dB - The decibel

# What is a decibel?

Unlike other units of measurement, such as the Volt, dB is not an absolute measure. Rather, dB expressed how much bigger ( or smaller ) one this is when compared to another.

## What is a logarithm?

ratio power of ten logarithm
.000001 \$10^{-6}\$ \$\log ( .000001 ) = -6\$
.00001 \$10^{-5}\$ \$\log ( .00001 ) = -5\$
.0001 \$10^{-4}\$ \$\log ( .0001 ) = -4\$
.001 \$10^{-3}\$ \$\log ( .001 ) = -3\$
.01 \$10^{-2}\$ \$\log ( .01 ) = -2\$
.1 \$10^{-1}\$ \$\log ( .1 ) = -1\$
1 \$10^{0}\$ \$\log ( 1 ) = 0\$
10 \$10^{1}\$ \$\log ( 10 ) = 1\$
100 \$10^{2}\$ \$\log ( 100 ) = 2\$
1,000 \$10^{3}\$ \$\log ( 1,000 ) = 3\$
10,000 \$10^{4}\$ \$\log ( 10,000 ) = 4\$
100,000 \$10^{5}\$ \$\log ( 100,000 ) = 5\$
1,000,000 \$10^{6}\$ \$\log ( 1,000,000 ) = 6\$

## dB for voltages

for 2 voltages, dB = \$20 * \log{ V_1 / V_2 }\$

 voltage ratio power of ten logarithm dB .000001 \$10^{-6}\$ \$\log ( .000001 ) = -6\$ -120dB .00001 \$10^{-5}\$ \$\log ( .00001 ) = -5\$ -100dB .0001 \$10^{-4}\$ \$\log ( .0001 ) = -4\$ -80dB .001 \$10^{-3}\$ \$\log ( .001 ) = -3\$ -60dB .01 \$10^{-2}\$ \$\log ( .01 ) = -2\$ -40dB .1 \$10^{-1}\$ \$\log ( .1 ) = -1\$ -20dB 1 \$10^{0}\$ \$\log ( 1 ) = 0\$ 0dB 10 \$10^{1}\$ \$\log ( 10 ) = 1\$ 20dB 100 \$10^{2}\$ \$\log ( 100 ) = 2\$ 40dB 1,000 \$10^{3}\$ \$\log ( 1,000 ) = 3\$ 60dB 10,000 \$10^{4}\$ \$\log ( 10,000 ) = 4\$ 80dB 100,000 \$10^{5}\$ \$\log ( 100,000 ) = 5\$ 100dB 1,000,000 \$10^{6}\$ \$\log ( 1,000,000 ) = 6\$ 120dB

## dB for power

for power, dB = \$10 * \log{ P_1 / P_2 }\$

 power ratio power of ten logarithm dB .000001 \$10^{-6}\$ \$\log ( .000001 ) = -6\$ -60dB .00001 \$10^{-5}\$ \$\log ( .00001 ) = -5\$ -50dB .0001 \$10^{-4}\$ \$\log ( .0001 ) = -4\$ -40dB .001 \$10^{-3}\$ \$\log ( .001 ) = -3\$ -30dB .01 \$10^{-2}\$ \$\log ( .01 ) = -2\$ -20dB .1 \$10^{-1}\$ \$\log ( .1 ) = -1\$ -10dB 1 \$10^{0}\$ \$\log ( 1 ) = 0\$ 0dB 10 \$10^{1}\$ \$\log ( 10 ) = 1\$ 10dB 100 \$10^{2}\$ \$\log ( 100 ) = 2\$ 20dB 1,000 \$10^{3}\$ \$\log ( 1,000 ) = 3\$ 30dB 10,000 \$10^{4}\$ \$\log ( 10,000 ) = 4\$ 40dB 100,000 \$10^{5}\$ \$\log ( 100,000 ) = 5\$ 50dB 1,000,000 \$10^{6}\$ \$\log ( 1,000,000 ) = 6\$ 60dB

## Some specific absolute dB measures

Abbreviation What is Measured Reference Value Notes
dBW power 1 Watt not seen that much
dBm power 1 milliwatt this is more common
dBV voltage 1 Volt not used that much
dBu voltage .775 Volts aka dBv — why .775 Volts?? see below?
dBmV voltage 1mV = .001 Volts
dbSPL sound pressure 'quietest sound ear can hear'

## Some examples, and typical signal levels

This link to an online dB calculator, will be helpful in the following examples: calculator

### Example: Consumer and Professional Line Level

If dB hasn't been confusing enough, the fact that 'line-level' can mean multiple things really puts the icing on the cake. There is perhaps more confusion about this than just about everything. If you understand the following, you should be able to stump quite a few folks in the world of audio.

First off, remember that when using dB for an absolute measure, we need to always be clear on what our reference is. Remember that dBV is dB, relative to 1 Volt, and dBu is dB relative to .775 Volts.

First we will look at converting between dBV and dBu. From the calculator, we see that 0dBu is -2.2dBV and that 0dBV is +2.2dBu — so to convert from dBu to dBV, we need to subtract 2.2 — alternatively, to convert from dbV to dBu, we need to add 2.2.

Here is the deal: Consumer line-level is expressed as -10dBV and Professional line level is +4dBu. Very often, you will here someone say that Consumer level is 14dB lower than Pro line-level. In doing this simple math, it is easy to forget that you first need to make sure that both measurements are using the same reference. In this example, we will convert everything to dBu and then determine what the real difference is.

-10dBV = (-10 + 2.2)dBu = -7.8dBu.

The difference between +4dBu and -7.8dBu is +4 - (-7.8) = +4 + 7.8 = 11.8dB, which is the real difference between consumer line level and professional line level.

### Example: Sound Pressure Level ( SPL )

Example Sound Typical dBSPL Pressure in 'Pascals' (Pa)
threshold of hearing 0 .00002
rustling leaves 20 .0002
normal conversation 60 .02
outboard motor 80 .2
convertible on freeway, top down 95 1.1
rock concert 120 20
eardrum perforates 160 2,000
shuttle launch 180 20,000

### Example: Shure SM58

( The following info is taken from specs )

Sensitivity = -54.5dBV/Pa (1.85mV) where 1 Pa = 94dBSPL

Interpreting this, we see that a fairly loud sound ( 94dBSPL, from a pressure of 1 Pa) will result in -54.5dBV signal. Using our online calculator, we get that it is a voltage of .0018Volts = 1.8mVolts.

If we want to get this signal up to professional line level ( +4dBu ), we will need to amplify it. This is the job of a microphone pre-amp. How much gain do we need to the pre-amp to be capable of?

First off, the sensitivity is given in dBV. We need to be careful of units, and convert this to dBu. Again, using the online calculator we get that:

-54.5dBV = -52.3dBu (to convert, add 2.2 to the dBV value)

So the gain needed …

+4dBu - (-52.3dBu) = +4dBu + 52.3dBu = 56.3dB of gain.

So typical mic preamps have at least 60dB of gain, and perhaps more for additional headroom. ( The Universal Audio Solo/610 has a max of 61dB of gain.

page revision: 15, last edited: 26 Sep 2009 21:28