Lecture
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
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.
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].
| D | P1 / P0 | F1 / F0 |
|---|---|---|
| 40 dB | 10,000 | 100 |
| 20 dB | 100 | ten |
| 10 dB | ten | ≈ 3.16 |
| 6 dB | ≈ 4 | ≈ 2 |
| 3 dB | ≈ 2 | ≈ 1.41 |
| 1 dB | ≈ 1.26 | ≈ 1.12 |
| 0 dB | one | one |
| −1 dB | ≈ 0.79 | ≈ 0.89 |
| −3 dB | ≈ 0.5 | ≈ 0.71 |
| −6 dB | ≈ 0.25 | ≈ 0.5 |
| −10 dB | 0.1 | ≈ 0.32 |
| −20 dB | 0.01 | 0.1 |
| −40 dB | 0.0001 | 0.01 |
Attitude 
two values of energy value 
and 
expressed in decibels, is determined by the formula:
From here:
or 
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
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].
| Unit | Designation | Energy change times |
Power change times |
Recalculation in ... | |||
|---|---|---|---|---|---|---|---|
| dB | B | Np | |||||
| decibel | dB, dB | 10 root of 10 ≈ 1.259 | 20 root of 10≈ 1,122 | one | 0.1 | ≈0.1151 | |
| bel | B, B | ten | root of 10 ≈ 3.162 | ten | one | ≈1,151 | |
| neper | Np, Np | e 2 ≈ 7.389 | e ≈ 2.718 | ≈8,686 | ≈0.8686 | one | |
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.
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.
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.
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.
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.
Schematic representation of the relationship between dBc (voltage source) and dBm (power dissipated into heat on a 600 ohm resistor)
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.
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.
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Microwave Devices and Antennas
Terms: Microwave Devices and Antennas