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The bel had its origin in the Bell Telephone Labs, where workers needed a convenient way to express power losses in telephone lines as power ratios. Because the bel is a power ratio of 10, and this is a rather large ratio, it is convenient to divide it into tenths of bels, or decibels, abbr. dB. Ten dB is 1 bel; thus the DECIBEL is ten times the common log of the ratio of two powers. The DECIBEL was originally called the "transmission unit," or TU, by the Bell Labs people. Because of the properties of logarithms, it is easy and convenient to form some "rules of thumb" about decibels. The common log of 2 is 0.301, so a power ratio of 2 is 3.01 dB, normally taken as 3 dB. Therefore, any two powers differing by a factor of 2 will be 3 dB apart, and this applies to any type of power whatever, so long as it is power. Two light bulbs of 100W and 50W differ by 3 dB, just as electric motors of 1 horsepower and 2 horsepower differ by 3 dB. So, any time a power is doubled, it is increased by 3 dB. An increase of 6 dB represents two doublings of power, or a power ratio of 4. If an orchestra increases its SOUND PRESSURE LEVEL by 3 dB, its acoustic power output will be doubled. Another rule of thumb that is useful to remember is that 10 dB is a power ratio of 10. Any time a power is increased tenfold, it is increased by 10 dB; thus, a 200W power amplifier will put out 10 dB more electrical power than a 20W amplifier, and its sound power output will also increase by 10 dB. Another way to think of decibels is to think in terms of percentages. We all know what 10 percent means, and nobody thinks of percentages as being quantities of anything. A DECIBEL is nothing more than a power change of 27 percent, 3 dB is a power change of 100 percent, and 10 dB is a power change of 1,000 percent. Decibels have caused untold confusion among AUDIO people, and most of this is due to the failure to realize that decibels are not quantities of anything and can represent only power ratios. The trouble starts when we measure audio signals in volts rather than watts. If we note that power is proportional to the square of VOLTAGE, then a power ratio would be the same as a ratio of two squared voltages. Then, because the log of a squared ratio is twice the log of the simple ratio, we can see that the number of decibels is twenty times the log of the voltage ratio between two signals. Therefore, we can still measure in volts and express power ratios in decibels simply by multiplying the log of the voltage ratio by 20 instead of 10. Thus, dB = 10 log10 (P1/P2)
= 20 log10 (E1/E2)
Because we usually measure voltages in audio circuits instead of power, we need some more rules of thumb for voltage ratios. Here they are: a doubling of voltage is a 6dB increase, or a power factor of 4. A tenfold increase in voltage is a 20dB increase, or a power factor of 100. In the DECIBEL equation, we could replace the power in the denominator with a fixed amount of power. Then, dB would represent the power in relation to this reference. For instance, if P2 in the equation above is always 1 milliwatt, then the DECIBEL level will represent a specific amount of power. In other words, 3 dB would be 2 mW, 10 dB would be 10 mW, etc. This is commonly done, and if the reference power is 1 mW, the measured quantity is in dBm; dBm = 10 log (P1/0.001) W. The reference power could be any value, and sometimes different values are used, for instance dBW uses a reference of 1 W. Thus X dBW is X dB above 1W, and 3 dBW is 2W, etc. Decibels are also used in measuring SOUND PRESSURE. Because sound pressure squared is proportional to sound power, sound pressure in decibels is equal to 20 times the pressure ratio. If a reference pressure is chosen, then we can measure actual sound levels in decibels, and this is done. The reference pressure is 20 micropascals, 1 Pa being a pressure of 1 newton per square meter; 20mPa is about the threshold of hearing at 1,000 Hz for most people, so it is a convenient reference. In any case, it has been agreed upon by all international standards. A sound pressure level in decibels is always referred to this standard pressure. The GAIN of an AMPLIFIER commonly is expressed in decibels, and this can lead to further confusion: an amplifier with 3 dB of gain literally means it doubles the power in the signal, and an amplifier with 60 dB gain would be expected to increase the power one million times. This would be true if the IMPEDANCE of the input and output of the amplifier were the same, but this is seldom the case in practice. For instance, a power amplifier typically has a high INPUT IMPEDANCE and a very low OUTPUT IMPEDANCE for driving a LOUDSPEAKER. The true power gain of such an amplifier is very high because the input signal has essentially no LOAD and thus supplies almost no CURRENT or power. This power gain could be correctly expressed in decibels if the actual input and output powers were taken into consideration. This, however, is rarely done; it works out correctly only if the two impedances are the same, as is sometimes the case in amplifiers used in broadcasting and some sound systems. The impedance of such units is usually 600 OHMS. When amplifier gains are expressed in decibels, what is almost always meant is VOLTAGE GAIN, and as we have seen, a simple voltage ratio cannot be expressed in decibels by the definition of the DECIBEL. The formula used to calculate amplifier gain is dB (gain) = 20 log [V(output)/V(input)] and again, it would be correct only if the impedances
at the input and output were the same. It is small wonder that decibels
cause so much confusion!
dBsee DECIBEL.dBFLiterally, decibels referred to 1 femtowatt, or 10 to the minus fifteenth power watts. The dBF are used to specify SIGNAL levels at the RF inputs to FM tuners.dBkThe signal level in DECIBELS referred to 1,000 watts. dBk is most often used in radio and television transmitting stations.dBmLiterally, decibels referred to 1 milliwatt. Strictly speaking, the 1mW must be dissipated in a LOAD of 600 OHMS. The dBm is used in stating power levels of signals in broadcast and recording consoles and in tape recorders. 1 dBm into 600 ohms will result in 0.775 VOLTS RMS. This causes some confusion. The dBm is a power level and only results in 0.775 V when the LOAD IMPEDANCE is 600 ohms. See also DECIBEL, dBm.dBmThe signal level in DECIBELS referred to 1 microwatt.dBVLiterally, decibels referred to 1 volt RMS. This is an unfortunate usage because decibels cannot properly refer to simple voltages. See also DECIBEL.dBWLiterally, decibels referred to 1 WATT. Power amplifier output levels are sometimes specified in dBW, a 100-W AMPLIFIER is then 20 dBW. Power rating in dBW is numerically equal to ten times the common logarithm of the power output in watts. See also DECIBEL.Dynamic RangeThe dynamic range of a sound is the ratio of the strongest, or loudest, part to the weakest, or softest, part; it is measured in DECIBELS. A full orchestra may have a dynamic range of 90 dB, meaning the softest passages are 90 dB less powerful than the loudest ones. Dynamic range is a power ratio, and has nothing to do with the absolute level of the sound. An AUDIO signal also has a dynamic range, which is sometimes confused with SIGNAL-TO-NOISE RATIO. Rarely is the dynamic range of an audio system as large as the dynamic range of an orchestra because of several factors. The inherent NOISE of the recording medium determines the softest possible recorded sound, and the maximum SIGNAL, capacity of the system (CLIPPING level) limits the loudest possible sound. Many times an extremely wide dynamic range is not desirable (e.g., in radio broadcasting for listening in cars) and broadcasters frequently use COMPRESSORS and LIMITERS to reduce the dynamic range of the signals before they are transmitted. This type of SIGNAL, PROCESSING distorts the music in a more or less noticeable way, symphonic music being the most sensitive to it. The dynamic range of recorded signals can be increased by VOLUME EXPANDERS, such as the ones made by the dbx Company.Signal-to-Noise RatioSignal-to-noise ratio is the ratio of the signal power at a certain reference point in a CIRCUIT to the noise power which would exist there if the signal were removed. This ratio is expressed in DECIBELS. For instance, if a tape recorder has a signal-to-noise (S/N) ratio of 50 dB, the signal power at the output is 50 dB above the noise power. Measurement of S/N ratio is complicated by several factors. In a tape recorder, for example, a signal is recorded at a high level, approaching the onset of audible DISTORTION, and its VOLTAGE is measured with a voltmeter. Usually the signal is a SINE WAVE. Then the signal is removed from the input, and the remaining noise consisting of tape noise, HUM, electronic noise, etc., is measured with the voltmeter. Because the noise will be mostly random in nature, the voltmeter should be a true RMS meter. The ratio of these two measurements expressed in dB is the signal-to-noise ratio. This measurement ignores any type of noise which is present only when the signal is present, such as modulation noise. The subjective audibility of the measured noise will not be well correlated to the rms measurement of it because of our ears' varying sensitivity to different frequencies. Therefore, a FILTER or WEIGHTING NETWORK is usually placed in the meter's input. The characteristics of this weighting network are not universally agreed upon, so when comparing noise specifications, as between European and American equipment, care must be taken to see that the measurements were similarly made. In DIGITAL audio systems, the signal-to-noise ratio is defined as the ratio of the maximum possible sine wave signal power to the QUANTIZATION noise power, also expressed in dB. This is an unambiguous measure in LINEAR PCM systems; but in all other PCM schemes, the quantization noise depends strongly on the level of the signal being encoded. See PCM for a discussion of NONLINEAR PCM systems. See also DYNAMIC RANGE.Sound Pressure, Sound Pressure LevelA sound wave progressing through air causes the instantaneous air pressure at any given point to vary above and below the barometric pressure in accordance with the WAVEFORM of the sound. This variation in pressure is used as a quantitative measure of the strength of the sound, and is called sound pressure. This is the quantity which a PRESSURE MICROPHONE. measures, and if it is expressed on a DECIBEL scale and referred to a pressure of 20 micropascals, it is called sound pressure level. The reference pressure is 0 dB on the scale, and corresponds to the threshold of hearing at 1,000 HERTZ for a normal human ear (20 micropascals). Sound pressure level is what is measured by a sound level meter. See also LEVEL.(end of quotation from the book)
Decibel Calculation ExamplesDecibel difference between 60W (P1) and 120W (P2):= 10 log (P1/P2) = 10 log (60/120) = 10 log 0.5 = 10 x (-0.3) = -3 (dB) Amplifier A has a voltage gain of 10 (i.e. 0.1V input comes out as 1V), and amplifier B has a voltage gain of 100. If we connect A and B in series, what is the total gain in Decibel?: The decibel gain of amp A = 20 log 10 = 20 x 1 = 20 (dB)or Total voltage gain A and B = 10 x 100 = 1000 What is the voltage equivalent of the signal level -40dBm?: Assume that the value we seek is X volts. ( log A = B is equivalent to A = 10B ) |