Signals - Adding Decibels

The decibel (dB) is a logarithmic unit used to express the ratio of two signal values - like power, sound power or pressure, voltage, intensity etc. - where one value is a reference value. 

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Adding Equal Signal Levels

The total signal level in decibel from equal signal sources can be calculated as

L_t =  10 log (n S / S_ref)

    = 10 log (S / S_ref) + 10 log (n) 

    = L_s + 10 log (n)                                                         (1)

where

L_t = total signal level (dB)

S = signal (signal unit)

S_ref = signal reference (signal unit)

n = number of sources

L_s = signal level from each single source (dB)

The signal units depends on the nature of the signal - W for power, Pa for pressure and so on.

Note! -  adding sound pressure levels.

Example - Total Sound Power from Two Identical Fans

For sound power it is common to use 10^-12 W as the reference sound power. Total sound power from two identical fans each generating 1 W in noise power can be calculated as

L_t =  10 log (2 (1 W) / (1 10^-12 W))

              = 123 dB

Sound power and sound power level are often used to specify the noise or sound emitted from technical equipment like fans, pumps or other machines. The "sound" measured with microphones or sensors (meters) are sound pressure.

Adding Equal Signals Units Calculator

S - signal (signal unit)

S_ref - signal reference (signal unit)

n - number of signal sources

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Adding Equal Signal Levels (decibels) Calculator

L_s - signal level from single source (decibel, dB)

n - number of signal sources

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Adding equal signal sources can be expressed graphically

Download and print Adding Signal Level of Equal Sources chart.

Note! Adding two identical sources (doubling the signal) will increase the total signal level with 3 dB (10 log(2)).

Adding Signals from Sources with different Strengths

The total signal level from sources with different strengths can be calculated as

L_t =  10 log ((S₁ + S₂ ... + S_n) / S_ref)                                               (2)

Example - Total Sound Power from Two different Fans

The total noise power from two fans - one with sound power 1 W and the other with sound power 0.5 W - can be calculated as

L_t =  10 log (((1 W) + (0.5 W)) / (1 10^-12 W))

      = 122 dB

Adding two signal sources with different levels can be expressed graphically in decibels as

Download and print Adding Sources with different Signal Levels.

Example - Adding Sound Power in Decibels

The sound power from one of the fans in the example above can be calculated as

L_s1 = 10 log((1 W) / (1 10^-12 W))

   = 120 dB  

The sound power from the other fan can be calculated as

L_s2 = 10 log((0.5 W) / (1 10^-12 W))

   = 117 dB  

The difference in decibel is

L_s1 - L_s2

= (120 dB) - (117 dB)

= 3 dB

From the table or diagram above a difference of 3 dB requires that 2 dB must be added to the highest sound pressure source as

L_t = (120 dB) + (2 dB)

     = 122 dB