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Technical Report: What is dB (Decibel)? 2

4. Decibels in various fields

Here, we will specifically describe how decibels are used in various fields.

4-1 Electrical and Telecommunications Systems

The gain and attenuation of transfer systems are often expressed in decibels, which are relative levels. Since voltage measurement is usually simpler, the transfer characteristics of amplifiers and filters are typically calculated using the voltage ratio to determine the decibel level.
For example, suppose a 1 mV signal is input to a circuit, and a 10 V voltage is generated at its output. In this case, the voltage amplification factor is 10,000 times, so using equation (3-4), the gain is 80 dB.
Below is an explanation of decibels, which are commonly used in electrical and telecommunications fields.

(1) dBm

In the field of power amplification, dBm is frequently used. This unit represents the absolute level of power, with 1 mW defined as 0 dBm. For example, what is 10 W in dBm? 10 W is 10⁴ mW, so it is 40 dBm (= 10 log (10⁴)). Similarly, what is 0.1 mW in dBm? 0.1 mW is 10⁻¹ mW, so it is -10 dBm. Although dBm is originally a unit of power, in transmission systems, by fixing the impedance, it is also used as the absolute level of voltage.
Now, if the impedance system is Z (Ω), and the voltage value of 0 dBm (1 mW) is V, then:

The relationship is as follows. Table 6 summarizes the voltage values for 0 dBm at various impedance values, derived from equation (4-1).

ImpedanceZ (Ω) Voltage value (V) Frequently used fields
50 0.224 Wireless systems
75 0.274 Video
600 0.775 telephone acoustic system

  • The relationship between voltage value V and decibel value X (dBm)

(Example 1) When the impedance is 50 Ω, 0.5 V corresponds to 7.0 dBm
(Example 2) When the impedance is 75 Ω, 1 V is 11.2 dBm
(Example 3) When the impedance is 600 Ω, 6 dBm is equal to 1.55 V

(2) dBV, dBμ

These are absolute voltage levels, with dBV defined as 1 V = 0 dBV and dBμ defined as 1 μV = 0 dBμ.

【Note】

The voltage values (true values) used for level conversion are basically all the RMS values of the signals.

dBV is commonly used in low-frequency measuring instruments such as FFT analyzers. In FFT analyzers, the input unit is initially voltage (V), so unless physical calibration is performed, the vertical axis unit of the power spectrum is expressed in [dBV]. The input voltage range is also typically in 10 dBV steps. For example, the input range of the DS-3000 series data station defines a voltage of 1 Vrms as 0 dBV (see Table 7).

Table 7 Input Range Table for DS-3000 Series

dBV VRMS V (peak)
20 10 ±14.14
10 3.162 ±4.471
0 1 ±1.414
−10 0.3162 ±0.4471
−20 0.1 ±0.1414
−30 31.62 m ±44.71 m
−40 10 m ±14.14 m

  • The relationship between voltage value V and decibel value X (dBV)

dBμ is a unit commonly used in wireless communication and is based on a voltage value of 1 μV. It should technically be written as dBμV, but the V is often omitted.

(3) dBμV/m

It is used to represent the electric field strength value that expresses radiated emission values such as EMC. It defines 1 μV/m as 0 dB.

(4) dBc

When evaluating the spectral characteristics of high frequencies or operational amplifiers, it is the relative level value of harmonics and noise components relative to the fundamental wave (carrier, "c" for Carrier). For example, if the fundamental wave is 10 dBm and its harmonics are -40 dBm, then the harmonics will be -50 dBc. This relationship holds true even if the vertical axis of the spectrum is dBV. It is used as a parameter to evaluate low distortion in operational amplifiers and other devices.

(5) dBV/√Hz

When measuring the self-noise characteristics of an amplifier, the power spectral density (PSD) is used for evaluation. The vertical axis of this PSD represents the effective value per unit frequency (1 Hz), so its unit is V²/Hz or V/√Hz. Converting this value to decibels gives dBV/√Hz.

4-2 Acoustic system

Decibels (dB) are frequently used to quantify the intensity (loudness) of sound. The main reasons for this are that the range of sound intensity (loudness) that humans can perceive is very wide, and that this perception is logarithmic (see Section 3.4, (3)). Decibels (dB) are commonly used to express absolute level values when quantifying sound volume.

(1) Sound pressure level [Lp]

Sound transmitted through the air is a minute pressure fluctuation (wave) centered around atmospheric pressure (static pressure), and the effective value of this fluctuation component is called sound pressure, which is measured in Pascals (Pa). As mentioned above, the sound pressure that humans can normally hear falls within a wide range of 10⁶ values, from 20 μPa to 20 Pa.

Sound pressure level is defined by the following formula:

【Note】

  1. Sound pressure level is the physical intensity (loudness) of sound, but in the field of noise measurement, a level that includes a frequency weight [A] determined based on human hearing characteristics is often used. This is specifically called the A-weighted sound pressure level (commonly known as the noise level) and is defined by the following formula.

In equations (4-6) and (4-7), the question arises as to how to specifically determine the sound pressure (the effective value of the instantaneous sound pressure). Typically, the following method is commonly used to determine the effective value from the instantaneous sound pressure waveform by averaging.

Exponential average
This method involves exponentially averaging the squared instantaneous sound pressure by a time weight τ to obtain the effective value at that time (instantaneous). The resulting decibel value is also a function of time. This is what is known as the instantaneous sound pressure level, and it is usually displayed every second on a sound level meter. In the JIS standard (JISC1509) for sound level meters, it is called the time-weighted sound level. In the field of acoustic measurement, the time weight τ (time constant) commonly used is Fast (0.125 s) or Slow (1 s).

Linear average
This method involves integrating the squared instantaneous sound pressure over a measurement time T (with equal weighting) and then averaging it to obtain the RMS value. The resulting decibel value is a representative value (a single value) for that measurement time. In the JIS standard (JIS C1509) for sound level meters, this is called the time-averaged sound level (equivalent sound level). If the frequency weight is [A], it becomes the "equivalent sound level" in the field of environmental noise.
For more details, please refer to Chapter 9, "Sound Level Meter Indications," on Ono Sokki website under "What is a Sound Level Meter?".

(2) Sound intensity level [LI]

Sound intensity is defined as the energy that passes through a unit area per unit time when sound waves travel through a medium such as air, and its unit is [W/ m²].


The level of sound intensity is defined by the following formula:

If a sound wave can be considered a plane wave, the relationship between sound intensity I and sound pressure p is:

Therefore, the level of sound intensity L1 is sound pressure level Lp It becomes approximately equal to this. The relationship between sound intensity and sound pressure is: Figure 5.1 from "5-1 Sound Pressure Level" on Ono Sokki website, under "What is a Sound Level Meter?" Please refer to.

(3) Sound power level [L W]

Sound waves propagating through a medium can be considered as a flow of energy, and this energy is called acoustic energy. Therefore, as a quantity that represents the magnitude of this acoustic energy, we consider the acoustic energy passing through a specified surface per unit time, and this is called "acoustic power" [P (W)].


The sound power level is defined by the following formula:

Acoustic power is primarily used to express the magnitude of acoustic energy radiated from a sound source. Within a specified frequency band, the total acoustic energy radiated by the sound source per unit time is called "acoustic output (acoustic power of the sound source)" [P (W)], and its acoustic power level is called "acoustic output level (acoustic power level of the sound source)" [LW] (dB).

(4) Acoustic energy level [L J]

For continuously occurring sounds, the above-mentioned acoustic power levels are used, but for single or transient sounds, energy should be used for evaluation.


The acoustic energy level [L J] is defined by the following formula:

【Note】
Energy is the integral of power. Its dimensions are (power) x (time). Conversely, power corresponds to energy per unit time. For example, in the field of electricity, power is measured in kW, while electrical energy is measured in kWh.

4-3 Vibration System

Similar to acoustic systems, absolute decibel values are frequently used in the field of vibration systems, particularly human body vibrations.

(1) Vibration acceleration level [LVa]

Acceleration signals are commonly used as the quantity for measuring vibration. Since actual vibrations are not simple waveforms like sine waves but complex signals containing various frequency components, the RMS value, which corresponds well to energy and power, is used to measure their magnitude.


The vibration acceleration level [LVa] is defined by the following formula:

The standard acceleration value is 10⁻⁵ m/s² according to JIS, but 10⁻⁶ m/s² according to ISO. In other words, there is a difference of 20 dB in vibration acceleration levels.


[example]
In the field of seismology, the practical unit is Gal, where 1 Gal is equal to 1 cm/s². Therefore, 1 Gal corresponds to 60 dB in JIS standards and 80 dB in ISO standards.

(2) Vibration level [LV]​

Vibration level is a level representation of the effective value of vibration acceleration after correcting for human vibration perception. The effect of vibration on the human body depends on its amplitude and frequency, and the perception differs between vertical and horizontal vibrations. Vertical vibrations are most easily perceived at frequencies of 4 to 8 Hz, while horizontal vibrations are most easily perceived at frequencies of 1 to 2 Hz. These are defined in JIS C 1510-1995 as the "overall frequency response of vibration perception characteristics."
For more details, please refer to the "Vibration Level Meter FAQ" section on Ono Sokki website.

The vibration level [LV] is defined by the following formula:

The vibration level is a decibel value with a similar meaning to the A-weighted sound pressure level (noise level) in acoustic systems.

【Note】
Similar to acoustic systems, there are several methods for determining the RMS value using the averaging method, as follows:

  • Exponential average
    This method involves exponentially averaging the squared values of instantaneous vibration waveforms with a time weight τ to obtain the effective value at that time (instantaneously). The resulting decibel value is also a function of time. This corresponds to the so-called instantaneous vibration (acceleration) level, which is usually displayed every second on a vibration level meter. In the JIS standard for vibration level meters (JIS C 1510-1995), the time weight τ (time constant, dynamic characteristic) is 0.63 s.

  • Linear average
    This method involves integrating the squared values of the instantaneous vibration waveform over a measurement time T (with equal weighting) and then averaging them to obtain the RMS value. The resulting decibel value is a representative value (a single value) for that measurement time. This value is called the equivalent vibration level LVeq, similar to how it is used in acoustic systems.