001 kilowatts (kW), 1000 mW = 1 W, 1 kW = 1000 W. Fundamentals of Telecommunications, Second Edition, by Roger L. Freeman ISBN 0-471-71045-8 Copyright © 2005 by Roger L. Freeman LEARNING DECIBELS AND THEIR APPLICATIONS We will start off in the power domain (watts are in the power domain, SO are milliwatts; volts and amperes are not). We will deal with volts and amperes later. Again, the decibel expresses a ratio. In the power domain (e.g., level is measured in watts or milliwatts), the decibel value of such a ratio is 10 X logarithm of the ratio. Consider this network: Network We are concerned about the ratio of P1/P2 or vice versa. Algebraically we express the decibel by this formula: dB value = 10 log (P1/P2) or 10 log(P2/P1). (C1.1) Some readers may feel apprehensive about logarithms. The logarithm (log) used here is to the number base 10. A logarithm is an exponent. In our case it is the exponent of the number 10 such as the log is 0 101 10 the log is 1 102 100 the log is 2 103 1000 the log is 3 104 = 10,000 the log is 4, etc. For numbers less than 1, we use decimal values, SO 10° = 1 the log is 0 the log is -1 10-2 0.01 the log is -2 10-3 0.001 the log is -3 10-4 0.0001 the log is -4, etc. Let us now express the decibel values of the same numbers: 10° = 1 dB value = 10 log 1 = 10 x 0 = 0 dB 101 10 log = dB value = 10 log 10 = 10 x 1 = 10 dB 102 = 100 log = dB value = 10 log 100 = 10 x 2 = 20 dB 103 = 1000 log = 3 dB value = 10 log 1000 = 10 x 3 = 30 dB 104 = 10,000 log = 4 dB value = 10 log 10,000 = 10 X 4 = 40 dB, etc. 10-1 0.1 log = -1 dB value = 10 log.1 = 10 X -1 = 10 dB 10-2 0.01 log = -2 dB value = 10 log. = 10 X -2 = -20 dB 10-3 = 0.001 log = -3 dB value = 10 log .001 = 10 X -3 = -30 dB 10-4 =0.0001 log = -4 dB value = 10 log .0001 = 10 -4 = -40 dB, etc. We now have learned how to handle power ratios of 10, 100, 1000, and SO on, and 0.1, 0.01, 0.001, and SO on. These, of course, lead to dB values of +10 dB, +20 dB, and +30 dB; -10 dB, -20 dB, -30 dB, and SO on. The next step we will take is to learn t