What are decibels. Encyclopedia of radio electronics and electrical engineering

Encyclopedia of radio electronics and electrical engineering / Beginner radio amateur

 Comments on the article

The decibel is a tenth of the Bel, a logarithmic unit named after the inventor of the telephone, Alexander Graham Bell (1847-1922). One Bel corresponds to a tenfold increase in signal power: 10 dB = 1 B = Ig10. Tenfold power attenuation corresponds to -10 dB = -1 B = Ig0,1. However, voltage or current with a tenfold change in power changes only 3,16 times (power is proportional to the square of voltage or current). Thus, the gain G or attenuation a, expressed in decibels, is:

G, α(dB) = 10lg(P2/P1) = 20lg(U2/U1).

Let's warn against common mistakes: there are no "voltage decibels" and "power decibels" - an amplifier with G \u20d 100 dB amplifies the signal power by 10 times, and the voltage (if the input and output impedances are equal) - by 10 times. The clause in brackets is essential - after all, alternating voltages and currents can be transformed, while leaving the power unchanged. It would never occur to anyone to say that a transformer that steps up the voltage by 20 times has a gain of 0 dB. Its gain is G = 0,1 dB, or even α = - 1...XNUMX dB, if we take into account insignificant losses. So, to use the formula

G = 20log(U2/U1),

you must first bring the input voltage U1 and output voltage U2 to the same resistances, while the formula G or α = 10lg(P2/P1) is used without restrictions.

It turned out that in decibels it is extremely convenient to measure the sound volume, signal power and voltage, amplification and attenuation (attenuation) of any circuits, long lines and filters. It was telegraph operators and telephonists who were the first to widely use decibels - to assess the attenuation and signal levels in the lines. The main advantage turned out to be that in calculations, multiplication and division are replaced by addition and subtraction, which are easy to do even in the mind, and on graphs built on a logarithmic scale, many curves become straight.

To read any value in decibels, you need an initial (zero) level. When calculating the gain and attenuation, the value of the considered value at the input of the device (P1, U1) serves as the initial level. If we are dealing with certain, specific quantities that have a dimension (the logarithm can only be taken from a dimensionless number), then the initial level must be set.

The zero volume level corresponds to the average threshold sensitivity of human hearing, at which the sound intensity (acoustic energy flux density) is 10-12 W/m2, and the sound pressure is 2·10-5 Pa. These are extremely small quantities. So, for example, the speed of oscillating air particles at such a sound strength is only 5 10-8 m / s, and the displacement of these particles from the equilibrium position (at a sound frequency of 1000 Hz) is only 2 10-11 m, which is comparable to the size molecules! This is the perfect organ of hearing that nature has created.

Let's say your loudspeaker develops a standard sound pressure of 0,2 Pa (at a distance of 1 m with an input electrical power of 0,1 W), which corresponds to a sound power (determined from the reference book) of 10 "4 W / m2. Let's find the volume in decibels:

10lg(10-4/10-12) = 80 dB, which is approximately the same as the volume of an orchestra. You can do without a reference book, using sound pressure data, given that sound power and loudness are proportional to the square of sound pressure (just like power is proportional to the square of voltage): loudness \u20d 0,2lg (2 / 10 5-80) \u1d XNUMX db. Table XNUMX is given for orientation. XNUMX relating loudness, sound intensity and sound pressure.

(click to enlarge)

It should be noted that the loudness scale in decibels has a powerful physical, even better, physiological justification. The fact is that the characteristic of the subjective perception of loudness is non-linear - it obeys a logarithmic law (as well as the characteristics of other sense organs). This means that in order to cause a noticeable increase in volume at low levels, you need to add very little power, and at high levels, quite a lot. However, as a percentage of the initial level, the increase will be the same value, for example, 26%. In decibels, this would be 10lg(1.26/1) = 1 dB. This is the "secret" of logarithmic scales - an increase in the argument by some causes a change in the function by some times.

The strength of the sound in the table. 1 can also be expressed in decibels, and for a frequency of 1000 Hz the values ​​will match the loudness values. At other frequencies in the audio range, the sensitivity of human hearing is somewhat different, and with equal sound strength, the subjectively perceived loudness is usually less. The dependence between the sound intensity and loudness for different frequencies (numbers near the curves) is shown in Fig. 36.

Inverse logarithmic, exponential dependence occurs in nature much more often than linear. The air pressure in the atmosphere decreases by a factor of e (e = 2,72 is the base of natural logarithms) for every next 8 km, the number of radioactive atoms and their mass are halved after a time equal to the half-life, etc. All similar dependences on graphs built on a logarithmic scale are displayed as straight lines.

Power is often measured relative to the 1mW level. This "zero" is taken as the standard telephone level, corresponding to a voltage of 0,775 V into a 600 ohm load. It is also extremely often used in microwave technology. To indicate this zero level, use (instead of dB) the notation dBm:

P(dBm) = 101d(P/1mW).

A power of 1 mW corresponds to 0 dBm, 1 W - +30 dBm, 0,1 mW - -10 dBm. Similarly, field strengths are often referenced at 1 µV/m, for example a field strength of 46 dBµV corresponds to 200 µV/m.

To facilitate the conversion of values ​​​​to decibels and vice versa, table is useful. 2. Only units of decibels are given in it, with tens the situation is much simpler. Every 10 dB gives an increase in power by a factor of 10 and voltage by a factor of 3,16. Let it be required to find out how many times the power and voltage of the signal at the output of the filter with an attenuation of 48 dB decrease. Note that 48 = 40 + 8, 40 dB gives an attenuation of 10000 times, and 8 dB another 6,3 times. Consequently, the filter output power is reduced by a factor of 63. The decrease in voltage can be found by taking the square root of this number. It turns out 000 - because the power is proportional to the square of the voltage. But we will continue the calculation in decibels. 250 dB gives 40 times and 100 dB - 8 times. Again it turns out 2,5 times.

Another example. The amplifier has a gain of 17 dB, the input and output impedances are equal, how many times is the voltage amplified? There is no 17 dB in the table, but 17 = 20 - 3.

A gain of 20 dB corresponds to a voltage increase of 10 times, and -3 dB means an attenuation of 1,4 times. Total: 10/1,4=7. Let's find the answer differently: 17 = 8 + 9; 8 dB corresponds to a voltage increase of 2,5 times, and 9 dB to 2,8 times. Let's multiply these numbers in our mind and get 2,5 2,8 = 7.

In conclusion, here is a useful graph related to the material presented in the section "This complicated Ohm's law"(Radio, 2002, No. 9, pp. 52, 53). There we considered the simplest circuit consisting of a generator with internal resistance r and a load with resistance R. It was shown that the maximum power is transferred to the load when the resistances are equal r = R. And what will happen if they are not equal?The power delivered to the load will turn out to be less, but by how much?In Fig. 37 the answer is given in decibels depending on the mismatch coefficient k = r/R.

(click to enlarge)

Question for self-test. Get the formula for the dependence of the power delivered to the load depending on the mismatch coefficient k, and then build a graph similar to Fig. 37. Think about what information on this graph is redundant and what needs to be done to simplify it?

Response. For a simple circuit containing a source with EMF E and internal resistance r and a load with resistance R (Fig. 4), the current is l \uXNUMXd E / (r + R).

This is true for both direct and alternating current. The voltage at the load will be U = ER / (r + R).

Find the power in the load P = U l = E²R/(r+R)².

When the load and source resistances are equal (R = r), this power is maximum and is P₀ = E²/4r.

Find the P/P Mismatch Loss₀ = 4rR/(r + R)².

If we divide both the numerator and denominator of the right side of the formula by R² and take into account that r/R = k (mismatch coefficient), then we get P/P₀ = 4k/(1+k)².

This is the formula by which the graph in Fig. 37. Of course, the formula gives the ratio P/P₀ "in times", and on the graph it is already translated into decibels. Let us explain with an example: for k = 2, the power ratio will be Р/Р₀ = 8/9. With the help of a slide rule (which the author still uses with great success despite the presence of several calculators and a computer), in a fraction of a second we find the loss due to a mismatch - 0,5 dB.

It is curious to note that the substitution k = 0,5 gives exactly the same loss value. This means that a halving of the load (both in the direction of its decrease and increase) gives the same decrease in power in the load. This is indeed the case, and the formula we have derived will remain the same when substituting k'= 1/k. Keep in mind that another definition of the mismatch coefficient is often found in the literature: k'= R/r, but the results of the loss calculation are the same.

Thus, the graph in Fig. 37, built on a logarithmic scale, is symmetrical with respect to the point k = 1. It was quite possible to get by with one half of it, taking values ​​of k either less than or greater than unity and indicating "k or 1/k" on the abscissa. This is the redundancy of the graph.

As you can see, even with a fairly significant mismatch (the load resistance differs from the internal resistance of the source by a factor of two), the losses due to the mismatch are very small. If, for example, we are dealing with an audio frequency amplifier, then a change in volume by 0,5 dB is practically not audible. In the area of ​​large mismatches (to " 1 or to " 1), the power loss due to the mismatch is already significant.

Author: V.Polyakov, Moscow

See other articles Section Beginner radio amateur.

Read and write useful comments on this article.

<< Back

Latest news of science and technology, new electronics:

Traffic noise delays the growth of chicks 06.05.2024

The sounds that surround us in modern cities are becoming increasingly piercing. However, few people think about how this noise affects the animal world, especially such delicate creatures as chicks that have not yet hatched from their eggs. Recent research is shedding light on this issue, indicating serious consequences for their development and survival. Scientists have found that exposure of zebra diamondback chicks to traffic noise can cause serious disruption to their development. Experiments have shown that noise pollution can significantly delay their hatching, and those chicks that do emerge face a number of health-promoting problems. The researchers also found that the negative effects of noise pollution extend into the adult birds. Reduced chances of reproduction and decreased fertility indicate the long-term effects that traffic noise has on wildlife. The study results highlight the need ... >>

Wireless speaker Samsung Music Frame HW-LS60D 06.05.2024

In the world of modern audio technology, manufacturers strive not only for impeccable sound quality, but also for combining functionality with aesthetics. One of the latest innovative steps in this direction is the new Samsung Music Frame HW-LS60D wireless speaker system, presented at the 2024 World of Samsung event. The Samsung HW-LS60D is more than just a speaker system, it's the art of frame-style sound. The combination of a 6-speaker system with Dolby Atmos support and a stylish photo frame design makes this product the perfect addition to any interior. The new Samsung Music Frame features advanced technologies including Adaptive Audio that delivers clear dialogue at any volume level, and automatic room optimization for rich audio reproduction. With support for Spotify, Tidal Hi-Fi and Bluetooth 5.2 connections, as well as smart assistant integration, this speaker is ready to satisfy your ... >>

A New Way to Control and Manipulate Optical Signals 05.05.2024

The modern world of science and technology is developing rapidly, and every day new methods and technologies appear that open up new prospects for us in various fields. One such innovation is the development by German scientists of a new way to control optical signals, which could lead to significant progress in the field of photonics. Recent research has allowed German scientists to create a tunable waveplate inside a fused silica waveguide. This method, based on the use of a liquid crystal layer, allows one to effectively change the polarization of light passing through a waveguide. This technological breakthrough opens up new prospects for the development of compact and efficient photonic devices capable of processing large volumes of data. The electro-optical control of polarization provided by the new method could provide the basis for a new class of integrated photonic devices. This opens up great opportunities for ... >>

Random news from the Archive Silicon formats proteins 22.02.2007 Swedish scientists have found that silicon particles are able to shape protein molecules. It is generally believed that particles of inorganic substances such as silicon oxide contribute to the fact that biological molecules lose their shape. "We decided to change this prejudice and prove that such particles, on the contrary, contribute to the structuring of organic substances," says Professor Bengt Harald Jonsson from the Linköping University (Sweden). To do this, scientists under his leadership synthesized short peptide chains with a specific distribution of positive charges. In the free state, these chains did not take any definite form. Then they were mixed with a solution of negatively charged spherical particles of silicon oxide with a diameter of 9 nm. Having come into contact with the particle, the peptide coiled into a spiral, and the complex of the particle and the peptide had enzymatic activity. According to the authors of the work, the phenomenon they discovered has two aspects: applied and fundamental. The first is related to the fact that this method can be useful for the recognition of organic molecules, controlled catalysis of chemical reactions, and the search for targets for medical drugs. And the second allows you to think about the origin of life. "Our study shows that peptides with amino acids were very likely to form complex structures as a result of interaction with clay particles," says the scientist.

Other interesting news:

▪ CD as a dosimeter

▪ Camera with microlenses mimics eagle vision

▪ Canon EOS M10 Mirrorless Camera

▪ Germany refuses cars with internal combustion engines

▪ Supermicro A1SA7-2750F motherboard has 17 SATA ports

News feed of science and technology, new electronics

Interesting materials of the Free Technical Library:

▪ section of the site Stories from the life of radio amateurs. Selection of articles

▪ article Poet, do not cherish the love of the people. Popular expression

▪ article Who Invented the Parachute? Detailed answer

▪ article Motorcycle fuel gauge. Personal transport

▪ article Simple LC oscillator. Encyclopedia of radio electronics and electrical engineering

▪ Article Wonderful thread. Chemical experience

Leave your comment on this article:

All languages ​​of this page

Arabic	Hebrew	Polish
Bengali	Hindi	Portuguese
Chinese	Italian	Spanish
English	Japanese	Turkish
French	Korean	Ukrainian
German	Malay	Vietnamese

Home page | Library | Articles | Website map | Site Reviews

www.diagram.com.ua
2000-2024