decibel

[Professor smith]

I learned that the decibel is a relative value. I don't understand why it's often used to refer to loudness or signal levels. I dont understand why logarithm is used. You often hear that 3db = double loudness. What does that mean?

How does the decibel work in electronics and sound pressure levels?

[SY]

What, they don't have Google in England?

Decibel - Wikipedia, the free encyclopedia

[nattawa]

Originally Posted by Professor smith

.....You often hear that 3db = double loudness. What does that mean?

How does the decibel work in electronics and sound pressure levels?

If memory serves 3db does not mean perceived double in loudness, but a barely distinshable change in loudness for an average human, which also means double/half in power.

Why logarithm? God knows. We were not created with sensations to lineally respond to physical quantities, loudness, sound frequency, brightness, and so on. Perhaps logarithm is one of the better ways to associate our sensations with physical quantities than a lineal system?

[DF96]

Those overseas may not realise that the teaching of logarithms in UK schools has deteriorated somewhat since we started using pocket calculators, so a whole generation now lacks the practical experience of logs which us old'uns have. When you have used log tables to routinely carry out multiplication in, say, a chemistry lab you get an understanding of them which makes decibels much easier to grasp.

[RJM1]

Actually 10db is twice/half the perceived loudness, 3db is twice/half the power, 6db is twice/half the voltage and one db is the minimal sound difference discernable by the average human ear.

[AndrewT]

a decibel is a tenth of a Bel.
A Bel, is a ratio, for this "relative to" can be understood as meaning the same in respect to the reference.

3dB = 0.3Bel
That is exactly the same as saying the ratio is 2:1, whereas -3dB is a ratio of 1:2

In electronics the reference will be stated or sometimes is understood by definition.
eg. dBV is relative to 1V
dBm is relative to 1mW into 600r
dBu is relative to 0.7747V
dBW is relative to 1W

Be careful with mixing up voltage and power. These are treated differently.
Power ratio in dB is {10 * Log (P1 / P2)}
Voltage ratio in dB is {20 * Log (V1 / V2)}

dBSPL is sound pressure relative to a reference.
Usually this reference is the physical pressure just at the threshold of human hearing. It is defined in precise terms as xPascal.
According to Wikipeadia the threshold of human hearing at 1kHz is 20uPa rms. This is equivalent to 0dB 1kHz.

At other frequencies the 0dB (threshold of hearing) reference pressure will be different.

Log is used because the Scientists and Physicists before us decided the best way to express this ratio was to use the formulae, as defined, so that all of us can understand where we are all at.
You do not need to know why they chose logarithms, simply accept that is what they decided so we can universally talk/write to each other without ambiguity.

[DF96]

dBm is relative to 1mW, whatever the impedance. It may be 600R for audio, or 50R for radio.

Log is used for expressing ratios because most humans used to find adding to be easier than multiplying. Now that many humans are equally baffled by both, it may be time to stop using dB!

[lineup]

I knew it originated from Alexander Graham Bell.
Any unit we use has got his 'old father' and uses his name.

Eventually, international standards bodies adopted the base-10 logarithm of the power ratio as a standard unit,
named the bel in honor of the Bell System's founder and telecommunications pioneer Alexander Graham Bell.

[Fogonazo]

Some information:

[DF96]

That article from Elektor is a useful summary, but it contains a couple of mistakes. Firstly, dB is simply a ratio between two quantities - one of them does not have to be some "clearly defined and indicated reference level". That is why you can specify amplifer gain in dB.

dBm is relative to 1mW - no impedance needs to be specified unless you want to calculate a signal voltage. So 3dBm in a 600ohm circuit is exactly the same power as 3dBm in a 50ohm circuit: 2mW.

dBu is 0.775V, which just happens to be 1mW into 600ohms.

The article says, correctly, that dB for voltage and power are worked out differently but it doesn't say why. It is because power is proportional to voltage^2.