Decibels (dB)

This is a term that crops up often in technical specifications and literature, and yet it is not easy to find out what it means. The Decibel is not something that can be measured, like  a Voltage, it is a word that describes a ratio, like the term 'percentage'.

The human ear can hear sounds over an extremely wide range of intensity. From the quietest whisper (called the threshold of hearing) to the loudest uncomfortable sound imaginable, the intensity ratio can be in excess of 1,000,000,000,000:1 (that is, the quietest whisper multiplied by 10, 12 times over)

Fortunately for us, our senses do not need to resolve such a huge number of implied sound levels. In fact, if we started with the quietest sound, then increased it until it was just noticeably louder, we would find that we would only need to increase it like this about 60 times before the sound became unbearable. In technical terms, it means our ears have a logarithmic response to sound intensity. To further illustrate this, if we were listening to a sound that had an acoustic power of 1/10 Watt, and we added another 1/10 Watt, we would be well aware of the increase. If the power was now 1 Watt, and we added 1/10 Watt, it is unlikely we would notice the difference.

In order to cope with the massive power ratio mentioned earlier, a new unit was introduced - the Bel - named after the Scottish inventor Alexander Graham Bell, who did so much in the 19th and early 20th century to advance the science of sound. The Bel represents a tenfold increase in sound, there being 12 Bels over our huge hearing range.

The Bel represents quite a large change, so it is more common to talk in terms of Decibels (dB), which are 1/10 of a Bel. Whereas the Bel is a factor of 10, a Decibel is a factor of 1.26 (If you multiply 1.26 by itself 10 times, you get 10). The Decibel therefore is a logarithmic quantity, which matches the way our hearing works.

The minimum detectable change in volume that our ears can detect is about 2 dB. This figure is the same, regardless of how loud the original sound was.

If the volume of a piece of music was increased at a linear rate, we would notice a rapid increase in sound to begin with, then very little change as we passed the half-way mark, and virtually no change as we approach 100%. Many older PC soundcard sliders behave like this.

If the volume was increased at a rate of 1dB/second we would perceive the change as a smooth gradual increase. If it increased at 10dB/second it would still be a smooth increase, but would occur more rapidly.

In both these last cases our ears perceive the increase as a linear change, when in fact the intensity (if we were to measure it) would increase logarithmically - it would start increasing slowly, then more rapidly as time progressed. This is one of the reasons why the Decibel is so useful when dealing with sound - it relates so well with the way our hearing works.

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There are, of course, good scientific/mathematical/engineering reasons why the Decibel is such a popular unit of reference. Decibels can be used to describe gain and attenuation in a circuit, signal-to-noise ratios, dynamic range of signals, relative sensitivities of microphones and loudspeakers, sound pressure levels, and many other ratiometric measurements.

There's no easy way around the next step in our understanding - we have to look at simple maths to see what the Decibel numbers mean.

If we are working with what can be classed as primary quantities (Voltage, Current, Sound Pressure etc) then this relationship exists :

Decibels = 20 x Log10(Ratio)

If we are working with secondary (primary-squared) quantities such as power, then the following relationship exists :

Decibels = 10 x Log10(Ratio)

This is where a lot of confusion arises. Because these two equations exist, it is tempting to think that there are, say, Voltage Decibels and Power Decibels. This is not strictly the case, but there are times when you need to specify which units you are referring to. Here are some explanations of this :

Firstly, consider a voltage across a load resistor. If we double the voltage, the increase is :

20 x Log10(2) = 6.02 dB (engineers round this to 6dB)

Because the voltage has doubled, the power in the resistor will increase by a factor of 4, so the increase is :

10 x Log10(4) = 6.02 dB  (6dB)

So, you can see that, providing we are dealing with a common resistive point in the circuit, the Decibel result is the same, irrespective of whether we are measuring Voltage or Power. This is where the confusion arises - a doubling in voltage gives a 6dB increase, whereas a doubling in power only gives a 3dB increase. These two conditions are not equivalent however, as they were in the above example, that is why the Decibel ratios (3dB vs. 6dB) are different.

There are times when it is inappropriate to associate voltage ratios with power ratios. Take an amplifier for example. This may have a voltage gain of 20dB (10x), but a power gain of 60dB (1,000,000 x). In this example it is inadequate to just make a statement about the 'gain' of the amplifier, and attach a dB figure to it. We should specify whether we mean Voltage or Power gain (it is, however, common to assume Voltage gain by default). Even then, knowing one gain does not imply we can work out the other unless we have input and load resistance specified.

In all these calculations, a positive Decibel ratio implies an increase, and a negative one a decrease. This is a natural consequence of using the logarithm operator.

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Now we should be beginning to understand where the Decibel fits into the scheme of things, and it's time to look at how to interpret specifications that use them, and how to put them to use ourselves.

Signal-to-noise (S/N) ratios are often specified. These invariably refer to the  ratio between the signal and noise r.m.s. voltages under specified conditions. Magnetic tapes are sometimes quoted as providing a certain  S/N ratios. This refers to the strongest signal that can be impressed on the tape in relation to the background noise of a blank tape. Amplifier specifications often quote S/N ratios in dB. This allows us to assess how low the self-noise of the amplifier is in relation to the largest undistorted signal it can handle.

Sensitivities are often quoted in Decibels (e.g. -55dB). On their own, these values are meaningless unless we know the test conditions and the reference level. For example, for a microphone we need to know the sound pressure level and the reference voltage level in order to calculate what the output voltage will be. If we were comparing two microphones however, and we knew the test method was the same for both, then this specification would be meaningful. If microphone A was -55dB and microphone B was -65dB, then microphone A would be 10dB (approx. 3 times) more sensitive than microphone B.

SPL (Sound Pressure Level). Loudspeakers often have their efficiency quoted in SPL (dB) units. Once again, these units are generally meaningless unless they can be compared with a known reference, or two speakers are being compared. If the SPL for speaker A was 96dB, and for speaker B was 102dB, then the 6dB difference would be quite noticeable. If the SPL for speaker B had been 99dB, the audible difference would be marginal.

Noise Level. This is the ratio of sound intensity at a given location, referred to an accepted standard representing the threshold of hearing. Typical figures would range from 15dB for a recording studio, through 30dB for a cinema, 40dB for a library or quiet household, 60dB for a noisy office/store/mall, 80dB for a powerful (unsilenced) vacuum cleaner (at 1 metre), to 110dB for front stage at a pop concert.

Dynamic Range is another term often quoted in Decibels. This is the ratio of the largest signal to the smallest signal that can be handled by a system or component. Our ears have a dynamic range of about 120dB (even greater in young people)