 reduced, the gain in decibels results in a negative value. Figure 3.21 presents an element in a telecommunications network with a certain input power and an output power. The formulas of loss (attenuation) and gain are given in the figure as well. In telecommunications systems we usually have many elements in a chain. If the overall gain or loss needs to be calculated, all gain figures (which Introduction to Telecommunications Network Engineering Gain dB Loss in dB Overall gain: g=g * g Overall gain in dB: gd = 91,db + 92,dB For example, a gain of 100000000 corresponds to the gain of 80 dB Figure 3.21 Gain, loss, and decibels. often are very large or small numbers) must be multiplied. If the gain of each element is presented in decibels, the figures (which usually have values of less than 100) are added along the chain to determine the overall gain in decibels as shown in Figure 3.21. Decibels allow us to add small positive or negative numbers instead of multiplying with very large or very small numbers. For example, a gain of 100,000,000 corresponds to a gain of 80 dB. Note that the decibel is the measure of power gain and, if we are inter- ested in how voltage level changes, the impedances must be considered. The voltage and power gains are the same only if the impedances at the points where the power and voltage are measured are the same. The following for- mula gives the power gain if input and output voltages and impedance are known: (3.12) The impedances in the preceding equation are assumed to be real numbers. 3.8.2 Power Levels In the previous section we expressed power ratios in decibels. That does not tell us anything about the actual power in watts, only the ratio. Instead of expressing the actual power in watts, we can use the decibel-based figures for Signals Carried over the Network this measurement also. Power levels in practical systems may vary from picowatts to tens of watts, corresponding to variations from 1 to 1,000,000,000,000. Power measures based on decibels can be used to express this wi