Decibel Power Ratios

In this system, the output of the signal is twice as strong as the input to the system. As you can see, this constant multiplication of the ratios can be wearisome, and the products can be extremely small or large. Therefore, the discovery that adding the logarithms of the numbers would yield the same result as this calculation led early scientists to develop the unit of measure called the bel. The bel, named in honor of Alexander Graham Bell, expresses the logarithmic ratio between the input and output of any given component, circuit, or system. 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) and taking the base 10 logarithm (log ₁₀) of the resulting quotient. Thus, if an amplifier doubles the power, the quotient will be 2. When you consult a logarithm table, you will find that the base 10 logarithm of 2 is 0.3; so the power gain of the amplifier is 0.3 bel. Experience has shown that the bel is a rather large unit that is difficult to apply. A more practical, easier unit to apply is the decibel (1/10 bel). Any figure expressed in bels can be converted to decibels by multiplying the value by 10. Thus the ratio of 0.3 bel is equal to 3 decibels. The reason the decibel system is used to express signal strength is shown in table 1-2. For example, saying that a reference signal has increased 50 dB is much easier than saying that the output has increased 100,000 times. The basis of the decibel measuring system is the amount of increase or decrease from a reference level. Whether the input power is increased from 1 watt to 1-4 100 watts or from 1,000 watts to 100,000 watts, the amount of increase, or gain, is still 100 times or 20 dB. Examine table 1-2 again, taking particular note of the power ratios for source levels 3 dB and 6 dB. As the table illustrates, an increase of 3 dB represents a doubling of power. The reverse is also true. If a signal decreases by 3 dB, half of the power is lost. For example, a 1,000-watt signal decreased by 3 dB will equal 500 watts, while a 1,000-watt signal increased by 3 dB will equal 2,000 watts. Table 1-2.—Decibel Power Ratios When you speak of the dB level of a signal, you are actually speaking of the logarithmic comparison between the input and output signals. The input signal is normally used as the reference signal. In some instances, a standard reference signal must be used in place of the input signal. The most widely used reference level is a 1-milliwatt signal (600-ohm load). When the 1-milliwatt reference is used, the standard decibel abbreviation of dB is changed to dBm; dBms are used as an indication of power, while dBs are used to indicate the ratio between the input and output. A signal level of +3 dBm is 3 dB above 1 milliwatt, and a signal level of –3 dBm is 3 dB below 1 milliwatt. Whether you are using dB or dBm, a plus sign (+) or no sign indicates that the output level is