Technical Report: What is dB (Decibel) 2

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

Gain and attenuation in transmission systems often use relative level values in decibels. Since voltage measurement is usually simpler, voltage ratios are taken to calculate decibels in the transfer characteristics of amplifiers and filters.
For example, if a signal of 1 mV is input to a certain circuit, an output voltage of 10 V is generated. In this case, the voltage gain is 10,000 times, so using equation (3-4), the "gain is 80 dB."
Below, we will introduce decibels commonly used in electrical and communication systems.

In the field of power amplification, dBm is often used. This unit defines the absolute power level value of 1 mW as 0 dBm. For example, how many dBm is 10 W? 10 W is 10 ⁴ mW, so it becomes 40 dBm (= 10 log (10 ⁴)). Similarly, how many dBm is 0.1 mW? 0.1 mW is 10^-1 mW, so it becomes −10 dBm. dBm is originally a unit of power, but in transmission systems, it is also used as the absolute voltage level value by fixing the impedance.
Now, if the impedance system is Z (Ω), and the voltage value of 0 dBm (1 mW) is V;

This is the relationship. Table 6 summarizes the voltage values corresponding to 0 dBm at various impedance values derived from equation (4-1).

(Example 1) At 50 Ω, 0.5 V is 7.0 dBm
(Example 2) At 75 Ω, 1 V is 11.2 dBm
(Example 3) At 600 Ω, 6 dBm is 1.55 V

These are the absolute level values of voltage, where dBV is defined as 0 dBV for 1 V, and dBμ is defined as 0 dBμ for 1 μV.

Notice

The leveled voltage values (true values) are basically treated as the effective values of all signals.

dBV is commonly used in low-frequency measurement instruments such as FFT analyzers. Since the default input unit for FFT analyzers is voltage (V), the vertical axis of the power spectrum is labeled in [dBV] unless the physical quantity is calibration.In addition, the input voltage range is typically set in 10 dBV steps. For example, the input range of the DS-3000 series data stations defines a voltage of 1 Vrms as 0 dBV (see Table 7).

Table 7: Input Range of the DS-3000 Series

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

It is used to express the electric field strength values representing radiation emission values such as those from EMC. This defines 1 μV/m as 0 dB.

When evaluating the spectral characteristics of high-frequency signals and operational amplifiers (OP amps), the relative level values of harmonics and noise components are based on the fundamental wave (the carrier, denoted as "c"). For example, if the fundamental wave is 10 dBm and a harmonic is -40 dBm, that harmonic would be -50 dBc. This relationship holds true even if the vertical axis of the spectrum is in dBV. It is used as a parameter to evaluate low distortion in devices like OP amps.

When measuring the self-noise characteristics of an amplifier, it is evaluated using power spectral density (PSD), where the vertical axis represents the effective value per unit frequency (1 Hz), so the unit is V ² /Hz or V/√Hz. The value converted to decibels is dBV/√Hz.

Decibels (dB) are often used to quantify the intensity (loudness) of sound. The main reason for this is that the range of sound intensity that humans can perceive is very wide, and our perception is logarithmic in nature (see section 3.4 (3)). The absolute level value representation of decibels (dB) is commonly used for quantifying sound volume.

Sound transmitted through air is a minute pressure fluctuation (wave) centered around atmospheric pressure (static pressure), and the effective value of that fluctuation component is called sound pressure, with the unit of sound pressure being Pa (Pascal). As mentioned above, the sound pressure that humans can typically hear ranges from 20 μPa to 20 Pa, covering a wide range of values of 10 ⁶.

The sound pressure level is defined by the following formula.

Notice

In equations (4-6) and (4-7), the issue arises regarding how to specifically determine the sound pressure (the effective value of instantaneous sound pressure). Typically, the method used to obtain the effective value from the instantaneous sound pressure waveform is the averaging method, which is commonly employed.

Exponential average
is a method to calculate the effective value at a moment (instant) by exponentially averaging the square value of the instantaneous sound pressure over a time weighting τ, making the decibel value to be calculated a function of time. The so-called instantaneous sound pressure level corresponds to this, and sound level meters typically display it every second. In the JIS standard for sound level meters (JISC1509), it is referred to as time-weighted sound level. In the field of acoustic measurement, the time weighting τ (time constant) commonly uses Fast (0.125 s) and Slow (1 s).

Linear average
The method of averaging the squared value of the instantaneous sound pressure over a measurement time T (with equal weighting) to obtain the effective value, and the decibel value derived from this will be a representative value (one value) for that measurement time. In the JIS standard for sound level meters (JIS C1509), this is referred to as the time-averaged sound level (equivalent sound level). If the frequency weighting is [A], it becomes the "equivalent noise level" in the field of environmental noise.
For more details, please refer to Ono Sokki's homepage "What is a sound level meter" in Chapter 9: Indications of the sound level meter.

The energy that passes through a unit area in a unit time of sound waves traveling through a medium such as air is called sound intensity, and the unit is [W/m ²].

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

When sound waves can be considered plane waves, the relationship between sound intensity I and sound pressure p is:

Therefore, the sound intensity level L₁ is almost equal to the sound pressure level L_p. The relationship between sound intensity and sound pressure can be found in Ono Sokki homepage "What is a sound level meter" figure 5.1 of "5-1 Sound Pressure Level (sound pressure level)".

Sound waves propagating through a medium can be considered as a flow of energy, which is referred to as acoustic energy. Therefore, the quantity that represents the magnitude of this acoustic energy is the acoustic power, denoted as P (W), which is defined as the amount of acoustic energy passing through a specified surface per unit time.

The sound power level is defined by the following formula.

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

For continuously occurring sounds, the above acoustic power level is used, but for transient or single sounds, it is necessary to evaluate based on energy.

The acoustic energy level [L _J] is defined by the following equation.

[Note]
Energy is the integral of power. Its dimension is (power) X (time). Conversely, power corresponds to energy per unit time. For example, in the field of electricity, electric power is measured in KW, while electric energy is measured in kWh.

Just like in acoustic systems, absolute decibel values are often used in the field of vibration systems, particularly in relation to human body vibrations.

Acceleration signals are commonly used for measuring vibrations. Actual vibrations are complex signals that include various frequency components, rather than simple waveforms like sine waves. Therefore, the effective value, which corresponds well to energy or power, is used as a measure of magnitude.

The vibration acceleration level [L_Va] is defined by the following formula.

The reference acceleration value is 10^-5 m/s ² according to JIS, while ISO uses 10^-6 m/s ² as the standard. In other words, there is a difference of 20 dB in the vibration acceleration level.

[Example]
In the field of earthquakes, there is a practical unit called Gal, where 1 Gal is 1 cm/s ², thus 1 Gal corresponds to 60 dB in JIS and 80 dB in ISO.

The vibration level is the leveled effective value of vibration acceleration that has been corrected for human vibration perception. The effects of vibration on the human body depend on amplitude and frequency, and the perception differs between vertical and horizontal directions. In vertical vibrations, frequencies of 4 to 8 Hz are most easily felt, while in horizontal vibrations, frequencies of 1 to 2 Hz are most easily perceived, as specified in JIS C 1510-1995 as the "comprehensive frequency response of vibration perception characteristics."
For more details, please refer to "Frequently Asked Questions about Vibration Level Meters".

The vibration level [L _V] is defined by the following formula.

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

【Note】
Similar to audio systems, there are the following methods to obtain the effective value using the average method.