# 9: Interfaces, Structures, and Enumerations in visual C# Writer code 128b in visual C# 9: Interfaces, Structures, and Enumerations

THE TRAPEZOID RULE
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SOLUTION Refer to Fig. 4.8 as we reason along. Let f (x) = x 2 .
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The multiplicative constant, 10 in this example, gives us a way to compare the relative strength differences between two quantities. That is, if the difference between IdB1 and IdB2 is 10 dB, then the intensity of I1 is ten times the strength of I2 . Note that since the multiplicative factor in (15.1) is 20, a difference of 20 dB indicates that one signal has a magnitude 20 times as large as the other. The log function is a useful measure of signal strength for two good reasons. First, quantities can often vary quite a bit in strength sometimes over many orders of magnitude. By using the logarithm we can rescale that variation down to a more manageable number. One famous example where this behavior is apparent is the Richter scale used to characterize the strength of earthquakes. The details of the Richter scale don t concern us; all that is important for our purposes is that this is a logarithmic quantity. This means that each increment on the Richter scale describes an order-of-magnitude increase in strength. An earthquake that is a 7 on the Richter scale is 10 times as strong as an earthquake that is a 6. In our case, using logarithms allows us to scale down a wide range of frequencies into a small scale that can be visualized and plotted more easily. This works in a way similar to the Richter scale. In our case, when the magnitude of the frequency increases by a factor of 10, then log increases by 1. The second reason that using logarithms is useful is that log(AB) = log A + log B (15.3)
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Let ( t) = 75 10t2 + t. Of course the rate of loss of air is given by ( 1) . We therefore calculate ( 1) = lim ( 1 + h) ( 1) h h 0 [75 10( 1 + h) 2 + ( 1 + h) ] [75 10 12 + 1] h h 0 [75 ( 10 + 20h + 10h2 ) + ( 1 + h) ] [66] h h 0 19h 10h2 h h 0
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One should check that the inputs and outputs can interface with standard logic levels such as ICL or TTL. Whereas telecommunications equipment normally operates with 75- impedances, high-speed general circuit applications will probably require 50- connections. A general-purpose test set will probably have programmable output levels and offsets, e.g., 0.25 to 2 V p-p with 10 mV resolution. Both data and inverted-data outputs usually are provided. In high-speed testers, check the jitter specification on the clock and data outputs. This usually is specified in picoseconds (e.g., 10 ps RMS) when transmitting a PRBS. Wave shape also is important and is defined by the transition times and overshoot. A poor wave shape from the pattern generator may limit the testing and hence the quality of development work. One final point, sometimes overlooked in digital systems, is the return loss or impedance matching at the tester input and output. Compared to analog systems, return loss is not quite so important; anything less than 10 to 15 dB return loss, however, may cause problems with transmission-line reflections and degraded pulse shape. This is particularly important when testing very high-speed systems and components. The G.703 interface specification gives recommended return loss values for telecommunication systems.
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Refer to the text in this chapter if necessary. Answers are in the back of the book. 1. An ultracentrifuge operates on the principle of a. electrophoresis. B. spinning very fast. c. sedimentation. D. gravity. 2. The various forms of EM spectroscopy typically measure some property of the EM radiation as a function of A. wavelength. B. intensity. C. speed of light. d. density. 3. Oxygen-free hemoglobin absorbs 10 times more light at 690 nm than fully oxygenated hemoglobin. If a sample of hemoglobin is found to absorb only 5 times as much light as fully oxygenated hemoglobin, what percentage of the hemoglobin molecules have oxygen bound to them (Assume that each hemoglobin molecule is either fully bound or fully unbound.) A. 5% B. 10% C. 50% D. 690% 4. Fluorescence is the opposite of A. darkness. B. incandescence. c. absorption. D. X-ray crystallography. 5. A mass spectrograph characterizes molecules according to their molecular weight by A. placing them on a scale. B. weighing them in a vacuum. C. ionizing them and passing them through a magnetic field in a vacuum. D. ionizing them and passing them through an electric field in a gel. 6. In order for X-ray crystallography to work, A. the X-rays must be focused using a glass crystal. B. the X-rays must be bound to the molecules being studied. C. the molecules must be in a regular, repeating arrangement. D. the molecules must not cause electromagnetic interference.
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