 is the approximation and which is the mathematically derived exact value. Using 5 dB instead of 4.77 dB for a factor of 3 is a little bit looser, but much of the time the difference between a factor of 3 and a factor of 3.16228 is not that important. We are not endorsing sloppy arithmetic, only using notation that articulates what needs to be communicated and is typical in the field of radio engineering. Table 1.1 shows some decibel values converted to their ratios. After a while in radio, or just about any other part of electrical engineering, the decibel scale seems easy and natural. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Radio Engineering Concepts Key Radio Concepts So far we have a ratio scale of decibels, but we have no units. The most familiar ap- plication of decibels in everyday life (for most of us anyway) is sound pressure level (SPL). A committee decreed that a pressure wave of 0.0002 dynes per square centime- ter is the unit of sound pressure level, the 0-dB point. We denote this very quiet level as 0 dB SPL. A subway train that is 1,000,000,000 times louder, 90 dB louder, is there- fore 90 dB SPL. And if I buy a pair of earplugs that say "15 dB attenuation" right on the box, I can expect the resulting subway sound level in my ears to be 75 dB SPL, which is 90 dB SPL minus 15-dB earplug attenuation. In the radio world, our 0-dB point, 0 dBm, is 1 mW of ERP. A 1-W radio signal 30 dBm, a 100-W radio signal is 50 dBm, and a received power level of 10 fW is 110 dBm. Losing 99.99999999999 percent between the transmitter and the receiver is ex- pressed as 130 dB of path loss in our decibel notation. Most of the time in radio engineering we stay in the decibel-ratio world of units. The magnitude range is one reason, but there is an even more compelling reason to think in terms of decibels rather than absolute amounts. The perf