Decibel is a special unit that is a little different from other measuring units in everyday practices. This is non physical unit but more mathematical understanding. Decibel (dB) units are similar to percent (%), just different calculation and purpose. As a percent units so decibels are used to compare two quantities. As whole value in percents is expressed as 100% so decibels is more complex and it is a ratio of two independent quantities. Decibels mostly are used for energetic parameters like power or voltage and current.

Decibel (dB), equal to 0.1 bel (B) . Bel – is a decimal logarithm of ratio of two powers. If these powers P1 and P2, then expression looks like:

N_P=lg(P2/P1) [B]

In physical nature any power can be compared: electrical, acoustic, mechanical. Important part is that both variables were expressed in same units – watts, mili-watts, horse powers (HP).

Practically speaking Bel (B) is way to big unit. Even big ratios of power gives a small B. For instance P2/P1=100, lg100=2. If P2/P1=1000, lg100=3. So the big difference 100 and 1000 in bels will be 2B and 3B. For more detailed and convenient use bels are converted in decibels like 2B->20dB:

D_P=10lg(P2/P1)

As bels and decibels is a ratio of two value, the operations using bels or decibels are the same as with logarithms.

Positive decibels usually mean signal magnitude(in amplifiers) while negative decibels means energy loss (in filters, voltage dividers). Good point of decibels is that they are widely used and because of universality. It is ease to represent values from 1 to millions in convenient form (graphically).

But there are some disadvantages. Calculating decibels requires reference tables of logarithms and decibels. Another disadvantage is that there is no absolute reference point for decibels as there is no 0 watts in decibels.

For instance if we measure sound level, the reference point is taken air pressure as 20 micropascals, or 0.02 mPa – close to limit of sensitivity of human ear. Then if wee hear 20 log (p₂/p₁) = 86 dB sound it means log (p₂/p₁) = 4.3 and p₂/p₁ = 10^4.3 is about p₂/p₁ = 20,000. This is a loud but not dangerous level of sound, if it is not maintained for very long.

Important part is that if measured quantity is equal to reference level, then we get 0dB: 10log 1 = 0dB.

Few most common values in following table:

INCREASE IN POWER LEVELS (WATTS)
dB=10*log(P1/P2)
DeciBels   Output Signal Strength
3dB           2x
6dB           4x
10dB (1 Bel)  10x
20dB         100x
30dB       1,000x
40db      10,000x
ATTENUATION OF AMPLITUDE (VOLTS or AMPS)
dB=20*log(A1/A2)
DeciBels   Output Signal Strength
-3dB        0.707x
-6dB        0.5x
-10dB        0.316x
-20dB        0.1x
-30dB        0.032x
-40db        0.010x

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This entry was posted on Thursday, January 4th, 2007 at 12:32 pm and is filed under Electronics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.