Decibel. Isotropic decibel

Decibele (Russian designation: dB ; international: dB ) is the common unit of white, equal to one tenth of this unit. Bel expresses the ratio of two values ​​of the energy value by the decimal logarithm of this ratio.

The ratio Dp of two values ​​of the energy quantity P, such as power, energy, energy density, etc., expressed in decibels, is determined by the formula:

Dp = 10 lg (P1 / P0)

It follows that an increase in the energy value by 1 dB means an increase of 10 ^ 0.1 ≈ 1.259 times.

Energy values ​​are proportional to the squares of force values (or field values , as is customary in international documents), such as sound pressure, voltage, electric current, etc., therefore the ratio Df of two values ​​of force value F, expressed in decibels, is determined by formula:

Df = 20 lg (F1 / F0)

It follows that an increase in the power value by 1 dB means an increase of 10 ^ 0? 05 ≈ 1,122 times.

Decibel refers to units that are not part of the International System of Units (SI), but in accordance with the decision of the International Committee of Measures and Weights, it is allowed to be used without restrictions in conjunction with SI units. Mainly used in telecommunications, acoustics, radio engineering, in the theory of automatic control systems

Content

• 1. History
• 2Determination
  • 2.1 Energy values
  • 2.2 Force values
  • 2.3 Determination of units of white
  • 2.4Comparison of logarithmic units
• 3Application
  • 3.1 Acoustics
  • 3.2Convenience decibel use
• 4Basic values ​​and level designations
  • 4.1Special notation
• 5Notes
• 6SM. also

Story

Distribution of the decibel originates from the methods used to quantify the loss (attenuation) of the signal in the telegraph and telephone lines. The loss unit was originally the mile of a standard cable (English mile of standard cable - msc). 1 msc is the power ratio of a signal with a frequency of 800 Hz at the two ends of a cable 1 m long (approximately 1.6 km), having a distributed resistance of 88 Ohms (per loop) and a distributed capacitance of 0.054 μF [7]. This ratio of power, converted into sound vibrations, was close to the smallest distinguishable average listener difference of two signals in volume. However, the standard cable mile was frequency-dependent, and it could not be a full-fledged unit of the power ratio [8].

In 1924, Bell Phone received a favorable response to the new unit definition among the members of the International Telegraph Union in Europe: instead of msc, the transmission unit (TU). The transmission unit was determined in such a way that it was ten times the decimal logarithm of the ratio of the measured power to the original power [9]. The convenience of this definition was in approximate correspondence between the old and the new units (1 msc is approximately 0.9 TU). In 1928, Bell Phone Company renamed the TU transmission unit to decibels [10], which became one tenth of the newly defined unit of the logarithmic power ratio, named Bel in honor of the American scientist Alexander Bell [11]. The unit bel is rarely used, while the decibel is widespread [12].

In April 2003, the International Committee for Weights and Measures (CIPM) considered the recommendation to include a decibel in the International System of Units (SI), but declined the proposal [13]. However, decibels are recognized by other international organizations, such as the International Electrotechnical Commission (IEC) and the International Organization for Standardization (ISO) [14]. IEC allows the use of decibels with power and energy values, and this recommendation is followed by many national standards organizations, such as the National Institute of Standards and Technology in the United States.

Definition

Decibels are usually used to measure or express the ratio of like energy values, such as power, energy, intensity, power flux density, power spectral density, etc., as well as force values ​​such as voltage, current, field strength, sound pressure and so on. Often the generally accepted initial (or reference) value is used as one of the ratio values ​​(in the denominator). Then the ratio expressed in decibels is called the level of the corresponding physical quantity (for example, power level, voltage level, etc.) [1] [2].

Energy values

Attitude two values ​​of energy value and expressed in decibels, is determined by the formula:

From here:

or

Force values

Energy values ​​are proportional to the squares of force values. For example, in an electrical circuit dissipated into heat on a load with resistance under tension is determined by the formula:

Hence the ratio of two quantities:

The logarithmic relation in the particular case, with :

Thus, the preservation of numerical values ​​in decibels in the transition from the ratio of power to the ratio of voltages at the same load requires that the following relationship holds:

Dp = Du where Du = 20 lg (U1 / U0)

From here:

U1 / U0 = 10 ^ (0.05 Du) or U1 = Uo 10 ^ 0.05 Du

Unit definition is white

Bel (Russian designation: B; international: B) expresses the ratio of two powers as the decimal logarithm of this ratio.

According to GOST 8.417-2002], bel is a unit of the logarithmic ratio of a physical quantity to a physical quantity of the same name taken as the initial one. For energy values ​​(P): 1 B = lg (P2 / P1) with P2 = 10P1; for force values ​​(F): 1 Б = 2 lg (F2 / F1) with F2 = 100,5 F1.

Thus, the protein corresponds to a ratio of 10 for energy values ​​or a ratio of 100.5 ≈ 3.162 for force values.

Bel is rarely used both without a prefix and with any other SI prefixes, except for deci . For example, instead of the one-thousandth of white, it is preferable to use the hundredth of a decibel (the standard recording will be not 5 MB, but 0.05 dB) [16].

Comparison of logarithmic units

Application

Decibels are widely used in areas of technology where measurement or representation of quantities varying in a wide range is required: in radio engineering, antenna technology, information transmission systems, automatic control and control, in optics, acoustics (the volume level of sound is measured in decibels), etc. So, in decibels, it is customary to measure or indicate the dynamic range (for example, the loudness range of a musical instrument), the attenuation of a wave during propagation in an absorbing medium, the attenuation coefficient of a radio frequency Amplifier cable, gain and noise figure.

Acoustics

Sound pressure is a force quantity, and sound intensity, proportional to the square of the sound pressure, is an energy quantity. For example, if the volume of the sound (subjectively determined by its intensity) increased by 10 dB, then this means that the intensity of the sound increased 10 times, and the sound pressure increased by approximately 3.16 times.

The use of decibels when specifying the volume of a sound is due to the human ability to perceive sound in a very large range of changes in its intensity. The use of a linear scale is almost inconvenient. In addition, based on the Weber-Fechner law, the sensation of loudness of sound is proportional to the logarithm of its intensity. Hence the convenience of a logarithmic scale. The range of sound pressure values ​​from the minimum human hearing threshold (20 μPa) to the maximum, which causes pain, is approximately 120 dB. For example, the statement “sound volume is 30 dB” means that the sound intensity is 1000 times higher than the human hearing threshold.

To express the volume of sound, the units of background and sleep are also used, taking into account the frequency and subjective sensitivity of sound by humans.

Usability decibels

First of all, it should be noted the convenience of decibel compared with the unit Bel. For practical applications, Bel turned out to be too large a unit, often involving the fractional recording of the value of a logarithmic quantity. The following amenities are somehow connected with the use of not only decibels, but a logarithmic scale and logarithmic values ​​in general.

• The character of changes in the course of many physical and biological processes in the organs of sense of man and animals is not proportional to the amplitude of the input, but to the logarithm of the input (see Weber-Fechner Law). This feature makes the use of logarithmic scales, logarithmic quantities and their units quite natural. For example, one of such scales is a musical evenly tempered frequency scale.
• A logarithmic scale provides a visual graphical representation and simplification of the analysis of a quantity varying within very wide limits (examples are antenna pattern, amplitude-frequency characteristic (AFC) of the automatic control system). The same applies to the frequency response characteristics of electric filters (see logarithmic amplitude-phase frequency response). In this case, the shape of the curve is simplified and it is possible to use a piecewise linear approximation, in which the rate of decrease of the frequency response has the dimension dB / decade or dB / oct. Simplifies the analysis of the frequency response of filters made up of series-connected links with frequency characteristics that are independent of each other. It should be noted that the construction of graphs on a logarithmic scale requires a certain skill (see Logarithmic paper).
• The logarithmic representation of some relative values ​​in some cases simplifies mathematical operations with them, in particular, multiplication and division are replaced by addition and subtraction. For example, if the intrinsic gains of series-connected amplifiers are expressed in decibels, then the total gain is found as the sum of the intrinsic coefficients.

Reference Values ​​and Level Labels

If one of the values ​​of the ratio (in the denominator) is the generally accepted initial (or reference) quantity X ref, then the ratio expressed in decibels is called the level (sometimes called the absolute level ) of the corresponding physical quantity X and is denoted by L X (from English. ).

In accordance with current standards, if necessary, indicate the initial value of its value is placed in brackets for the logarithmic value. For example, the L P level of sound pressure P can be written: L P (out. 20 μPa) = 20 dB, and using international notation - L P (re 20 µPa) = 20 dB ( re is an abbreviation of English reference ). It is allowed to indicate the value of the initial value in brackets behind the level value, for example: 20 dB (out. 20 μPa). A short form is also used, for example, the L W power level W can be written: L W (1 mW) = 30 dB, or L W = 30 dB (1 mW). The value “1” of the initial value can be omitted, for example, L W = 30 dB (mW). That is, if only the dimension of the initial value is indicated in parentheses, but the value of the value is not indicated, then it is assumed that it is equal to "1". Special abbreviations are widely used to shorten the recording, for example: L W = 30 dBm. Recording means that the power level is +30 dB with respect to 1 mW, that is, the power is 1 W.

Special notation

Some special designations are given, which in an extremely brief form indicate the value of the initial (reference) value, in relation to which the corresponding level, expressed in decibels, is determined. For the following reference values, the voltage is understood to mean its rms (effective) value.

• dBW (Russian dBW ) - reference power 1 watt. For example, a power level of +30 dBW corresponds to a power of 1 kW.
• dBm (Russian dBm ) - reference power 1 mW.
• dBm0 (Russian dBm0 ) - reference power of 1 mW. The designation is used in telecommunications to indicate the absolute power level, reduced to the so-called zero relative level point.
• dBV (Russian dBV ) - reference voltage of 1 V.
• dBuV or dBμV (Russian dBµV ) is a reference voltage of 1 µV.

Schematic representation of the relationship between dBc (voltage source) and dBm (power dissipated into heat on a 600 ohm resistor)

• dBu (Russian dBc ) - reference voltage (root of 0.600) ≈ 0.775 V, corresponding to a power of 1 mW at a load of 600 ohms.
• dBrn - the reference voltage corresponds to the thermal noise power of an ideal resistor with a resistance R equal to 50 Ohms at room temperature in the 1 Hz frequency band: U t.th.sq.th (4k TR * 1 Hz) = 9 * 10 ^ -10 B. This value corresponds to a voltage level of –61 dBμV or a power level of −168 dBm.
• dBFS (from English. full scale - “full scale”) - the reference signal (power, voltage) corresponds to the full scale of the analog-to-digital converter.
• dB SPL (from sound pressure level , “ sound pressure level ”) is the reference value of the amplitude of sound pressure of 20 μPa, corresponding to the hearing threshold of harmonic sound oscillation with a frequency of 1 kHz.
• dB (A) , dB (B) , dB (C) - these symbols are used to denote a weighted sound pressure level relative to 20 µPa, when measurements are used with filters with appropriate standard frequency characteristics.
• dBc (Russian dBc ) - the reference value corresponds to the radiation power at the carrier frequency (English carrier ).
• dBi (Russian dBi ) - isotropic decibels. The designation is used to describe the characteristics of the antenna (directional gain, gain) compared to a hypothetical isotropic antenna, which radiates energy uniformly in all directions.

Isotropic decibel ( dBi ) is a type of decibel. It characterizes an ideal antenna, in which the radiation pattern looks like an ideal sphere. As a rule, unless otherwise specified, the gain characteristics of real antennas are given relative to the gain of an isotropic antenna. That is, when they say that the gain of any antenna is 12 dB, 12 dBi is implied.

• dBd (Russian dBd ) - decibel relative to the half-wave vibrator (dipole). The designation is used to describe the characteristics of the antenna compared to a half-wave vibrator (0 dBd = 2.15 dBi).
• dBsm (from English square meter , Russian dBq.m or dB (m²) ) - decibels relative to one square meter. It characterizes the effective scattering surface of a diverter in radar.

By analogy, compound units [1] [2] are formed, for example, the power spectral density level: dBW / Hz is the “decibel” analog of the W / Hz unit (power at the nominal load in the 1 Hz frequency band centered on a given frequency) - here is the reference level 1 W / Hz.