What is a decibel? Basic decibel meter. What is measured in decibels, dimensionless units, relative values, their features

Over the past six months we have had good news in Slavutich. During this time, no more, no less, two new fighters were revealed. And what’s especially pleasing is that both are technically very competent guys. With the encouragement 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, to be fair, it would be better to launch this somewhere on a team.....

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

I can include enough antennas in Kenwood:

Good old mechanics

I received a question in the guest book:

"Hello, Egor. I've been looking at your site for a couple of years now. My hobby is next to your amateur radio. Solder more. I noticed that there are a lot of descriptions simple solutions problems. I want to ask you. There is no FM radio in my city. The nearest radio stations are in regional centers. I started with a regular vertical one :-) Weak signal. To reliably receive music, I made a simple directional antenna at 108 MHz (two frames), but sometimes I have to go out into the yard and turn it towards three large cities. Because the radio stations are different. Is it possible to somehow make it work well this way? "End quote.

I already answered a similar question once. AND key phrase there was: "You will be surprised at the difference when switching to external antenna" :-) True, there was a question about receiving satellites. Well, it doesn’t matter. It’s just that the solution that I proposed then works well and costs practically nothing :-) But miracles don’t happen in nature. Either it’s simple and not good enough, but from all sides, or simple and good, but on the one hand, in the case of Leonid, we can consider the question of what. it may be more effective to solve the rotation issue than the antenna gain problem. In order not to send via a link, I’m simply copying a piece of old material. He's short: ......in principle, two colinear elements or the same number of Yagi or squares are enough. It is, of course, desirable

Double Kharchenko

Even people as far from radio engineering as zoologists noted its undoubted advantages: a very convenient geometric layout and good gain. In Africa, they look for lions with radio collars with such an antenna :-) If you go by the size of what was shown on TV, then it was a range of about 300-400 MHz, maybe a little more. But they needed a clear direction towards the beast, but we need the opposite: high instincts from all sides. Therefore, the usual layout of the Kharchenko antenna (biquadrate) does not suit us. As usual, we will use amateur radio imagination, a little radio engineering and mechanics. So, first, let's remember how an ordinary butterfly works. However, there are a dime a dozen descriptions on the Internet. So it's very short. A single frame with a perimeter equal to the wavelength has an input impedance from 240 ohms (if the shape of the loop vibrator) to 120 ohms if the shape of the frame is a circle. But at the same time, it emits levels approximately the same for horizontal and vertical polarizations. There is a slight difference, of course:

Merry Christmas!

On behalf of my loved ones and especially my wife Irina UY2RY (her tree and photo:-) I wish all radio amateurs a Merry Christmas! I wish you health, happiness and, of course, success in our multifaceted hobby.

Telegram UR8RF

Radio Promin

I love everyone. Today, November 17, on Radio Promin on protyazhi 40 Khvylin Volodymyr UY2UQ learned about amateur radio. You can listen to it on the Radio Promin website in the audio archive on November 17.
Hour 15:14:14 - 15:54:38 http://promin.fm/page/9.html?name=Audioarhiv1http://promin.fm/page/9.html?name=Audioarhiv1
73! With the car Oleksandr UR8RF

EN5R Islands Activity

EN5R Islands Activity: UIA award

Sound recording

The third and final area of audio processing in HAM radio is programs for recording and editing audio. If you noticed, sometimes interesting enough events happen on the air to record them and then let others listen to them. And when you work in a contest, there is no need to strain your vocal cords too much - write it down necessary phrases, and then in the contest logger just press the desired button playback :-). For example, I work in SSB contests very rarely, but my N1MM has soundtracks for two or three tests. :-) But everyday communication with people and subsequent playback of sent audio files shows that this topic is relevant for almost everyone: sent files and Low quality and very large in volume and, most importantly, in formats that I sometimes see for the first time. It's no secret that the most suitable mp3 format for us is fast and easy, allowing everyone specific case select the saving option - either quality prevails, or we save volume. In MP3 format, all this can be easily adjusted depending on the task at hand. More about this below, but for now

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

Really, convenient units? But, as it turns out, they are not convenient for everyone! It can be said that most people who are not well versed in physics, mathematics and engineering do not understand logarithmic units such as decibels. Some even believe that logarithmic values do not apply to modern digital technology, and to the times when a slide rule was used for engineering calculations!

A little history

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

An important tool for practical use logarithms were tables of logarithms. The first such table was compiled by the English mathematician Henry Briggs in 1617. Building on the work of John Napier and others, English mathematician and Church of England clergyman William Oughtred invented the slide rule, which was used by engineers and scientists (including this author) for the next 350 years until it was replaced by pocket calculators in the mid-1970s. .

Definition

Logarithm is the inverse operation of raising to a power. The number y is the logarithm of the number x to base b

if equality is maintained

In other words, the logarithm of a given number is an exponent to which the number, called the base, must be raised to get given number. It can be said more simply. A logarithm is the answer to the question “How many times must one number be multiplied by itself to get another number.” For example, how many times must you multiply the number 5 by itself to get 25? The answer is 2, that is

By the above definition

Classification of logarithmic units

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

By using absolute logarithmic units express physical quantities that are compared with a certain fixed value. For example, dBm (decibel milliwatt) is an absolute logarithmic unit of power that compares power to 1 mW. Note that 0 dBm = 1 mW. Absolute units are great for describing single size, and not the ratio of two quantities. Absolute logarithmic units of measurement of physical quantities can always be converted into other, ordinary units of measurement of these quantities. For example, 20 dBm = 100 mW or 40 dBV = 100 V.

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

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

It should also be noted that converting logarithmic units to regular units is often not possible. However, this only happens in cases where they talk about relationships. For example, the voltage gain of an amplifier of 20 dB can only be converted into “folds”, that is, into a dimensionless value - it will be equal to 10. At the same time, sound pressure measured in decibels can be converted into pascals, since sound pressure is measured in absolute logarithmic units, that is, relative to the reference value. Note that the transmission coefficient in decibels is also a dimensionless quantity, although it has a name. It's a total mess! But we'll try to figure it out.

Logarithmic amplitude and power units

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

10 log₁₀(P₁/P₂) dB

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

20 log₁₀(P₁/P₂) dB.

Examples of relative logarithmic quantities and units

Common units

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

You can convert N, B and dB on the “Sound Converter” page.

Music, acoustics and electronics

s = 1000 ∙ log₁₀(f₂/f₁)

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

Communication and data transfer

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

Electronic sound reproduction and recording equipment

Other units and quantities

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

Power, signal level (absolute)

Voltage (absolute)

Electrical resistance (absolute)

dBohm, dBohm or dBΩ(decibel ohm, amplitude ratio) - absolute resistance in decibels relative to 1 ohm. This unit of measurement is convenient when considering a large range of resistances. For example, 0 dbω = 1 ω, 6 dbω = 2 ω, 10 dbω = 3.16 ω, 20 dbω = 10 ω, 40 dbω = 100 ω, 100 dbω = 100,000 ω, 160 dbω = 100,000 ω and so on Further.

Acoustics (absolute sound level, sound pressure or sound intensity)

Radar. Absolute values on a logarithmic scale are used to measure radar reflectivity compared to some reference value.

dBZ or dB(Z)(amplitude ratio) - absolute coefficient of radar reflectivity in decibels relative to the minimum cloud Z = 1 mm⁶ m⁻³. 1 dBZ = 10 log (z/1 mm⁶ m³). This unit shows the number of droplets per unit volume and is used by weather radar stations (meteo-radar). The information obtained from measurements in combination with other data, in particular, the results of polarization and Doppler shift analysis, makes it possible to estimate what is happening in the atmosphere: whether it is raining, snowing, hail, or a flock of insects or birds flying. For example, 30 dBZ corresponds to light rain, and 40 dBZ corresponds to moderate rain.
dBη(amplitude ratio) - the absolute factor of the radar reflectivity of objects in decibels relative to 1 cm²/km³. This value is convenient if you need to measure the radar reflectivity of flying biological objects, such as birds, bats. Weather radars are often used to monitor such biological objects.
dB(m²), dBsm or dB(m²)(decibel square meter, amplitude ratio) - an absolute unit of measurement of the target's effective scattering area (EPR, English radar cross section, RCS) in relation to square meter. Insects and weakly reflective targets have a negative cross section, while large passenger aircraft have a positive cross section.

Communication and data transfer. Absolute logarithmic units are used to measure various parameters related to the frequency, amplitude, and power of transmitted and received signals. All absolute values in decibels can be converted into ordinary units corresponding to the measured value. For example, the noise power level in dBrn can be converted directly to milliwatts.

Other absolute logarithmic units. There are many such units in different branches of science and technology, and here we will give only a few examples.

Richter earthquake magnitude scale contains conventional logarithmic units (decimal logarithm is used) used to estimate the strength of an earthquake. According to this scale, the magnitude of an earthquake is defined as the decimal logarithm of the ratio of the amplitude of seismic waves to an arbitrarily chosen very small amplitude that represents magnitude 0. Each step of the Richter scale corresponds to an increase in the amplitude of the vibrations by a factor of 10.
dBr(decibel relative to the reference level, amplitude or power ratio, set explicitly) - logarithmic absolute unit of measurement of any physical quantity specified in the context.
dBSVL- vibrational velocity of particles in decibels relative to the reference level 5∙10⁻⁸ m/s. The name comes from English. sound velocity level - sound speed level. The oscillatory speed of particles of the medium is otherwise called acoustic speed and determines the speed with which the particles of the medium move when they oscillate relative to the equilibrium position. The reference value 5∙10⁻⁸ m/s corresponds to the vibrational velocity of particles for sound in air.

Quite often in popular radio engineering literature, in the description electronic circuits The unit of measurement used is decibel (dB or dB).

When studying electronics, a novice radio amateur is accustomed to such absolute units measurements as Ampere (current), Volt (voltage and emf), Ohm ( electrical resistance) and many others, with the help of which one or another electrical parameter (capacitance, inductance, frequency) is quantified.

As a rule, it is not difficult for a novice radio amateur to figure out what an ampere or a volt is. Everything is clear here, there is an electrical parameter or quantity that needs to be measured. Eat First level reference, which is accepted by default in the formulation of this unit of measurement. Eat symbol this parameter or value (A, V). Indeed, as soon as we read the inscription 12 V, we understand that we are talking about a voltage similar, for example, to the voltage of a car battery.

But as soon as you see an inscription, for example: the voltage has increased by 3 dB or the signal power is 10 dBm, then many people are perplexed. Like this? Why is voltage or power mentioned, but the value is indicated in some decibels?

Practice shows that not many beginning radio amateurs understand what a decibel is. Let's try to dispel the impenetrable fog over such a mysterious unit of measurement as the decibel.

A unit of measurement called Bel Bell Telephone Laboratory engineers began to use it for the first time. A decibel is a tenth of a Bel (1 decibel = 0.1 Bel). In practice, it is the decibel that is widely used.

As already mentioned, the decibel is a special unit of measurement. It is worth noting that decibel is not part of official system SI units. But, despite this, the decibel gained recognition and took a strong place along with other units of measurement.

Remember, when we want to explain a change, we say that, for example, it became 2 times brighter. Or, for example, the voltage dropped 10 times. At the same time, we set a certain reference threshold, relative to which a change of 10 or 2 times occurred. These “times” are also measured using decibels, only in logarithmic scale.

For example, a change of 1 dB corresponds to a change in energy value by a factor of 1.26. A change of 3 dB corresponds to a change in energy value by a factor of 2.

But why bother so much with decibels if relationships can be measured in times? There is no clear answer to this question. But since decibels are actively used, this is probably justified.

There are still reasons to use decibels. Let's list them.

Part of the answer to this question lies in the so-called Weber-Fechner law. This is an empirical psychophysiological law, that is, it is based on the results of real, not theoretical experiments. Its essence lies in the fact that any changes in any quantities (brightness, volume, weight) are felt by us, provided that these changes are logarithmic in nature.

Graph of the dependence of the sensation of loudness on the strength (power) of sound. Weber-Fechner law

For example, the sensitivity of the human ear decreases with increasing volume level sound signal. That is why, when choosing a variable resistor that is planned to be used in the volume control of an audio amplifier, it is worth choosing an exponential dependence of the resistance on the angle of rotation of the control knob. In this case, when you turn the volume control slider, the sound in the speaker will increase smoothly. The volume adjustment will be linear, since the exponential dependence of the volume control compensates for the logarithmic dependence of our hearing and in total will become linear. This will become more clear when you look at the picture.

Dependence of the resistance of the variable resistor on the angle of rotation of the engine (A-linear, B-logarithmic, B-exponential)

Shown here are graphs of the resistance of variable resistors different types: A – linear, B – logarithmic, C – exponential. As a rule, on variable resistors domestic production indicates what kind of dependence it has variable resistor. Digital and electronic regulators volume.

It is also worth noting that the human ear perceives sounds, the power of which varies by a whopping 10,000,000,000,000 times! Thus, the most loud noise differs from the quietest that our ears can detect by 130 dB (10,000,000,000,000 times).

The second reason widespread use decibel is the ease of calculation.

Agree that it is much easier to use small numbers like 10, 20, 60,80,100,130 (the most commonly used numbers when calculating decibels) compared to the numbers 100 (20 dB), 1000 (30 dB), 1000,000 (60 dB), 100,000,000 (80 dB), 10 000 000 000 (100 dB), 10 000 000 000 000 (130 dB). Another advantage of decibels is that they are simply added together. If you carry out calculations in times, then the numbers must be multiplied.

For example, 30 dB + 30 dB = 60 dB (in times: 1000 * 1000 = 1000,000). I think this is all clear.

Also, decibels are very convenient when graphic construction various dependencies. All graphs such as antenna radiation patterns and amplitude-frequency characteristics of amplifiers are performed using decibels.

Decibel is dimensionless unit of measurement. We have already found out that a decibel actually shows how many times any quantity (current, voltage, power) has increased or decreased. The difference between decibels and times is only that the measurement occurs on a logarithmic scale. To somehow designate this and attribute the designation dB . One way or another, when assessing, you have to move from decibels to times. You can compare using decibels any units of measurement (not just current, voltage, etc.), since the decibel is a relative, dimensionless quantity.

If a “-” sign is indicated, for example, –1 dB, then the value of the measured quantity, for example, power, decreased by 1.26 times. If no sign is placed in front of decibels, then we are talking about an increase, an increase in value. This is worth considering. Sometimes instead of the “-” sign they talk about attenuation, a decrease in gain.

Transition from decibels to times.

In practice, most often you have to move from decibels to times. There is a simple formula for this:

Attention! These formulas are used for so-called “energy” quantities. Such as energy and power.

m = 10 (n / 10), where m is the ratio in times, n is the ratio in decibels.

For example, 1dB is equal to 10 (1dB / 10) = 1.258925...= 1.26 times.

Likewise,

at 20 dB: 10 (20 dB / 10) = 100 (increase in value by 100 times)

at 10 dB: 10 (10dB / 10) = 10 (10x increase)

But it's not that simple. There are also pitfalls. For example, the signal attenuation is -10 dB. Then:

at -10 dB: 10 (-10 dB / 10) = 0.1

If the power from 5 W decreased to 0.5 W, then the decrease in power is equal to -10 dB (a 10-fold decrease).

at -20 dB: 10 (-20dB / 10) = 0.01

It's similar here. When the power is reduced from 5 W to 0.05 W, in decibels the power drop will be -20 dB (a 100-fold decrease).

Thus, at -10 dB the signal power decreased by 10 times! Moreover, if we multiply the initial signal value by 0.1, we will obtain the signal power value at attenuation of -10 dB. That is why the value 0.1 is indicated without “times”, as in the previous examples. Take this feature into account when substituting decibel values with a “-” sign into the formula data.

Transition from times to decibels can be done using the following formula:

n = 10 * log 10 (m), where n is the value in decibels, m is the ratio in times.

For example, a 4-fold increase in power will correspond to a value of 6.021 dB.

10 * log 10 (4) = 6.021 dB.

Attention! To recalculate the ratios of such quantities as voltage And current strength There are slightly different formulas:

(Current strength and voltage are so-called “power” quantities. Therefore, the formulas are different.)

To go to decibels: n = 20 * log 10 (m)

To go from decibels to times: m = 10 (n/20)

n – value in decibels, m – ratio in times.

If you have successfully reached these lines, then consider that you have taken another significant step in mastering electronics!

Areas of use

The decibel was originally used to measure ratios energy(power, energy) or security forces(voltage, current) quantities. In principle, decibels can be used to measure anything, but currently it is recommended to use decibels only for level measurements power and some other power-related quantities. So decibels are used today in acoustics to measure sound volume and in electronics for measurement power electrical signal . Sometimes dynamic range is also measured in decibels (for example, sounds musical instruments). The decibel is also a unit of sound pressure.

Power measurement

As mentioned above, whites were originally used to assess the ratio capacity, therefore, in the canonical, usual sense, a value expressed in bels means the logarithmic ratio of two capacity and is calculated by the formula:

value in bels =

Where P 1 / P 0 - ratio of the levels of two powers, usually measurable to the so-called supporting, basic (taken as the zero level). To be more precise, this is - "white in power". Then the ratio of two quantities in "decibels by power" calculated by the formula:

value in decibels (by power) =

Measurement of non-power quantities

Formulas for calculating level differences in decibels frail(non-energy) quantities such as voltage or current strength, differ from the above! But ultimately, the ratio of these quantities, expressed in decibels, is also expressed through the ratio of the powers associated with them.

So for linear circuit equality is true or

From here we see that a means

whence we get the equality: which is the connection between "white in power" And "voltage white" in the same circuit.

From all this we see that when comparing the values of voltages (U 1 and U 2) or currents (I 1 and I 2), their ratios in decibels are expressed by the formulas:

decibels by voltage = decibels by current =

It can be calculated that when measuring power, a change of 1 dB corresponds to a power increase (P 2 /P 1) of ≈1.25893 times. For voltage or current, a change of 1 dB will correspond to an increment of ≈1.122 times.

Calculation example

Suppose that the power P 2 is 2 times greater than the initial power P 1, then

10 log 10 (P 2 /P 1) = 10 log 10 2 ≈ 3 dB,

that is, a change in power by 3 dB means its increase by 2 times. Similarly, the power change is 10 times:

10 log 10 (P 2 /P 1) = 10 log 10 10 = 10 dB,

and 1000 times

10 log 10 (P 2 /P 1) = 10 log 10 1000 = 30 dB,

Conversely, to get times from decibels (dB), you need

For power - for voltage (current) .

For example, knowing the reference level (P 1) and the value in dB, you can find the power value, for example, with P 1 = 1 mW and a known ratio of 20 dB:

Similarly for voltage, with U 1 = 2 V and a ratio of 6 dB:

It is quite possible to carry out calculations in your head; to do this, it is enough to remember an approximate simple table (for capacities):

1 dB 1.25 3 dB 2 6 dB 4 9 dB 8 10 dB 10 20 dB 100 30 dB 1000

The addition (subtraction) of dB values corresponds to the multiplication (division) of the ratios themselves. Negative dB values correspond to reverse relationship. For example, reducing power by 40 times is 4*10 times or −6 dB-10 dB = −16 dB. An increase in power by 128 times is 2^7 or 3 dB*7=21 dB. An increase in voltage by 4 times is equivalent to an increase in power by 4*4=16 times, which is 2^4 or 3 dB*4=12 dB.

Practical use

Since the decibel is not an absolute, but a relative value and is calculated differently for different physical quantities (see above), additional conventions exist to avoid confusion when using decibels in practice.

Most often you need to know the ratio of two levels (voltages), expressed in decibels; there are several values that are easy to remember:

6 dB - 2:1 ratio

20 dB - 10:1 ratio

40 dB - 100:1 ratio

60 dB - 1000:1 ratio

80 dB - 10000:1 ratio

100 dB - ratio 100000:1

120 dB - ratio 1000000:1

Intermediate values can be easily calculated using the formula - 20*Lg(U1/U2), where U1 is the signal level (voltage), U2 is the noise level (voltage), recall that measurements are carried out with an rms millivoltmeter, or a spectrum analyzer with an IEC filter (A), where IEC - International Electrotechnical Commission

Why use decibels at all and operate with logarithms, if the same thing can be expressed by the usual percentages or shares? Let's imagine that in a completely dark room we turn on a light bulb of some aperture. At the same time, the room is strikingly different in appearance before and after switching on. The change in illumination, expressed in dB, is also huge, theoretically infinite. Let's say that we now turn on another similar light bulb. Now the effect will be completely different, maybe even a person will not immediately notice the changes if it is turned on smoothly. And in decibels it will be only 3 dB. So, in practice, in decibels it is convenient to measure both highly variable quantities and almost constant ones.

Legend

For different physical quantities the same numerical value , expressed in decibels, can match different levels signals (or rather, level differences). Therefore, in order to avoid confusion, such “specific” units of measurement are denoted by the same letters “dB”, but with the addition of an index - a generally accepted designation for the physical quantity being measured. For example, “dBV” (decibel relative to volt) or “dBμV” (decibel relative to microvolt), “dBW” (decibel relative to watt), etc. In accordance with international standard IEC 27-3, if it is necessary to indicate the original value, its value is placed in parentheses behind the designation of the logarithmic value, for example for the sound pressure level: L P (re 20 µPA) = 20 dB; L P (ref. 20 µPa) = 20 dB

Application in automatic control theory

Decibel also used in theories automatic regulation and management(TAU) and is one of the most important parameters when comparing the amplitudes of the output and input signals.

Reference level

Although the decibel is used to determine the ratio of two quantities, decibels are sometimes used to measure absolute values. To do this, it is enough to agree on what level of the measured physical quantity will be taken as the reference level (conditional 0). In practice, the following reference levels and special designations for them are common:

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:

dBV for a 50-ohm microwave circuit corresponds to (dBm−13 dB);
dBμV for a 50-ohm microwave circuit corresponds to (dBm+107 dB)
dBV for a 75-ohm TV circuit corresponds to (dBm−11 dB);
dBµV for a 75 ohm TV circuit corresponds to (dBm+109 dB)

You should clearly remember the mathematical rules:

you cannot multiply or divide relative units;
summation or subtraction relative units is produced regardless of their original dimension and corresponds to the multiplication or division of absolute ones.

For example, applying a power of 0 dBm, equivalent to 1 mW, or 0.22 V, or 107 dBμV, to one end of a 50-ohm cable with a gain of −6 dB, the output power will be −6 dBm, equivalent to 0.25 mW (4 times less power) or 0.11 V (half the voltage) or 101 dBµV (the same 6 dB less).

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

Steps

Comparison table of noise levels in decibels

The table below describes decibel levels in ascending order, and corresponding examples of sound sources. Information is also provided about negative consequences for hearing opposite each noise level.

Decibel levels for different noise sources

Decibels	Example source	Health effects
0	Silence	None
10	Breath	None
20	Whisper	None
30	Quiet background noise in nature	None
40	Sounds in the library, quiet background noise in the city	None
50	Calm conversation, normal suburban background noise	None
60	Office or restaurant noise, loud conversation	None
70	TV, highway noise from 15.2 meters (50 feet) away	The note; some people find it unpleasant
80	Noise from factory, food processor, car wash from 6.1 meters (20 feet) away	Possible hearing damage with prolonged exposure
90	Lawn mower, motorcycle from a distance of 7.62 m (25 ft)	High potential for hearing damage with prolonged exposure
100	Boat motor, jackhammer	High probability serious damage hearing loss after long-term exposure
110	Loud rock concert, steel mill	It may hurt immediately; there is a very high likelihood of serious hearing damage with prolonged exposure
120	Chainsaw, thunder	Usually there is immediate pain
130-150	Fighter taking off from an aircraft carrier	There may be immediate hearing loss or a ruptured eardrum.

Measuring sound levels using instruments

Use your computer. Co special programs and equipment, it is easy to measure the noise level in decibels directly on the computer. Below are just some of the ways you can do this. Please note that using better recording equipment will always give best result; in other words, the microphone built into your laptop may be sufficient for some tasks, but high quality external microphone will give a more accurate result.

Use the mobile app. To measure sound level anywhere, mobile applications will come in handy. Microphone on your mobile device It probably won't produce the same quality as an external microphone connected to your computer, but it can be surprisingly accurate. For example, reading accuracy is mobile phone may well differ by 5 decibels from professional equipment. Below is a list of programs for reading sound level in decibels for different mobile platforms:
- For Apple devices: Decibel 10th, Decibel Meter Pro, dB Meter, Sound Level Meter
- For Android devices: Sound Meter, Decibel Meter, Noise Meter, deciBel
- For Windows phones: Decibel Meter Free, Cyberx Decibel Meter, Decibel Meter Pro
Use a professional decibel meter. It's usually not cheap, but it may be the easiest way to get precise measurements the sound level you are interested in. Also, such a device is called a “sound level meter”, this is a specialized device (can be bought in an online store or specialized stores) that uses sensitive microphone to measure the noise level around and display exact value in decibels. Since such devices are not used in great demand, they can be quite expensive, often starting at $200 even for entry-level devices.
- Please note that the decibel/sound level meter may have a slightly different name. For example, another similar device called a noise meter does the same thing as a sound level meter.
Mathematical calculation of decibels
1. Find out the sound intensity in watts/meter square. IN Everyday life, decibels are used as a simple measure of loudness. However, everything is not so simple. In physics, decibels are often thought of as convenient way expressions of the "intensity" of a sound wave. The greater the amplitude of a sound wave, the more energy it transmits, the more air particles vibrate along its path, and the more intense the sound itself. Because of the direct relationship between sound wave intensity and decibel volume, it is possible to find the decibel value by knowing only the sound level intensity (which is usually measured in watts/meter square)
  - Note that for normal sounds the intensity value is very low. For example, a sound with an intensity of 5 × 10 -5 (or 0.00005) watts/meter square corresponds to approximately 80 decibels, which is approximately the volume of a blender or food processor.
  - To better understand the relationship between intensity and decibel level, let's solve a problem. Let's take this as an example: Let's assume that we are sound engineers, and we need to get ahead of the level of background noise in a recording studio in order to improve the quality of the recorded sound. After installing the equipment, we recorded background noise intensity 1 × 10 -11 (0.00000000001) watt/meter square. Using this information, we can then calculate the background noise level of the studio in decibels.
2. Divide by 10 -12. If you know the intensity of your sound, you can easily plug it into the formula 10Log 10 (I/10 -12) (where "I" is the intensity in watts/meter square) to get the decibel value. First, divide 10 -12 (0.000000000001). 10 -12 displays the intensity of a sound with a rating of 0 on the decibel scale, by comparing the intensity of your sound to this number you will find its ratio to the starting value.
  - In our example, we divided the intensity value 10 -11 by 10 -12 and got 10 -11 / 10 -12 = 10 .
3. Let's calculate Log 10 from this number and multiply it by 10. To complete the solution, all you have to do is take the base 10 logarithm of the resulting number and then finally multiply it by 10. This confirms that decibels are a base 10 logarithmic value - in other words, a 10 decibel increase in noise level indicates a doubling sound volume.
  - Our example is easy to solve. Log 10 (10) = 1. 1 ×10 = 10. Therefore, the value of background noise in our studio is equal to 10 decibels. It's quite quiet, but is still picked up by our high-quality recording equipment, so we'll probably need to eliminate the source of the noise to achieve better results. High Quality records.
4. Understanding the logarithmic nature of decibels. As stated above, decibels are logarithmic values to base 10. For any given value decibel, noise that is 10 decibels larger is twice as loud as the original, and noise that is 20 decibels larger is four times louder, and so on. This makes it possible to designate a large range of sound intensities that can be perceived by the human ear. The loudest sound a person can hear without experiencing pain is a billion times louder than the quiet sound which a person can hear. By using decibels we avoid using huge numbers to describe ordinary sounds, three numbers are enough for us instead.
  - Think about what is easier to use: 55 decibels or 3 × 10 -7 watts/square meter? Both values are equal, but instead of using the scientific notation (as a very small fraction of a number), it is much more convenient to use decibels, which are a kind of simple shorthand for easy everyday use.