In this system, the output of the signal is twice asstrong as the input to the system.As you can see, this constant multiplication of theratios can be wearisome, and the products can beextremely small or large. Therefore, the discoverythat adding the logarithms of the numbers would yieldthe same result as this calculation led early scientiststo develop the unit of measure called the bel.The bel, named in honor of Alexander GrahamBell, expresses the logarithmic ratio between the inputand output of any given component, circuit, orsystem. The bel maybe expressed in voltage, current,sound levels, or power. The formula is as follows:The gain of an amplifier can be expressed in bels(N) by dividing the output (P1) by the input (P2) andtaking the base 10 logarithm (log _{10}) of the resultingquotient. Thus, if an amplifier doubles the power, thequotient will be 2. When you consult a logarithmtable, you will find that the base 10 logarithm of 2 is0.3; so the power gain of the amplifier is 0.3 bel.Experience has shown that the bel is a rather largeunit that is difficult to apply. A more practical, easierunit to apply is the decibel (1/10 bel). Any figureexpressed in bels can be converted to decibels bymultiplying the value by 10. Thus the ratio of 0.3 belis equal to 3 decibels.The reason the decibel system is used to expresssignal strength is shown in table 1-2. For example,saying that a reference signal has increased 50 dB ismuch easier than saying that the output has increased100,000 times.The basis of the decibel measuring system is theamount of increase or decrease from a reference level.Whether the input power is increased from 1 watt to1-4100 watts or from 1,000 watts to 100,000 watts, theamount of increase, or gain, is still 100 times or20 dB. Examine table 1-2 again, taking particularnote of the power ratios for source levels 3 dB and 6dB. As the table illustrates, an increase of 3 dBrepresents a doubling of power. The reverse is alsotrue. If a signal decreases by 3 dB, half of the poweris lost. For example, a 1,000-watt signal decreased by3 dB will equal 500 watts, while a 1,000-watt signalincreased by 3 dB will equal 2,000 watts.Table 1-2.—Decibel Power RatiosWhen you speak of the dB level of a signal, youare actually speaking of the logarithmic comparisonbetween the input and output signals. The inputsignal is normally used as the reference signal. Insome instances, a standard reference signal must beused in place of the input signal. The most widelyused reference level is a 1-milliwatt signal (600-ohmload). When the 1-milliwatt reference is used, thestandard decibel abbreviation of dB is changed todBm; dBms are used as an indication of power, whiledBs are used to indicate the ratio between the inputand output.A signal level of +3 dBm is 3 dB above 1milliwatt, and a signal level of –3 dBm is 3 dB below1 milliwatt. Whether you are using dB or dBm, a plussign (+) or no sign indicates that the output level is