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Decibel values are calculated according to the logarithm of the ratio of change. Suppose a sound produces a power of P watts on your eardrums, and then it changes (either getting louder or softer) to a level of Q watts. The change in decibels is obtained by dividing out the ratio Q/P, taking its base-10 logarithm, and then multiplying the result by 10: dB = 10 log (Q/P) As an example, suppose a speaker emits 1 W of sound, and then you turn up the volume so that it emits 2 W of sound power. Then P = 1 and Q = 2, and dB = 10 log (2/1) = 10 log 2 = 10 0.3 = 3 dB. This is the minimum detectable level of volume change if you aren t expecting it: a doubling of the actual sound power. If you turn the volume level back down again, then P/Q = 1/2 = 0.5, and you can calculate dB = 10 log 0.5 = 10 -0.3 = 3 dB. A change of plus or minus 10 dB is an increase or decrease in sound power of 10 times. A change of plus or minus 20 dB is a hundredfold increase or decrease in sound power. It is not unusual to encounter sounds that range in loudness over plus/minus 60 dB or more a millionfold variation.

As stated in the preceding paragraphs, perceived levels of sound change according to the logarithm of the actual sound power level. The same is true for various other phenomena, too, such as visiblelight intensity and radio-frequency signal strength. Specialized units have been defined to take this into account. The fundamental unit of sound-level change is called the decibel, symbolized as dB. A change of +1 dB is the minimum increase in sound level that you can detect if you are expecting it. A change of 1 dB is the minimum detectable decrease in sound volume, when you are anticipating the change. Increases in volume are given positive decibel values, and decreases in volume are given negative decibel values. If you aren t expecting the level of sound to change, then it takes about +3 dB or 3 dB to make a noticeable difference. Changes in intensity, when expressed in decibels, are sometimes called gain and loss. Positive decibel changes represent gain, and negative decibel changes represent loss. The sign (plus or minus) is usually absent when speaking of changes in terms of decibel gain or decibel loss. If you say that a certain system causes 5 dB of loss, you are saying that the gain of that circuit is 5 dB.

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YOU VE SEEN HOW INDUCTIVE AND CAPACITIVE REACTANCE CAN BE REPREsented along a line perpendicular to resistance. In this chapter, you ll put all three of these quantities R, XL, and XC together, forming a complete, working definition of impedance. You ll also get acquainted with admittance, impedance s evil twin. To express the behavior of alternating-current (ac) circuits, you need two dimensions, because ac has variable frequency along with variable current. One dimension (resistance) will suffice for dc, but not for ac. In this chapter and the two that follow, the presentation is rather mathematical. You can get a grasp of the general nature of the subject matter without learning how to do all of the calculations presented. The mathematics is given for those of you who wish to gain a firm understanding of how ac circuits behave.

Calculating Decibel Values Decibel values are calculated according to the logarithm of the ratio of change. Suppose a sound produces a power of P watts on your eardrums, and then it changes (either getting louder or softer) to a level of Q watts. The change in decibels is obtained by dividing out the ratio Q/P, taking its base10 logarithm (symbolized as log10 or simply as log), and then multiplying the result by 10. Mathematically:

For the longest time, access described the manner in which customers reached the network for the transport of voice services In the last 20 years, however, that definition has changed dramatically In 1981 (20 years ago), IBM changed the world when it introduced the PC, and in 1984 the Macintosh arrived, bringing well-designed and organized computing power to the masses Shortly thereafter, hobbyists began to take advantage of emergent modem technology and created online databases, the first bulletin board systems that enabled people to send simple text messages to each other This accelerated the modem market dramatically, and before long, data became a common component of local loop traffic At that time, there was no concept of Instant Messenger or of the degree to which e-mail would fundamentally change the way people communicate and do business.

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