Decibel measurement online. Optical line attenuation measurement. In animal husbandry and clerical activities

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

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

History of origin

As it turned out as a result of long-term research, the susceptibility is not directly related to the absolute level of sound propagation. It is a measure of the power applied to a given unit of area that is in the zone of exposure to sound waves, which is measured in decibels today. As a result, a curious proportion was established - the more space belongs to the useful area of \u200b\u200bthe human ear, the better it is for the perception of minimum powers.

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

In the original version, the unnamed scale had 14 values \u200b\u200b- from 0 to 13, where human whispering was "3" and spoken language was "6". Subsequently, this scale found wide application, and its units were called bels. To obtain more accurate data on a logarithmic scale, the original unit was increased 10 times - this is how decibels were formed.

General information

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

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

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

Despite its wide area of \u200b\u200bapplication, most people know that decibels are used to determine the degree of loudness. This value characterizes the waves per square meter. Thus, an increase in volume of 10 decibels is comparable to a doubling of sound intensity.

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

Application area

Telecommunications designers today use the decibel as the base unit for conducting comparative characteristics devices displayed on a logarithmic scale. Such possibilities are provided by the design feature of this quantity, which is a logarithmic unit of different levels used for attenuation or, conversely, power amplification.

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

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

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

It is possible to use these dimensionless units both for physical quantities related to the second order - energy or power, and for quantities related to the first order - current or voltage. Decibels open up the possibility of measuring the relationship between all physical quantities, and in addition, with their help, absolute values \u200b\u200bare compared.

Sound volume

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

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

The ability of different people to perceive sounds is in the range of loudness from 10 to 15 dB, and in some cases even higher. The perceived range of sound intensity ranges from 20 to 20 thousand Hertz. The easiest to perceive sounds are located in the frequency range from 3 to 4 kHz. This frequency is commonly used in telephones, as well as in medium and long wave radio broadcasting.

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

Permissible noise levels in residential premises

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

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

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

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

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

Operating noise level

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

In offices

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

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

In animal husbandry and clerical activities

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

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

In production and transport

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

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

Limiting noise level

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

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

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

Critical noise level

Noise power at around 135 dB is considered unacceptable, a person who finds himself in the zone of sound of such a force gets a concussion. The noise level of 140 dB also leads to concussion, such a sound accompanying the launch of a jet plane. At a noise level of 145 dB, a fragmentation grenade explodes.

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

Impact on the body of inaudible sounds

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

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

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

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

Influence of noise from office equipment and methods of protection

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

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

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

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

The question of converting dB to dBm and vice versa is often heard from clients, met on specialized forums. However, as much as one would not like, it is impossible to convert power into attenuation.

If the power 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 optical power, 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) - 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 (Pin). 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, this 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 attenuation measurement optical line greatly simplified, which is 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

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

Convenient units, aren't they? But, as it turns out, they are not convenient for everyone! It can be said that most people who are poorly versed in physics, mathematics, and technology do not understand logarithmic units such as decibels. Some even believe that logarithmic values \u200b\u200bdo not refer to modern digital technology, but to the days when a slide rule was used for engineering calculations!

A bit of history

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

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

Definition

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

if equality is met

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

By the above definition

Classification of logarithmic units

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

Via absolute logarithmic units express physical quantities that are compared with a certain fixed value. For example, dBm (decibel milliwatts) is the absolute logarithmic unit of power, which compares power to 1 mW. Note that 0 dBm \u003d 1 mW. Absolute units are great for describing single valuerather than a ratio of two quantities. Absolute logarithmic units of measurement of physical quantities can always be converted into other, usual units of measurement of these quantities. For example, 20 dBm \u003d 100 mW or 40 dBV \u003d 100 V.

On the other hand, relative logarithmic units are used to express a physical quantity in the form of a ratio or proportion of other physical quantities, for example, in electronics, where a decibel (dB) is used for this. Logarithmic units are well suited for describing, for example, transmission ratio 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 just special names that are used in conjunction with dimensionless units. Note also that the decibel is often used with various suffixes, which are usually attached to the dB abbreviation with a hyphen, such as dB-Hz, a space as in dB SPL, without any symbol between dB and the suffix, as in dBm, or enclosed in quotation marks as in units of dB (m²). We will talk about all these units later in this article.

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

Amplitude and Power Logarithmic Units

Power... It is known that power is proportional to the square of the amplitude. For example, electric powerdefined by the expression P \u003d U² / R. That is, a 10-fold change in amplitude is accompanied by a 100-fold change in power. The ratio of two values \u200b\u200bof power in decibels is determined by the expression

10 log₁₀ (P₁ / P₂) dB

Amplitude... Due to the fact that the power is proportional to the square of the amplitude, the ratio of the two amplitude values \u200b\u200bin decibels is described by the expression

20 log₁₀ (P₁ / P₂) dB.

Examples of relative logarithmic values \u200b\u200band units

• Common units



• dB (decibel) - a logarithmic dimensionless unit used to express the ratio of two arbitrary values \u200b\u200bof the same physical quantity. For example, in electronics, decibels are used to describe signal gain in amplifiers or attenuation in cables. The decibel is numerically equal to the decimal logarithm of the ratio of two physical quantities, multiplied by ten for the power ratio and multiplied by 20 for the amplitude ratio.
• B (bel) is 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 \u200b\u200bof the same physical quantity. Unlike the decibel, neper is defined as the natural logarithm for expressing the difference between two quantities x₁ and x₂ by the formula:
  

  R \u003d ln (x₁ / x₂) \u003d ln (x₁) - ln (x₂)

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





s \u003d 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, the measured parameter is usually compared with the corresponding parameter. standard type antennas.




• Communication and data transmission



• dBc or dBc (carrier decibel, power ratio) is the dimensionless power of the radio signal (radiation level) in relation to the radiation level at the carrier frequency, expressed in decibels. Defined as S dBc \u003d 10 log₁₀ (P carrier / P modulation). If the dBc value is positive, then the power of the modulated signal is greater than the power of the unmodulated carrier. If the dBc value is negative, then the power of the modulated signal is less than the power of the unmodulated carrier.
• Electronic equipment for sound reproduction and sound recording




• Other units and quantities

Examples of absolute logarithmic units and decibel values \u200b\u200bwith suffixes and reference levels

• Power, signal level (absolute)

• Voltage (absolute)

• Electrical resistance (absolute)
• dBΩ, dBohm or dBΩ (decibel ohms, amplitude ratio) - absolute resistance in decibels relative to 1 ohm. This unit of measure is convenient when considering a large resistance range. For example, 0 dBΩ \u003d 1 Ω, 6 dBΩ \u003d 2 Ω, 10 dBΩ \u003d 3.16 Ω, 20 dBΩ \u003d 10 Ω, 40 dBΩ \u003d 100 Ω, 100 dBΩ \u003d 100,000 Ω, 160 dBΩ \u003d 100,000,000 Ω, and so on Further.
• Acoustics (absolute sound level, sound pressure or sound intensity)

• Radar... Log-scale absolute values \u200b\u200bare used to measure radar reflectivity compared to a reference value.



• dBZ or dB (Z) (amplitude ratio) - the absolute coefficient of radar reflectivity in decibels relative to the minimum cloud Z \u003d 1 mm⁶ m⁻³. 1 dBZ \u003d 10 log (z / 1 mm⁶ m³). This unit indicates the number of droplets per unit of volume and is used by meteorological radar stations (meteorological radars). The information obtained from measurements in combination with other data, in particular, the results of the analysis of polarization and Doppler shift, allows you to assess what is happening in the atmosphere: whether it is raining, snowing, hail, or a flock of insects or birds. For example, 30 dBZ corresponds to light rain and 40 dBZ to moderate rain.
• dBη (amplitude ratio) - the absolute factor of radar reflectivity of objects in decibels relative to 1 cm² / km³. This value is convenient if you want to measure the radar reflectivity of flying biological objects, such as birds and bats. Weather radars are often used to monitor such biological objects.
• dB (m²), dBsm or dB (m²) (decibel square meter, amplitude ratio) is an absolute unit of measurement of the effective scattering area of \u200b\u200ba target (RCS, English radar cross section, RCS) in relation to square meter... Insects and low-reflective targets have a negative effective scattering area, while large passenger aircraft have a positive one.
• Communication and data transmission. Absolute logarithmic units are used to measure various parameters related to the frequency, amplitude, and power of transmitted and received signals. All absolute values \u200b\u200bin decibels can be converted to common 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, which represents a magnitude of 0. Each step of the Richter scale corresponds to an increase in vibration amplitude by 10 times.
• dBr (decibel relative to the reference level, the ratio in amplitude or in power, is specified explicitly) - a logarithmic absolute unit of measurement of any physical quantity specified in a context.
• dBSVL - vibrational velocity of particles in decibels relative to the reference level 5 ∙ 10⁻⁸ m / s. The name comes from the English. sound velocity level - sound speed level. The vibrational velocity of the particles of the medium is otherwise called the acoustic velocity and determines the speed with which the particles of the medium move when they oscillate about the equilibrium position. The reference value 5 ∙ 10⁻⁸ m / s corresponds to the vibrational particle velocity for sound in air.

The network is full of such calculators, but I also wanted to make my own. I'm sure I won't surprise anyone by saying that it also works here JavaScript, and all the computational load falls on your browser. If there are empty fields, it means that your browser does not work with JavaScript-th, and calculations won't work :(

19 Dec 2017 the EMC unit was introduced. Perhaps he is more in line with your needs?

Terms of use simple to the point of disgrace. Change the value of any of the values, and all other values \u200b\u200bwill be recalculated automatically.

Conversion of the ratios of the incident and reflected power into the VSWR value:

Just in case, a hint for use:
Recalculate dBμV in dBm (dBμV in dBm) In the "Voltage, dBμV" field, enter the voltage value in decibel-microvolts. If your value is in decibel-millivolts (dBmV, dBmV), just add 60 dB to it (0 dBmV ≡ 60 dBμV). Do not forget that in order to convert voltage into power, you also need to know the load resistance! Recalculate dBm in dBμV (dBm in dBμV) In the "Power, dBm" field, enter the power value in decibel-milliwatts. If your value is in decibel-watts, just subtract 30 dB from it (0 dBW ≡ 30 dBm). Do not forget that in order to convert power into voltage, you also need to know the load resistance! Recalculate decibels at times Enter the level change in decibels in the table, and the calculator will show how many times the voltage and power will change. The calculator does not like negative numbers and replaces them with positive ones. Convert times to decibels Enter in the table the change in the voltage level or signal power in the appropriate field, and you will find out how many decibels it is. At the same time, the change in the second value will be recalculated. The calculator does not like negative numbers and replaces them with positive ones. Indeed, an increase of 0.5 times is a 2-fold decrease, and there is no physical difference. But it's clearer! Recalculate the power ratio in SWR Enter your values \u200b\u200bof the incident and reflected powers in the corresponding fields. If instead of values \u200b\u200byou have a difference, immediately write this difference in the field for difference and ignore the two upper fields Convert SWR to the power ratio Enter the SWR value in the corresponding field and the calculator will calculate the power ratio, and for the specified value P FWD enter the corresponding P value REF

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

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

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

But as soon as an inscription is encountered, for example: the voltage has increased by 3 dB or the signal power is 10 dBm (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 novice 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.

The unit of measure named Bel Bell's telephone lab engineers were first used. A decibel is a tenth of a Bel (1 decibel \u003d 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 the decibel is not part of the official SI system of units. But, despite this, the decibel gained recognition and took a firm 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 countdown threshold, relative to which there was a change in 10 or 2 times. With the help of decibels, these "times" are also measured, only in logarithmic scale.

For example, a 1 dB change corresponds to a 1.26-fold change in energy value. A change of 3 dB corresponds to a 2-fold change in the energy value.

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

There are still reasons for using 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, loudness, weight) are felt by us, provided that these changes are of a logarithmic nature.

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

For example, the sensitivity of the human ear decreases with increasing volume. 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 taking with an exponential dependence of 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 grow smoothly. The volume control will be linear, since the exponential relationship of the volume control will compensate for the logarithmic dependence of our hearing and will become linear in total. This will become clearer by looking at the drawing.

The 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 the graphs of the dependence of the resistance of variable resistors different types: A - linear, B - logarithmic, C - exponential. As a rule, on variable resistors of domestic production, it is indicated what dependence the variable resistor has. Digital and electronic volume controls are based on the same principles.

It is also worth noting that the human ear perceives sounds, the power of which differs by a colossal amount of 10,000,000,000,000 times! Thus, the most loud noise differs from the quietest that our hearing can pick up by 130 dB (10,000,000,000,000 times).

The second reason for the widespread use of decibels is the ease of calculation.

Agree that it is much easier when calculating to use small numbers like 10, 20, 60,80,100,130 (the most commonly used numbers when calculating in 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 simply add up. If you carry out calculations at times, then the numbers must be multiplied.

For example, 30 dB + 30 dB \u003d 60 dB (at times: 1000 * 1000 \u003d 1000 000). I think this is clear.

Also decibels are very handy for plotting various dependencies graphically. All graphs such as antenna radiation patterns, amplitude-frequency characteristics of amplifiers are performed using decibels.

Decibel is dimensionless unit... We have already found out that the decibel actually shows how many times a value (current, voltage, power) has increased or decreased. The difference between decibels and times is only that the measurement takes place on a logarithmic scale. To somehow denote this and assign the designation dB ... One way or another, when evaluating, you have to go from decibels to times. Any unit of measurement (not only current, voltage, etc.) can be compared with the help of decibels, since the decibel is a relative, dimensionless quantity.

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

Going from decibels to times.

In practice, most often you have to go 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 \u003d 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) \u003d 1.258925… \u003d 1.26 times.

Similarly,

at 20dB: 10 (20dB / 10) \u003d 100 (increase in value 100 times)

at 10dB: 10 (10dB / 10) \u003d 10 (10x magnification)

But, not everything is so simple. There are also pitfalls. For example, signal attenuation is -10 dB. Then:

at -10dB: 10 (-10dB / 10) \u003d 0.1

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

at -20dB: 10 (-20dB / 10) \u003d 0.01

Here it is similar. With a decrease in power from 5 W to 0.05 W, in decibels, the power drop will be -20 dB (a decrease of 100 times).

Thus, at -10 dB, the signal power decreased 10 times! Moreover, if we multiply the initial value of the signal by 0.1, then we will get the value of the signal power with attenuation of -10 dB. That is why the value of 0.1 is indicated without "times", as in the previous examples. Consider this feature when substituting decibel values \u200b\u200bwith a "-" sign in the formula data.

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

n \u003d 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 would correspond to a value of 6.021 dB.

10 * log 10 (4) \u003d 6.021 dB.

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

(Amperage and voltage are so-called "power" quantities. Therefore, the formulas are different.)

To convert to decibels: n \u003d 20 * log 10 (m)

To go from decibels to times: m \u003d 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!