major factor limiting multimode-fiber bandwidth. Pulse spreading caused by chromatic dispersion can be calculated as follows: D tchrom = D (l )D l L, (3) where D(l ) is the chromatic-dispersion parameter measured in picoseconds per nanometer- kilometer, thus, we have ps/nm-km.; L is the transmission length over the fiber in km; and D l is the spectral width of a light source in nm (the characteristic of how many wavelengths this source radiates). Given the spectral width of a light source and the transmission length, a chromatic dispersion parameter becomes a critical characteristic of an optical fiber that determines the pulse spread caused by chromatic dispersion. Manufacturers specify the chromatic-dispersion parameter for optical fibers either by giving its value or via a formula. The formula D(l ) = (S0/4)l [1 – (l 0/l )4] (4) is, where S0 is the zero-dispersion slope in ps/(nm2-km), l 0 is the zero-dispersion wavelength, and l is the operating wavelength. A conventional singlemode fiber has the following typical values of these characteristics: S0 = 0.090 ps2/nm-km and l 0 = 1312 nm. Thus, for three commonly used operating wavelengths of 850 nm, 1300 nm, and 1550 nm , the values of a dispersion parameters of -89.433 ps/nm-km, -1.095 ps/nm-km, and 16.972 ps/nm-km. result It follows from Equation 4 that the chromatic-dispersion parameter, D (l ), is zero at the zero-dispersion wavelength. The value of l 0 is determined by the dispersive properties of the material from which the fiber core is made. The formula for a chromatic dispersion parameter can be derived as follows: An information light pulse, consisting of a group of spectral components, D l , travels at group velocity, vg, is equal to:
where w (rad/s) is a radian frequency and b (1/m) is a phase constant also called longitudinal propagation, or wave, constant. (For definition and detailed discussion of the meaning of group velocity see [1].) Letting t g
be a propagation delay per kilometer of the path length -- a unit propagation delay (ns/km). Both vg and t g are wavelength-dependent. To derive Equation 3, first expand t g into the Taylor series: t g (l ) = t g( l 0) + (l - l 0) ¶ t g/ ¶ l + ½ ( l - l 0 )2 ¶ t g2/ ¶ l 2 + ... , (7) where t g( l 0) is the unit propagation delay for the chosen wavelength, l 0. Further, limit the analysis to a linear approximation and denote: D(l ) = ¶ t g/¶ l , (8) where D(l ) is the chromatic dispersion parameter. Then given the notations D tchrom = t g(l ) - t g( l 0) and D l = (l - l 0), Equation (3) result. To step from Equation (8) to Equation (4), the formula t g = t g(l ) is employed in explicit form. Building this formula theoretically, that is deriving it based on a theoretical description of fiber material, is not productive. A graph describing this dependence is usually obtained experimentally. In such a case, the common approach is to find the mathematical expression describing the experimental graph as accurately as possible. Such a formula is known as a Sellmeier equation. There are several forms of the Sellmeier equation. The industry has accepted as its standard "Recommendation 455-80" of the Electronic Industries Alliance defining three-term t g = A + B 2 + C -2 (9) and five-term Sellmeier equation t g = A + B 4 + C 2 + D -4 + E -2 , (10) where coefficients should be determined experimentally. A three-term equation is used for a regular fiber at 1300 nm and five-term is used at 1550 nm. To derive Equation (4) from a three-term Sellmeier equation, consider ¶ t g/¶ l = 0. Find the zero-dispersion wavelength, l 04 = C/B. Then ¶ t g/¶ l takes the form ¶ t g/¶ l = 2B (l - l 04/l 3). Take ¶ D/¶ l , which is the slope S0 by definition. This yields S0 = ¶ 2 t g/ ¶ l 2 = 8B at l 0. Substitute S0 = 8B, Equation 4 results. D (l ) = ¶ t g/¶ l = S0/4[l - (l 04/l 3)] (11) This derivation is within the mathematical knowledge of engineering technology students, while delivering important information necessary to understand the origin and nature of chromatic dispersion.
Reference: 1. Djafar K. Mynbaev and Lowell L. Scheiner, Fiber-Optic Communications Technology, Upper Saddle River, N.J.: Prentice Hall, 2001.
Dr. Djafar K. Mynbaev NYCTC 300 Jay Street, V-733 Brooklyn, NY 11201 Phone: 718.260.5304 Fax: 718.254.8643 e-mail: dmynbaev@nyctc.cuny.edu |
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