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The Decibel Defined

The Decibel is the unit used to express relative differences in signal strength. It is expressed as the base 10 logarithm of the ratio of the powers of two signals:
dB = 10 log (P1/P2)
Signal amplitude can also be expressed in dB. Since power is proportional to the square of a signal's amplitude (e.g., a power ratio of 100 is equivalent to an amplitude ratio of 10), dB is expressed as follows:
dB = 20 log (A1/A2)
Logarithms are useful as the unit of measurement because (1) signal power tends to span several orders of magnitude and (2) signal attenuation losses and gains can be expressed in terms of subtraction and addition.

For example, suppose that a signal that passes through two channel segments is first attenuated in the ratio of 20 to 1 on the first leg and 7 to 1 on the second. The total signal degradation is in the ratio of 140 to 1. Expressed in dB, this becomes 13.01 (10 log 20) + 8.45 (10 log 7) = 21.46 dB.

The following table helps to indicate the order of magnitude associated with dB:
1 dB attenuation means that 0.79 of the input power survives
3 dB attenuation means that 0.50 of the input power survives
10 dB attenuation means that 0.1 of the input power survives
20 dB attenuation means that 0.01 of the input power survives
30 dB attenuation means that 0.001 of the input power survives
40 dB attenuation means that 0.0001 of the input power survives
NOTE: Many times dB ratios are expressed using a third letter (or letters), e.g. dBm -- the third letter is a reference level for the log operation. For instance, dBm is used to define dB levels in a 50 Ohm RF system, using a 1 milliwatt reference level.

Thanks: Randy H. Katz, Independent Partner
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Other Information About the dB:

"Decibel - dB", — a good explanation from the HANDBOOK FOR ACOUSTIC ECOLOGY, Barry Truax, editor, Second Edition, 1999.

Cisco Systems, "Introduction to Optical Fibers, dB, Attenuation and Measurements"

"How to cheat with dBs - An Intuitive Approach", by Chris Scott — a useful article on approximating when the calculator is back in the office.

"The diaBolical dB — Understanding Logarithmic Scales And The deciBel", A well-written introductory article by LeCroy Labs.

"Decibels and Power" — another good introductory article by Jim Lesurf, University of St. Andrews, Scotland

dB/Watts/ERP/EIRP Calculator

Online dB converter, with notes

Power Conversion Online Calculator, from

"What is a Decibel?" — good introductory tutorial from the University of New South Wales, Australia

"What is a decibel, and what is the loudest sound I can listen to before it hurts my ears?" — introductory material from HowStuffWorks

"Intensity and the Decibel Scale" — a high school physics tutorial on sound waves

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