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For example, the passband of a LC resonant circuit is the differences of frequency at +3db and -3db.

Why do we prefer dB?

Kevin Vermeer
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Jichao
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  • the "3 dB point" is actually 10⋅log10(1/2) = -3.0102999566398... dB. It's chosen because 1/2 power is exactly where the asymptotes meet if you plot it on a log-log plot (I believe). – endolith May 29 '11 at 18:16
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    dB doesn't represent the difference, but rather the ratio. It is another way to write percentage. For an attenuator, "power reduced to 50%" and "power reduced by 3dB" mean the same thing, but put two attenuators in series and 3dB + 3dB is easier to computer than 50% * 50%. – markrages Jun 02 '11 at 22:33
  • Neper (Np) is pretty common too, especially in RF engineering. Neper's are like dB's, though based on ln(value) instead of 20.log(value). – jippie Oct 18 '12 at 19:16

4 Answers4

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Many processes in nature are either of logarithmic nature (like human senses) or have a great dynamic range.

Describing them on a logarithmic scale and expressing differences in dB has several advantages:

  • often the absolute difference doesn't matter, but the ratio (that's what dB is used for) does (e.g. signal-to-noise ratio)
  • smaller numbers can be used
  • there's an approximately linear relation between measurement and perceived sensation
  • chained attenuations or amplifications can be expressed by addition instead of multiplication (easier to calculate in the head)

Here's another video about it.

AndreKR
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5

In many cases, voltage ratios are expressed in terms of dB rather than absolute numbers because there are many relationships which end up being linear when expressed in terms of dB. It is simpler, for example, to say that an N-stage low-pass filter will attenuate frequencies above the cutoff by \$(6 \times N) \frac{dB}{octave}\$ than it is to say that it will attenuate frequencies above the cutoff by a ratio of \$({\frac{f_c}{f}})^N\$.

Adam Lawrence
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supercat
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  • Right idea, but mixing two concepts. First, dB is a _ratio_ relative to some reference, not an absolute value. Second, as you point out, it's a logarithmic representation of that ratio rather than a linear one. – Chris Stratton May 30 '11 at 18:18
  • @Chris Stratton: By "absolute number" I didn't mean an absolute quantity, but rather a "bare" number without a dB suffix, as distinct from one with such a suffix. I should also have mentioned that it's easier to compare things that attenuate by 40, 50, 60, and 120dB than things which scale a signal by 0.01, 0.0033, and 0.001, and 0.000001. – supercat May 31 '11 at 16:21
  • the word you want is 'linear' not 'absolute' – Chris Stratton May 31 '11 at 16:31
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dB is useful since it is a relative expression. +/-3dB is a doubling or halving of power.

morten
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dB are often used because the human senses have a logarithmic response, to increase the dynamic range.

Around 3dB gives a sensation of doubling or halving the stimulus, as well as doubling or halving the physical value. That value seems to apply to all human senses, and is one reason why 3dB is so ubiquitous. Psychophysics, a branch of experimental psychology, has a long history of investigating this stuff. The minimal amount of change that can be detected is around 1dB (the Just Noticeable Difference or JND). 0dB is the absolute threshold, below which the stimulus isn't detected.

Leon Heller
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  • do you mean the change of voice? – Jichao May 29 '11 at 18:14
  • It applies to hearing – Leon Heller May 29 '11 at 18:18
  • I think general consensus is that 1 dB is the smallest change in sound level detectable by humans. – morten May 29 '11 at 18:29
  • http://hyperphysics.phy-astr.gsu.edu/hbase/sound/db.html#c4 – endolith May 29 '11 at 18:37
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    "0dB is the absolute threshold, below which the stimulus isn't detected." What do you mean by this? 0 dB is by definition a ratio of 1 - ie, no change. Do you perhaps mean 0 dB relative to some reference power? – Chris Stratton May 30 '11 at 07:44
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    @Chris - it's not 0 dB relative to some reference, but 0 dB *as* a reference. We talk about sound levels of 90 dB, but that's always compared to some other level. Which is the 0 dB level. There are several dB scales each with its own reference. On the dBm scale for instance 0 dB is 775mV in 600 Ohm, or 1 mW. – stevenvh May 30 '11 at 09:50
  • When we are talking about sound, dB is used for sound pressure and the reference (0 dB) is 20µPa, which is considered the smallest pressure detectable by a normal human ear. – AndreKR May 30 '11 at 11:14
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    @stevenh If you talk aboout 0dB as a reference, you are mis-speaking. dB is always a ratio, relative to some reference. "x dBm" is a power stated by its ratio to a milliwat, but "x dB" is only a ratio, since no reference is given. You must give a reference to state a power logarithmically. – Chris Stratton May 30 '11 at 15:29
  • @Chris - wow, tough crowd :-). Talking about dBm, 1mW is the reference to which everything else is compared. Everybody working with dBm knows what this reference is. So, if you have a 1 mW signal, that's 0 dBm higher than the reference, only by convention the "higher than the reference" is dropped, and we say it's a 0 dBm signal. Likewise, a 10 mW signal is 10 dBm (compared to the reference). – stevenvh May 30 '11 at 16:58
  • This isn't correct, at least not as I'm reading it. In acoustics a +3dB SPL is a doubling of acoustical power input (how much air the speakers are moving), it doesn't have anything to do with human perception. An actual doubling of sound pressure is +6dB SPL and a doubling of loudness as perceived by a human is +10dB SPL. – Mark May 30 '11 at 17:38
  • The rules I've mentioned above are just 'estimates' they are rounded off and when considering the human perception numbers like +10dB = double loudness, a proper weighing curve needs to be applied based on level (A,B or C) to compensate for the perceived frequency response of the ear. – Mark May 30 '11 at 18:04
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    @stevenh "Everybody working with dBm knows what this reference is" yes, they know what the reference is because the 'm' in 'dBm' refers to the milliwatt reference. But if someone just says 'dB' there is no reference. You can perhaps argue that 'dB SPL' encodes a reference power in the definition of 'SPL' - but 'dB' by itself is a ratio, and it's improper to use it as a power. – Chris Stratton May 30 '11 at 18:11
  • @Mark: "+3 dB SPL" is an absolute level. "+3 dB" is a relative level. +3 dB SPL is +3 dB above 0 dB SPL, approximately the minimum that humans can hear. The reference level for SPL in air is 20 µPa, while in water or other contexts is 1 µPa. – endolith Jun 07 '11 at 19:27
  • @endolith When I say "+3dB SPL" i mean an increase of 3dB SPL over whatever the current level is. – Mark Jun 07 '11 at 22:27
  • @Mark: That's not what "+3 dB SPL" means, though. It means "3 dB above 20 µPa". [ref](https://ccrma.stanford.edu/~jos/st/DB_SPL.html) [ref](http://www.jimprice.com/prosound/db.htm#spl) [ref](http://wiki.answers.com/Q/What_is_the_difference_between_dB_SPL_and_dB_SL) [ref](http://www.rane.com/par-d.html#dB_SPL) – endolith Jun 08 '11 at 00:39