dB (decibel) is commonly used in measurements. We have introduced it in technical reports and measurement columns. However, for those who are new to measurement, it is difficult to understand dB itself. Thus, from this time, I will explain it in three parts without using mathematical formulas simply as much as possible.

1) dB is a logarithm.

In our daily lives, we are surrounded by a world of numbers such as 1, 2, 3, 4, 5..., which are called natural numbers. We also often use the numbers smaller than 1 such as 0.1, 0.2, 0.3 ..., which are called decimal numbers. When using natural numbers and decimal numbers, there is no problem when using with numbers in relatively narrow range of digits such as 0.1 to 100. However, when using with numbers in a wide range of digits such as 0.001 to 1,000,000, you have to be careful about miscounting due to many digits.
In such cases, we often use a power representation. For examples, when expressing in a power of 10, one million is expressed as 1,000,000=10⁶. The number with the upper right of 10 (6 in this case) is called the exponent. In other words, the meaning of the exponent is "the 6^th power of 10 denotes one million." The logarithm is a different expression of the meaning of this exponent. Considering whether the number one million is 10 to the n-th power, the number expressing whether it is the n-th power is called the logarithm. In the above case, one million = 1,000,000 is 10 to the 6th power, so the logarithm is 6. As you all know, exponent and logarithm actually represent the same number. However, they are expressed differently, thus they are defined as different terms.

When logarithms are used in this way, as shown in table 1, even if the number of digits is large, such as 1μ (micro) or 10M (mega), it can be simply expressed in numbers with a small digits. When considering whether a number is "10" to the n-th power, the logarithm at this time is called the common logarithm.

Table 1． Natural number and common logarithm

2) dB is one tenth of B.

dB is originally B (bell) with the SI prefix d (deci). It is the “deci” that you learned as 1ℓ = 10dℓ in elementary school. In other words, the value of B (bell) multiplied 10 times is the dB value. 7B is equivalent to 70 dB. As you know, other major SI prefixes are h (hect: 100 times), k (kilo: 1000 times), M (mega: 1 million times), G (giga: 1 billion times), c (centimeter: 1 /100 times), m (millimeter: 1/1000 times), μ (micro: 1/million times), and n (nano: 1/billion times).

3) What is B (bell)

Then, let’s look into B (bell).
B (Bell) is named after Alexander Graham Bell, who invented the telephone, and expresses the power transmission attenuation in the telephone. The definition of B (bell) is a logarithmic quantity of the ratio of reference physical quantity to measured physical quantity. There is a rule that the logarithm used here is expressed as the common logarithm, that is, a power of 10. For example, 2 B (2 bell) is 10², which is 100 times, 3 B (3 bell) is 10³, which is 1000 times, and -1 B (-1 bell) is 10^-1, which is 1/10 times. By the way, 0 B (0 bell) is 10⁰, which means that it is multiplied by 1 and is equivalent to the reference value. B (bell) was first used as a comparative expression of electric power as explained above, however, now it is used as a unit to express the ratio of various energies such as light, sound, and vibration.

That’s all for this column.
Next time, I would like to explain why dB came to have the SI prefix d (decibel), and the power gain and voltage gain of dB.

(KH)

[ Reference ]
For further detail information, please refer to the page: What is dB?

No.6 Various measurement instrument: What is dB? (Part 1)