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Jaycar Electronics Reference Data Sheet: DECIBELS.PDF (1)

UNDERSTANDING DECIBELS
You don’t have to be involved very long in electronics, hifi or professional audio before you come across the term decibels , or its contraction ‘dB’. And because of the very general way in which these terms are used, it can often be hard working out what they mean, and why they’re being used. Here’s a quickexplanation of what it’s all about. Early last century, when engineers were building the first telephone networks, they needed to be able to measure the performance of their cables, amplifiers, channel filters and so on. They soon discovered that because the human ear responded to both the frequency and loudness of sounds in a non-linear or logarithmic fashion, their measurements and comparisonsbetween signals were a lot more meaningful if they were made in logarithmic terms too. For comparing signal strengths they used at first a unit called the B e l , named in honour of Alexander Graham Bell, the inventor of the telephone. This was defined simply as the logarithm of the ratio of two signal power levels. So two signals were said to differ by one Bel if the logarithm of their power ratio was1.0. In other words, if one signal had a power level 10 times that of the other, because log(10) = 1. It was soon found, though, that the Bel was far too large a unit; the human ear could easily detect much smaller differences between signals. So engineers began to use a unit 10 times smaller, which not surprisingly they dubbed the d e c i B e l or ‘decibel’ — or just ‘dB’ for short.Mathematically the difference between two signals or signal levels is defined as: where P1 and P2 are the two signal power levels. The decibel turned out to be a very practical way to compare two signals, because a signal difference of 1.0dB corresponds closely to the smallest change in sound level that the human ear can detect — what psychologists and audiologists call a ‘just noticeable difference’ (JND).Now as you can see, the decibel is strictly speaking a way of comparing p o w e r l e v e l s , where the two levels may be measured in watts, milliwatts, microwatts or even kilowatts. However because signal voltages are proportional to power level, providing the impedance level is constant (or the same, in different circuits), you can also work out a ratio in decibels from the voltage ratio: whereV1 and V2 are the two voltage levels, and the multiplier ‘20’ comes in because the power level is proportional to the square of the voltage level (and squaring is equivalent to doubling the logarithm). So knowing two signal voltage levels, we can work out their difference in decibels — providing they are associated with the same impedance level. As you can see, though, the decibel strictly isn’ta unit of absolute measurement like the metre, the kilogram, the ohm or the volt. It’s basically just a unit of relative measurement; a way of comparing one signal level against another. Nowadays decibels are used exactly like this in many different areas of electronics — measuring the frequency response of preamplifiers, amplifiers, filters, microphones and speakers, comparing the optical outputlevels of lasers or the microwave power output of transistors and ICs, and so on. For example you may have noticed that the frequency response of things like amplifiers and filters is often measured between the points where the response is ‘3dB down’. Ever wondered why those points are chosen? Because a drop of 3dB corresponds to h a l v i n g the power level, which is very clearly noticeable.Other handy ‘rules of thumb’ to remember about decibels are that: l a 20dB difference corresponds to a drop or gain of 10 times the voltage. l a 10dB difference corresponds to a drop or gain of 10 times the power, or 3.162 times the voltage. l a 6dB difference corresponds to a halving or doubling in voltage. l a 3dB difference corresponds to a drop in voltage to 0.708 of the original level, or a...