Conversion of dBm to dB (dBm to dB), relationship between power and attenuation. Examples of relative logarithmic values \u200b\u200band units. Comparing decibels to percent

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

A long time ago, Alexander Bell found out that a person stops hearing a sound if the power of the source of this sound is less than 10 -12 W / m 2, and if it exceeds 10 W / m 2, then prepare your ears for unpleasant pain - this is a pain threshold.

As you can see, the difference between 10 -12 W / m 2 and 10 W / m 2 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 further it is even more interesting.

Get to the point

We found out that decibel is equal to 1/10 bel, but how to apply it in life? Here's an example:

• 0 dB - nothing is heard
• 15 dB - barely audible (rustle of foliage)
• 50 dB - clearly audible
• 60 dB - Noisy

Why is this necessary, if you can, for example, say: "the sound power level is 0.1 W / m 2". 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:

What is expressed in bels as the ratio of the level of the measured signal to a certain reference one. 1 Bel \u003d lg (P 1 / P 0), where P 0 is the sound power of the audibility threshold, but to get a decibel, you just need to multiply by 10: 1 dB \u003d 10 * lg (P 1 / P 0)

In this way 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 can be seen that decibels can be compared to any signals (and not only sound power), since decibels are dimensionless.

Features:

The confusion with decibels comes from the fact that there are several "types" of them. They are conventionally called amplitude and power (energy).

Formula 1 dB \u003d 10 * lg (P 1 / P 0) -compares two energy quantities in decibels. In this case, power. And the formula 1 dB \u003d 20 * lg (A 1 / A 0) -compares two amplitude values. For example, voltage, current, etc.
The transition from amplitude decibels to energy decibels and back is very simple. It is simply required to convert “non-energetic” quantities into energetic ones. I will show this with the example of current and voltage.

From the definition of power P \u003d UI \u003d U 2 / R \u003d I 2 * R. Substitute in 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 \u200b\u200bwill be carried out in the same way. More details, as always, can be found in textbooks and reference books.

Why complicate things?

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

Thus, the decibel allows from calculus in "parrots", i.e. go at times to more specific and small values. Which can be quickly added and subtracted in your mind. And if you still want to evaluate the attitude in parrots by a known value in decibels, then it is enough to remember a simple mnemonic rule (I spied on Revich):

If the ratio is greater than one, then it will be positive dB (+3 dB), and if it is less, it will be negative (-3 dB). In this way:

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

And now for an example. Suppose we were told that the signal is amplified by 50 dB. A 50db \u003d 10db + 20db + 20db \u003d 3 * 10 * 10 \u003d 300 times. Those. the signal was amplified 300 times.

So the decibel is just a convenient engineering convention that has been introduced as a result of some practical measurements and the benefits of practical use.

When measuring something (like voltage), we usually think in direct units (in volts). But sometimes it is preferable to use a relative scale. In this case, the most commonly used unit of measurement is the decibel (dB), a powerful tool that confuses beginners. With the knowledge of the origin of this term and one simple rule, difficulties can be excluded, and the value of a quantity expressed in decibels can be understood.

Alexander Graham Bell became famous for the invention of the telephone. Less well known is his work on determining the threshold of hearing. In 1890 he founded the Association of the Deaf and Hard of Hearing, which is still active today. He was the first scientist to quantify the sense of hearing and found that auditory sensitivity does not depend on the actual power level of the sound wave reaching our ear, but on its logarithm.

Bell found that a child's hearing threshold is about 10 -12 W / m 2, and the level at which pain occurs is about 10 W / m 2. Thus, the range of loudness normally perceived by a person is 13 orders of magnitude!

Based on the values \u200b\u200bobtained, Bell determined the sound power scale from 0 to 13. The units of loudness of this scale are called bels (the last "l" from his name was dropped). The sound level of a quiet whisper is about 3 beats, and that of normal speech is about 6 beats.

Since the sensation of loudness is based on a logarithmic scale of power level, the conversion between power and loudness on the Bell scale is as follows: loudness (in bels) \u003d lg (P1 / P0), where P0 is the audibility threshold of the sound.

Therefore, a sound level of 4 bels corresponds to a sound power of 10 4 P0.

Bel became in fact the standard unit of measurement for the logarithm of the ratio of two energy levels: the ratio expressed in bels is lg (P1 / P0), i.e. an increase of 3 bels corresponds to an increase of 1000 times. If the new value decreases, then the logarithm of the ratio becomes negative. To do the reverse transformation, you need to raise 10 to the power equal to bels.

The most important feature of whites is that they refer only to the ratio of two powers or two energies. If there is a need to describe the ratio of two amplitude signals, for example, voltages, then it is possible only to rely on the ratio of the powers associated with these voltages. Power is proportional to the square of the voltage or current: V 2 and I 2.

The ratio of the two voltages, expressed in bels, is related to the ratio of their powers: lg (P1 / P0) \u003d 2lg (V1 / V0). Therefore, the voltage ratio is V1 / V0 \u003d log10 (white * 2).

It has become common enough to express the ratio in tenths of a bel or in decibels (dB). The ratio of the two powers in dB is 10lg (P1 / P0), and the voltage ratio is 10 2lg (V1 / V0). To obtain the voltage ratio, it is necessary to perform the conversion V1 / V0 \u003d 10 (dB / 20).

Sometimes it is quite tricky to determine what is considered an amplitude value and what is energy. Voltage, current, impedance, electric or magnetic field strength and the swing of any wave processes are considered to be amplitude values. When a measurement is made in decibels, the logarithm of the ratio of the squares of these quantities is calculated. Energy, power and intensity are energy quantities and are used directly in relation to the logarithm.

For example, 5% of the voltage from one circuit is transferred to the other circuit. The stress ratio in this case is 0.05. To measure in decibels, take the logarithm of the voltage ratio, multiply it by 2 to get the ratio in bels, and then multiply by 10 to get the ratio in dB: 20lg (0.05) \u003d -26 dB coupling between signals.

The table lists some commonly used decibel values \u200b\u200band ratios of amplitudes and powers.

Radio 1967, 12

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

What is a decibel? First of all, decibel (abbreviated designation - dB) is not a physical quantity, like, say, watt, volt, ampere, but a mathematical concept. In this respect, decibels have some similarities with percentages. Like percentages, decibels are relative values \u200b\u200band are applicable to the assessment of a wide variety of phenomena, regardless of their nature. But, if percentages express some value related to the whole, taken as a unit, then the decibel is based on a broader concept that characterizes the ratio of two independent, but identical quantities. However, one must remember that the term "decibel" is always associated only with powers and with some reservations about voltages and currents. The physical nature of the power is not specified and can be any - electrical, acoustic, electromagnetic.

A decibel, as the prefix deci indicates, 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 \u003d 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 pertinent to recall here that the decimal logarithm of a number is the exponent to which the number 10 must be raised to get this number. For example: Lg (100) \u003d 2, since 10 2 \u003d 10 * 10 \u003d 100; Lg (1000) \u003d 3, since 10 3 \u003d 10 * 10 * 10 \u003d 1000.

For numbers greater than one, their logarithms will be positive, and if numbers are less than one, their logarithms are negative. Negative logarithms are preceded by a “-” (minus) sign, for example: Lg (0,1) \u003d - 1; Lg (0.01) \u003d - 2.

In the case when the initial signal is less than the final one, that is, P2 / P1 is greater than 1, which is the case in amplifiers, the number of decibels will be positive, and if the initial level is greater than the final one, that is, P2 / P1 is less than 1, then the number of decibels will be negative. The second case corresponds to the attenuation (attenuation) of the signal. When both powers are the same and P2 / P1 \u003d 1, then the decibel number is zero.

There is a simple relationship between the decibels of gain and attenuation: 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 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 prerequisite must be observed: the resistances of the loads at which the voltages U1 and U2 are measured or through which the measured currents I1 and I2 flow must be the same. In this case, the formulas for calculating decibels are as follows:

N dB \u003d 20 Lg (P2 / P1); N dB \u003d 20 Lg (I2 / I1)

Decibels are used not only to compare two values. They are also convenient for evaluating specific values \u200b\u200bof powers, 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 value compared with it will be characterized by a certain number of decibels. In this case, zero decibel corresponds to the power equal to the first, which is often called zero. For the conditional zero level of the electrical signal, the power P \u003d 1 mW (0.001 W), released at the active resistance R \u003d 600 Ohm, is taken - just as when measuring the temperature, the temperature of ice melting at normal atmospheric pressure is taken as zero degrees. At this power at the indicated resistance, the voltage drop is:

U \u003d (PR) 0.5 \u003d (0.001 * 600) 0.5 \u003d 0.775 V,

and the flowing current:

I \u003d (P / R) 0.5 \u003d (0.001 / 600) 0.5 \u003d 1.29 mA.

These values \u200b\u200b- 0.775 V and 1.29 mA are taken as zero decibels of electric voltage and current.

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

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

Suppose that as a result of the improvement of the output stage of the low frequency amplifier, its output power has increased from 10 to 20 W. So the power increment will be:

P2 / P1 \u003d 20/10 \u003d 2

According to the table in the column "Power ratio" the number closest to 2 will be 1.99. In the column "Decibels" this number corresponds to 3 dB. Therefore, doubling the output power corresponds to a 3dB gain increase. If, for some reason, the output power of the amplifier has decreased from 20 W to 10 W, then the new power ratio will be P2 / P1 \u003d 10/20 \u003d 0.5. But now the change in power means attenuation and will be expressed as -3 dB.

When performing actions with decibels, it must be remembered that the sum of two numbers in decibels is equivalent to the product of the absolute values \u200b\u200bof the numbers to which they correspond, therefore, in order to show an increase (or decrease) in power, for example, twice, three times or four times, it is necessary to add to the initial 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 with the 1 mW standard zero level noted above. Let us assume that a microphone of the MD-44 type, the output level of which is 78 dB, is connected to an amplifier that can develop 40 W of undistorted power. However, in the work it turned out that an amplifier with such a microphone develops only 10 watts. The question is, what sensitivity should the microphone be in order 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 \u003d 4. This ratio (according to the table - 3.98) corresponds to 6 dB. Therefore, you need a microphone with a recoil level of - 72 dB, that is, 6 dB more than the MD-44 microphone (-78 dB), since: - 78 dB + 6 dB \u003d -72 dB. This requirement is met, for example, by the MD-41 microphone.

Table 1. Decibels and the corresponding ratios of powers, voltages and currents

Another example. A voltage of 8 V with a frequency of 100 MHz is applied to a piece of cable of the RK-1 type with a length of 50 m. What will be the voltage at the output of the segment if it is known (from the handbook) that at this frequency the cable introduces an attenuation of 0.096 dB per meter? The power supply and the load have the same resistance equal to the waveform. Obviously, the attenuation introduced by the cable is: 0.096 * 50 \u003d 4.8 dB. Table 1 for this attenuation (-4.8 dB) the voltage ratio is not specified. Let's use the fact that the table shows the ratio for +4.8 dB, which is 1.74. This means that at the end of the segment, the signal will be 1 / 1.74 ≈ 0.57 of the input, i.e. 8 * 0.57 ≈ 4.6 V.

When you need to determine the values \u200b\u200bof decibels or ratios that are not in the table, you need to proceed as follows. Suppose you want to find a power ratio corresponding to 24 dB. Representing 24 dB as a 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 get that 24 dB corresponds to a power ratio of 251.2.

At the output of the amplifier at medium frequencies, a voltage of U1 \u003d 30 V develops, and at the edges of the passband, a voltage of U2 \u003d 21 V. The amplifier, therefore, introduces frequency distortion - the upper and lower audio frequencies are amplified worse ("overwhelms") than the average. The ratio of these values \u200b\u200bwill be

U2 / U1 \u003d 21/30 \u003d 0.7

According to the table, we find that the frequency distortion of this amplifier at the edges of the passband is -3 dB.

Decibels are also widely used in acoustics, where they are, in essence, the main unit for quantifying sound intensity. This is explained by the property of our ear to react to sounds, the intensity of which differs by a factor of millions. But the ear's sensitivity to sounds of different strengths is not the same - in silence and at low intensity (whisper, rustle) it is maximum, and at high intensity (the roar of an aircraft, the roar of cars) it is minimal. In this respect, a hearing aid is similar to an AGC radio.

This phenomenon can be explained by the following example. Let's say the amplifier develops 10 watts at the output. Increasing the output power to 20 watts will sound like a slight increase in volume. In order for the ear to feel twice as loud, an almost tenfold increase in the amplifier output power (≈10 dB) is required. And in order for the ear to perceive a 4 times increase in volume, the power must be increased by 100 times (≈20 dB).

Physiologists, 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 strength by several times will appear to the ear as a change in loudness approximately in the logarithm of this number of times. The use of decibels in acoustics turns out to be very convenient, since auditory perception and the assessment of the intensities of sounds are in strict connection and, moreover, a change in sound intensity by 1 dB is captured by the ear as a barely noticeable change in volume.

Table 2. AVERAGE NOISE LEVELS

A comparative assessment of the average loudness levels of some household and industrial noises in decibels relative to the hearing threshold of the human ear, taken as a zero level, is given in Table. 2. Measurement of sound intensity is carried out using special devices - sound level meters, the scales of which are graded directly in decibels.

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

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

Electrical engineers use various parameters when familiarizing themselves with an electrical circuit, measuring the absolute values \u200b\u200bof voltage, resistance, inductance. Each is conventionally designated, it is easy to determine them from the initial reading level to the measured value, for example, the current in amperes. But there are also inscriptions next to capacity, frequency or other electrical parameter, which have a quantitative designation, in the form of decibels.

The use of the dB base unit is widely used by telecommunications designers to compare performance in different equipment. With the help of a specific unit numerically expressed, it is determined how much the signal is amplified or attenuated.

Often measuring some kind of electrical size, straight units stand in the view, but experts have appreciated the use of a relative scale, in which decibels stand up as a powerful tool that came to science thanks to the scientist Graham Bell.

He became world famous after the invention of telephones, but he did a lot of research work, determining the hearing threshold in humans. For this, the scientists founded the Association for People, which operates to this day.

Who created the scale for measuring loudness

Alexander Bell was the first to quantify the auditory sense. He established the dependence of auditory sensitivity on logarithms, instead of the power of sound waves. The researcher found the hearing thresholds of children and adults, determined at what values \u200b\u200bit occurs that a normal person needs 13 edges of the range for loudness to be perceived without harm to health.

These data became the basis for the production of a logarithm scale, in which the sound power is divided into units, which are called bels. By this distinction, it has been established that a quiet whisper is equal to three bels, and normal speech is six. This logarithmic measurement is its standard value, determined by the ratio of energies in two levels. In the decoding, which is measured in decibels, the general expression of loudness is embedded, bel is raised to tenths for the convenience of handling numbers.

Concepts about sound, noise level and their sources

In terms of physical characteristics, sound and noise are distinguished by their special natural phenomena. The pressure in the air changes, which acts on the eardrums in the ears with the help of peculiar vibrations, and the sound is received. It continues to move through the human organs with transformed electrical impulses, reaching. A person is able to accept a wide range of sound pressure, which is expressed in decibels.

Sound propagation occurs at different frequencies, which affects the sensitivity of the ears of both animals and humans.
The differences between sounds and noises are purely subjective, which are determined by the sources of occurrence. Depending on the environment that surrounds a person, they are internal, associated with equipment:

• engineering
• technological
• household
• sanitary

External sources include noise arising from:

• vehicle
• industrial organizations
• energy enterprises
• various institutions dependent on people's livelihoods (stadiums, sports grounds, entertainment events)

Noise is heard in apartments, sometimes reaching 60 dB, from sanitary and engineering equipment:

• elevators
• pumps
• garbage chutes
• ventilation units

In houses they hear:

• musical equipment
• in operating mode devices and instruments
• household appliances

When moving around the apartment (moving bulky objects), sound vibrations occur, which turn into structural noise. The operation of fans and elevator winches in buildings emit both structural and air noise flow, which enters the premises through the ventilation ducts.

To prevent the operation of mechanical equipment from being heard, vibration isolating devices are installed. In high-rise buildings from the movement between the floors of the elevator winch, shock and pushing actions of guides, rattling of door leaves, the propagation of sound effects occurs both by air and constructively.

In addition to the irritating effect on the body of noise at home, a person is exposed to exceeding the permissible standards in public service, during production processes.

Industry has an abundance of noise generated during production. The rumbling of production is often heard from the compressed air. It is called impulse: the occurrence occurs when valves and cylinders are blown, equipment is cleaned, cooled, transported, sorted.

If sounds are characterized by certain timbres, spectral colors, and people can easily recognize their sources. For example, the sound of music, a children's cry, a dog barking. Then the noises coming from random oscillatory and non-periodic processes do not have specific sources. It can be the hubbub of the crowd, the crackling of construction sites, the hum of cars, the noise of the street.

Therefore, defining noise as a phenomenon, it is compared with a complex of uncontrolled sounds that adversely affect human health, annoying, interfering with a pleasant pastime. They are classified into types:

• air
• structural
• drums

Interference from television, radio, quarrels of neighbors spread through the air. Structurally, the crackle of partitions, the creak of flooring, ceiling structures in houses, audibility from operating mechanisms, a screwdriver, a processor, a vacuum cleaner are transmitted. Percussion sounds belong to the varieties of structurally disordered sound vibrations. They can be heard from neighboring apartments located on the upper floors, when a chair falls, furniture is moved.

Noise actions, their permissible value

The appearance of any noise pollution manifests itself as an increasing sound level, above existing in nature, causing irritation factors. Together, sound signals give a living creature time to evaluate them, to adapt.

High power causes damage to the auditory organs, there is a feeling of pain, shocking actions. Innovative developments have led to an alarming increase in noisy environments, allowing not only annoying emotions, but also a decrease in auditory acuity. From a violation of acoustic comfort, a person experiences stress, insomnia, and increased pressure.

The main threat is partial or complete hearing loss.

Rumble, screeching, clanking in raised tones leads to scattering of attention, decreased ability to work, productivity from work, especially if it is mental work. A person loses the ability to focus on the main operation, to make important decisions. Normal, nerve cells are disrupted. From their weakening, there is a failure in the coordination of various organs.

Examples of noise effects on the human body

The environment for hearing is a volume level of up to 30 dB. There is a permissible limit that does not exceed 80 dB, but after 60 dB a person begins to feel uncomfortable.

An increase in sound up to 120 dB causes pain, after 140 dB an intolerable feeling occurs. Even metal does not withstand 180 dB, its fatigue arises, and by increasing the level, destruction of the structure can occur. Noisy industries are famous for their loudness up to 110 dB. Apartments always excite many residents with their sound insulation; entire design bureaus are working on this, developing methods and new noise-absorbing materials.

It is known that increasing noise:

• from 61 dB - upsets the autonomic nervous system
• 91 dB - decreases hearing
• 116 dB is considered a pain threshold
• 140 dB - causes rupture of eardrums
• 151 dB - is unbearable
• 179 dB - Threat to life

Exceeding the permissible noise standards adversely affects the mental development of children. It is harmful for adolescents to often visit discos where music sounds up to 100 dB, sometimes amplifiers are specially placed and the rumble becomes equal to an electric train.

The noise background of megalopolises is increasing proportionally with constantly increasing technological processes. There have appeared many, forcing researchers to solve problems, to develop various regulations in order to protect a person from sound effects.

Buildings are protected with sound insulation products that reflect sound energy. All of them are flexible, resilient and multi-layered, perform the main task, clog surfaces, do not let sounds through.

How irritating rumble and soothing sounds affect the auditory organ

It is impossible to completely protect the living space of people from the sound background. Among them there are useful signals that have a beneficial effect on a person. With their help, they communicate, navigate, work.

It is known that streams murmur, birds sing, leaves rustle beneficial to the nervous system. A gentle song, the roar of sea waves can relieve nervous stress. Sounds were punished in the Middle Ages, condemning the condemned to be for a long time under the blows of bells. A harmonious lullaby made even a restless child calm down and fall asleep.

The receipt of certain sound signals in the human brain causes discomfort, irritation, and fatigue. People experience subjective sensations from what they hear, and pathological changes can occur in the organs of hearing.

An annoying hubbub can affect systems:

• central
• nervous
• cardiovascular
• endocrine
• digestive

It has been determined that an increased noise level affects a person as follows:

• decreased hearing function, adaptation from hearing fatigue up to partial or permanent hearing loss
• impaired ability to communicate through speech
• irritable, restless behavior
• physiological reactions change,
• mental deterioration
• decreases productivity

The actions of sound waves serve as specific stimuli of the auditory organs, with a certain frequency and intensity.

Scientist studies on noise

The effect of loud signals on hearing prompted a person to study their characteristics theoretically and practically. The purpose of such a study is to identify the threshold of the threatening effect of noise, on this basis to develop documents and substantiate the hygienic norms of various contingents of residents, depending on where they are and what they are in.

This could be:

• house
• public building
• production facility
• educational institution
• hospital, clinic
• preventive institutions
• dormitory area
• industrial district
• recreation area

In theory, scientists have coped with the task of studying the pathogenesis, methods of exposure to noise, adaptation of the body in an unfavorable environment, the consequences of a long stay in it. Numerous experiments have been carried out. This is a difficult research work, since there are significant differences in the noise sensitivity of citizens from their age, gender, social group.

A person reacts differently to sound effects depending on whether he is in a state of agitation or inhibited; which process prevails at this moment.

In percentage terms, people are divided into the perception of sounds with sensitivity:

• 35% - increased
• 55% - normal
• 10% - do not perceive noise

Acoustic stress affects the psychological and physiological state of residents and depends on the area:

• individual biorhythmic profile
• sleep patterns
• physical activity
• stress
• nervous state
• drinking and smoking

Sociologists say that most of all city citizens complain about the hum of cars (70%), the rumble from industrial enterprises occupies the middle line (20%), and domestic hubbub is in last place (10%). At the same time, 50% feel anxiety, 30% are irritated, and 20% do not complain at all. Citizens who suffer from damage to the neurovascular system or digestive organs.

From this, diseases occur or worsen:

• gastritis
• intestines

Residents permanently residing in the area of \u200b\u200bstreets with a high level of noise deteriorate their health, and the number of medical visits increases.

Basic rules to protect your hearing

It is difficult for a person who has the invaluable gift of hearing to imagine that one can lose it. For this, there are preventive measures to prevent unpleasant consequences:

1. Treatment. Especially important in childhood. With ear infections of a bacterial nature, competent and timely treatment is necessary. In addition to infections, many diseases carry dangerous complications of the hearing aid.
2. Reduce visits to establishments with increased noise levels. In restaurants, bars, concert halls, people talk in a raised voice, you should think about choosing a place and the length of your stay there.
3. No need to neglect protective equipment for people whose activities take place in an increased noise level, and over 80 dB it is very loud.
4. Long-term use of headphones is harmful.
5. The volume from the radio, televisions, radio tape recorders should be muted whenever possible.
6. Cleanliness is the guarantee of health, and the ears must be constantly cleaned of sulfur deposits, the use of cotton swabs is not approved by doctors, they recommend rinsing with water.

They are simple, and dry technical knowledge about decibels will help solve a practical problem, but will not preserve a person's hearing. It is necessary to take good care of your health, avoid noisy gatherings, protect your home from the penetration of extraneous sounds. Specialists will always come to the rescue: a doctor will cure, a builder will install sound insulation.

Nov 28, 2016 Violetta Healer

When measuring the parameters of radio equipment, it is often necessary to deal with relative values \u200b\u200bexpressed 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 values \u200b\u200bin 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 into decibels (a similar formula is valid for currents):

For example, if the output of U2 is at twice the level of U1, the ratio is +6 dB (Ig2 \u003d 0.301). If U2\u003e U1 10 times, then the signal ratio is 20 dB (Ig10 \u003d 1). If U1\u003e 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 \u200b\u200b0 ...- 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 output voltage value after setting the attenuation is at the intersection of the horizontal and vertical graph (the values \u200b\u200bin decibels are added arithmetically).

The value of the output voltage in the table is indicated in microvolts (1 μV \u003d 10-6 V). I

Using this table, it is not difficult to solve the inverse problem - by the required voltage, determine what signal attenuation should be set on 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 \u003d 106 dB will be required on the attenuator. The power ratio of the two signals in decibels is calculated by the formula:

The formula for 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 the practical use of dB, it is important to know the absolute value of the ratio of 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 \u003d U2 / U1 or K \u003d 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 signal power amplification by 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.

Over the past six months, we have good news in Slavutych. Neither more nor less during this time two new fighters have opened. And what makes me especially happy is that both are technically very competent guys. With the suggestion of Gennady UN7FGO and the support of our fellows Andrey and Boris, I became interested in Arduinism. The project of radio beacons seemed especially interesting to me. Probably due to the fact that in terms of antennas and transceivers I am rich :-) And I can afford to spend money on electricity. Although, for good reason, it would be better to run it somewhere on a collective ...

In short, the essence of the question. There is an idea (and probably will be in the hardware) an arduino controller that can control the Kenwood TS2000X. Who can remember, it ranges from 160 meters to 30 centimeters. Arduino assigns the time, frequency, direction where to turn the antennas (for example, to the north) and transmits the callsign, 10-digit WW locator, and with the announcement successively 4 power gradations: PWR 100 w (4 seconds carrier), 50 watts (4- carrier per second), 25 watts ... and 5 watts. Then follows the command to the antenna controllers (G-800DXA and G5500) to turn to the east and everything along the FOR loop 1 to the number of ranges. Then south, then west. Then a range change.

I can include enough antennas in Kenwood:

EN5R Islands Activity

EN5R Islands Activity: UIA award

The question of converting dB to dBm and vice versa is often heard from clients, met on specialized forums. However, no matter how much one would like, it is impossible to convert power into attenuation.

If the power of the optical signal is measured in dBm, then to determine the attenuation A (dB), it is necessary to subtract the signal power at the output from the signal power at the input to the line. But about all this in order.

Optical power, or the power of optical radiation, is the fundamental parameter of an optical signal. It can be expressed in the usual units of measurement - Watt (W), milliwatt (mW), microwatt (μW). And also in logarithmic units - dBm.

Attenuation of the optical signal (A) is a value that shows how many times the signal power at the output of the communication line (P out) is less than the signal power at the input of this line (P in). Attenuation is expressed in dB (deciBell) and can be determined using the following formula:

Figure 1 - The formula for calculating optical attenuation if the optical power is expressed in W

A bit strange, isn't it? Slide rules and tables are a thing of the past, at least for young installers they have long been replaced by a calculator. And even taking into account the use of a calculator - such a formula is not very convenient. Therefore, to simplify the calculations, it was decided to convert the power units to the logarithmic format and thus get rid of the logarithms in the formula:

Figure 2 - Conversion of power from mW to dBm

To convert dBm to W and vice versa, you can also use the table:

As a result of recalculation, the formula for calculating optical attenuation (Fig. 1) turns into:

Figure 3 - Conversion of dBm to dB (dBm to dB), relationship between power and attenuation

Considering the fact that all optical power meters known to the author use dBm as the main unit of measurement, using the formula in Fig. 3, an engineer can determine the attenuation level even in his head. In addition, many devices have the function of setting the reference level, due to which the user is given the loss value immediately in dB.

In this case, the measurement of the optical line attenuation is greatly simplified, as demonstrated in the following video.

Optical line attenuation measurement

A measured value of attenuation in dB is often sufficient. However, in order to represent how many times the input signal has decreased, you can use the formula:

m \u003d 10 (n / 10)

where m is the ratio in times, n is the ratio in decibels

you can also use the following table:

Table 1 - conversion of dB at times

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 different 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 is allowed to 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 quantities 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 \u200b\u200bare 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 \u003d 100, then 10 is called the base of the logarithm, and the number 2 - the logarithm of 100 and denote log 10 100 \u003d 2 or lg 100 \u003d 2 (read like this: "the logarithm of one hundred at base ten is two").

Logarithms with base 10 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 \u003d 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 \u003d 20 dB, 4.62 B \u003d 46.2 dB, etc.

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

Decibel operations do not differ from logarithm operations.

2 dB \u003d 1 dB + 1 dB → 1.259 * 1.259 \u003d 1.585;
3dB → 1.259 3 \u003d 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”.

Similarly, you can create a table for negative decibels. Minus 1 dB characterizes a decrease in power by 1 / 0.794 \u003d 1.259 times, that is, also by about 26%.

Remember that:

⇒ If R 2 \u003d P 1 i.e. P 2 / P 1 \u003d 1 then N dB = 0 , because lg 1 \u003d 0 .

⇒ If P 2 \u003e 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 same number of decibels with different signs correspond to inverse numbers of ratios. If, for example, the relation R 2 /R 1 \u003d 2 → 3 dB then –3 dB → 1/2 , i.e. 1 / R 2 /R 1 \u003d 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 \u003d 10k , because lg 10 k \u003d k .

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

And one more feature: the curve, which determines the decibel values \u200b\u200bdepending on the power ratios, first grows rapidly, then its growth slows down.

Knowing the number of decibels corresponding to one power ratio, one can 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 possibility of using 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 in 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, you can 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 of the ratio of voltages and currents is equal to. 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 \u200b\u200bthat are often encountered in practice and the ratios of powers and voltages (currents) that characterize them, given in Table. 1.

Table 1. Frequent decibel values \u200b\u200bof power and voltage

Using this table and the properties of logarithms, it is easy to calculate what arbitrary values \u200b\u200bof the logarithms correspond to. For example, 36 dB of power can be represented as 30 + 3 + 3, which corresponds to 1000 * 2 * 2 \u003d 4000. We get the same result by representing 36 as 10 + 10 + 10 + 3 + 3 → 10 * 10 * 10 * 2 * 2 \u003d 4000.

COMPARISON OF DECIBELS WITH PERCENTAGES

Earlier it was noted that the concept of decibels has some similarities with percent. Indeed, since the percentage expresses 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 display formulas for converting decibels to percentages of a ratio:

Table 2 is a translation of some of the most common decibel values \u200b\u200binto percentages of ratios. Various intermediate values \u200b\u200bcan be found from the nomogram in Fig. 1.

Figure: 1. Converting decibels into percentages of ratios according to the nomogram

Table 2. Converting decibels to percentages

Consider 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 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 corresponds to a –6 dB change?

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 radio 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, \u003d –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.

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

Fiber optic cables have significantly lower attenuation values \u200b\u200bin the range from 0.2 to 3 dB for 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 transmission distance. The signal attenuation graph in fiber optic cables is shown in Fig. 3.

Figure: 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 \u003d 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.

It is obvious that the attenuation introduced by a piece of cable is K \u003d –0.13 dB / m * 50 m \u003d –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 \u003d 8 V * 0.47 \u003d 3.76 V.

This example illustrates a very important point: losses in a line or cable grow extremely rapidly with increasing length. For a 1 km length 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

Negative feedback is usually introduced into audio frequency amplifiers in order to improve their performance. If the voltage gain of the device without feedback is equal 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 are 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 devices. Surround sound is only provided when good separation channels, i.e. in the absence of signal penetration from one channel to another. In practical terms, this requirement cannot be fully satisfied, and mutual leakage of signals occurs mainly through the nodes common to both channels. The channel separation quality is characterized by the so-called transient attenuation 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 - 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, as they are amplified by all subsequent stages. Intrinsic noise degrades the real 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 from - the specified or nominal output power of the useful signal together with noise; R w - 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 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 decibel number 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 components of the background are multiples of the mains frequency (50, 100, 150 and 200 Hz) and, when measured, are separated from the total interference voltage using bandpass 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 design imperfections (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) \u200b\u200ba useful signal with a power R from and noise power R w , then the signal-to-noise ratio at the input will be (R from /R w ) in After strengthening the attitude (R from /R w ) 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 gain.

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

Value 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 \u003d 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 determines another important parameter of many amplifying 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 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 indicator of how the volume control is operating.

These examples are far from being exhausted practical cases of application of decibels to the estimation of parameters of radio-electronic devices. Knowing general rules, the use of these units, one can understand how they are used in other conditions not covered here. Faced with an unfamiliar term, defined in decibels, one should clearly imagine the ratio of which two quantities it corresponds. 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, one should always pay attention to the ratio of which units - power or voltage - corresponds to each specific case, that is, which 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 various devices (amplifiers, dividers, filters) from frequency external influence... To construct a 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 \u200b\u200bare plotted along the frequency axis on a linear scale, that is, 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 the lowest frequencies it is compressed, and the higher frequencies are stretched.

Frequency characteristics are usually plotted on the so-called logarithmic scale. On the frequency axis, in a scale convenient for work, values \u200b\u200bare plotted that are proportional not to the frequency itself f and the logarithm lgf / f o where f about - the frequency corresponding to the origin. Values \u200b\u200bare labeled against axis marks f ... To construct the logarithmic frequency response, a special logarithmic graph paper is used.

When carrying out theoretical calculations, they usually use not just the frequency f , and the value ω \u003d 2πf which is called the circular frequency.

Frequency f about , 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 AT occupies a strip in decades f B / f H \u003d 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 upper frequencies of the octave, but is 0.707 f AT .

Frequencies found in this way are called root mean squares.

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 middle frequencies, if desired.

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

On the frequency axis on 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 \u200b\u200bof powers, as well as voltages and currents. When the value of one of the terms under the sign of the logarithm 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, the power equal to the power of the conditional comparison level corresponds to zero decibels, since at N P \u003d 0 R 2 \u003d P 1 therefore this level is usually called 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 quantity R 0 is put in the denominator, while the power is expressed in positive decibels P\u003e 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 by a 600 ohm resistor. The choice of these parameters occurred historically: initially, the decibel as a unit of measurement appeared in technology telephone connection... 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 \u003d 1 mW \u003d 10 –3 W: P r \u003d 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, that is, almost all the powers that one has to meet fall into within the first hundred decibels. Powers less than 1 mW will be expressed in negative decibels.

Decibels, specified relative to 1 mW, are called decibel-milliwatts and are denoted as dBm or dBm. The most common values \u200b\u200bfor zero levels are summarized in Table 3.

In a similar way, 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 decibels of the presented parameter are reported relative to a certain level is emphasized by the term "level": noise level, power level, volume 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 \u003d 1 mW ... This microphone parameter is called standard microphone sensitivity ... Typical test conditions are considered to be a sound pressure of 1 Pa at a frequency of 1 kHz, a load resistance for a dynamic microphone - 250 Ohm.

Table 3. Zero levels for measuring named numbers

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 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 measure - 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 sound intensity is related to the sound pressure and the vibrational velocity of air particles by a simple relationship:

J \u003d pv

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

v \u003d p / (ρc)

here ρ is the density of the medium, kg / m3; from - 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 \u003d 420 kg / m2 * s; for water ρ c \u003d 1.5 * 106 kg / m2 * s.

You can write that:

J \u003d 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 separate concepts that characterize electrical and acoustic phenomena, and 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 corresponds 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 evaluated 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 with a change in sound intensity of about 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.

Likewise, decibels represent the ratio of two sound intensities:

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 \u200b\u200bof acoustic values \u200b\u200band 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, that is, the difference between the maximum and minimum values \u200b\u200bin a given frequency range of different emitters and receivers of sound: microphones, loudspeakers, etc. In this case, the counting is usually carried out from the average value of the considered value, 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, it is necessary to deal with sounds, the values \u200b\u200bof which must be expressed in specific numbers. Acoustic measurement equipment is more complex than equipment for electrical measurements, and is significantly inferior in accuracy. 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 \u200b\u200bof which are known. For the same purpose, to measure and study acoustic signals, they are converted into electrical ones.

The absolute values \u200b\u200bof powers, intensities of sounds and sound pressures can also be expressed in decibels, if in the above formulas you specify the values \u200b\u200bof 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 following 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 r \u003d 15 m.

The sound intensity at a distance r \u003d 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 affected 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 \u200b\u200bof the intensity (W / m2), add them, and this sum is 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 \u200b\u200bof 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 one of this 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 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 \u003d 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 different frequencies will seem 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 in approximately the same way 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 volume level of sound of any frequency is characterized by the value of a level equal in volume to a sound 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 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 to give the impression of equal loudness with a tone of 1 kHz of a given intensity (Fig. 4).

Figure: 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: a "blockage" of the characteristic, ie, a decrease in the transmission coefficient, is shown here by an increase, not a decrease, of 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 \u200b\u200bfor 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 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 called, compensated controls. Simultaneously with the adjustment of the input signal value in the direction of decrease, such regulators 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 (assessed by ear) is approximately equivalent to a change in volume level by 10 phon. This dependence is the basis for assessing the sound loudness. For a unit of loudness called sleep , conventionally adopted a volume level of 40 background. The doubled loudness, equal to two sleep, corresponds to 50 phon, four sleep corresponds to 60 phon, etc. The conversion of loudness levels into volume units is facilitated by the graph in Fig. five.

Figure: 5. Relationship between volume and volume

Most of the sounds that we 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 a hearing estimate of noise that may differ from the readings of measuring instruments. This is explained by the fact that at equal levels of noise loudness (in backgrounds), the most irritating 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 volume 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 to be 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 are the so-called effective levels of perceived noise, expressed in EPNdB. The EPNdB system allows 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 sleep volume unit, the noise unit 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. For the rest, 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 \u003d 50 RNdB, 4 noi \u003d 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 to 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.

Figure: 6. Portable digital sound level meter

Modern sound level meters are very compact, which makes it possible to measure even in hard-to-reach places. Of the domestic sound level meters, one can name the device of the company "Octava-Electrodesign" "Octava-110A" (http://www.octava.info/?q\u003dcatalog/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 characteristics AND and FROM ; the rest are allowed.

Figure: 7. Standard frequency characteristics of sound level meters

Characteristic AND 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 AND ... 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 AND , 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 AND regardless of the actual sound intensity level.

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

Characteristic FROM 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 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 pht, 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 correspond to the level of perceived noise by a person than according to other characteristics. 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 Fast , the device manages to follow the rapid changes in sound levels, in the position Slow 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 ( AND ), dB ( AT ), dB ( FROM ) 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 continuous or intermittent noise are the 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 normalized parameter is the sound level in dB ( AND ).

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

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, time of day and the location of the object. For example, in the daytime, the allowable noise level 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, a rough estimate of the loudness levels of various noises can be carried out using the table. five.

Table 5. Noises and their assessment