What is a decibel. Basic meter decibels

WHAT ARE DECIBELS?

Universal logarithmic units decibels are widely used in quantitative estimates of the parameters of various audio and video devices in our country and abroad. In radio electronics, in particular, in wire communication, technology for recording and reproducing information, decibels are a universal measure.

Decibel is not a physical quantity, but a mathematical concept

In electroacoustics, the decibel is essentially the only unit for characterizing various levels - sound intensity, sound pressure, loudness, and also for evaluating the effectiveness of means of dealing with noise.

The decibel is a specific unit of measurement that is not similar to any of those that we have to meet in everyday practice. The decibel is not an official unit in the SI system, although, according to the decision of the General Conference on Weights and Measures, it can be used without restrictions in conjunction with the SI, and the International Chamber of Weights and Measures recommended its inclusion in this system.

The decibel is not a physical quantity, but a mathematical concept.

In this respect, decibels have some similarities with percentages. Like percentages, decibels are dimensionless and serve to compare two values ​​of the same name, in principle very different, regardless of their nature. It should be noted that the term "decibel" is always associated only with energy quantities, most often with power and, with some reservations, with voltage and current.

A decibel (Russian designation - dB, international designation - dB) is a tenth of a larger unit - bela 1.

Bel is the decimal logarithm of the ratio of the two powers. If two powers are known R 1 and R 2 , then their ratio, expressed in bels, is determined by the formula:

The physical nature of the compared powers can be any - electrical, electromagnetic, acoustic, mechanical, it is only important that both values ​​are expressed in the same units - watts, milliwatts, etc.

Let us briefly recall what a logarithm is. Any positive 2 number, both whole and fractional, can be represented by another number to a certain extent.

So, for example, if 10 2 = 100, then 10 is called the base of the logarithm, and the number 2 - the logarithm of 100 and denote log 10 100 = 2 or lg 100 = 2 (read like this: "the logarithm of one hundred at base ten is two").

Base 10 logarithms are called decimal logarithms and are most commonly used. For numbers divisible by 10, this logarithm is numerically equal to the number of zeros per unit, and for other numbers it is calculated on a calculator or found from tables of logarithms.

Logarithms with base e = 2.718 ... are called natural. In computing, logarithms with base 2 are commonly used.

Basic properties of logarithms:

Of course, these properties are also valid for decimal and natural logarithms. The logarithmic way of representing numbers is often very convenient, since it allows you to replace multiplication by addition, division by subtraction, raising to a power by multiplication, and extracting a root by division.

In practice, bel turned out to be too large, for example, any power ratios in the range from 100 to 1000 fit within one bel - from 2 B to 3 B. Therefore, for greater clarity, we decided to multiply the number showing the number of bels by 10 and count the resulting product an indicator in decibels, i.e., for example, 2 B = 20 dB, 4.62 B = 46.2 dB, etc.

Usually, the power ratio is expressed immediately in decibels using the formula:

Operations with decibels are the same as operations with logarithms.

2 dB = 1 dB + 1 dB → 1.259 * 1.259 = 1.585;
3dB → 1.259 3 = 1.995;
4 dB → 2.512;
5 dB → 3.161;
6 dB → 3.981;
7 dB → 5.012;
8 dB → 6.310;
9 dB → 7.943;
10 dB → 10.00.

The → sign means “match”.

Similarly, you can create a table for negative decibels. Minus 1 dB characterizes a decrease in power by 1 / 0.794 = 1.259 times, that is, also by about 26%.

Remember that:

⇒ If R 2 = P 1 i.e. P 2 / P 1 = 1 , then N dB = 0 , because lg 1 = 0 .

⇒ If P 2 > P l , then the number of decibels is positive.

⇒ If R 2 < P 1 , then decibels are expressed in negative numbers.

Positive decibels are often referred to as gain decibels. Negative decibels usually characterize energy losses (in filters, dividers, long lines) and are called attenuation or loss decibels.

There is a simple relationship between the decibels of gain and damping: the opposite numbers of ratios correspond to the same number of decibels with different signs. If, for example, the relation R 2 /R 1 = 2 → 3 dB , then –3 dB → 1/2 , i.e. 1 / R 2 /R 1 = P 1 /R 2

⇒ If R 2 /R 1 represents a power of ten, i.e. R 2 /R 1 = 10 k , where k - any integer (positive or negative), then NdB = 10k , because lg 10 k = k .

⇒ If R 2 or R 1 is equal to zero, then the expression for NdB loses its meaning.

And one more feature: the curve, which determines the decibel values ​​depending on the power ratios, first grows rapidly, then its growth slows down.

Knowing the number of decibels corresponding to one power ratio, it is possible to recalculate for another - close or multiple ratio. In particular, for power ratios that differ by a factor of 10, the decibel number differs by 10 dB. This feature of decibels should be well understood and firmly remembered - it is one of the foundations of the entire system.

The advantages of the decibel system include:

⇒ versatility, that is, the ability to use in assessing various parameters and phenomena;

⇒ huge differences in converted numbers - from units to millions - are displayed in decibels as numbers of the first hundred;

⇒ natural numbers representing powers of ten are expressed in decibels as multiples of ten;

⇒ reciprocal numbers are expressed in decibels by equal numbers, but with different signs;

⇒ both abstract and named numbers can be expressed in decibels.

The disadvantages of the decibel system include:

⇒ low visibility: to convert decibels into ratios of two numbers or to perform the opposite actions, calculations are required;

⇒ Power ratios and voltage (or current) ratios are converted to decibels using different formulas, which sometimes leads to errors and confusion;

⇒ decibels can only be measured relative to a level that is not equal to zero; absolute zero, for example 0 W, 0 V, is not expressed in decibels.

Knowing the number of decibels corresponding to one power ratio, it is possible to recalculate for another - close or multiple ratio. In particular, for power ratios that differ by a factor of 10, the decibel number differs by 10 dB. This feature of decibels should be well understood and firmly remembered - it is one of the foundations of the entire system.

Comparing two signals by comparing their powers is not always convenient, since expensive and complex instruments are required to directly measure electrical power in the audio and radio frequency ranges. In practice, when working with equipment, it is much easier to measure not the power that is released at the load, but the voltage drop across it, and in some cases, the flowing current.

Knowing the voltage or current and resistance of the load, it is easy to determine the power. If measurements are carried out on the same resistor, then:

These formulas are very often used in practice, but note that if voltages or currents are measured at different loads, these formulas do not work and other, more complex dependencies should be used.

Using the technique that was used to compile the power decibel table, you can similarly determine what 1 dB is equal to the ratio of voltages and currents. A positive decibel will be 1.122, and a negative decibel will be 0.8913, i.e. 1 dB of voltage or current characterizes the increase or decrease of this parameter by about 12% with respect to the initial value.

The formulas were derived under the assumption that the load resistances are active and there is no phase shift between voltages or currents. Strictly speaking, one should consider the general case and take into account the presence of a phase angle for voltages (currents), and for loads not only active, but impedance, including reactive components, but this is important only at high frequencies.

It is useful to remember some of the decibel values ​​that are often encountered in practice and the ratios of powers and voltages (currents) that characterize them, given in Table. one.

Table 1. Frequent decibel values ​​of power and voltage

Using this table and the properties of logarithms, it is easy to calculate what arbitrary values ​​of the logarithms correspond to. For example, 36 dB of power can be represented as 30 + 3 + 3, which corresponds to 1000 * 2 * 2 = 4000. We get the same result by representing 36 as 10 + 10 + 10 + 3 + 3 → 10 * 10 * 10 * 2 * 2 = 4000.

COMPARISON OF DECIBELS WITH PERCENTAGES

Earlier it was noted that the concept of decibels has some similarities with percent. Indeed, since the percentage is the ratio of a number to another, conventionally taken as one hundred percent, the ratio of these numbers can also be represented in decibels, provided that both numbers characterize power, voltage or current. For the power ratio:

For the ratio of voltages or currents:

You can also derive formulas for converting decibels to percentages of a ratio:

Table 2 is a translation of some of the most common values ​​of decibels in percentages of ratios. Various intermediate values ​​can be found on the nomogram in Fig. one.

Rice. 1. Converting decibels to percentages of ratios according to the nomogram

Table 2. Converting decibels to percentages

Let's look at two practical examples to illustrate the conversion of percentage to decibels.

Example 1. What is the harmonic level in decibels in relation to the level of the fundamental frequency signal corresponds to a THD of 3%?

Let's use fig. 1. Through the point of intersection of the vertical line of 3% with the "voltage" graph, draw a horizontal line until it crosses the vertical axis and we get the answer: –31 dB.

Example 2. What percentage of voltage attenuation does the –6 dB change correspond to?

Answer. 50% of the original value.

In practical calculations, the fractional part of the numerical value of decibels is often rounded to an integer, however, an additional error is introduced into the calculation results.

DECIBELS IN RADIO ELECTRONICS

Let's consider a few examples that explain the technique of using decibels in electronics.

Attenuation in the cable

Energy losses in lines and cables per unit length are characterized by the attenuation coefficient α, which, with equal input and output line resistances, is determined in decibels:

where U 1 - voltage in an arbitrary section of the line; U 2 - voltage in another section, spaced from the first by a unit of length: 1 m, 1 km, etc. For example, a high-frequency cable of the RK-75-4-14 type at a frequency of 100 MHz has an attenuation coefficient α, = –0.13 dB / m, a twisted pair cable of category 5 at the same frequency has an attenuation of the order of –0.2 dB / m, and for a cable of category 6 it is slightly less. The signal attenuation plot in an unshielded twisted pair cable is shown in Fig. 2.

Rice. 2. A graph of the signal attenuation in an unshielded twisted pair cable

Fiber optic cables have significantly lower attenuation values ​​in the range from 0.2 to 3 dB at a cable length of 1000 m. All optical fibers have a complex attenuation dependence on wavelength, which has three "transparency windows" 850 nm, 1300 nm and 1550 nm ... "Window of transparency" means the smallest loss at the maximum signal transmission distance. The signal attenuation graph in fiber optic cables is shown in Fig. 3.

Rice. 3. Graph of signal attenuation in fiber optic cables

Example 3. Find what will be the voltage at the output of a piece of cable RK-75-4-14 length l = 50 m, if a voltage of 8 V at a frequency of 100 MHz is applied to its input. The load resistance and the characteristic impedance of the cable are equal, or, as they say, are matched with each other.

Obviously, the attenuation introduced by a piece of cable is K = –0.13 dB / m * 50 m = –6.5 dB. This decibel value roughly corresponds to a voltage ratio of 0.47. This means that the voltage at the output end of the cable U 2 = 8V * 0.47 = 3.76V.

This example illustrates a very important point: losses in a line or cable grow extremely rapidly with increasing length. For a 1 km section of cable, the attenuation will already be –130 dB, that is, the signal will be attenuated more than three hundred thousand times!

The attenuation largely depends on the frequency of the signals - in the audio frequency range it will be much less than in the video range, but the logarithmic law of attenuation will be the same, and with a long line length, the attenuation will be significant.

Audio Amplifiers

In order to improve their quality indicators, negative feedback is usually introduced into audio amplifiers. If the open-loop voltage gain of the device is TO , and with feedback To OS then the number showing how many times the gain changes under the action of feedback is called depth of feedback ... It is usually expressed in decibels. In a working amplifier, the coefficients TO and TO OS determined experimentally, unless the amplifier is excited with an open feedback loop. When designing an amplifier, first calculate TO and then determine the value To OS in the following way:

where β is the transmission coefficient of the feedback circuit, i.e. the ratio of the voltage at the output of the feedback circuit to the voltage at its input.

The feedback depth in decibels can be calculated using the formula:

Stereo devices have to fulfill additional requirements compared to monaural ones. The surround sound effect is ensured only with good channel separation, that is, without the penetration of signals from one channel to another. In practical terms, this requirement cannot be fully satisfied, and mutual leakage of signals occurs mainly through nodes common to both channels. The channel separation quality is characterized by the so-called crosstalk damping a PZ A measure of the crosstalk in decibels is the ratio of the output powers of both channels when the input signal is applied to only one channel:

where R D - maximum output power of the operating channel; R SV is the free channel output power.

Good channel separation corresponds to a crosstalk of 60-70 dB, excellent –90-100 dB.

Noise and background

At the output of any receiving-amplifying device, even in the absence of a useful input signal, an alternating voltage can be detected, which is caused by the inherent noise of the device. The reasons that cause intrinsic noise can be both external - due to interference, poor filtering of the supply voltage, and internal, due to the intrinsic noise of radio components. Noise and interference arising in the input circuits and in the first amplifier stage are most affected, since they are amplified by all subsequent stages. Intrinsic noise degrades the actual sensitivity of the receiver or amplifier.

Noise is quantified in several ways.

The simplest one is that all noises, regardless of the cause and place of their occurrence, are recalculated to the input, i.e., the noise voltage at the output (in the absence of an input signal) is divided by the gain:

This voltage, expressed in microvolts, is a measure of the intrinsic noise. However, for evaluating a device from the point of view of interference, it is not the absolute value of the noise that is important, but the ratio between the useful signal and this noise (signal-to-noise ratio), since the useful signal must be reliably distinguished from the background of interference. The signal-to-noise ratio is usually expressed in decibels:

where R With - the specified or nominal output power of the useful signal together with noise; R NS - output power of noise when the source of the useful signal is off; U c - signal and noise voltage across the load resistor; U Sh - noise voltage across the same resistor. So it turns out the so-called. "Unweighted" signal-to-noise ratio.

Often the signal-to-noise ratio is given in the parameters of audio equipment, measured with a weighting filter ("weighted"). The filter allows you to take into account the different sensitivity of a person's hearing to noise at different frequencies. The most commonly used filter is type A, in which case the designation usually indicates the unit of measurement "dBA" ("dBA"). The use of a filter usually gives better quantitative results than for unweighted noise (usually the signal-to-noise ratio is 6-9 dB higher), therefore (for marketing reasons) equipment manufacturers often indicate exactly the "weighted" value. For more information on weighing filters, see the Sound Meters section below.

Obviously, for the successful operation of the device, the signal-to-noise ratio must be higher than some minimum acceptable value, which depends on the purpose and requirements for the device. For Hi-Fi equipment, this parameter should be at least 75 dB, for Hi-End equipment - at least 90 dB.

Sometimes, in practice, they use the inverse ratio, characterizing the noise level relative to the useful signal. The noise level is expressed in the same decibels as the signal-to-noise ratio, but with a negative sign.

In the descriptions of receiving and amplifying equipment, the term background level sometimes appears, which characterizes in decibels the ratio of the components of the background voltage to the voltage corresponding to a given nominal power. The background components are multiples of the mains frequency (50, 100, 150 and 200 Hz) and during measurement are isolated from the total interference voltage using band-pass filters.

The signal-to-noise ratio does not allow, however, to judge which part of the noise is directly caused by the elements of the circuit, and which is introduced as a result of imperfections in the design (pickup, background). To assess the noise properties of radio components, the concept is introduced noise factor ... Noise figure is rated in terms of power and is also expressed in decibels. This parameter can be characterized as follows. If at the input of the device (receiver, amplifier) ​​a useful signal with a power R With and noise power R NS , then the signal-to-noise ratio at the input will be (R With /R NS ) in After strengthening the attitude (R With /R NS ) out will be less, since the amplified intrinsic noise of the amplifying stages will also be added to the input noise.

The noise figure is the ratio expressed in decibels:

where TO R is the power amplification factor.

Therefore, noise figure represents the ratio of the output noise power to the amplified input noise power.

Meaning Rsh.in determined by calculation; Psh.out measured and TO R usually. known from calculation or after measurement. An ideal amplifier in terms of noise should only amplify useful signals and should not introduce additional noise. As follows from the equation, for such an amplifier, the noise figure is F Sh = 0 dB .

For transistors and ICs intended for operation in the first stages of amplifying devices, the noise figure is regulated and given in the reference books.

The self-noise voltage also determines another important parameter of many amplifying devices - the dynamic range.

Dynamic range and adjustments

Dynamic range is the ratio of the maximum undistorted output power to its minimum value, expressed in decibels, at which the admissible signal-to-noise ratio is still ensured:

The lower the noise floor and the higher the undistorted output power, the wider the dynamic range.

The dynamic range of sound sources - orchestra, voice, is determined in a similar way, only here the minimum sound power is determined by the background noise. In order for the device to transmit both the minimum and maximum amplitudes of the input signal without distortion, its dynamic range must be no less than the dynamic range of the signal. In cases where the dynamic range of the input signal exceeds the dynamic range of the device, it is artificially compressed. This is done, for example, when recording.

The effectiveness of the manual volume control is checked at two extreme positions of the control. First, with the regulator in the maximum volume position, a voltage of 1 kHz is applied to the input of the audio frequency amplifier, such that a voltage corresponding to a certain specified power is established at the amplifier output. Then the volume control knob is turned to the minimum volume, and the voltage at the amplifier input is raised until the output voltage again becomes equal to the initial one. The ratio of the input voltage with the knob in the minimum volume position to the input voltage at the maximum volume, expressed in decibels, is an indication of how the volume control is operating.

The given examples are far from being exhausted practical cases of application of decibels to the estimation of parameters of radioelectronic devices. Knowing the general rules for the application of these units, one can understand how they are used in other conditions not considered here. Faced with an unfamiliar term, defined in decibels, one should clearly imagine the ratio of which two quantities it corresponds to. In some cases, this is clear from the definition itself, in other cases, the relationship between the components is more complicated, and when there is no clear clarity, one should refer to the description of the measurement procedure in order to avoid serious errors.

When operating with decibels, you should always pay attention to the ratio of which units - power or voltage - each specific case corresponds to, i.e. what coefficient - 10 or 20 - should come before the sign of the logarithm.

LOGARITHMIC SCALE

The logarithmic system, including decibels, is often used when constructing amplitude-frequency characteristics (AFC) - curves depicting the dependence of the transfer coefficient of various devices (amplifiers, dividers, filters) on the frequency of external influences. To construct the frequency response, a number of points characterizing the output voltage or power at a constant input voltage at different frequencies are determined by calculation or experiment. The smooth curve connecting these points characterizes the frequency properties of the device or system.

If numerical values ​​are plotted along the frequency axis in a linear scale, i.e., in proportion to their actual values, then such a frequency response will be inconvenient for use and will not be visual: in the region of lower frequencies it is compressed, and in the region of higher frequencies it is stretched.

Frequency characteristics are usually plotted on the so-called logarithmic scale. On the frequency axis, in a scale convenient for work, values ​​are plotted that are proportional not to the frequency itself f , and the logarithm lgf / f o , where f O - the frequency corresponding to the origin. Values ​​are labeled against axis marks f ... To build logarithmic frequency response, a special logarithmic graph paper is used.

When carrying out theoretical calculations, they usually use more than just the frequency f , and the value ω = 2πf which is called the circular frequency.

Frequency f O , corresponding to the origin, can be arbitrarily small, but cannot be equal to zero.

On the vertical axis, the ratio of the transmission coefficients at different frequencies to its maximum or average value is plotted in decibels or in relative numbers.

The logarithmic scale allows a wide range of frequencies to be displayed on a small section of the axis. On such an axis, equal ratios of two frequencies correspond to sections of equal length. The interval characterizing the tenfold increase in frequency is called decade ; twice the frequency ratio corresponds octave (this term is borrowed from music theory).

Frequency range with cutoff frequencies f H and f V occupies a strip in decades f B / f H = 10m , where m - the number of decades, and in octaves 2 n , where n - number of octaves.

If the bandwidth of one octave is too wide, then intervals with a lower frequency ratio of half an octave or a third of an octave can be used.

The average frequency of an octave (half-octave) is not equal to the arithmetic mean of the lower and higher frequencies of the octave, but is equal to 0.707 f V .

Frequencies found in this way are called rms.

For two adjacent octaves, the mid frequencies also form octaves. Using this property, one and the same logarithmic frequency series can be considered either as octave boundaries or as their mid-frequencies, if desired.

On logarithmic forms, the center frequency bisects the octave series.

On the frequency axis in a logarithmic scale, for every third of an octave there are equal axis segments, each one third of an octave long.

When testing electroacoustic equipment and performing acoustic measurements, it is recommended to use a number of preferred frequencies. The frequencies of this series are members of a geometric progression with a denominator of 1.122. For convenience, some frequencies have been rounded to within ± 1%.

The interval between the recommended frequencies is one-sixth of an octave. This was not done by chance: the series contains a sufficiently large set of frequencies for different types of measurements and picks up the series of frequencies at intervals of 1/3, 1/2 and a whole octave.

And one more important property of a number of preferred frequencies. In some cases, not an octave, but a decade is used as the main frequency interval. So, the preferred range of frequencies can be considered equally as binary (octave) and decimal (decade).

The denominator of the progression on the basis of which the preferred frequency range is built is numerically equal to 1 dB of voltage, or 1/2 dB of power.

REPRESENTATION OF NAMED NUMBERS IN DECIBELS

Until now, we assumed that both the dividend and the divisor under the sign of the logarithm have an arbitrary value and to perform the decibel conversion it is important to know only their ratio, regardless of the absolute values.

In decibels, you can also express specific values ​​of powers, as well as voltages and currents. When the value of one of the terms under the logarithm sign in the previously considered formulas is given, the second term of the ratio and the number of decibels will uniquely determine each other. Therefore, if you set any reference power (voltage, current) as a conditional comparison level, then another power (voltage, current), compared with it, will correspond to a strictly defined number of decibels. In this case, a power equal to the power of the conditional comparison level corresponds to zero decibels, since at N P = 0 R 2 = P 1 therefore this level is usually referred to as zero. Obviously, at different zero levels, the same specific power (voltage, current) will be expressed in different decibels.

where R is the power to be converted to decibels, and R 0 - zero power level. The magnitude R 0 is put in the denominator, while the power is expressed in positive decibels P> P 0 .

The conditional power level with which the comparison is made, in principle, can be anything, but not everyone would be convenient for practical use. Most often, a power of 1 mW is selected as the zero level, dissipated across a 600 ohm resistor. The choice of these parameters occurred historically: initially, the decibel as a unit of measurement appeared in the technology of telephone communication. The characteristic impedance of overhead two-wire copper lines is close to 600 ohms, and a power of 1 mW is developed without amplification by a high-quality carbon telephone microphone on a matched load impedance.

For the case when R 0 = 1 mW = 10 –3 W: P R = 10 lg P + 30

The fact that the decibels of the presented parameter are reported relative to a certain level is emphasized by the term "level": noise level, power level, loudness level

Using this formula, it is easy to find that relative to the zero level of 1 mW, the power of 1 W is defined as 30 dB, 1 kW as 60 dB, and 1 MW is 90 dB, i.e., almost all the powers that you have to meet fall into within the first hundred decibels. Powers less than 1 mW will be expressed in negative decibels.

Decibels, specified with respect to 1 mW level, are called decibel-milliwatts and stand for dBm or dBm. The most common values ​​for zero levels are summarized in Table 3.

Similarly, you can present formulas for expressing voltages and currents in decibels:

where U and I - voltage or current to be converted, a U 0 and I 0 - zero levels of these parameters.

The fact that the decibels of the presented parameter are reported relative to a certain level is emphasized by the term "level": noise level, power level, loudness level.

Microphone sensitivity , i.e. the ratio of the electrical output to the sound pressure acting on the diaphragm, is often expressed in decibels by comparing the power delivered by a microphone at its nominal load impedance to a standard zero power level P 0 = 1 mW ... This microphone parameter is called standard microphone sensitivity ... Typical test conditions are considered to be a sound pressure of 1 Pa with a frequency of 1 kHz, a load resistance for a dynamic microphone - 250 Ohm.

Table 3. Zero levels for measuring named numbers

Designation		Description
int.	Russian
dBc	dBc	the reference is the level of the carrier or fundamental harmonic in the spectrum; for example, “distortion is –60 dBc”.
dBu	dBu	a reference voltage of 0.775 V, corresponding to a power of 1 mW at a load of 600 ohms; for example, the standardized signal level for professional audio equipment is +4 dBu, i.e. 1.23 V.
dBV	dBV	reference voltage 1 V at rated load (for household appliances usually 47 kOhm); for example, the standardized signal level for consumer audio equipment is –10 dBV, i.e. 0.316 V
dBμV	dBμV	reference voltage 1mkV; for example, “the sensitivity of the receiver is –10dBμV”.
dBm	dBm	reference power of 1 mW, corresponding to a power of 1 milliwatt at a nominal load (in telephony 600 Ohm, for professional equipment usually 10 kOhm for frequencies less than 10 MHz, 50 Ohm for high-frequency signals, 75 Ohm for television signals); for example, "the sensitivity of a cell phone is -110 dBm"
dBm0	dBm0	the reference power in dBm at the reference point. dBm - The reference voltage corresponds to the thermal noise of an ideal 50 ohm resistor at room temperature in a 1 Hz bandwidth. For example, "the noise level of the amplifier is 6 dBm0"
dBFS		(English Full Scale - "full scale") the reference voltage corresponds to the full scale of the device; for example, "the recording level is –6 dBfs"
dBSPL		(English Sound Pressure Level - "sound pressure level") - reference sound pressure of 20 μPa, corresponding to the audibility threshold; for example, "volume 100 dBSPL". dBPa - reference sound pressure 1 Pa or 94 dB sound scale dBSPL; for example, “for a volume of 6 dBPa, the mixer was set to +4 dBu, and the recording control was –3 dBFS, the distortion was –70 dBc”.
dBA, dBB, dBC, dBD		reference levels are selected in accordance with the frequency characteristics of standard "weight filters" of type A, B, C or D, respectively (filters reflect curves of equal loudness for different conditions, see below in the section "Sound level meters")

The power delivered by a dynamic microphone is naturally extremely low, much less than 1 mW, and the sensitivity level of the microphone is therefore expressed in negative decibels. Knowing the standard level of microphone sensitivity (it is given in the passport data), you can calculate its sensitivity in voltage units.

In recent years, to characterize the electrical parameters of radio equipment, other quantities have also begun to be used as zero levels, in particular 1 pW, 1 μV, 1 μV / m (the latter is used to assess the field strength).

Sometimes it becomes necessary to recalculate the known power level P R or voltage P U given relative to one zero level R 01 (or U 01 ) another R 02 (or U 02 ). This can be done using the following formula:

The ability to represent both abstract and named numbers in decibels leads to the fact that the same device can be characterized by different decibel numbers. This duality of decibels must be borne in mind. A clear understanding of the nature of the parameter being determined can serve as protection against errors.

To avoid confusion, it is advisable to state the reference level explicitly, eg –20 dB (relative to 0.775 V).

When converting power levels to voltage levels and vice versa, it is imperative to take into account the resistance that is standard for this task. In particular, the dBV for a 75 ohm TV circuit is (dBm – 11dB); dBμV for 75 ohm TV circuit corresponds to (dBm + 109dB).

Decibels in acoustics

Until now, speaking of decibels, we have operated in electrical terms - power, voltage, current, resistance. Meanwhile, logarithmic units are widely used in acoustics, where they are the most frequently used unit in quantitative assessments of sound quantities.

Sound pressure R represents the excess pressure in the medium in relation to the constant pressure that exists there before the appearance of sound waves (unit of measurement - pascal (Pa)).

An example of a sound pressure (or sound pressure gradient) receiver is most types of modern microphones that convert this pressure into proportional electrical signals.

The intensity of sound is related to the sound pressure and the vibrational speed of air particles by a simple relationship:

J = pv

If a sound wave propagates in free space, where there is no sound reflection, then

v = p / (ρc)

here ρ is the density of the medium, kg / m3; With - the speed of sound in the medium, m / s. Product ρ c characterizes the environment in which the propagation of sound energy occurs, and it is called specific acoustic resistance ... For air at normal atmospheric pressure and a temperature of 20 ° С ρ c = 420 kg / m2 * s; for water ρ c = 1.5 * 106 kg / m2 * s.

You can write that:

J = p 2 / (ρс)

everything that has been said about converting electrical quantities to decibels applies equally to acoustic phenomena

If you compare these formulas with the previously derived formulas for cardinality. current, voltage and resistance, it is easy to find an analogy between the individual concepts that characterize electrical and acoustic phenomena, and the equations describing the quantitative relationships between them.

Table 4. The relationship between electrical and acoustic performance

The analogue of electrical power is acoustic power and sound intensity; the analogue of voltage is sound pressure; the electric current corresponds to the vibrational speed, and the electrical resistance - to the specific acoustic resistance. By analogy with Ohm's law for an electrical circuit, we can talk about the acoustic Ohm's law. Consequently, everything that has been said about the conversion of electrical quantities into decibels applies equally to acoustic phenomena.

The use of decibels in acoustics is very convenient. The intensities of sounds that have to be dealt with in modern conditions can differ hundreds of millions of times. Such a huge range of changes in acoustic quantities creates great inconvenience when comparing their absolute values, and when using logarithmic units, this problem is removed. In addition, it was found that the loudness of a sound when assessed by ear increases approximately in proportion to the logarithm of the sound intensity. Thus, the levels of these quantities, expressed in decibels, correspond fairly closely to the loudness perceived by the ear. For most people with normal hearing, a change in the volume of a 1 kHz sound is felt when the sound intensity changes by about 26%, that is, by 1 dB.

In acoustics, by analogy with electrical engineering, the definition of decibels is based on the ratio of two powers:

where J 2 and J 1 - acoustic powers of two arbitrary sound sources.

Likewise, the ratio of two sound intensities is expressed in decibels:

The last equation is valid only if the acoustic impedances are equal, in other words, the constancy of the physical parameters of the medium in which the sound waves propagate.

The decibels determined by the above formulas are not related to the absolute values ​​of acoustic values ​​and are used to evaluate sound attenuation, for example, the effectiveness of sound insulation and noise suppression and suppression systems. The unevenness of the frequency characteristics is expressed in a similar way, i.e. the difference between the maximum and minimum values ​​in a given frequency range of various emitters and receivers of sound: microphones, loudspeakers, etc. range) relative to the value at a frequency of 1 kHz.

In the practice of acoustic measurements, however, as a rule, one has to deal with sounds, the values ​​of which must be expressed in specific numbers. The equipment for carrying out acoustic measurements is more complex than the equipment for electrical measurements, and in terms of accuracy it is significantly inferior to it. In order to simplify the measurement technique and reduce the error in acoustics, preference is given to measurements relative to reference, calibrated levels, the values ​​of which are known. For the same purpose, to measure and study acoustic signals, they are converted into electrical ones.

The absolute values ​​of powers, intensities of sounds and sound pressures can also be expressed in decibels, if in the above formulas you specify the values ​​of one of the terms under the sign of the logarithm. By international agreement, the reference level of sound intensity (zero level) is considered to be J 0 = 10 –12 W / m 2 ... This negligible intensity, under the influence of which the amplitude of the vibrations of the tympanic membrane is less than the size of an atom, is conventionally considered to be the hearing threshold of the ear in the frequency range of the highest hearing sensitivity. It is clear that all audible sounds are expressed with respect to this level only in positive decibels. The actual hearing threshold for people with normal hearing is slightly higher and is equal to 5-10 dB.

To represent the intensity of sound in decibels relative to a given level, use the formula:

The intensity value calculated by this formula is usually called sound intensity level .

The sound pressure level can be expressed in a similar way:

In order for the levels of sound intensity and sound pressure in decibels to be numerically expressed in one quantity, the value must be taken as the zero sound pressure level (sound pressure threshold):

Example. Let us determine what level of intensity in decibels is created by an orchestra with a sound power of 10 W at a distance of r = 15 m.

The sound intensity at a distance r = 15 m from the source will be:

Intensity level in decibels:

The same result will be obtained if you convert not the intensity level to decibels, but the sound pressure level.

Since the sound intensity level and the sound pressure level are expressed in the same number of decibels at the place of sound reception, in practice the term “level in decibels” is often used without specifying which parameter these decibels refer to.

Having determined the level of intensity in decibels at any point in space at a distance r 1 from a sound source (by calculation or experiment), it is easy to calculate the intensity level at a distance r 2 :

If the sound receiver is simultaneously influenced by two or more sound sources and the sound intensity in decibels produced by each of them is known, then to determine the resulting value of the decibels should be converted into absolute values ​​of the intensity (W / m2), added them, and this sum again converted into decibels. In this case, it is impossible to add decibels at once, since this would correspond to the product of the absolute values ​​of the intensities.

If there is n several identical sound sources with the level of each L J , then their total level will be:

If the intensity level of one sound source exceeds the levels of the others by 8-10 dB or more, only this one source can be taken into account, and the effect of the rest can be neglected.

In addition to the considered acoustic levels, sometimes you can also find the concept of the sound power level of a sound source, determined by the formula:

where R - sound power of the characterized arbitrary sound source, W; R 0 - initial (threshold) sound power, the value of which is usually taken equal to P 0 = 10 –12 W.

VOLUME LEVELS

The ear's sensitivity to sounds of different frequencies is different. This dependence is quite complex. At low sound intensity levels (up to about 70 dB), the maximum sensitivity is 2-5 kHz and decreases with increasing and decreasing frequency. Therefore, sounds of the same intensity, but of different frequencies, will seem to the ear to be different in volume. With an increase in sound power, the frequency response of the ear flattens out and at high intensity levels (80 dB and above) the ear reacts approximately the same to sounds of different frequencies of the sound range. It follows from this that the intensity of sound, which is measured by special broadband devices, and the loudness, which is recorded by the ear, are not equivalent concepts.

The loudness level of sound of any frequency is characterized by the value of the level equal in loudness to sound with a frequency of 1 kHz

The volume level of sound of any frequency is characterized by the value of the level equal in volume to a sound with a frequency of 1 kHz. Loudness levels are characterized by so-called equal loudness curves, each of which shows what level of intensity at different frequencies the sound source must develop in order to give the impression of equal loudness with a tone of 1 kHz of a given intensity (Fig. 4).

Rice. 4. Curves of equal loudness

Equal loudness curves represent essentially a family of ear frequency responses on a decibel scale for different intensity levels. Their difference from the usual frequency response is only in the way of construction: the "blockage" of the characteristic, that is, a decrease in the transmission coefficient, is shown here by an increase, not a decrease in the corresponding section of the curve.

The unit characterizing the loudness level, in order to avoid confusion with the decibels of intensity and sound pressure, has been assigned a special name - background .

The sound volume level in backgrounds is numerically equal to the sound pressure level in decibels of a pure tone with a frequency of 1 kHz, equal to it in volume.

In other words, one hum is 1 dB SPL of a 1 kHz tone, corrected for the frequency response of the ear. There is no constant relationship between the two, these units: it changes depending on the volume of the signal and its frequency. Only for currents with a frequency of 1 kHz, the numerical values ​​for the loudness level in backgrounds and the intensity level in decibels coincide.

Referring to Fig. 4 and to trace the course of one of the curves, for example, for a level of 60 background, it is easy to determine that to ensure equal loudness with a tone of 1 kHz at a frequency of 63 Hz, a sound intensity of 75 dB is required, and at a frequency of 125 Hz, only 65 dB.

High quality audio amplifiers use manual volume controls with loudness, or, as they are also called, compensated controls. Such controls, simultaneously with the adjustment of the input signal value in the direction of decrease, provide an increase in the frequency response in the low-frequency region, due to which a constant sound timbre is created for the hearing at different sound reproduction volumes.

Studies have also found that a twofold change in sound volume (as estimated by ear) is approximately equivalent to a change in volume level by 10 phon. This dependence is used as the basis for assessing the sound loudness. For a unit of loudness called dream , conventionally adopted a volume level of 40 background. The doubled loudness, equal to two sleep, corresponds to 50 phon, four sleep - 60 phon, etc. The conversion of loudness levels into loudness units is facilitated by the graph in Fig. 5.

Rice. 5. Relationship between volume and volume

Most of the sounds that you have to deal with in everyday life are noisy in nature. Characterizing the loudness of noise based on comparison with pure 1 kHz tones is straightforward, but results in the perceived noise by ear may be at odds with the readings of the measuring instruments. This is explained by the fact that at equal levels of noise loudness (in backgrounds), the most annoying effect on a person is produced by noise components in the range of 3-5 kHz. Noises can be perceived as equally unpleasant, although their loudness levels are not equal.

The annoying effect of noise is more accurately assessed by another parameter, the so-called perceived noise level ... A measure of the perceived noise is the sound level of uniform noise in an octave band with an average frequency of 1 kHz, which, under given conditions, is judged by the listener as equally unpleasant with the noise being measured. Perceived noise levels are expressed in PNdB or PNdB units. Their calculation is carried out according to a special method.

Further development of the noise estimation system is the so-called effective levels of perceived noise, expressed in EPNdB. The EPNdB system allows for a comprehensive assessment of the nature of the influencing noise: the frequency composition, discrete components in its spectrum, as well as the duration of the noise exposure.

By analogy with the unit of loudness sleep, the unit of noise has been introduced - Noah .

For one Noah adopted noise level of uniform noise in the 910-1090 Hz band at a sound pressure level of 40 dB. In other respects, nois are similar to dreams: a twofold increase in noise corresponds to an increase in the perceived noise level by 10 RNdB, i.e. 2 noi = 50 RNdB, 4 noi = 60 RNdB, etc.

When working with acoustic concepts, it should be borne in mind that the intensity of sound is an objective physical phenomenon that can be accurately determined and measured. It really exists regardless of whether anyone hears it or not. The loudness of the sound determines the effect that the sound produces on the listener, and is, therefore, a purely subjective concept, since it depends on the state of the human hearing organs and his personal properties for the perception of sound.

NOISE METERS

To measure all kinds of noise characteristics, special devices are used - sound level meters. The sound level meter is a self-contained portable device that allows you to measure directly in decibels levels of sound intensity over a wide range relative to standard levels.

The sound level meter (Fig. 6) consists of a high-quality microphone, a broadband amplifier, a sensitivity switch that changes the gain in 10 dB steps, a frequency response switch and a graphical indicator, which usually provides several options for presenting the measured data - from numbers and tables to graphs.

Rice. 6. Portable digital sound level meter

Modern sound level meters are very compact, which allows measurements in hard-to-reach places. From domestic sound level meters, one can name the device of the company "Octava-Electrodesign" "Octava-110A" (http://www.octava.info/?q=catalog/soundvibro/slm).

Sound level meters allow the determination of both general sound intensity levels in measurements with a linear frequency response and sound levels in backgrounds when measured with frequency responses similar to those of the human ear. The measurement range of sound pressure levels is usually in the range from 20-30 to 130-140 dB relative to the standard sound pressure level of 2 * 10-5 Pa. With interchangeable microphones, the measurement level can be expanded up to 180 dB.

Depending on the metrological parameters and technical characteristics, domestic sound level meters are divided into the first and second classes.

The frequency characteristics of the entire path of the sound level meter, including the microphone, are standardized. There are five frequency characteristics in total. One of them is linear within the entire operating frequency range (symbol Lin), four others approximately repeat the characteristics of the human ear for pure tones at different volume levels. They are named by the first letters of the Latin alphabet. A, B, C and D ... The form of these characteristics is shown in Fig. 7. The frequency response switch is independent of the range switch. For sound level meters of the first class, characteristics are required A, B, C and Lin ... Frequency response D - additional. Sound level meters of the second class must have the characteristics A and WITH ; the rest are allowed.

Rice. 7. Standard frequency characteristics of sound level meters

Characteristic A simulates the ear at about 40 fon. This characteristic is used when measuring weak noise - up to 55 dB and when measuring loudness levels. In practical conditions, the frequency response with correction is most often used. A ... This is explained by the fact that, although the perception of sound by a person is much more complicated than a simple frequency dependence that determines the characteristic A , in many cases the instrument's measurements are in good agreement with hearing noise estimates at low volume levels. Many standards - domestic and foreign - recommend the assessment of noise by the characteristic A regardless of the actual sound intensity level.

Characteristic V repeats the characteristic of the ear at level 70 background. It is used when measuring noise in the range of 55-85 dB.

Characteristic WITH uniform in the range 40-8000 Hz. This characteristic is used when measuring significant loudness levels - from 85 phon and above, when measuring sound pressure levels - regardless of the measurement limits, as well as when connecting devices to a sound level meter for measuring the spectral composition of noise in cases where the sound level meter does not have a frequency response Lin .

Characteristic D - auxiliary. It represents the average of the ear at about 80 phon, taking into account the increase in its sensitivity in the band from 1.5 to 8 kHz. When using this characteristic, the readings of the sound level meter more accurately than according to other characteristics correspond to the level of perceived noise by a person. This characteristic is mainly used when assessing the irritating effect of high-intensity noise (aircraft, high-speed cars, etc.).

The sound level meter also includes a switch Fast - Slow - Pulse , which controls the time characteristics of the device. When the switch is in position Quickly , the device manages to monitor rapid changes in sound levels, in the position Slowly the instrument shows the average value of the measured noise. Time characteristic Pulse used for recording short sound impulses. Some types of sound level meters also contain an integrator with a time constant of 35 ms, which simulates the inertia of human sound perception.

When using a sound level meter, the measurement results will differ depending on the set frequency response. Therefore, when recording readings, to avoid confusion, the type of characteristic at which the measurements were made is also indicated: dB ( A ), dB ( V ), dB ( WITH ) or dB ( D ).

To calibrate the entire path of the microphone - meter, the sound level meter kit usually includes an acoustic calibrator, the purpose of which is to create uniform noise of a certain level.

According to the currently valid instruction "Sanitary Standards for Permissible Noise in Premises of Residential and Public Buildings and on the Territory of Residential Development", the standardized parameters of constant or intermittent noise are sound pressure levels (in decibels) in octave frequency bands with average frequencies of 63, 125, 250, 500, 1000, 2000, 4000, 8000 Hz. For intermittent noise, such as noise from passing vehicles, the standardized parameter is the sound level in dB ( A ).

The following total sound levels have been established, measured on the A scale of the sound level meter: living quarters - 30 dB, auditoriums and classrooms of educational institutions - 40 dB, residential areas and recreation areas - 45 dB, working premises of administrative buildings - 50 dB ( A ).

For a sanitary assessment of the noise level, corrections from –5 dB to +10 dB are introduced into the sound level meter readings, which take into account the nature of the noise, the total time of its action, the time of day and the location of the object. For example, in the daytime, the allowable noise norm in residential premises, taking into account the amendment, is 40 dB.

Depending on the spectral composition of the noise, the approximate norm of the maximum permissible levels, dB, is characterized by the following figures:

High frequency from 800 Hz and above	75-85
Medium frequency 300-800 Hz	85-90
Low frequency below 300 Hz	90-100

In the absence of a sound level meter, an approximate assessment of the loudness levels of various noises can be carried out using the table. 5.

Table 5. Noises and their assessment

Loudness rating aurally	Level noise, dB	Source and location of noise measurement
Deafening	160	Damage to the tympanic membrane.
	140-170	Jet engines (close up).
	140	Noise Tolerance Limit.
	130	Pain threshold (sound is perceived as pain); piston aircraft engines (2-3 m).
	120	Thunder overhead.
	110	High-speed powerful motors (2-3 m); riveting machine (2-3 m); very noisy workshop.
Very loud	100	Symphony orchestra (loudness peaks); woodworking machines (in the workplace)
	90	Outdoor loudspeaker; noisy street; metal-cutting machines (in the workplace).
	80	Radio receiver loudly (2m)
Loud	70	Bus salon; scream; a policeman's whistle (15 m); medium noisy street; noisy office; large store hall
Moderate	60	Calm conversation (1 m).
	50	Light car (10-15 m); calm office; living quarters.
Weak	40	Whisper; reading room.
	60	Rustle of paper.
	20	Hospital ward.
Very weak	10	Quiet garden; radio center studio.
	0	Hearing threshold

1 A. Bell is an American scientist, inventor and businessman of Scottish descent, the founder of telephony, the founder of the Bell Telephone Company, which determined the development of the telecommunications industry in the United States.
2 Logarithms of negative numbers are complex numbers and will not be considered further.

The logarithmic scale and logarithmic units are often used when it is necessary to measure a certain quantity that varies over a large range. Examples of such quantities are sound pressure, earthquake magnitude, luminous flux, various frequency-dependent quantities used in music (musical intervals), antenna feeders, electronics and acoustics. Logarithmic units allow you to express the ratios of quantities that vary over a very large range using convenient small numbers, much like it is done with exponential notation of numbers, when any very large or very small number can be represented in short form in the form of mantissa and order. For example, the sound power of the Saturn launch vehicle was 100,000,000 watts or 200 dB SWL. At the same time, the sound power of a very quiet conversation is 0.000000001 W or 30 dB SWL (measured in decibels with respect to sound power of 10⁻¹² watts, see below).

Convenient units, aren't they? But, as it turns out, they are not convenient for everyone! It can be said that most people who are poorly versed in physics, mathematics, and engineering do not understand logarithmic units such as decibels. Some even believe that logarithmic values ​​do not belong to modern digital technology, but to the days when a slide rule was used for engineering calculations!

A bit of history

The invention of logarithms simplified computation, since they made it possible to replace multiplication with addition, which is much faster than multiplication. Among the scientists who made a significant contribution to the development of the theory of logarithms, one can note the Scottish mathematician, physicist and astronomer John Napier, who published in 1619 an essay describing natural logarithms, which greatly simplified calculations.

An important tool for the practical use of logarithms were tables of logarithms. The first such table was compiled by the English mathematician Henry Briggs in 1617. Based on the work of John Napier and others, the English mathematician and Church of England priest William Ouhtred invented the slide rule, which was used by engineers and scientists (including the author of this article) for the next 350 years, until it was replaced by pocket calculators in the mid-seventies of the last century. ...

Definition

Logarithm is the inverse operation to exponentiation. Number y is the logarithm of x to base b

if equality is respected

In other words, the logarithm of a given number is an exponent to which the number, called the base, must be raised to get the given number. It can be put simply. The logarithm is the answer to the question "How many times do you need to multiply one number by itself to get another number." For example, how many times do you have to multiply 5 by itself to get 25? The answer is 2, i.e.

By the above definition

Classification of logarithmic units

Logarithmic units are widely used in science, technology, and even in everyday activities such as photography and music. There are absolute and relative logarithmic units.

Via absolute logarithmic units express physical quantities that are compared with a certain fixed value. For example, dBm (decibel milliwatts) is the absolute logarithmic unit of power, which compares power to 1 mW. Note that 0 dBm = 1 mW. Absolute units are great for describing single value rather than the ratio of two quantities. Absolute logarithmic units of measurement of physical quantities can always be converted into other, usual units of measurement of these quantities. For example, 20 dBm = 100 mW or 40 dBV = 100 V.

On the other side, relative logarithmic units are used to express a physical quantity in the form of a ratio or proportion of other physical quantities, for example, in electronics, where a decibel (dB) is used for this. Logarithmic units are well suited for describing, for example, the transfer ratio of electronic systems, that is, the relationship between the output and the input signals.

It should be noted that all relative logarithmic units are dimensionless. Decibels, nepers, and other names are just special names that are used in conjunction with dimensionless units. Note also that the decibel is often used with various suffixes, which are usually attached to the dB abbreviation with a hyphen, for example dB-Hz, a space as in dB SPL, without any symbol between dB and a suffix as in dBm, or enclosed in quotation marks as in units of dB (m²). We will talk about all these units later in this article.

It should also be noted that converting logarithmic units to common units is often not possible. However, this only happens when people talk about relationships. For example, the voltage transfer coefficient of an amplifier of 20 dB can only be converted to "times", that is, to a dimensionless value - it will be equal to 10. At the same time, the sound pressure measured in decibels can be converted into pascals, since the sound pressure is measured in absolute logarithmic units, that is, relative to the reference value. Note that the transfer coefficient in decibels is also a dimensionless quantity, although it has a name. Complete confusion turns out! But we will try to figure it out.

Amplitude and Power Logarithmic Units

Power... It is known that power is proportional to the square of the amplitude. For example, electrical power, defined by the expression P = U² / R. That is, a 10-fold change in amplitude is accompanied by a 100-fold change in power. The ratio of two values ​​of power in decibels is determined by the expression

10 log₁₀ (P₁ / P₂) dB

Amplitude... Due to the fact that the power is proportional to the square of the amplitude, the ratio of the two amplitude values ​​in decibels is described by the expression

20 log₁₀ (P₁ / P₂) dB.

Examples of relative logarithmic values ​​and units

• Common units



• dB (decibel)- a logarithmic dimensionless unit used to express the ratio of two arbitrary values ​​of the same physical quantity. For example, in electronics, decibels are used to describe the amplification of a signal in amplifiers or the attenuation of a signal in cables. The decibel is numerically equal to the decimal logarithm of the ratio of two physical quantities, multiplied by ten for the power ratio and multiplied by 20 for the amplitude ratio.
• B (bel)- rarely used logarithmic dimensionless unit of measurement of the ratio of two physical quantities of the same name, equal to 10 decibels.
• N (neper)- dimensionless logarithmic unit of measurement of the ratio of two values ​​of the same physical quantity. Unlike the decibel, neper is defined as the natural logarithm for expressing the difference between two quantities x₁ and x₂ by the formula:
  

  R = ln (x₁ / x₂) = ln (x₁) - ln (x₂)

  
  You can convert H, B and dB on the "Sound Converter" page.
• Music, acoustics and electronics





s = 1000 ∙ log₁₀ (f₂ / f₁)

• Antenna technology. The logarithmic scale is used in many relative dimensionless units to measure various physical quantities in antenna technology. In these units, the measured parameter is usually compared with the corresponding parameter of the standard antenna type.




• Communication and data transmission



• dBc or dBc(carrier decibel, power ratio) is the dimensionless power of the radio signal (radiation level) in relation to the radiation level at the carrier frequency, expressed in decibels. Defined as S dBc = 10 log₁₀ (P carrier / P modulation). If the dBc value is positive, then the power of the modulated signal is greater than the power of the unmodulated carrier. If the dBc value is negative, then the power of the modulated signal is less than the power of the unmodulated carrier.
• Electronic equipment for sound reproduction and sound recording




• Other units and quantities

Examples of absolute logarithmic units and decibel values ​​with suffixes and reference levels

• Power, signal level (absolute)

• Voltage (absolute)

• Electrical resistance (absolute)
• dBΩ, dBohm or dBΩ(decibel ohms, amplitude ratio) - absolute resistance in decibels relative to 1 ohm. This unit of measure is convenient when considering a large resistance range. For example, 0 dBΩ = 1 Ω, 6 dBΩ = 2 Ω, 10 dBΩ = 3.16 Ω, 20 dBΩ = 10 Ω, 40 dBΩ = 100 Ω, 100 dBΩ = 100,000 Ω, 160 dBΩ = 100,000,000 Ω, and so on Further.
• Acoustics (absolute sound level, sound pressure or sound intensity)

• Radar... Log-scale absolute values ​​are used to measure radar reflectivity in relation to a reference value.



• dBZ or dB (Z)(amplitude ratio) - the absolute coefficient of radar reflectivity in decibels relative to the minimum cloud Z = 1 mm⁶ m⁻³. 1 dBZ = 10 log (z / 1 mm⁶ m³). This unit indicates the number of droplets per unit of volume and is used by meteorological radar stations (meteorological radars). The information obtained from the measurements in combination with other data, in particular, the results of the analysis of polarization and Doppler shift, makes it possible to assess what is happening in the atmosphere: whether it is raining, snowing, hail, or a flock of insects or birds flying. For example, 30 dBZ corresponds to light rain and 40 dBZ to moderate rain.
• dBη(amplitude ratio) - the absolute factor of radar reflectivity of objects in decibels relative to 1 cm² / km³. This value is convenient if you need to measure the radar reflectivity of flying biological objects, such as birds and bats. Weather radars are often used to monitor such biological objects.
• dB (m²), dBsm or dB (m²)(decibel square meter, amplitude ratio) is an absolute unit of measurement of the effective scattering area of ​​a target (RCS, English radar cross section, RCS) in relation to a square meter. Insects and low-reflective targets have a negative effective scattering area, while large passenger aircraft have a positive one.
• Communication and data transmission. Absolute logarithmic units are used to measure various parameters related to the frequency, amplitude and power of transmitted and received signals. All absolute values ​​in decibels can be converted to common units corresponding to the measured value. For example, the power level of noise in dBrn can be converted directly to milliwatts.

• Other absolute logarithmic units. There are many such units in different branches of science and technology, and here we will give just a few examples.
• Richter earthquake magnitude scale contains conventional logarithmic units (decimal logarithm is used) used to estimate the severity of an earthquake. According to this scale, the magnitude of an earthquake is defined as the decimal logarithm of the ratio of the amplitude of seismic waves to an arbitrarily chosen very small amplitude, which represents a magnitude of 0. Each step of the Richter scale corresponds to an increase in vibration amplitude by 10 times.
• dBr(decibel relative to the reference level, the ratio in amplitude or in power, is specified explicitly) - a logarithmic absolute unit of measurement of any physical quantity specified in a context.
• dBSVL- vibrational velocity of particles in decibels relative to the reference level 5 ∙ 10⁻⁸ m / s. The name comes from the English. sound velocity level - sound speed level. The vibrational velocity of the particles of the medium is otherwise called the acoustic velocity and determines the speed with which the particles of the medium move when they vibrate relative to the equilibrium position. The reference value 5 ∙ 10⁻⁸ m / s corresponds to the vibrational particle velocity for sound in air.

When carrying out measurements of parameters of radio equipment it is quite often necessary to deal with relative values ​​expressed in decibels [dB]. In decibels, the intensity of sound, the gain of a stage in voltage, current or power, transmission loss or signal attenuation, etc. are expressed.

The decibel is a universal logarithmic unit. The widespread use of the representation of quantities in dB is associated with the convenience of a logarithmic scale, and when calculating decibels obey the laws of arithmetic - they can be added and subtracted if the signals have the same shape.

There is a formula for converting the ratio of two voltages to the number of decibels (a similar formula is valid for currents):

For example, if the output of U2 is at twice the level of U1, then this ratio is +6 dB (Ig2 = 0.301). If U2> U1 10 times, then the signal ratio is 20 dB (Ig10 = 1). If U1> U2, then the sign of the ratio changes by minus 20 dB.

For example, for a measuring generator, the attenuator for attenuating the output signal can be graduated in dB. In this case, to convert a value from decibels to an absolute value, the result will be obtained faster if you use the already calculated table. 6; 1. It has a discreteness of 1 dB (which is quite enough in most cases) and a range of values ​​0 ...- 119 dB.

Tab. 6.1 can be used to convert the decibels of attenuator attenuation to the output voltage level. For the convenience of using the table, it will be necessary to set a voltage level of 1 V (effective or amplitude) at the generator output in the absence of attenuation (0 dB at the attenuator). In this case, the corresponding desired value of the output voltage after setting the attenuation is at the intersection of the horizontal and vertical graph (the values ​​in decibels are added arithmetically).

The value of the output voltage in the table is indicated in microvolts (1 μV = 10-6 V). I

Using this table, it is not difficult to solve the inverse problem - by the required voltage, determine how much attenuation of the signal should be set at the attenuator in decibels. For example, in order to obtain a voltage of 5 μV at the output of the generator, as can be seen from the table, an attenuation of 100 + 6 = 106 dB will need to be set on the attenuator. The power ratio of the two signals in decibels is calculated using the formula:

The formula for the power is valid provided that the input and output impedances of the device are the same, which is often done in high-frequency devices to facilitate their matching with each other.

To determine the power, you can use the calculated table. 6.2

Often, in practical use of dB, it is important to know the absolute value of the ratio of the two quantities, i.e. how many times the voltage or power at the output is greater than at the input (or vice versa). If the ratio of the two quantities is designated: K = U2 / U1 or K = P2 / P1, then you can use the table. 6.3 to convert the value from dB to times (K) and vice versa.

So, for example, an antenna amplifier provides a signal power amplification of 28 dB. From table. 6.3 it can be seen that the signal is amplified by a factor of 631.

Literature: I.P. Shelestov - Useful schemes for radio amateurs, book 3.

] Usually, decibels are used to measure the loudness of a sound. The decibel is the decimal logarithm. This means that an increase in volume of 10 decibels indicates that the sound has become twice as loud as the original. Sound volume in decibels is usually described by the formula 10Log 10 (I / 10 -12) where I is the sound intensity in watts / square meter.

Steps

Comparison table of noise levels in decibels

The table below describes the decibel levels in ascending order and their corresponding examples of sound sources. It also provides information on the negative effects on hearing in front of each noise level.

Decibel levels for different noise sources

Decibels	Source example	Impact on health
0	Silence	Absent
10	Breath	Absent
20	Whisper	Absent
30	Quiet background noise in nature	Absent
40	Sounds in the library, quiet background noise in the city	Absent
50	Calm conversation, normal suburban background noise	Absent
60	Office or restaurant noise, loud conversation	Absent
70	TV, highway noise from 15.2 meters (50 feet)	The note; some are unpleasant
80	Noise from factory, food processor, car wash from a distance of 6.1 meters (20 feet)	Potential Hearing Damage with Prolonged Exposure
90	Lawnmower, motorcycle from 7.62 m (25 ft)	High probability of hearing damage from prolonged exposure
100	Outboard motor, jackhammer	Serious hearing damage is highly likely with prolonged exposure
110	Loud rock concert, steel mill	It can hurt right away; very likely to cause serious hearing damage with prolonged exposure
120	Chain saw, thunder	There is usually momentary pain
130-150	Takeoff of a fighter from an aircraft carrier	Immediate hearing loss or ruptured eardrum may occur.

Sound level measurement with instruments

Use your computer. With special software and hardware, it's easy to measure the noise level in decibels right on your computer. Below are just some of the ways you can do this. Note that using better quality recording equipment will always give better results; in other words, the microphone built into your laptop may be sufficient for some tasks, but a high quality external microphone will give more accurate results.

1. Use a mobile app. To measure the sound level anywhere, mobile applications will come in handy. The microphone on your mobile device may not be as good as an external microphone connected to your computer, but it can be surprisingly accurate. For example, the reading accuracy on a mobile phone may well differ by 5 decibels from professional equipment. Below is a list of programs for reading the sound level in decibels for different mobile platforms:

   • For Apple devices: Decibel 10th, Decibel Meter Pro, dB Meter, Sound Level Meter
   • For Android devices: Sound Meter, Decibel Meter, Noise Meter, deciBel
   • For Windows phones: Decibel Meter Free, Cyberx Decibel Meter, Decibel Meter Pro

2. Use a professional decibel meter. This is usually not cheap, but it may be the easiest way to get accurate measurements of the sound level you are interested in. Also called a "sound level meter", this is a specialized device (available from an online store or specialty store) that uses a sensitive microphone to measure the noise level around it and gives an accurate decibel reading. Since such devices are not in great demand, they can be quite expensive, often starting at $ 200, even for entry-class devices.

   • Note that the decibel / sound level meter may call it slightly differently. For example, another similar device called a "noise meter" does the same thing as a sound level meter.

   Calculating decibels

   1. Find out the sound intensity in watts / square meter. In everyday life, decibels are used as a simple measure of loudness. However, things are not so simple. In physics, decibels are often viewed as a convenient way of expressing the "intensity" of a sound wave. The greater the amplitude of the sound wave, the more energy it transfers, the more air particles vibrate in its path, and the more intense the sound itself. Due to the direct relationship between the intensity of a sound wave and loudness in decibels, it is possible to find the value of decibels, knowing only the intensity of the sound level (which is usually measured in watts / square meter)

      • Note that the intensity value is very low for normal sounds. For example, a sound with an intensity of 5 × 10 -5 (or 0.00005) watt / meter square corresponds to approximately 80 decibels, which is approximately the volume of a blender or food processor.
      • For a better understanding of the relationship between intensity and decibel level, let's solve one problem. For example, let's take this: let's assume that we are sound engineers and we need to get ahead of the background noise in the recording studio to improve the quality of the recorded sound. After installing the equipment, we recorded the background noise intensity 1 × 10 -11 (0.00000000001) watt / square meter... Then, using this information, we can calculate the background noise level of the studio in decibels.

   2. Divide by 10 -12. If you know the intensity of your sound, you can easily plug it into the formula 10Log 10 (I / 10 -12) (where "I" is the intensity in watts / meter square) to get the decibel value. First, divide 10 -12 (0.000000000001). 10 -12 displays the intensity of sound with a score of 0 on the decibel scale, comparing the intensity of your sound with this number, you will find its ratio to the initial value.

      • In our example, we divided the intensity value 10 -11 by 10 -12 and got 10 -11 / 10 -12 = 10 .

   3. Let's calculate the Log 10 of this number and multiply it by 10. To complete the solution, all you have to do is take the base 10 logarithm of the resulting number and then finally multiply it by 10. This confirms that decibels are log base 10 - in other words, a 10 decibel increase in noise level is a doubling sound volume.

      • Our example is easy to solve. Log 10 (10) = 1.1 × 10 = 10. Therefore, the value of the background noise in our studio is 10 decibels... It's quiet enough, but still picked up by our high quality recording equipment, so we probably need to eliminate the noise source to achieve a higher quality recording.

   4. Understanding the logarithmic nature of decibels. As mentioned above, decibels are logarithmic values ​​with base 10. For any given decibel value, 10 decibel noise is twice as loud as the original, and 20 decibel noise is four times as loud, and so on. This makes it possible to designate a wide range of sound intensities that can be perceived by the human ear. The loudest sound a person can hear without experiencing pain is a billion times louder than the quietest sound a person can hear. By using decibels, we avoid using huge numbers to describe ordinary sounds — instead, we only need three digits.

      • Think about which is easier to use: 55 decibels or 3 × 10 -7 watts / square meter? Both values ​​are equal, but instead of using the scientific notation (as a very small fraction of a number), it is much more convenient to use decibels, which are sort of a simple abbreviation for easy everyday use.

The decibel is a relative unit of measurement, it is not like other known quantities, therefore it was not included in the SI system of generally accepted units of measurement. However, many calculations allow the use of decibels on a par with absolute units of measurement, and even use them as a reference value.

Decibels are determined by belonging to physical quantities, therefore they cannot be attributed to mathematical concepts. This is easy to imagine if we draw a parallel with percentages, with which decibels have a lot in common. They do not have specific dimensions, but at the same time they are very convenient when comparing 2 values ​​of the same name, even if they are different in nature. So it's not hard to imagine what is measured in decibels.

History of origin

As it turned out as a result of long-term research, the susceptibility is not directly related to the absolute level of sound propagation. It is a measure of the power applied to a given unit of area that is in the zone of exposure to sound waves, which is measured in decibels today. As a result, a curious proportion was established - the more space belongs to the usable area of ​​the human ear, the better it is for the perception of minimum powers.

Thus, the researcher Alexander Graham Bell was able to establish that the perception limit of the human ear is 10 to 12 watts per square meter. The data obtained covered a very wide range, which was represented by only a few values. This created certain inconveniences and the researcher had to create his own measurement scale.

In the original version, the unnamed scale had 14 values ​​- from 0 to 13, where human whispering had the value "3" and spoken language - "6". Subsequently, this scale was widely used, and its units were called bels. To obtain more accurate data on a logarithmic scale, the original unit was increased 10 times - this is how decibels were formed.

General information

First of all, it should be noted that the decibel is one tenth of the Bel, which is the decimal form of the logarithm that determines the ratio between the 2 powers. The nature of the capacities to be compared is arbitrary. The main thing is that the rule is observed, representing the compared powers in equal units, for example, in watts. Due to this feature, decibel designations are used in different areas:

• mechanical;
• electric;
• acoustic;
• electromagnetic.

Since practical application showed that Bel turned out to be a rather large unit, for better clarity, it was proposed to multiply its value by ten. Thus, the generally accepted unit appeared - the decibel, in which sound is measured today.

Despite its wide area of ​​application, most people know that decibels are used to determine the degree of loudness. This value characterizes the waves per square meter. Thus, an increase in volume of 10 decibels is comparable to a doubling of sound intensity.

In the legislation, the decibel was recognized as the calculated value of the noise level of a room. It was the defining characteristic for calculating the permissible noise power in residential buildings. This value makes it possible to measure the permissible noise level in decibels in the apartment and to reveal the facts of violation, if necessary.

Application area

Telecommunications designers today use the decibel as the base unit for comparing device performance on a log scale. Such possibilities are provided by the design feature of this value, which is a logarithmic unit of different levels used for attenuation or, conversely, power amplification.

The decibel is widely used in various fields of modern technology. What is measured in decibels today? These are various values ​​that vary over a wide range that can be applied:

• in systems related to the transfer of information;
• radio engineering;
• optics;
• antenna technology;
• acoustics.

Thus, decibels are used to measure the characteristics of the dynamic range, for example, they can measure the loudness of a certain musical instrument. And also it becomes possible to calculate the damped waves at the moment of their passage through the absorbing medium. Decibels allow you to determine the gain or to fix the noise figure generated by the amplifier.

It is possible to use these dimensionless units both for physical quantities related to the second order - energy or power, and for quantities related to the first order - current or voltage. Decibels open up the possibility of measuring the relationship between all physical quantities, and in addition, with their help, absolute values ​​are compared.

Sound volume

The physical component of the loudness of the sound impact is determined by the level of the available sound pressure acting on a unit of contact area, which is measured in decibels. The noise level is formed from the chaotic fusion of sounds. A person reacts to low frequencies or, conversely, sounds of high frequency as to quieter sounds. Midrange sounds will be perceived as louder despite the same intensity.

Taking into account the uneven perception of sounds of different frequencies by the human ear, a frequency filter was created on an electronic basis, capable of transmitting an equivalent degree of sound with a unit of measurement, which is expressed in dBa - where "a" denotes the use of a filter. This filter, based on the measurement normalization, is able to simulate a weighted sound level value.

The ability of different people to perceive sounds is in the range of loudness from 10 to 15 dB, and in some cases even higher. The perceived limits of sound intensity are frequencies from 20 to 20 thousand Hertz. The easiest sounds for perception are located in the frequency range from 3 to 4 kHz. It is customary to use this frequency in telephones, as well as in radio broadcasting on medium and long waves.

Over the years, the range of perceived sounds narrows, especially in the high-frequency spectrum, where the sensitivity can be reduced to 18 kHz. This leads to a general hearing impairment that affects many older people.

Acceptable noise level in residential premises

With the use of decibels, it became possible to determine a more accurate noise scale for ambient sounds. It reflects characteristics that are superior in accuracy compared to the original scale created in due time by Alexander Bell. Using this scale, the legislative authorities have determined the noise level, the norm of which is valid within the residential premises intended for the recreation of citizens.

Thus, a value of "0" dB means complete silence, from which ringing in the ears is heard. The next value of 5 dB also determines complete silence in the presence of a small background sound that drowns out the internal processes of the body. At 10 dB, indistinct sounds become distinguishable - all kinds of rustles or rustling of foliage.

A value of 15 dB is in the clear range of the quietest sounds, such as the ticking of a wristwatch. With a sound power of 20 dB, you can make out the cautious whispering of people at a distance of 1 meter. The 25 dB mark allows you to hear more clearly a conversation in a whisper and a rustle from friction of soft tissues.

30 dB defines how many decibels are allowed in an apartment at night and is compared to silent conversation or the ticking of a wall clock. At 35 dB, muffled speech can be heard clearly.

The 40 decibel level determines the sound intensity of normal conversation. It is loud enough to communicate freely within the room, watch TV or listen to music tracks. This mark determines how many decibels are allowed in the apartment during the day.

Operating noise level

Compared to the permissible noise level in decibels in an apartment, in production and in office activities, other sound levels are allowed during working hours. Restrictions of a different order apply here, clearly adjusted for each type of occupation. The basic rule in these conditions is to avoid noise levels that can adversely affect human health.

In offices

The noise level value of 45 dB is within the limits of good audibility and is comparable to the noise of a drill or an electric motor. Noise of 50 dB is also characterized by excellent audibility limits and is the same strength as the sound of a typewriter.

The noise level of 55 decibels remains within excellent audibility, it can be represented by the example of a simultaneous sonorous conversation between several people at once. This indicator is taken as the upper mark acceptable for office space.

In animal husbandry and clerical activities

The noise level of 60 dB is considered to be elevated, this level of noise can be found in offices where many typewriters are working at the same time. The indicator of 65 dB is also considered increased and it can be fixed when the printing equipment is operating.

The noise level, reaching 70 dB, remains elevated and is found on livestock farms. A noise value of 75 dB is the extreme noise level and can be noted in poultry farms.

In production and transport

With a mark of 80 dB, a loud sound level sets in, prolonged exposure to which will result in partial hearing loss. Therefore, when working in such conditions, it is recommended to use ear protectors. The noise level of 85 dB is also within the loud sound level, which can be compared with the operation of the equipment of a weaving mill.

The noise figure of 90 dB remains within the loud sound range, such a noise level can be registered when a train is moving. The noise level of 95 dB reaches the extreme limits of loud sound, such a noise level can be detected in a metal rolling shop.

Limit noise level

The noise level at around 100 dB reaches the limits of excessively loud sound, it can be compared to the rolling of thunder. Work in such conditions is considered harmful to health and is performed within the framework of a certain length of service, after which a person is considered unfit for harmful work.

The noise value of 105 dB is also within the limits of an excessively loud sound, the noise of such a force is created by a gas cutter when cutting metal. The noise level of 110 dB remains within the limits of an excessively loud sound, such an indicator is recorded during the takeoff of the helicopter. The noise level of 115 dB is considered the limit for the boundaries of excessively loud sound, such noise is emitted by a sandblaster.

The noise level of 120 dB is considered unbearable and can be compared to the operation of a jackhammer. The noise level of 125 dB is also characterized by an unbearable noise level, which is reached by the aircraft at the start. The maximum noise level in dB is considered to be the limit at around 130, after which the pain threshold sets in, which not everyone is able to endure.

Critical noise level

The noise level at around 135 dB is considered unacceptable; a person who finds himself in the area of ​​such a sound will receive a concussion. The noise level of 140 dB also leads to concussion, such a sound accompanying the launch of a jet plane. At a noise level of 145 dB, a fragmentation grenade explodes.

The rupture of a cumulative projectile on tank armor reaches 150-155 dB, the sound of such a force leads to concussion and injuries. Above 160 dB, a sound barrier occurs, sound exceeding this limit leads to rupture of the ear eardrums, disintegration of the lungs and multiple shock wave injuries, resulting in instant death.

Impact on the body of inaudible sounds

A sound with a frequency below 16 Hz is called infrared, and if its frequency exceeds 20 thousand Hz, then such a sound is called ultrasound. The eardrums of the human ear are incapable of picking up sounds of this frequency, so they are outside the range of human hearing. The decibels, in which sound is measured today, also determine the meanings of inaudible sounds.

Low frequency sounds, ranging from 5 to 10 Hz, are poorly tolerated by the human body. Such an impact can activate malfunctions in the work of internal organs and affect brain activity. In addition, the intensity of low frequencies affects bone tissue, provoking joint pain in people suffering from various diseases or injured.

The everyday sources of ultrasound are various vehicles, and they can also be thunderclaps or the operation of electronic equipment. Such influences are expressed in the heating of tissues, and the strength of their influence depends on the distance to the active source and on the degree of sound.

There are also certain restrictions for public places of work with inaudible range. The maximum infrared sound power should be kept within 110 dBa, and the ultrasound power is limited to 125 dBa. Even a short-term stay in areas where the sound pressure exceeds 135 dB of any frequency is strictly prohibited.

Influence of noise from office equipment and methods of protection

The noise emitted by a computer and other organizational equipment can be higher than 70 dB. In this regard, experts do not recommend installing a large number of this equipment in one room, especially if it is not large. It is recommended to install noisy units outside the premises where there are people.

To reduce the level of noise in finishing works, materials with sound-absorbing properties are used. In addition, you can use curtains made of thick fabric or, in extreme cases, bears, covering the eardrums from the impact.

Today, in the construction of modern buildings, there is a new standard that determines the degree of sound insulation of premises. The walls and ceilings of the buildings of apartment buildings are checked for noise resistance. If the soundproofing level is below the acceptable limit, the building cannot be put into operation until the problems are corrected.

In addition, today they set limits on the strength of the sound for various signaling and warning devices. For fire protection systems, for example, the sound strength of the warning signal should be between 75 dBa and 125 dBa.