What is a decibel? Encyclopedia of radio electronics and electrical engineering

Encyclopedia of radio electronics and electrical engineering / Beginner radio amateur

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When measuring something (like voltage) we usually think in direct units (volts). But sometimes it is more preferable to use a relative scale. In this case, the most commonly used unit is the decibel (dB) - a powerful tool that confuses beginners. With knowledge of the origin of this term and one simple rule, difficulties can be eliminated, and the meaning of a quantity expressed in decibels can be understood.

Alexander Graham Bell became famous for inventing the telephone. Less well known are his works on the determination of the threshold of audibility. In 1890 he founded the Deaf and Hard of Hearing Association, which is still active today. He was the first scientist to quantify the sense of hearing and established that auditory susceptibility does not depend on the actual power level of the sound wave reaching our ear, but on its logarithm.

Bell found that a child's hearing threshold is about 10^-12 W / m², and the level at which pain occurs is about 10 W / m². Thus, the range of loudness normally perceived by a person is 13 orders of magnitude!

Based on the values ​​obtained, Bell determined the sound power scale from 0 to 13. The loudness units of this scale are called bels (the last "l" from his surname was discarded). The sound level of a soft whisper is about 3 bels, and that of normal speech is about 6 bels.

Since the perception of loudness is based on a logarithmic scale of power level, the conversion between power and loudness on the Bell scale is as follows: loudness (in bels) = log(P1/P0), where P0 is the threshold for hearing sound.

Therefore, a sound level of 4 bela corresponds to a sound power of 10⁴xP0.

The bel has become the de facto standard unit for measuring the logarithm of the ratio of two energy levels: the ratio expressed in bels is log(P1/P0), i.e. an increase of 3 bela corresponds to an increase of 1000 times. If the new value decreases, then the logarithm of the ratio becomes negative. To do the reverse conversion, you need to raise 10 to a power equal to bels.

The most important feature of whites is that they refer only to the ratio of two powers or two energies. If there is a need to describe the ratio of two amplitude signals, for example, voltages, then it is only possible to rely on the ratio of the powers associated with these voltages. Power is proportional to the square of voltage or current: V² и I².

The ratio of two voltages, expressed in bels, is related to the ratio of their powers: log(P1/P0) = 2log(V1/V0). Therefore, the voltage ratio is V1/V0 = 10^(white/2).

It has become quite common to express the ratio in tenths of a bela, or in decibels (dB). The ratio of the two powers in dB is 10log(P1/P0) and the ratio of the voltages is 10•2log(V1/V0). To obtain the voltage ratio, it is necessary to perform the conversion V1/V0 = 10^(dB/20).

Sometimes it is quite tricky to determine what is considered an amplitude value, and what is energy. Voltage, current, impedance, electric or magnetic field strengths, and ranges of any wave processes are considered to be amplitude quantities. When measured in decibels, the logarithm of the ratio of the squares of these values ​​is calculated. Energy, power and intensity are energy quantities, and in relation to the logarithm they are used directly.

For example, 5% of the voltage of one circuit is transferred to another circuit. The stress ratio in this case is 0,05. To measure in decibels, take the logarithm of the voltage ratio, multiply it by 2 to get the ratio in bels, and then multiply by 10 to get the ratio in dB: 20log(0,05) = -26 dB of signal-to-signal coupling.

The table shows some frequently used values ​​in decibels and ratios of amplitudes and powers.

Amplitude ratio	Power ratio	Value in dB
0,7	0,5	-3
0,5	0,25	-6
0,3	0,1	-10
0,1	0,01	-20
0,05	0,003	-25
0,01	10-4	-40
0,001	10-6	-60

Publication: cxem.net

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