Intel  Pentium II P2
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Intel  Pentium II P2
Fuse shortcircuit performance characteristics are published in the form of peak letthrough (Ip) graphs and I 2t graphs. Ip (peak current) is simply the peak of the shaded triangular waveform, which increases as the fault current increases, as shown in Fig. 1.34(b). The electromagnetic forces, which can cause mechanical damage to equipment, are proportional to Ip2 . I 2t represents heat energy measured in units of A2 s (ampere squared seconds) and is documented on I 2t graphs. These I 2t graphs, as illustrated in Fig. 1.34(c), provide three values of I 2t: minimum melting I 2t, arcing I 2t,...
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 FIGURE 1.33 Timecurrent characteristic curves. Fuse shortcircuit performance characteristics are published in the form of peak letthrough (Ip) graphs and I 2t graphs. Ip (peak current) is simply the peak of the shaded triangular waveform, which increases as the fault current increases, as shown in Fig. 1.34(b). The electromagnetic forces, which can cause mechanical damage to equipment, are proportional to Ip2 . I 2t represents heat energy measured in units of A2 s (ampere squared seconds) and is documented on I 2t graphs. These I 2t graphs, as illustrated in Fig. 1.34(c), provide three values of I 2t: minimum melting I 2t, arcing I 2t, and total clearing I 2t. I 2t and Ip shortcircuit performance characteristics can be used to coordinate fuses and other equipment. In particular, I 2t values are often used to selectively coordinate fuses in a distribution system. © 2000 by CRC Press LLC
 FIGURE 1.34 (a) Fuse shortcircuit operation. (b) Variation of fuse peak letthrough current Ip . (c) I 2 t graph. Selective Coordination In any power distribution system, selective coordination exists when the fuse immediately upstream from a fault operates, leaving all other fuses further upstream unaffected. This increases system reliability by isolating the faulted branch while maintaining power to all other branches. Selective coordination is easily assessed by © 2000 by CRC Press LLC
 comparing the I 2t characteristics for feeder and branch circuit fuses. The branch fuse should have a total clearing I 2t value that is less than the melting I 2t value of the feeder or upstream fuse. This ensures that the branch fuse will melt, arc, and clear the fault before the feeder fuse begins to melt. Standards Overload and shortcircuit characteristics are well documented by fuse manufacturers. These characteristics are standardized by product standards written in most cases by safety organizations such as CSA (Canadian Standards Association) and UL (Underwriters Laboratories). CSA standards and UL specify product designa tions, dimensions, performance characteristics, and temperature rise limits. These standards are used in con junction with national code regulations such as CEC (Canadian Electrical Code) and NEC (National Electrical Code) that specify how the product is applied. IEC (International Electrotechnical Commission—Geneva, Switzerland) was founded to harmonize electrical standards to increase international trade in electrical products. Any country can become a member and participate in the standardswriting activities of IEC. Unlike CSA and UL, IEC is not a certifying body that certiﬁes or approves products. IEC publishes consensus standards for national standards authorities such as CSA (Canada), UL (USA), BSI (UK) and DIN (Germany) to adopt as their own national standards. Products North American lowvoltage distribution fuses can be classiﬁed under two types: Standard or Class H, as referred to in the United States, and HRC (high rupturing capacity) or currentlimiting fuses, as referred to in Canada. It is the interrupting rating that essentially differentiates one type from the other. Most Standard or Class H fuses have an interrupting rating of 10,000 A. They are not classiﬁed as HRC or currentlimiting fuses, which usually have an interrupting rating of 200,000 A. Selection is often based on the calculated available shortcircuit current. In general, shortcircuit currents in excess of 10,000 A do not exist in residential applications. In commercial and industrial installations, shortcircuit currents in excess of 10,000 A are very common. Use of HRC fuses usually means that a fault current assessment is not required. Standard—Class H In North America, Standard or Class H fuses are available in 250 and 600V ratings with ampere ratings up to 600 A. There are primarily three types: onetime, timedelay, and renewable. Rating for rating, they are all constructed to the same dimensions and are physically interchangeable in standardtype fusible switches and fuse blocks. Onetime fuses are not reusable once blown. They are used for generalpurpose resistive loads such as lighting, feeders, and cables. Timedelay fuses have a speciﬁed delay in their overload characteristics and are designed for motor circuits. When started, motors typically draw six times their full load current for approximately 3 to 4 seconds. This surge then decreases to a level within the motor fullload current rating. Timedelay fuse overload characteristics are designed to allow for motor starting conditions. Renewable fuses are constructed with replaceable links or elements. This feature minimizes the cost of replacing fuses. However, the concept of replacing fuse elements in the ﬁeld is not acceptable to most users today because of the potential risk of improper replacement. HRC HRC or currentlimiting fuses have an interrupting rating of 200 kA and are recognized by a letter designation system common to North American fuses. In the United States they are known as Class J, Class L, Class R, etc., and in Canada they are known as HRCIJ, HRCL, HRCIR, and so forth. HRC fuses are available in ratings up to 600 V and 6000 A. The main differences among the various types are their dimensions and their short circuit performance (Ip and I 2t) characteristics. © 2000 by CRC Press LLC
 One type of HRC fuse found in Canada, but not in the United States, is the HRCIIC or Class C fuse. This fuse was developed originally in England and is constructed with boltontype blade contacts. It is available in a voltage rating of 600 V with ampere ratings from 2 to 600 A. Some higher ampere ratings are also available but are not as common. HRCIIC fuses are primarily regarded as providing shortcircuit protection only. Therefore, they should be used in conjunction with an overload device. HRCIR or Class R fuses were developed in the United States. Originally constructed to Standard or Class H fuse dimensions, they were classiﬁed as Class K and are available in the United States with two levels of short circuit performance characteristics: Class K1 and Class K5. However, they are not recognized in Canadian Standards. Under fault conditions, Class K1 fuses limit the Ip and I 2t to lower levels than do Class K5 fuses. Since both Class K1 and K5 are constructed to Standard or Class H fuse dimensions, problems with inter changeability occur. As a result, a second generation of these K fuses was therefore introduced with a rejection feature incorporated in the end caps and blade contacts. This rejection feature, when used in conjunction with rejectionstyle fuse clips, prevents replacement of these fuses with Standard or Class H 10kA I.R. fuses. These rejection style fuses are known as Class RK1 and Class RK5. They are available with timedelay or nontime delay characteristics and with voltage ratings of 250 or 600 V and ampere ratings up to 600 A. In Canada, CSA has only one classiﬁcation for these fuses, HRCIR, which have the same maximum Ip and I 2t currentlimiting levels as speciﬁed by UL for Class RK5 fuses. HRCIJ or Class J fuses are a more recent development. In Canada, they have become the most popular HRC fuse speciﬁed for new installations. Both timedelay and nontimedelay characteristics are available in ratings of 600 V with ampere ratings up to 600 A. They are constructed with dimensions much smaller than HRCIR or Class R fuses and have end caps or blade contacts which ﬁt into 600V Standard or Class Htype fuse clips. However, the fuse clips must be mounted closer together to accommodate the shorter fuse length. Its shorter length, therefore, becomes an inherent rejection feature that does not allow insertion of Standard or HRCIR fuses. The blade contacts are also drilled to allow bolton mounting if required. CSA and UL specify these fuses to have maximum shortcircuit currentlimiting Ip and I 2t limits lower than those speciﬁed for HRCIR and HRCIIC fuses. HRCIJ fuses may be used for a wide variety of applications. The timedelay type is commonly used in motor circuits sized at approximately 125 to 150% of motor fullload current. HRCL or Class L fuses are unique in dimension but may be considered as an extension of the HRCIJ fuses for ampere ratings above 600 A. They are rated at 600 V with ampere ratings from 601 to 6000 A. They are physically larger and are constructed with boltontype blade contacts. These fuses are generally used in low voltage distribution systems where supply transformers are capable of delivering more than 600 A. In addition to Standard and HRC fuses, there are many other types designed for speciﬁc applications. For example, there are medium or highvoltage fuses to protect power distribution transformers and medium voltage motors. There are fuses used to protect sensitive semiconductor devices such as diodes, SCRs, and triacs. These fuses are designed to be extremely fast under shortcircuit conditions. There is also a wide variety of dedicated fuses designed for protection of speciﬁc equipment requirements such as electric welders, capacitors, and circuit breakers, to name a few. Trends Ultimately, it is the electrical equipment being protected that dictates the type of fuse needed for proper protection. This equipment is forever changing and tends to get smaller as new technology becomes available. Present trends indicate that fuses also must become smaller and faster under fault conditions, particularly as available shortcircuit fault currents are tending to increase. With free trade and the globalization of industry, a greater need for harmonizing product standards exists. The North American fuse industry is taking big steps toward harmonizing CSA and UL fuse standards, and at the same time is participating in the IEC standards process. Standardization will help the electrical industry to identify and select the best fuse for the job—anywhere in the world. © 2000 by CRC Press LLC
 Deﬁning Terms HRC (high rupturing capacity): A term used to denote fuses having a high interrupting rating. Most low voltage HRCtype fuses have an interrupting rating of 200 kA rms symmetrical. I2 t (ampere squared seconds): A convenient way of indicating the heating effect or thermal energy which is produced during a fault condition before the circuit protective device has opened the circuit. As a protective device, the HRC or currentlimiting fuse lets through far less damaging I 2t than other protective devices. Interrupting rating (I.R.): The maximum value of shortcircuit current that a fuse can safely interrupt. Related Topic 1.1 Resistors References R .K. Clidero and K .H. Sharpe, Application of Electrical Construction, Ontario, Canada: General Publishing Co. Ltd., 1982. Gould Inc., Shawmut Advisor, Circuit Protection Division, Newburyport, Mass. C. A. Gross, Power Systems Analysis, 2nd ed., New York: Wiley, 1986. E. Jacks, High Rupturing Capacity Fuses, New York: Wiley, 1975. A. Wright and P.G. Newbery, Electric Fuses, London: Peter Peregrinus Ltd., 1984. Further Information For greater detail the “Shawmut Advisor” (Gould, Inc., 374 Merrimac Street, Newburyport MA 01950) or the “Fuse Technology Course Notes” (Gould Shawmut Company, 88 Horner Avenue, Toronto, Canada M8Z5Y3) may be referred to for fuse performance and application. © 2000 by CRC Press LLC
 Dorf, R.C., Wan, Z., Paul, C.R., Cogdell, J.R. “Voltage and Current Sources” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
 2 Voltage and Current Sources Richard C. Dorf 2.1 Step, Impulse, Ramp, Sinusoidal, Exponential, and University of California, Davis DC Signals Step Function • The Impulse • Ramp Function • Sinusoidal Zhen Wan Function • DCSignal University of California, Davis 2.2 Ideal and Practical Sources Clayton R. Paul Ideal Sources • Practical Sources University of Kentucky, Lexington 2.3 Controlled Sources What Are Controlled Sources? • What Is the Signiﬁcance of J. R. Cogdell Controlled Sources? • How Does the Presence of Controlled Sources University of Texas at Austin Affect Circuit Analysis? 2.1 Step, Impulse, Ramp, Sinusoidal, Exponential, and DC Signals Richard C. Dorf and Zhen Wan The important signals for circuits include the step, impulse, ramp, sinusoid, and dc signals. These signals are widely used and are described here in the time domain. All of these signals have a Laplace transform. Step Function The unitstep function u(t) is deﬁned mathematically by ì1, ï t ³ 0 u(t ) = í ï0, î t < 0 Here unit step means that the amplitude of u(t) is equal to 1 for t ³ 0. Note that we are following the convention that u(0) = 1. From a strict mathematical standpoint, u(t) is not deﬁned at t = 0. Nevertheless, we usually take u(0) = 1. If A is an arbitrary nonzero number, Au(t) is the step function with amplitude A for t ³ 0. The unit step function is plotted in Fig. 2.1. The Impulse The unit impulse d(t), also called the delta function or the Dirac distribution, is deﬁned by © 2000 by CRC Press LLC
 u(t) Kd(t) 1 (K) t t 0 1 2 3 0 FIGURE 2.1 Unitstep function. FIGURE 2.2 Graphical representation of the impulse Kd(t) d(t ) = 0, t ¹ 0 e ò e d(l ) d l = 1, for any real number e > 0 The ﬁrst condition states that d(t) is zero for all nonzero values of t, while the second condition states that the area under the impulse is 1, so d(t) has unit area. It is important to point out that the value d(0) of d(t) at t = 0 is not deﬁned; in particular, d(0) is not equal to inﬁnity. For any real number K, K d(t) is the impulse with area K. It is deﬁned by K d(t ) = 0, t ¹ 0 e ò e K d(l ) d l = K , for any real number e > 0 The graphical representation of K d(t) is shown in Fig. 2.2. The notation K in the ﬁgure refers to the area of the impulse K d(t). The unitstep function u(t) is equal to the integral of the unit impulse d(t); more precisely, we have t u(t ) = ò¥ d(l ) d l , all t except t = 0 Conversely, the ﬁrst derivative of u(t), with respect to t, is equal to d(t), except at t = 0, where the derivative of u(t) is not deﬁned. Ramp Function The unitramp function r(t) is deﬁned mathematically by r(t) ìt , t ³ 0 r (t ) = í î0, t < 0 1 Note that for t ³ 0, the slope of r(t) is 1. Thus, r(t) has unit slope, which is the reason r(t) is called the unitramp t 0 1 2 3 function. If K is an arbitrary nonzero scalar (real num ber), the ramp function Kr(t) has slope K for t ³ 0. The FIGURE 2.3 Unitramp function unitramp function is plotted in Fig. 2.3. The unitramp function r(t) is equal to the integral of the unitstep function u(t); that is, t r (t ) = ò ¥ u (l ) d l © 2000 by CRC Press LLC
 A cos(wt + q) A p + 2q p  2q 2w 2w t 0 3p + 2q q 3p  2q 2w w 2w –A FIGURE 2.4 The sinusoid A cos(wt + q) with –p/2 < q < 0. Conversely, the ﬁrst derivative of r(t) with respect to t is equal to u(t), except at t = 0, where the derivative of r(t) is not deﬁned. Sinusoidal Function The sinusoid is a continuoustime signal: A cos(wt + q). Here A is the amplitude, w is the frequency in radians per second (rad/s), and q is the phase in radians. The frequency f in cycles per second, or hertz (Hz), is f = w/2p. The sinusoid is a periodic signal with period 2p/w. The sinusoid is plotted in Fig. 2.4. Decaying Exponential In general, an exponentially decaying quantity (Fig. 2.5) can be expressed as a = A e –t/t where a = instantaneous value A = amplitude or maximum value e = base of natural logarithms = 2.718 … t = time constant in seconds t = time in seconds The current of a discharging capacitor can be approxi mated by a decaying exponential function of time. FIGURE 2.5 The decaying exponential. Time Constant Since the exponential factor only approaches zero as t increases without limit, such functions theoretically last forever. In the same sense, all radioactive disintegrations last forever. In the case of an exponentially decaying current, it is convenient to use the value of time that makes the exponent –1. When t = t = the time constant, the value of the exponential factor is 1 1 e  t t = e 1 = = = 0.368 e 2.718 In other words, after a time equal to the time constant, the exponential factor is reduced to approximatly 37% of its initial value. © 2000 by CRC Press LLC
 i(t) K t 0 FIGURE 2.6 The dc signal with amplitude K. DC Signal The direct current signal (dc signal) can be deﬁned mathematically by i(t) = K –¥ < t < +¥ Here, K is any nonzero number. The dc signal remains a constant value of K for any –¥ < t < ¥. The dc signal is plotted in Fig. 2.6. Deﬁning Terms Ramp: A continually growing signal such that its value is zero for t £ 0 and proportional to time t for t > 0. Sinusoid: A periodic signal x(t) = A cos(wt + q) where w = 2pf with frequency in hertz. Unit impulse: A very short pulse such that its value is zero for t ¹ 0 and the integral of the pulse is 1. Unit step: Function of time that is zero for t < t0 and unity for t > t0. At t = t0 the magnitude changes from zero to one. The unit step is dimensionless. Related Topic 11.1 Introduction References R.C. Dorf, Introduction to Electric Circuits, 3rd ed., New York: Wiley, 1996. R.E. Ziemer, Signals and Systems, 2nd ed., New York: Macmillan, 1989. Further Information IEEE Transactions on Circuits and Systems IEEE Transactions on Education 2.2 Ideal and Practical Sources Clayton R. Paul A mathematical model of an electric circuit contains ideal models of physical circuit elements. Some of these ideal circuit elements (e.g., the resistor, capacitor, inductor, and transformer) were discussed previously. Here we will deﬁne and examine both ideal and practical voltage and current sources. The terminal characteristics of these models will be compared to those of actual sources. © 2000 by CRC Press LLC
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