dB (decibels) are commonly used in everyday measurements.
We have previously introduced this in our technical reports and measurement columns.
However, for those new to measurement who find dB itself difficult to understand, we will explain it in an easy-to-understand way over the next three installments, using as few mathematical formulas as possible.
dB is logarithmic
In our daily lives, we live in a world of numbers such as 1, 2, 3, 4, 5, and so on. These numbers are called natural numbers. We also deal with numbers smaller than 1, such as 0.1, 0.2, 0.3, and these are called decimals. When using natural numbers or decimals, there are no particular problems when dealing with numbers in a relatively small range of digits, such as 0.1 to 100. However, when dealing with numbers in a wide range of digits, such as 0.001 to 1,000,000, the number of zeros to write becomes large, and we must be careful not to miscount the number of digits.
In such cases, we often use exponential notation. For example, the number one million can be expressed as 1,000,000 = 106, which is a power of 10 and makes it simpler with fewer digits. The number in the exponent of 10 (in this case, 6) is called the exponent. In other words, the meaning of the exponent is "10 raised to the power of 6 equals one million." A logarithm is a way of expressing this meaning of the exponent in a different way. We consider what power of 10 the number one million is, and the number that expresses how many times that power it is is called the logarithm. For example, in the previous example, one million = 1,000,000 is 10 to the power of 6, so the logarithm in this case is the number 6. As you can see, exponents and logarithms actually represent the same number, but they are defined as different words because they are expressed in different ways.
As shown in Table 1, using logarithms allows us to express even large numbers, such as 1 μ (micro) or 10 M (mega), with fewer, more manageable digits. In particular, when considering numbers that are not "2" or "3" but rather powers of "10", the logarithm used in this case is called a common logarithm.
Table 1. Relationship between natural numbers and logarithms (common logarithms).
| Decimal number | Prefix notation | (Commonly used) logarithm |
| 0.0000001 | 100n (nano) | -7 |
| 0.000001 | 1µ (micrometer) | -6 |
| 0.00001 | 10µ (micrometers) | -5 |
| 0.0001 | 100µ (micrometers) | -4 |
| 0.001 | 1m (millimeter) | -3 |
| 0.01 | 10m (millimeters) | -2 |
| 0.1 | 100m (millimeter) | -1 |
| natural numbers | Prefix notation | (Commonly used) logarithm |
| 1 | 0 | |
| 10 | 1 | |
| 100 | 2 | |
| 1,000 | 1k (kilometer) | 3 |
| 10,000 | 10k (kilometers) | 4 |
| 100,000 | 100k (kilometers) | 5 |
| 1,000,000 | 1M (mega) | 6 |
dB is one-tenth of B
dB originally comes from B (bel) with the SI prefix d (deci) added. This is the same d (deci) that you learned in elementary school, like 1 liter = 10 d liters. In other words, the dB value is the value in B (bel) expressed as 10 times that value. For example, 7B and 70 dB mean the same quantity. Other major SI prefixes include h (hecto: 100 times), k (kilo: 1000 times), M (mega: 1 million times), G (giga: 1 billion times), c (centi: 1/100 times), m (milli: 1/1000 times), μ (micro: 1/1 million times), and n (nano: 1/1 billion times), as you may already know.
B (Bell)
So what is B (Bell)? B (Bell) is named after Alexander Graham Bell, the inventor of the telephone, and represents the attenuation of power transmission in telephones. The definition of B (Bell) is a quantity expressed logarithmically as the ratio of a measured physical quantity to a reference physical quantity. There is a convention here that the logarithm used is the common logarithm, that is, expressed as a power of 10. For example, 2B (2 Bells) is 10^ 2, so it is 100 times, 3B (3 Bells) is 10^ 3, so it is 1000 times, and -1B (-1 Bell) is 10^-1, so it is 1/10 times. Incidentally, 0B (0 Bells) is 100, so it means it is 1 time and is the same as the reference value. As explained above, B (Bell) was initially used as a comparative expression of power, but nowadays it is used as a unit to express the ratio of various energies such as light, sound, and vibration.
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This concludes our introductory lesson.
Next time, I'd like to explain why dB uses the SI prefix 'd' (deci), and further discuss the power gain and voltage gain in dB.
Below are our technical reports on dB and a selection of past measurement columns.
If this column has piqued your interest in dB, please read on.
【reference】
Ono Ono Sokki Technical Report: "What is dB (Decibel)?"
Ono Sokki Measurement Column: "About dB (Decibel)"
(Excerpt from the email newsletter issued on January 19, 2022)
