decibel (dB)

The logarithmic ratio of two signal amplitudes:

for signals in volts. For power ratios, the formula is

The rigorous definition of decibel (since deci means tenth) is 10 times the logarithm of a ratio, but for convenience in electronics, decibels implicitly assumes that you are dealing with power ratios. Therefore, the simple mathematical shortcut is often used in the first formula given above, where instead of squaring the voltages to get the power ratio, you multiply by 20 instead of 10. Obviously, the result is the same, but often leads to a significant amount of confusion.

You can interactively use the formula for decibels in this link.

Common rules of thumb deal with what is the doubling of the amplitude of a signal. Using the above formulae, it is 6 dB, if we are talking about voltage. This, however, is a quadrupling of power. A doubling of power is 3 dB. An example of this is when dealing with filter bandwidth -- the half-power bandwidth is the bandwidth at which the power is dropped to one half (that is, 3 dB), which corresponds to a voltage drop to 70.7%.

Note that many quantities are expressed in decibels: sound pressure level, sound power level, sound intensity level, transmission loss, and so on. Although they all have “units” of decibels, they are typically NOT interchangeable because they use different reference levels.

Add and subtract dB according to the following formula:

This you can interactively use this formula in the following link for

• decibel addition
• For decibel subtraction, use the same link and enter the dB value with a minus sign.
  

Units:
dB

Additional References

Related NI Products:

• Sound and Vibration Toolset
  
  Helpful Web Sites:
  
• In Depth Essay on Decibels
  
• Table of Relationship between percentage error and decibels
  
  

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