# The Naked Scientists Forum

### Author Topic: How does the decibel scale work?  (Read 13951 times)

#### chris

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##### How does the decibel scale work?
« on: 28/12/2006 04:16:08 »
Audiophiles (e.g. Neil) - can anyone explain why the decibel scale starts off as minus numbers and then passes 0 to enter the positive numbers - is this because it is a log scale?

Chris

#### syhprum

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##### Re: How does the decibel scale work?
« Reply #1 on: 28/12/2006 08:37:54 »
The decibel scale is basically a method of expressing power ratios on a logarithmic scale.
For example if an audio amplifier is supplying a power of 1mW to a loudspeaker and the volume is turned up so that it supplies 1W the power level will have increased 1000 times, the log of which is 3 hence the power is now +3 Bel normally expressed as 30 decibel.

Decibels are a measure of relative power and are meaningless unless a reference level is specified, when they are used in reference to sound levels 0 db is taken as the smallest sound pressure the ear can perceive which is taken as 0.00002 dyne/cm square (20 micro Pa ) at 2KHz the maximum sound level then corresponds to 194 db.
When decibels are used to designate the power levels in audio amplifiers 0 db input level normally means 1 mw in 600 ohms (about 2v peak to peak)

#### Heliotrope

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##### Re: How does the decibel scale work?
« Reply #2 on: 28/12/2006 10:59:38 »
In the electronic fiels of radio transmission etc... 0 dB is also taken to be 1 mW, usually into 50 Ohms.
So a 47dB RF amp has an output of 50 Watts when fed with a miliwatt (0dBm).
The units are very important :
dBm means power referenced to 1 mW as 0 dBm. So 2mW = +3dBm.
The power doubles every 3 dBm (or dB).
The power is 10 times greater for every 10dBm.
0dBm = 1mW
10dBm = 10mW
20dBm = 100mW
30dBm = 1000mW = 1W

I always think of it in terms of doubling (+3dB) rather than logarithmically because it enables me to use the old binary powers to calculate rapidly in my head.

There are many forms of power units too and they can get very confusing.
dBc
dBm
dBSPL
dBu
dBa

etc... etc...

You have to be very careful when designing something that you're using the same units.

#### chris

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##### Re: How does the decibel scale work?
« Reply #3 on: 28/12/2006 13:16:33 »
Thanks for these points, but I'm still not sure I understand why my decibel meter on my recording equipment starts off with negative numbers and then reaches 0 and then goes positive.

#### Heliotrope

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##### Re: How does the decibel scale work?
« Reply #4 on: 28/12/2006 13:47:02 »
Ahhh right.

I'll bet you it's really a VU meter (volume unit meter) and not a proper power meter.
VU meters do not give an accurate representation of power.
They are not designed to.
What they do, and do very well, is give you information about what level of signal you're putting into them and at what level you can expect distortion. They average out the input signal smoothing it a bit so that it doesn't respond to the highest transient peaks. This gives you a more realistic measure of how your ears are going to perceive the sound in terms of it's loudness rather than the actual incident power on them.

The ranges start off at minuses because the designer of the meter decided that a certain, nominal level was to be referenced to zero and the highest peak signal was to be x and the lowest signal visible to be y. That zero level should be the correct point at which the input signal will not be distorted at all and will give high fidelity reproduction with some headroom for cranking things up a little should you need to.

Most signals are below the nominal level so they appear as minuses. Loud things will go above the zero point.

#### Heliotrope

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##### Re: How does the decibel scale work?
« Reply #5 on: 28/12/2006 13:53:22 »
It's all down to where you choose to put your reference.
A bit like temperature.
That's why I prefer Kelvin to anything else as I know exactly where I am and don't have to bother shifting my zero for Farenheit and/or Celsius.

#### lightarrow

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##### Re: How does the decibel scale work?
« Reply #6 on: 28/12/2006 14:12:43 »
Thanks for these points, but I'm still not sure I understand why my decibel meter on my recording equipment starts off with negative numbers and then reaches 0 and then goes positive.

Vdb = 10*log10(V/V0)

where: V is the absolute voltage level; V0 is the reference voltage level; Vdb is the voltage level in decibel.

log10(X) means: logaritm of X in base 10: 10L = X where L is the logaritm.

If X < 1 the logaritm is negative. But, in this case, X < 1 --> V < V0; so, if V < V0, Vdb is negative.

« Last Edit: 28/12/2006 14:17:45 by lightarrow »

#### syhprum

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##### Re: How does the decibel scale work?
« Reply #7 on: 28/12/2006 17:14:07 »
The power level in a circuit is proportional to V^2               so Vdb = 20*log (V/V0)

#### lightarrow

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##### Re: How does the decibel scale work?
« Reply #8 on: 29/12/2006 20:41:50 »
The power level in a circuit is proportional to V^2               so Vdb = 20*log (V/V0)
Thank you for the correction.

#### Sandwalker

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##### Re: How does the decibel scale work?
« Reply #9 on: 30/12/2006 23:20:24 »
Note ten decibels = 1 Bell (named after AGB) - so sayeth the QI book GI, so it must be right!

#### The Naked Scientists Forum

##### Re: How does the decibel scale work?
« Reply #9 on: 30/12/2006 23:20:24 »