 (29)3 = 1/2 log10 (38) + log 10(60) - 3 log 10 (29). The logarithm of a number has two components: its characteristic and its mantissa. The characteristic is an integer and the mantissa is a decimal. If the number in question is 10 or its multiple, the logarithm has a characteristic only, and its mantissa is .000000++ Consider Table B.1 containing selected the powers of 10. APPENDIX LEARNING DECIBELS AND THEIR APPLICATIONS C.1 LEARNING DECIBEL BASICS When working in the several disciplines of telecommunications, a clear understanding of the decibel (dB) is mandatory. The objective of this appendix is to facilitate this understanding and to encourage the reader to take advantage of this useful tool. The decibel relates to a ratio of two electrical quantities such as watts, volts, and amperes. If we pass a signal through some device, it will suffer a loss or achieve gain. Such a device may be an attenuator, amplifier, mixer, transmission line, antenna, subscriber loop, trunk, or a telephone switch, among others. To simplify matters, let's call this generic device a network, which has an input port and an output port, as shown: Signal Signal input output Network The input and output can be characterized by a signal level, which can be measured in either watts (W), amperes (A), or volts (V). The decibel is a useful tool to compare input- to-output levels or vice versa. Certainly we can say that if the output level is greater than the input level, the device displays a gain. The signal has been amplified. If the output has a lower level than the input, the network displays a loss. In our discussion we will indicate a gain with a positive sign (+) such as +3 dB, +11 dB, +37 dB; and a loss with a negative sign (-): -3 dB, -11 dB, -43 dB. At the outset it will be more convenient to use the same unit at the output of a network as at the input, such as watts. If we use watts, for example, it is watts or any of its metric derivatives. Remember: 1 W = 1000 milliwatts (mW), 1 W = 1,000,000 (1 x 106) microwatts (wW), 1 W = 0.