Using the converter “Levels in dBm (dBm or dBmW), dBV (dBV), watts and other units. Permissible noise standards, or how many decibels in...

Radio 1967, 12

A decibel is a specific unit of numerical expression for the amplification or attenuation of a signal. In decibels, gain and attenuation coefficients, selectivity of receivers, unevenness of frequency characteristics, sound intensity and many parameters of various radio equipment, devices, transmission lines, antennas and other devices are evaluated. Many voltmeters and avometers have decibel scales.

What is a decibel? First of all, the decibel (abbreviated as dB) is not a physical quantity, like, say, watt, volt, ampere, but a mathematical concept. In this respect, decibels have some similarities to percentages. Like percentages, decibel is a relative value and is applicable to the assessment of a wide variety of phenomena, regardless of their nature. But, if percentages express some value related to a whole taken as a unit, then the decibel is based on a broader concept that characterizes the ratio of two independent, but identical quantities. We must, however, remember that the term “decibel” is always associated only with powers and with some reservations with voltages and currents. The physical nature of the powers is not specified and can be anything - electrical, acoustic, electromagnetic.

A decibel, as indicated by the prefix "deci", is a tenth of another, larger unit - Bel. And Bel is the decimal logarithm of the ratio of two powers. If two powers P1 and P2 are known, then their ratio, expressed in decibels, is defined as:

N dB =10 Lg (P2/P1)

where P1 is the power corresponding to the initial signal level, and P2 is the power corresponding to the final signal level.

It is appropriate to recall here that the decimal logarithm of a number is the exponent to which the number 10 must be raised to obtain a given number. For example: Lg(100) = 2, since 10 2 = 10*10 = 100; Lg(1000) = 3, since 10 3 = 10*10*10 = 1000.

Numbers greater than one will have positive logarithms, and numbers less than one will have negative logarithms. Negative logarithms are preceded by a “-” (minus) sign, for example: Lg(0.1) = - 1; Lg(0.01) = - 2.

In the case when the initial signal is less than the final signal, that is, P2/P1 is greater than 1, which occurs in amplifiers, the number of decibels will be positive, and if the initial level is greater than the final level, that is, P2/P1 is less than 1, then the number of decibels will be negative. The second case corresponds to attenuation (attenuation) of the signal. When both powers are the same and P2/P1= 1, then the number of decibels is zero.

There is a simple relationship between gain and attenuation decibels: if, for example, a ratio of 10 corresponds to 10 dB, then -10 dB expresses the inverse ratio, that is, 0.1.

Comparing two signals by comparing their powers is not always convenient. In many cases, it turns out that it is easier to measure not the power in the load, but the voltage drop across it or the current flowing. But at the same time, a mandatory condition must be observed: the resistance of the loads on which the voltages U1 and U2 are measured or through which the measured currents I1 and I2 flow must be the same. The formulas for calculating decibels in this case are as follows:

N dB =20 Lg (P2/P1); N dB =20 Lg (I2/I1)

Decibels are used not only to compare two quantities. They are also convenient for estimating specific power values, as well as voltages and currents, if we assume that the value of one of the terms of the ratio included in the above formulas is unchanged. Then any other quantity compared with it will be characterized by a certain number of decibels. In this case, zero decibels corresponds to a power equal to the first, which is often called zero. The conditional zero level of the electrical signal is taken to be the power P = 1 mW (0.001 W), released at the active resistance R = 600 Ohm - just as when measuring temperature, the melting temperature of ice at normal atmospheric pressure is taken as zero degrees. At this power across the indicated resistance the voltage drop is equal to:

U = (PR) 0.5 = (0.001*600) 0.5 = 0.775 V,

and the flowing current:

I = (P/R) 0.5 = (0.001/600) 0.5 = 1.29 mA.

These values ​​- 0.775 V and 1.29 mA are taken as zero decibels electrical voltage and current.

If a circuit with an active resistance of 600 Ohms generates power greater than 1 mW, that is, a voltage drop greater than 0.775 V and a current greater than 1.29 mA, the levels will be positive. When the power, voltage or current is less than these values, the levels are negative.

Decibels and the corresponding ratios of powers, voltages and currents are given in table. 1.

Let us assume that as a result of improving the final stage of the low-frequency amplifier, its output power increased from 10 to 20 W. This means the power increase will be:

P2/P1 = 20/10 = 2

According to the table in the “Power Ratio” column, the number closest to 2 will be 1.99. In the “Decibels” column, this number corresponds to 3 dB. Therefore, doubling the output power corresponds to a 3 dB increase in gain. If for some reason the output power of the amplifier decreased from 20 W to 10 W, then the new power ratio will be P2/P1 = 10/20 = 0.5. But now the change in power means attenuation and will be expressed as -3 dB.

When performing operations with decibels, we must remember that the sum of two numbers in decibels is equivalent to the product of the absolute values ​​of the numbers to which they correspond, therefore, in order to show an increase (or decrease) in power, for example, doubling, tripling or quadrupling, it is necessary to add to the original number of decibels (or subtract) 3 dB, 4.8 dB or 6 dB, respectively.

Decibels are often used to express the sensitivity of microphones by comparing their power output during factory testing to the above standard zero level of 1 mW. Let's assume that a microphone type MD-44, whose output level is 78 dB, is connected to an amplifier that can develop 40 W of undistorted power. However, in work it turned out that the amplifier with such a microphone develops only 10 W. The question is, what sensitivity should the microphone be for the amplifier to deliver full power? The ratio of the maximum power (40 W) of the amplifier to the received power (10 W) is 40/10 = 4. This ratio (according to the table - 3.98) corresponds to 6 dB. Therefore, you need a microphone with a return level of - 72 dB, that is, 6 dB more than the MD-44 microphone (-78 dB), since: - 78 dB + 6 dB = -72 dB. This requirement is met, for example, by the MD-41 microphone.

Table 1. Decibels and their corresponding power, voltage and current ratios

Another example. A voltage of 8 V with a frequency of 100 MHz is applied to a section of RK-1 type cable 50 m long. What will be the voltage at the output of the segment if it is known (from the reference book) that at this frequency the cable introduces an attenuation of 0.096 dB per meter? The power source and load have the same resistance, equal to the wave resistance. Obviously, the attenuation introduced by the cable is: 0.096*50 = 4.8 dB. In table 1 for this attenuation (-4.8 dB) the voltage ratio is not specified. Let's take advantage of the fact that the table shows the ratio for +4.8 dB, which is equal to 1.74. This means that at the end of the segment the signal will be 1/1.74 ≈ 0.57 from the input, i.e. 8 * 0.57 ≈ 4.6 V.

When you need to determine decibel values ​​or ratios that are not in the table, you must proceed as follows. Suppose we need to find the power ratio corresponding to 24 dB. Presenting 24 dB as the sum of 10 + 14 dB, we find in the table the power ratios for each of the terms; they are equal to 10 and 25.12. Multiplying these ratios, we obtain that 24 dB corresponds to a power ratio of 251.2.

At the output of the amplifier at medium frequencies a voltage U1 = 30 V develops, and at the edges of the passband a voltage U2 = 21 V develops. The amplifier, therefore, introduces frequency distortion- the upper and lower sound frequencies are amplified worse (“overwhelms”) than the middle ones. The ratio of these quantities will be

U2/U1 = 21/30 = 0.7

From the table we find that frequency distortions of this amplifier at the edges of the passband are -3 dB.

Decibels are also widely used in acoustics, where they are essentially the basic unit for quantifying sound intensity. This is explained by the property of our ear to respond to sounds, the intensity of which differs millions of times. But the sensitivity of the ear to sounds of different strengths is not the same - in silence and at low intensity (whispering, rustling) it is maximum, and at high intensity (the roar of an airplane, the rumble of cars) it is minimal. In this respect, a hearing aid is similar to a radio receiver with an AGC system.

This phenomenon can be explained with the following example. Let's say the amplifier develops an output power of 10 W. Increasing the output power to 20 W will sound like a small increase in volume. In order for the ear to perceive twice the volume, an almost tenfold increase in the amplifier output power (≈10 dB) will be required. And in order for the ear to perceive a 4-fold increase in volume, the power must be increased 100 times (≈20 dB).

Physiological scientists, studying the properties of hearing, have established that the sensitivity of the ear is related to the intensity of sound exposure by a logarithmic law, that is, an increase in sound intensity several times will appear to the ear as a change in volume approximately by the logarithm of this number of times. The use of decibels in acoustics turns out to be very convenient, since auditory perception and assessment of sound intensities are strictly related and, moreover, a change in sound intensity by 1 dB is perceived by the ear as a barely noticeable change in volume.

Table 2. AVERAGE NOISE LEVELS

A comparative assessment of the average volume levels of some household and industrial noises in decibels relative to the hearing threshold of the human ear, taken as zero level, is given in Table. 2. Sound intensity is measured using special instruments - sound level meters, the scales of which are graduated directly in decibels.

The examples given here are far from exhausting the use of decibels in various calculations and measurements in amateur radio practice. We just wanted to show the ease of understanding decibels and the wide possibilities of using them.

Cand. tech. Sciences E. ZELDIN, engineer. K. DOMBROVSKY

In the last article we touched on the topic of cleaning ears with cotton swabs. It turned out that, despite the prevalence of such a procedure, self-cleaning ears can lead to perforation (rupture) of the eardrum and a significant decrease in hearing, up to complete deafness. However, improper ear cleaning is not the only thing that can damage our hearing. Excessive noise that exceeds sanitary standards, as well as barotrauma (injuries associated with pressure changes) can also lead to hearing loss.

To have an idea of ​​the danger that noise poses to hearing, it is necessary to familiarize yourself with the permissible noise standards for different times of the day, as well as find out what noise level in decibels certain sounds produce. In this way, you can begin to understand what is safe for your hearing and what is dangerous. And with understanding comes the ability to avoid harmful effects sound by ear.

According to sanitary standards, the permissible noise level, which does not harm hearing even with prolonged exposure to the hearing aid, is considered to be: 55 decibels (dB) during the daytime and 40 decibels (dB) at night. Such values ​​are normal for our ear, but, unfortunately, they are very often violated, especially within large cities.

Noise level in decibels (dB)

Indeed, the normal noise level is often significantly exceeded. Here are examples of just some of the sounds we encounter in our lives and how many decibels (dB) these sounds actually contain:

• Spoken speech ranges from 45 decibels (dB) to 60 decibels (dB), depending on the volume of the voice;
• Car horn reaches 120 decibels (dB);
• Heavy traffic noise – up to 80 decibels (dB);
• Baby crying – 80 decibels (dB);
• Various operation noise office equipment, vacuum cleaner – 80 decibels (dB);
• Noise of a running motorcycle, train - 90 decibels (dB);
• The sound of dance music in a nightclub is 110 decibels (dB));
• Airplane noise - 140 decibels (dB);
• Noise from repair work – up to 100 decibels (dB);
• Cooking on a stove - 40 decibels (dB);
• Forest noise from 10 to 24 decibels (dB);
• Lethal noise level for humans, explosion sound - 200 decibels (dB)).

As you can see, most of the noises that we encounter literally every day significantly exceed the permissible threshold. And these are just natural noises that we cannot do anything about. But there is also noise from TV and loud music, to which we expose our hearing aids. And with our own hands we cause enormous harm to our hearing.

What noise level is harmful?

If the noise level reaches 70-90 decibels (dB) and continues quite long time, then such noise with prolonged exposure can lead to diseases of the central nervous system. And prolonged exposure to noise levels of more than 100 decibels (dB) can lead to significant hearing loss, including complete deafness. Therefore, we get much more harm from loud music than pleasure and benefit.

What happens to hearing when exposed to noise?

Aggressive and prolonged noise exposure to the hearing aid can lead to perforation (rupture) of the eardrum. The consequence of this is decreased hearing and, as an extreme case, complete deafness. And although perforation (rupture) of the eardrum is a reversible disease (i.e., the eardrum can recover), the recovery process is long and depends on the severity of the perforation. In any case, treatment of perforation of the eardrum is carried out under the supervision of a doctor, who chooses a treatment regimen after examination.

The word "decibel" consists of two parts: the prefix "deci" and the root "bel". "Deci" literally means "tenth", i.e. tenth part of "bel". This means that in order to understand what a decibel is, you need to understand what a bel is and everything will fall into place.

A long time ago, Alexander Bell found out that a person stops hearing sound if the power of the source of this sound is less than 10-12 W/m2, and if it exceeds 10 W/m2, then prepare your ears for unpleasant pain - this is the pain threshold.

As you can see, the difference between 10 -12 W/m2 and 10 W/m2 is as much as 13 orders of magnitude. Bell divided the distance between the hearing threshold and the pain threshold into 13 steps: from 0 (10 -12 W/m2) to 13 (10 W/m2). Thus he determined the sound power scale.

Here you can say: “Oh, everything is clear!” - good! But then it gets even more interesting.

Get to the point

We found out that decibel equal to 1/10 Bel, but how to apply this in life? Let me give you this example:

• 0 dB - nothing can be heard
• 15 dB - barely audible (rustling leaves)
• 50 dB - Clearly audible
• 60 dB - Noisy

But why is this necessary, if you can, for example, say: “sound power level 0.1 W/m2”. The fact is that it has been experimentally established that a person feels a change in brightness, volume, etc. when they change logarithmically. Like this:

Which is expressed in bels as the ratio of the level of the measured signal to some reference signal. 1 Bel = log(P 1 / P 0), where P 0 is sound power hearing threshold, but to get a decibel you just need to multiply by 10: 1 dB = 10*lg(P 1 / P 0)

Thus decibel shows the logarithm of the ratio of the level of one signal to another and is used to compare two signals. From the formula, by the way, it is clear that decibels can be used to compare any signals (and not just sound power), since decibels are dimensionless.

Peculiarities

Confusion with decibels arises because there are several “types” of them. They are conventionally called amplitude and power (energy).

Formula 1 dB = 10*lg(P 1 / P 0) - compares two energy quantities in decibels. IN in this case power. And the formula 1 dB = 20*lg(A 1 /A 0) - compares two amplitude quantities. For example, voltage, current, etc.
It is very easy to go from amplitude decibels to energy decibels and back. It is simply necessary to convert “non-energy” quantities into energy ones. I will show this using the example of current and voltage.

From the definition of power P = UI = U 2 / R = I 2 * R. Substitute into 10*lg(P 1 /P 0) and after transformation we get 20*lg(A 1 /A 0) - everything is simple.

Transformations for other amplitude values ​​will be carried out in the same way. As always, you can read more in textbooks and reference books.

Why did everything have to be complicated?

You see, two quantities can differ millions of times. Thus, the simple ratio (P 1 /P 0) can give both very large and very small values. Agree that this is not very convenient in practice. This may also be one of the reasons for such a prevalence of decibels (along with a consequence of the Weber-Fechner law)

Thus, the decibel allows for calculation in “parrots”, i.e. in times move on to more specific and small quantities. Which you can quickly add and subtract in your head. But if you still want to evaluate the ratio in parrots by a known value in decibels, then it is enough to remember a simple mnemonic rule (I spotted it from Revici):

If the ratio of values ​​is greater than one, then it will be positive dB (+3 dB), and if less, it will be negative (-3 dB). Thus:

• 3 dB means increase/decrease the signal by a third
• 6 dB means increase/decrease by 2 times
• 10 dB corresponds to a change in value of 3 times
• 20 dB corresponds to a change of 10 times

And now for an example. Let us be told that the signal is amplified by 50 dB. A 50 dB = 10 dB + 20 dB + 20 dB = 3 * 10 * 10 = 300 times. Those. the signal was amplified 300 times.

So the decibel is just a convenient engineering convention that was introduced as a result of some practical measurements, as well as the benefits of practical use.

English decibel, dB) - psychophysical unit of stimulus intensity, one tenth of a bel: 1 bel = lg (I/Ithr), where / is the intensity of a given stimulus (for example, the physical brightness of light or sound intensity), I/Ithr is the intensity of the threshold stimulus ( absolute threshold value). On the one hand, the D. scale makes it possible to more adequately judge the subjective strength of various stimuli (in accordance with Fechner’s law); on the other hand, knowing the properties of logarithms, it is not difficult to estimate the relationship between physical characteristics. The D. scale also allows for more direct cross-modal comparisons of stimulus intensity (e.g., both sound intensity and light intensity of 130-140 dB are prohibitive and physically dangerous to the senses, while 60-70 dB is a level stimuli of medium volume and brightness). Wed. Hearing, Background. (B.M.)

DECIBEL (dB)

A unit of measurement commonly used to express the intensity of sound. It always expresses the relationship between two dimensions of pressure (physical forces). Should be determined standard use this term. The common system uses 0.0002 dynes/cm2 to measure sound; this corresponds to approximately the average human threshold for a tone of 1,000 Hz. The intensity of any given tone is thus expressed by dB = 10log,10I1,/I2, where I1 is the intensity in question and I2 is the standard. Since the relationship is logarithmic, an increase in decibels is accompanied by a geometric increase in intensity. At a distance of 5 feet (approx. 1.5 meters), a human whisper measures approximately 20 dB, normal speech measures approximately 60 dB, a jackhammer noise measures approximately 100 dB, and beyond the pain threshold there will be a wide range of sounds (eg, rock music) of approximately at 120 dB. Note, however, that a decibel is a measure of more than just sound intensity. Literally, a decibel is 1/10 of a white, a unit sometimes used to measure electrical voltage and light. Since this measurement is the ratio of two energies, it is logically not limited to sound pressure and can be used in other physical continuums.

Decibel (dB)

A standard unit of measurement for the intensity, or amplitude, of sound. Corresponds to one tenth of a bel, and one bel is the decimal logarithm of the energy (or intensity) ratio. To calculate the intensity in decibels, the formula is often used:

Ndb = 20 logRe/Pr,

where Ndb is the number of decibels, Pe is the sound pressure, which must be expressed in decibels, Pr is the standard pressure with which the measured pressure is compared and which is equal to 0.0002 dyn/cm2. The sound pressure, which must be expressed in decibels (Re), is compared with a certain standard pressure close in value to the threshold of human auditory sensitivity (for sound with a frequency of 1000 Hz).

WHAT ARE DECIBELS?

Universal logarithmic units decibels widely used for quantitative estimates parameters of various audio and video devices in our country and abroad. In radio electronics, in particular in wired communications, 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 serves essentially as the only unit for characterizing various levels - sound intensity, sound pressure, loudness, as well as for assessing the effectiveness of noise control measures.

The decibel is a specific unit of measurement, not similar to any of those encountered in everyday practice. The decibel is not an official unit in the SI system of units, 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 has recommended its inclusion in this system.

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

In this respect, decibels have some similarities to percentages. Like percentages, decibels are dimensionless and serve to compare two quantities of the same name, which are, 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 - 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 powers being compared can be anything - electrical, electromagnetic, acoustic, mechanical - it is only important that both quantities are expressed in the same units - watts, milliwatts, etc.

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

So, for example, if 10 2 = 100, then 10 is called the base of the logarithm, and the number 2 is the logarithm of the number 100 and is denoted log 10 100 = 2 or log 100 = 2 (read as follows: “the logarithm of one hundred to the base ten is equal to two”).

Logarithms with base 10 are called decimal logarithms and are the most commonly used. For numbers that are multiples of 10, this logarithm is numerically equal to the number of zeros behind the 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 computer technology Logarithms with base 2 are usually used.

Basic properties of logarithms:

Of course, these properties are also true for decimal and natural logarithms. The logarithmic method of representing numbers often turns out to be very convenient, since it allows you to replace multiplication with addition, division with subtraction, exponentiation with multiplication, and root extraction with division.

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

Typically, the power ratio is expressed directly in decibels using the formula:

Operations with decibels are no different from operations with logarithms.

2 dB = 1 dB + 1 dB → 1.259 * 1.259 = 1.585;
3 dB → 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 “matches.”

In a similar way, you can create a table for negative decibel values. Minus 1 dB characterizes a decrease in power by 1/0.794 = 1.259 times, i.e., also by about 26%.

Remember that:

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

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

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

Positive decibels are often called gain decibels. Negative decibels, as a rule, 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 attenuation: the same number of decibels with different signs correspond to the inverse numbers of ratios. If, for example, the relation R 2 /P 1 = 2 → 3 dB , That –3 dB → 1/2 , i.e. 1/R 2 /P 1 = P 1 /P 2

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

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

And one more feature: the curve that determines the decibel values ​​depending on the power ratios initially grows quickly, then its growth slows down.

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

The advantages of the decibel system include:

⇒ universality, i.e. the ability to be used when assessing various parameters and phenomena;

⇒ huge differences in converted numbers - from units to millions - are displayed in decibels in 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 as equal numbers, but with different signs;

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

The disadvantages of the decibel system include:

⇒ poor clarity: converting decibels into ratios of two numbers or performing the reverse operations requires calculations;

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

⇒ decibels can only be counted relative to a non-zero level; absolute zero, for example 0 W, 0 V, is not expressed in decibels.

Knowing the number of decibels corresponding to one power ratio, you can recalculate for another - a close or multiple ratio. In particular, for power ratios that differ by a factor of 10, the number of decibels differs by 10 dB. This decibel feature 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 for direct measurement electrical power in the audio and radio frequencies, expensive and complex instruments are required. In practice, when working with equipment, it is much easier to measure not the power released by the load, but the voltage drop across it, and in some cases, the current flowing.

Knowing the voltage or current and load resistance, 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 relationships should be used.

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

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

It is useful to remember some commonly encountered decibel values ​​in practice and the power and voltage (current) ratios that characterize them, given in Table. 1.

Table 1. Common decibel values ​​for power and voltage

Using this table and the properties of logarithms, it is easy to calculate what arbitrary logarithm values ​​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

It was previously noted that the concept of decibels has some similarities with percentages. Indeed, since a percentage expresses the ratio of one number to another, conventionally accepted 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 power ratio:

For voltage or current ratio:

You can also derive formulas for converting decibels into percentage ratios:

In table 2 shows the translation of some of the most common decibel values ​​into percentage ratios. Various intermediate values can be found from the nomogram in Fig. 1.

Rice. 1. Converting decibels into percentage ratios according to the nomogram

Table 2. Converting decibels to percentage ratios

Let's look at two practical examples to explain the conversion of percentages to decibels.

Example 1. To what level of harmonics in decibels relative to the fundamental frequency signal level does the coefficient correspond? nonlinear distortion at 3%?

Let's use fig. 1. Through the intersection point vertical line We will carry out 3% with the “voltage” graph horizontal line until it intersects with the vertical axis and we get the answer: –31 dB.

Example 2. What percentage reduction in voltage corresponds to a change of –6 dB?

Answer. At 50% of the original value.

In practical calculations, the fractional part of the numerical value of decibels is often rounded to a whole number, but this introduces an additional error into the calculation results.

DECIBELS IN RADIO ELECTRONICS

Let's look at a few examples that explain the method of using decibels in radio electronics.

Cable attenuation

Energy losses in lines and cables per unit length are characterized by the attenuation coefficient α, which, with equal input and output resistances of the line, 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 length: 1 m, 1 km, etc. For example, a high-frequency cable of type RK-75-4-14 has an attenuation coefficient α at a frequency of 100 MHz = –0.13 dB /m, a twisted pair cable of category 5 at the same frequency has an attenuation of about –0.2 dB/m, and a cable of category 6 is slightly less. The signal attenuation graph in an unshielded twisted pair cable is shown in Fig. 2.

Rice. 2. Graph of signal attenuation in an unshielded twisted pair cable

Fiber optic cables have significantly lower attenuation values ​​ranging from 0.2 to 3 dB over a cable length of 1000 m. All optical fibers have a complex attenuation versus wavelength relationship that has three "transparency windows" of 850 nm, 1300 nm and 1550 nm . “Transparency window” means the least loss at the maximum signal transmission range. Signal attenuation graph fiber optic cables shown in Fig. 3.

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

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

Obviously, the attenuation introduced by a cable segment 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 is U 2 = 8 V * 0.47 = 3.76 V.

This example illustrates a very important point: losses in a line or cable increase extremely quickly as their length increases. For a cable section 1 km long, the attenuation will be -130 dB, i.e. the signal will be weakened by more than three hundred thousand times!

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 amplifiers audio frequency In order to improve their quality indicators, negative feedback is usually introduced. If the open-loop voltage gain of the device is equal to TO , and with feedback TO OS that number showing how many times the gain changes under the influence of feedback is called depth of feedback . It is usually expressed in decibels. In a working amplifier, the coefficients TO And TO OS are determined experimentally, unless the amplifier is driven with an open feedback loop. When designing an amplifier, first calculate TO , and then determine the value TO OS as follows:

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 must meet additional requirements compared to mono devices. The surround sound effect is only possible when good separation channels, i.e. in the absence of penetration of signals from one channel to another. In practical conditions, this requirement cannot be fully satisfied, and mutual leakage of signals occurs mainly through nodes common to both channels. The quality of channel separation is characterized by the so-called transient attenuation a PZ A measure of crosstalk attenuation 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 current channel; R NE - output power of the free channel.

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

Noise and background

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

Noise can be quantified in several ways.

The simplest one is that all noise, regardless of the cause and place of its origin, is converted 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, serves as a measure of its own noise. However, to evaluate a device from the point of view of interference, it is not the absolute value of 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 interference. The signal-to-noise ratio is usually expressed in decibels:

Where R With - specified or rated output power of the useful signal along with noise; R w - noise output power when the useful signal source is turned off; U c - signal and noise voltage across the load resistor; U Sh - noise voltage across the same resistor. This is how the so-called “unweighted” signal-to-noise ratio.

Frequently, audio equipment parameters include the signal-to-noise ratio measured with a weighted filter. The filter allows you to take into account different sensitivity human 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”). Using 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 the “weighted” value. For more information on weighing filters, see the Sound Level Meters section below.

Obviously, for successful operation of the device, the signal-to-noise ratio must be higher than a certain minimum permissible value, which depends on the purpose and requirements for the device. For Hi-Fi class equipment this parameter must 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 number of decibels as the signal-to-noise ratio, but with a negative sign.

In 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 rated power. The background components are multiples of the mains frequency (50, 100, 150 and 200 Hz) and are measured from the total noise voltage using bandpass filters.

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

Noise figure is the ratio expressed in decibels:

Where TO r - power gain.

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

Meaning Rsh.in determined by calculation; Rsh.out is measured and TO r usually. known from calculation or after measurement. An ideal amplifier from a noise point of view 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 to operate in the first stages of amplification devices, the noise figure is regulated and given in reference books.

The self-noise voltage is also determined by another important parameter many amplification devices - 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 acceptable 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 - an orchestra, a voice - is determined in a similar way, only here the minimum sound power is determined by the background noise. In order for a 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 sound.

The effectiveness of the manual volume control is checked at two extreme positions of the control. First, with the regulator in position maximum volume A voltage with a frequency of 1 kHz is applied to the input of an audio amplifier of such a magnitude that a voltage corresponding to a certain specified power is established at the output of the amplifier. 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 original. The ratio of the input voltage with the control at minimum volume to the input voltage at maximum volume, expressed in decibels, is an indicator of the operation of the volume control.

The examples given do not exhaust the practical cases of applying decibels to assessing the parameters of radio-electronic devices. Knowing general rules, application of these units, it is possible to understand how they are used in other conditions not considered here. When encountering an unfamiliar term defined in decibels, you 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 complex, and when there is no clear clarity, you should refer to the description of the measurement technique in order to avoid serious errors.

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

LOGARITHMIC SCALE

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

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

Frequency characteristics are usually plotted on the so-called logarithmic scale. Along the frequency axis, values ​​that are not proportional to the frequency itself are plotted on a scale convenient for work. f , and the logarithm lgf/f o , Where f O - frequency corresponding to the reference point. Values ​​are written against the marks on the axis. f . To construct logarithmic frequency responses, special logarithmic graph paper is used.

When carrying out theoretical calculations, they usually use not just frequency f , and the size 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 various frequencies to its maximum or average value is plotted in decibels or in relative numbers.

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

Frequency range with cutoff frequencies f H And f IN occupies a stripe in decades f B /f H = 10m , Where m - the number of decades, and in octaves 2 n , Where n - number of octaves.

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

The average frequency of the octave (half octave) is not equal to the arithmetic mean of the lower and upper frequencies octaves, and is equal 0.707f IN .

Frequencies found in this way are called root mean square.

For two adjacent octaves, the mid frequencies also form octaves. Using this property, one can optionally consider the same logarithmic series of frequencies either as boundaries of octaves or as their average frequencies.

On forms with a logarithmic grid, the middle frequency divides the octave row in half.

On a frequency axis on a logarithmic scale, for every third of an octave there are equal segments of the axis, 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 terms of a geometric progression with a denominator of 1.122. For convenience, the values ​​of some frequencies have been rounded within ±1%.

The interval between recommended frequencies is one sixth of an octave. This was not done by chance: the series contains a fairly large set of frequencies for different types of measurements and includes 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 equally considered both as binary (octave) and as decimal (decadal).

The denominator of the progression, on the basis of which the preferred range of frequencies 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 logarithm sign have an arbitrary value and to perform decibel conversion it is important to know only their ratio, regardless of the absolute values.

Specific values ​​of powers, as well as voltages and currents can also be expressed in decibels. When the value of one of the terms under the logarithm sign in the previously discussed formulas is given, the second term of the ratio and the number of decibels will uniquely determine each other. Consequently, 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. Zero decibel in this case corresponds to power equal to the power of the conventional comparison level, since when N P = 0 R 2 =P 1 therefore this level is usually called zero. Obviously, at different zero levels the same specific power (voltage, current) will be expressed different numbers decibel.

Where R - power to be converted into decibels, and R 0 - zero power level. Magnitude R 0 is placed in the denominator, while power is expressed in positive decibels P > P 0 .

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

For the case when R 0 = 1 mW=10 –3 Tue: P r = 10 log P + 30

The fact that the decibels of the represented parameter are reported relative to a certain level is emphasized by the term “level”: interference level, power level, volume 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 encountered fit into within the first hundred decibels. Powers less than 1 mW will be expressed in negative decibel numbers.

Decibels defined relative to the 1 mW level are called decibel milliwatts and are denoted dBm or dBm. The most common values ​​for zero levels are summarized in Table 3.

In a similar way, we 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 represented parameter are reported relative to a certain level is emphasized by the term “level”: interference level, power level, volume level.

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

Table 3. Zero levels for measuring named numbers

The power developed 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 sensitivity level of the microphone (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 values ​​have begun to be used as zero levels, in particular 1 pW, 1 μV, 1 μV/m (the latter for estimating field strength).

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

The possibility of representing both abstract and named numbers in decibels leads to the fact that the same device can be characterized by different numbers of decibels. This duality of decibels must be kept 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 specify the reference level explicitly, for example –20 dB (relative to 0.775 V).

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

DECIBELS IN ACOUSTICS

Until now, when talking about decibels, we have used 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 a medium relative to the constant pressure existing there before the sound waves appear (unit is pascal (Pa)).

An example of sound pressure (or sound pressure gradient) receivers is most types of modern microphones, which convert this pressure into proportional electrical signals.

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

J=pv

If sound wave extends to free space, where there is no reflection of sound, then

v=p/(ρc)

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

We can write that:

J=p 2 / (ρс)

everything that has been said about the conversion of electrical quantities into decibels applies equally to acoustic phenomena

If we compare these formulas with the formulas derived earlier for power. current, voltage and resistance, then it is easy to detect an analogy between individual concepts characterizing electrical and acoustic phenomena and equations describing quantitative dependencies between them.

Table 4. Relationship between electrical and acoustic characteristics

The analogue of electrical power is acoustic power and sound intensity; The analogue of voltage is sound pressure; electric current corresponds to the oscillatory speed, and the electrical resistance corresponds to the specific acoustic impedance. By analogy with Ohm's law for electrical circuit we can talk about Ohm's acoustic 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 by hundreds of millions of times. Such a huge range of changes in acoustic quantities creates great inconvenience when comparing their absolute values, but when using logarithmic units this problem is eliminated. In addition, it has been established 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 volume perceived by the ear. For most people with normal hearing, a change in the volume of a 1 kHz sound is perceived as a change in sound intensity of approximately 26%, i.e., 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.

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

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

The decibels determined by the above formulas are not related to the absolute values ​​of acoustic quantities and are used to evaluate sound attenuation, for example, the effectiveness of sound insulation and noise suppression and attenuation systems. Uneven frequency characteristics are expressed in a similar way, i.e. the difference between the maximum and minimum values ​​in a given frequency range of various sound emitters and receivers: microphones, loudspeakers, etc. In this case, the counting is usually carried out from the average value of the value under consideration, or (when working in sound 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 meanings of which must be expressed specific numbers. The equipment for carrying out acoustic measurements is more complex than the equipment for electrical measurements, and is significantly inferior in accuracy. In order to simplify measurement techniques and reduce errors 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 signals.

The absolute values ​​of powers, sound intensities and sound pressures can also be expressed in decibels if in the above formulas they are specified by the values ​​of one of the terms under the logarithm sign. By international agreement, the sound intensity reference level (zero level) is considered to be J 0 = 10 –12 W/m 2 . This insignificant intensity, under the influence of which the amplitude of vibrations of the eardrum 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 greatest sensitivity of hearing. It is clear that all audible sounds are expressed relative to this level only in positive decibels. The actual hearing threshold for people with normal hearing is slightly higher and is 5-10 dB.

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

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

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

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

Example. Let us determine what intensity level in decibels is created by an orchestra with a sound power of 10 W at a distance 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 into decibels, but the sound pressure level.

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

By determining the level of intensity in decibels at any point in space at a distance r 1 from the sound source (calculated or experimentally), it is easy to calculate the intensity level at a distance r 2 :

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

If available 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 others can be neglected.

In addition to the considered acoustic levels, you can sometimes come across 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 sensitivity of the ear to sounds of different frequencies varies. This dependence is quite complex. At low sound intensity levels (up to approximately 70 dB), the maximum sensitivity is 2-5 kHz and decreases with increasing and decreasing frequency. Therefore, sounds of the same intensity but different frequencies will sound different in volume. As the sound intensity increases, the frequency response of the ear levels out and at high intensity levels (80 dB and above), the ear reacts approximately equally to sounds of different frequencies in the audio range. It follows from this that sound intensity, which is measured by special broadband devices, and volume, which is recorded by the ear, are not equivalent concepts.

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

The volume level of a sound of any frequency is characterized by the level of a sound equal in volume 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 a sound source must develop to give the impression of equal loudness to a 1 kHz tone of a given intensity (Fig. 4).

Rice. 4. Equal Loudness Curves

Equal loudness curves essentially represent a family of ear frequency responses on a decibel scale for different intensity levels. The difference between them and conventional frequency responses lies only in the method of construction: the “blockage” of the characteristic, i.e., a decrease in the transmission coefficient, is represented here by an increase rather than a decrease in the corresponding section of the curve.

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

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

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

If we refer to Fig. 4 and trace the course of one of the curves, for example, for a level of 60 von, it is easy to determine that to ensure equal volume with a 1 kHz tone 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 compensation, or, as they are also called, compensated controls. Such regulators, simultaneously with adjusting the input signal value downwards, provide an increase in the frequency response in the lower frequency region, due to which a constant sound timbre is created for the ear at different sound playback volumes.

Research has also established that a change in sound volume by half (as assessed by hearing) is approximately equivalent to a change in the volume level by 10 backgrounds. This dependence is the basis for estimating sound volume. Per unit of loudness, called dream , the volume level is conventionally assumed to be 40 background. Double volume equal to two sons corresponds to 50 backgrounds, four sons corresponds to 60 backgrounds, etc. The conversion of volume levels into volume units is made easier by the graph in Fig. 5.

Rice. 5. Relationship between loudness and loudness level

Most of the sounds we encounter in everyday life are noise in nature. Characterizing the loudness of noise based on comparison with pure tones of 1 kHz is simple, but leads to the fact that the assessment of noise by ear may diverge from the readings of measuring instruments. This is explained by the fact that at equal levels of noise volume (in the background), the most irritating effect on a person is exerted by noise components in the range of 3-5 kHz. Noises may be perceived as equally unpleasant even though their volume levels are not equal.

The irritating effect of noise is more accurately assessed by another parameter, the so-called perceived noise level . A measure of 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 rated by the listener as equally unpleasant as the measured noise. Perceived noise levels are characterized by units of PNdB or PNdB. They are calculated using a special method.

A further development of the noise assessment system is the so-called effective perceived noise levels, expressed in EPNdB. The EPNdB system allows you to comprehensively assess the nature of the impact noise: frequency composition, discrete components in its spectrum, as well as the duration of noise exposure.

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

In one Noah The noise level of uniform noise in the band 910-1090 Hz at a sound pressure level of 40 dB is assumed. In other respects, noi are similar to sons: a doubling of noise level corresponds to an increase in the level of perceived noise by 10 PNdB, i.e. 2 noi = 50 PNdB, 4 noi = 60 PNdB, etc.

When working with acoustic concepts, keep in mind that sound intensity represents an objective physical phenomenon that can be accurately defined and measured. It really exists whether anyone hears it or not. The loudness of a 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 person’s hearing organs and his personal abilities to perceive sound.

SOUND MEASURES

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

The sound level meter (Fig. 6) consists of a high-quality microphone, a wideband amplifier, a sensitivity switch that changes the gain in 10 dB steps, a frequency response switch and a graphic 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 to be taken in hard-to-reach places. Among the domestic sound level meters, one can name the device of the Octava-Electrodesign company “Octava-110A” (http://www.octava.info/?q=catalog/soundvibro/slm).

Sound level meters allow you to determine how general levels sound intensities when measured with a linear frequency response, and sound volume levels in the background when measured with frequency characteristics similar to those of the human ear. The range of measurements 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. Using 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 sound level meter path, including the microphone, are standardized. There are five frequency responses in total. One of them is linear within the entire operating frequency range ( symbol Lin), the other four approximate 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 appearance of these characteristics is shown in Fig. 7. The frequency response switch is independent of the measurement range switch. For class 1 sound level meters, the required characteristics are: 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 permitted.

Rice. 7. Standard frequency characteristics of sound level meters

Characteristic A imitates an ear at approximately 40 background. This characteristic is used when measuring weak noises - up to 55 dB and when measuring volume levels. In practical conditions, the frequency response with correction is most often used A . This is explained by the fact that, although human perception of sound is much more complex than the simple frequency dependence that determines the characteristic A , in many cases, the measurement results of the device are in good agreement with the assessment of auditory noise at low volume levels. Many standards - domestic and foreign - recommend that noise assessment be carried out according to the characteristics A regardless of the actual sound intensity level.

Characteristic IN 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 volume levels - from 85 von and above, when measuring sound pressure levels - regardless of the measurement limits, as well as when connecting devices to a sound level meter to measure 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 response of the ear at approximately 80 von, taking into account the increase in its sensitivity in the band from 1.5 to 8 kHz. When using this characteristic, the sound level meter readings more accurately than other characteristics correspond to the level of perceived noise by a person. This characteristic is used mainly when assessing the irritating effect of high-intensity noise (airplanes, high-speed cars, etc.).

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

When using a sound level meter, the measurement results will vary 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 ( IN ), dB ( WITH ) or dB ( D ).

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

According to the currently valid instruction “Sanitary standards for permissible noise in the premises of residential and public buildings and in residential areas,” the standardized parameters of continuous or intermittent noise are sound pressure levels (in decibels) in octave frequency bands with average frequencies 63, 125, 250, 500, 1000, 2000, 4000, 8000 Hz. For intermittent noise, for example noise from passing vehicles, the normalized parameter is the sound level in dB( A ).

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

For a sanitary assessment of the noise level, corrections are made to the sound level meter readings from –5 dB to +10 dB, 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, during the daytime, the permissible noise standard in residential premises, taking into account the amendment, is 40 dB.

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

In the absence of a sound level meter, an approximate estimate of the volume levels of various noises can be made using a table. 5.

Table 5. Noises and their assessment