ection at the end of this book. 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 Radio Engineering Concepts TABLE 1.1 Decibel Conversion to Ratios Factor Typical Percentage Decibels (exact ratio) rounding increase 1.02329 1.25892 25.89 1.58489 58.49 1.99526 99.53 0.30103 3.0103 100.00 2.51188 151.19 0.47712 4.7712 200.00 3.16227 216.23 3.98107 298.11 0.60206 6.0206 300.00 5.01187 401.19 0.77815 7.7815 500.00 6.30957 530.96 7.94328 694.33 900.00 9,900.00 1,000 10,000 100,000 10,000,000,000 10,000,000,000,000 factors multiply, SO a 2-bel change followed by a 3-bel change is a 5-bel change because 1000 times 100 is 100,000. Negative bels are reduction factors, so - 1 bel is a factor of 0.1 and -4 bels is a factor of 0.0001. Fractional bels require a little high-school mathematics. One-half of a bell would be the square root of 10, approximately 3.16228 on a calculator. Using a logarithm table or the LOG function on a calculator, we can see that a factor of 2 would be 0.30103 bel and a factor of 3 would be 0.47712 bel. Using the addition rule, we see that a factor of 6 is 0.30103 + 0.47712 = 0.77815 bel. The bel scale becomes more intuitive when we multiply the values by 10 and use decibels (dB) instead of bels. A factor of 10 is 10 dB, and a factor of 100,000 is 50 dB. And a path loss of 10,000,000,000,000 comes out as 130 dB. The fractions are easier to deal with in decibels, too. A factor of 2 is 3 dB. Sure, the exact value for a factor of 2 is 3.0103 dB and the exact value for 3 dB is 1.9952, but it is a very rare occasion where the 0.2 percent difference is going to be important enough to matter. After living in the engineering world for a few weeks, most of us use 3 dB for a factor of 2 and 6 dB for a factor of 4 as freely as 20 dB for a factor of 100. After 6 months, most of us do not even remember which of these