技術レポート dB（デシベル）とは 3

As explained so far, there are relative level values and absolute level values regarding decibel values. How should we perform addition or subtraction with these?

The following combinations can be considered.

In this case, it is possible to simply add or subtract decibel values.

[Example]
The combined amplification rate when connecting an A dB amplifier and a B dB amplifier is (A + B) dB.

In this case as well, numerical addition or subtraction of decibel values is possible.

[Example]
When a microphone with a sensitivity of -30 dB (re. 1 V/Pa) is connected to a preamplifier with an insertion loss of -2 dB, and a sound pressure of 1 Pa (sound pressure level 94 dB) is measured, an output voltage of -32 dBV (approximately 25 mV) is produced.

In this case, simple numerical addition or subtraction of decibel values is not possible. Regardless of whether it involves electrical or acoustic vibration systems, addition or subtraction must be done using power values. In other words, decibel values must be converted back to their true values, the addition or subtraction is performed on these true values, and then the result is converted back to decibels. This type of addition is referred to as energy addition (power addition, decibel summation).

For example, the sum (or difference) of the absolute level values L ₁ dB and L ₂ dB is L dB;

can be calculated as.

However, the addition of absolute level values does not hold much significance, while subtraction corresponds to the ratio of the actual values, so the difference in absolute decibels with the same reference value becomes meaningful as relative decibel values. For example, the sound pressure level difference D, commonly used in the acoustic performance of buildings, can be calculated as the difference in decibels.

[Example]
The combined sound pressure level value of 60 dB and 63 dB is obtained by substituting into equation (5-1);

The background noise was measured at 40 dB, and the sound pressure level was 45 dB. The corrected sound pressure level for the background noise is to be substituted into formula (5-1);

In a 1/3 octave band filter analysis, with levels of 72 dB at 800 Hz, 76 dB at 1 kHz, and 74 dB at 1.25 kHz, the level of the 1/1 octave band filter analysis centered at 1 kHz is;

[Note]
The average of absolute level values is calculated using a method that adds the true values and takes the average. This type of average is called energy average (power average, decibel average). For example, the average sound pressure level L dB of sound pressure levels L ₁ dB, L ₂ dB, and L ₃ dB is;

For example, the average levels of 80 dB, 82 dB, and 84 dB, when substituted into equation (5-3), result in 82.3 dB. However, according to existing standards, it is also possible to calculate the average using the numerical values of the decibel levels. This method is sometimes referred to as the arithmetic mean of decibel values. In this example;

It will be 82 dB. For the calculation of the decibel value, please also refer to Ono Sokki homepage "What is a sound level meter" Chapter 12 "Calculation of Decibels (dB)".