DB transcript. Converting values ​​from decibels to absolute values ​​and power

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, this 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

People really like certain sounds, such as music. It lifts your spirits and sometimes even induces a feeling of bliss. Santa Claus Parade in Toronto (Canada), 2010.

General information

Sound level determines its loudness and is used in acoustics - the science that studies the level and other properties of sound. When people talk about volume, they often mean sound level. Some sounds are very unpleasant and can cause a range of psychological and physiological problems, while other sounds, such as music, the sound of surf and birdsong, are calming, appealing to people and improve their mood.

Table of values ​​in decibels and ratios of amplitudes and powers

This table shows how the logarithmic scale allows you to describe very large and very small numbers representing ratios of powers, energies or amplitudes.

The human ear is very sensitive and can hear sounds from a whisper at a distance of 10 meters to the noise of jet engines. The sound power of a firecracker can be 100,000,000,000,000 times greater than the weakest sound that the human ear can hear (20 micropascals). This is a very big difference! Because the human ear can detect such a wide range of sound volumes, a logarithmic scale is used to measure sound intensity. On the decibel scale, the weakest sound, called the hearing threshold, is at 0 decibel level. A sound that is 10 times louder than the threshold of audibility has a level of 20 decibels. If a sound is 30 times louder than the threshold of audibility, its level will be 30 decibels. Below are examples of the volume of different sounds:

• Hearing threshold - 0 dB
• Whisper - 20 dB
• Quiet conversation at a distance of 1 m - 50 dB
• Powerful vacuum cleaner at a distance of 1 m - 80 dB
• Sound that may cause hearing impairment with prolonged exposure - 85 dB
• Portable media player at full volume - 100 dB
• Pain threshold - 130 dB
• Fighter turbojet engine at a distance of 30 m - 150 dB
• Flash and sound M84 hand grenade at a distance of 1.5 m - 170 dB

Music

Music, according to archaeologists, has been decorating our lives for at least 50,000 years. It surrounds us everywhere - music is present in all cultures, and, according to scientists, it unites us with other people - in society, in the family, in an interest group. Mothers sing lullabies to their babies; people go to concerts; dances, both folk and modern, take place to the music. Music attracts us with its regularity and rhythm, as we often look for order and clarity in everyday life.

Noise pollution

Unlike music, some sounds make us feel very unpleasant. Noise caused by human activities that disturbs people or harms animals is called noise pollution. It causes a number of psychological and physiological problems in humans and animals, such as insomnia, fatigue, blood pressure disorders, hearing loss due to loud noise, and other problems.

Sources of noise

Noise can be caused by many factors. Transport is one of the main noise pollutants of the environment. Airplanes, trains and cars make a lot of noise. Equipment at various plants in the industrial area is also a source of noise. People living near wind turbines often complain about noise and related illnesses. Repair work, especially those involving the use of jackhammers, tends to produce a lot of noise. In some countries, people keep dogs, often for safety reasons. These dogs, most often those that live in the yard, bark if other dogs and strangers are nearby. This is not so noticeable during the day when there is already a lot of noise around, but it is very clearly audible at night. Noise in residential areas is also often caused by loud music in homes, bars and restaurants.

]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 about the negative effects on hearing is also provided for each noise level.

Measuring sound levels using instruments

Use your computer. With 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 higher quality recording equipment will always produce better results; In other words, your laptop's built-in microphone may be sufficient for some tasks, but a high-quality external microphone will provide more accurate results.

1. Use the mobile app. To measure sound levels anywhere, mobile applications will come in handy. The microphone on your mobile device probably won't produce the same quality as an external microphone connected to your computer, but it can be surprisingly accurate. For example, the reading accuracy on a 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

2. Use a professional decibel meter. This is usually not cheap, but it may be the easiest way to get accurate measurements of the sound level you are interested in. Also called a “sound level meter”, this is a specialized device (can be bought in an online store or specialized stores) that uses a sensitive microphone to measure the noise level around and gives an exact value in decibels. Since such devices are not 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 seen as a convenient way of expressing 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 small. 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 background noise level 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 still picked up by our high-end recording equipment, so we probably need to eliminate the source of the noise to achieve a higher quality recording.

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 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.