A look at the dB system

    Sometimes the decibel seems like it is one of the hardest concepts in audio to understand.  However, upon close examination it is exactly quite simple & can be very useful.
    The decibel (dB) was created as a short-form for levels to make communication between audio engineers / technicians easier.  It uses the logarithmic scale, because it allows large measurements to be expressed by smaller numbers.  It is also used because the ear's sensitivity works on a logarithmic scale rather than a linear scale.
    The decibel is really 1/10 of a Bel. (Unit named after Alexandra Graham Bell, that is why the "B" is capital)  It can be mathematically expressed by the following equation:

dB = 10 X log (P₁ ¸ P₂)
To calculate dB using a calculator, first divide the 2 levels out (P₁ ¸ P₂), then hit LOG & lastly multiply the value by 10.
ie: 10 X log (2 ¸ 1)
= 10 X log 2 (on the calculator hit 2, then LOG, then multiply by 10)
= 3.01
= 3 dB

    It is extremely important to understand that the decibel is a comparison between two levels rather than the power value itself.  For example, the ratio between 2 watts & 1 watt is 3 dB.  (10 log (2 ¸ 1))  This 3 dB is the same value as the ratio between 100 watts& 50 watts.  In a nutshell, the decibel is a comparative system that expresses a ratio between 2 levels.  Usually the 2nd level is 1 dB,  therefore a 3 : 1 ratio would represent 3 dB.

    As stated earlier, the dB is a useful shorthand that allows smaller numbers to represent large numbers with many digits.  Here's an example:

123, 456, 789 : 1  =  81 dB
 

A Closer Look at the dB

  As you can see, the dB system has the potential of saving lots of time & confusion when used properly.  However, you may also notice that the dB ratio doesn't have any units attached.  When a standard reference value is used for 0 dB, then any number of dB higher or lower than the stated zero reference may be used to describe a certain quantity.  For example:

    "The output level is 10 dB above 1 watt"  --From this we can calculate the value of 10 dB, because we have something to relate 10 dB with.  10 dB would represent 10 watts.  If the level was "10 dB above 1 milliwatt", then the result would be 0.01 watts or 10 milliwatts.

    The term dBm expresses an electrical power level that is used in reference to 1 milliwatt. (0 dBm = 1 milliwatt)
So using the same example:  "10 dB above 1 milliwatt", this could be represented by just saying "10 dBm."  Pretty straight forward, eh?

    DBu expresses a voltage level referenced to 0.775 volts.  DBu is actually equivalent to that of dBm ONLY IF it is driven through 600 ohms.  However, dBu isn't dependent upon the load because it is always 0.775 volts. This is just saying that IF 10 dBm were driven through 600 ohms, it would be the equivalent to dBm.

Here's a chart that can be used as a reference: