de power range in an easy way. The level of absolute power is often expressed in dBm, where the actual power is compared to 1-mW power. The power level in dBm is given by the expression 10 log10(P/1 mW) dBm. If we need to know absolute power in watts, we can easily calculate it from the given dBm value. Absolute power level dBm is commonly used instead of the absolute power in watts to express, for example, the optical output and received power of optical line systems or the received radio signal strength of a mobile telephone. It is very handy to use power levels in dBm together with gain or attenuation in decibels. Assume that the input power level in Figure 3.21 is given in dBms and we know gain in decibels. Then we obtain the out- put power level in dBm simply by adding input level and gain. This comes Pout = g . Pin Pout/1mWg.Pin/1mW Post. (3.13) To illustrate the use of decibels, we will look at some examples. Let us consider the radio relay system shown in Figure 3.22. Antenna gains and radio link loss are usually measured or given in decibels and receiver sensitiv- ity in dBm. To determine the received power level, we first change 9R,dB = 30 dB Radio link Ldb = 110 dB P2=?W Attenuation of the fiber 0.5 dB/km P1,dBm 0dBm Optical fiber link P2,dBm = ? dBm / 40 km Figure 3.22 Example radio relay and optical fiber systems. Introduction to Telecommunications Network Engineering transmission power P1 = 1W into dBm power level according to 10 log10(P1/1 mW) dBm = +30 dBm. Then we simply derive the received power level as P2,dBm = +30 dBm + 30 dB -110 dB +30 dB = -20 dBm. If we need the received power expressed in watts, we solve the equation -20 dBm = 10 g10(P2/1 mW) dBm to get P2 = 10 uW. Another example in Figure 3.22 shows an optical line system where transmission power level and length and attenuation of the fiber are given. Total fiber attenuation becomes Ldb = 40 km . 0.5 dB/km = 20 dB and then received power level will become P2,dBm = P1,dBm - 20 dB = -20 dBm. We have reviewed the main two types of decibe