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 ratios 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 short form by its mantissa and exponent. 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 belong to modern digital technology, but to the times when slide rules were 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 the practical use of logarithms were logarithm tables. 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 indicator of the power to which a number, called the base, must be raised to obtain the 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 a physical quantity in the form of a ratio or proportion of other physical quantities, for example in electronics, where the decibel (dB) is used. Logarithmic units are well suited to describe, for example, the gain of electronic systems, that is, the relationship between 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, electrical power given by 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 determined 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 of a standard antenna type.




• 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 and 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 effective scattering area of ​​a target (EPR, English radar cross section, RCS) in relation to a 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 the 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.

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

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

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

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

Get to the point

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

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

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

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

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

Peculiarities

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

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

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

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

Why did everything have to be complicated?

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

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

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

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

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

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

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

19 Dec 2017 an EMC unit converter has appeared. Perhaps it better suits your needs?

Terms of use simple as hell. Change the value of any of the values, and all other values ​​will be recalculated automatically.

Converting the ratio of incident and reflected power to SWR:

Just in case, a hint for use:
Recalculate dBµV V dBm(dBμV to dBm) In the “Voltage, dBμV” field, enter the voltage value in decibel-microvolts. If you have a value in decibel-millivolts (dBmV), just add 60 dB to it (0 dBmV ≡ 60 dBmV). Don't forget that to convert voltage into power, you also need to know the load resistance! Recalculate dBm V dBµV(dBm in dBμV) In the “Power, dBm” field, enter the power value in decibel-milliwatts. If you have a value in decibel-watts, just subtract 30 dB from it (0 dBW ≡ 30 dBm). Don't forget that to convert power into voltage, you also need to know the load resistance! Convert decibels by times Enter in the table the change in level in decibels, 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 In the table, enter the change in 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 quantity will be recalculated. The calculator does not like negative numbers and replaces them with positive ones. In fact, an increase of 0.5 times is a decrease of 2 times, and physically there is no difference. But it’s clearer this way! Convert the power ratio to SWR. Enter your values ​​of incident and reflected power in the appropriate fields. If instead of values ​​you have their difference, immediately enter this difference in the field for the difference and ignore the two upper fields Convert SWR to power ratio Enter the SWR value in the appropriate field, and the calculator will calculate the power ratio, and for the specified value P FWD will enter the corresponding value P REF

Quite often in popular radio engineering literature, in the description of electronic circuits, a unit of measurement is used - 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 (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. There is an initial reference level, 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, 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 the decibel is not part of the official SI system of 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 of the 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 of different types: A – linear, B – logarithmic, C – exponential. As a rule, on domestically produced variable resistors 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 varies by a whopping 10,000,000,000,000 times! Thus, the loudest sound differs from the quietest sound that our ears can detect 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 to use small numbers like 10, 20, 60,80,100,130 (the most commonly used numbers when calculating in decibels) in calculations 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.

Decibels are also very convenient for graphically plotting 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 -20dB: 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 electrical signal power. Sometimes dynamic range (for example, the sound of musical instruments) is also measured in decibels. The decibel is also a unit of sound pressure.

Power measurement

As mentioned above, whites were originally used to assess the ratio capacities, therefore, in the canonical, usual sense, a value expressed in bels means the logarithmic ratio of two capacities 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 a linear chain the following equality holds:

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 inverse ratios. 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, different signal levels (or rather, level differences) may correspond. 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 a volt) or “dBμV” (decibel relative to a microvolt), “dBW” (decibel relative to a watt), etc. In accordance with the international standard IEC 27-3, if it is necessary to indicate the original value, its value is placed in in brackets after the designation of a logarithmic value, for example for 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 theory of automatic regulation and control(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 of relative units is carried out 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).