1. The birth background of dB
dB is the abbreviation of "decibel" in English, where deci means one-tenth and Bel means "Bei". Decibel, decibel is one tenth of a bel. "Bei" is the abbreviation of "Bell" and is a unit named after the outstanding scientist Alexander Graham Bell. Bell obtained a patent for the invention of the telephone in 1876 and made a huge breakthrough in the application and development of the telephone. Bel is not a unit of the International System of Units (System International), but due to the rules of the International System of Units, the first letter of the unit symbol represented by a person's name must be capitalized, so we see that the B in dB should be capitalized. Since the unit "Bel" is relatively large and inconvenient to use, the more commonly used unit is one-tenth of a Bel, which is decibel.
dB is often used to characterize the sound pressure level SPL (Sound Pressure Level). The unit of sound pressure is Pascal, Pa. The reference value of sound pressure is 20μPa. This value represents the average audible threshold of the human ear at 1000Hz, or the average minimum sound pressure fluctuation value that can be perceived by the human ear at 1000Hz. Sound is the sound pressure fluctuation superimposed on the atmospheric pressure, which is 1.01325×10^5Pa. Compared with atmospheric pressure, the amplitude fluctuation of sound pressure is very small. The audible sound pressure amplitude fluctuation range of the human ear is 2×10^-5Pa~20Pa. This sound pressure amplitude fluctuation range is very large, and the ratio between the two reaches 10^6. It seems that from a linear perspective, this fluctuation range of sound pressure amplitude is very inconvenient. If there are too many digits, it will give you a headache to read. You have to count the digits carefully. This is the case for me anyway. I don’t know if it is the same for you! Is there any lazy method that can easily reflect the amplitude of this fluctuation? Master Bell has long been thinking: Is there a good way to solve this problem? Therefore, the concept of sound pressure level expressed in dB was introduced. He found that the response of our human ears to sound intensity is in logarithmic form, which roughly means that when the intensity of sound increases to a certain level, human hearing will become less sensitive, which approximates the logarithmic unit scale. This allowed the logarithmic unit to be used to represent the proportion of changes in human hearing, and thus the sound pressure level expressed in logarithmic dB form was born. The audible sound pressure amplitude fluctuation range of the human ear is 2×10^-5Pa~20Pa, and the corresponding decibel number expressed in amplitude dB is 0~120dB. Therefore, when the sound pressure level is expressed in decibels, it is characterized More convenient. In the real world, the decibel levels of sound in various common situations are as shown in the figure below.
Use a graph to represent the sound pressure amplitude and decibels, as shown in the following table:
2. Definition of dB
The first point to understand dB is to know that it represents the relative relationship between two physical quantities with the same unit. That is, the ratio of two electrical or sound powers, or the ratio of two voltage or current values or similar sound quantities. It is also a unit that measures the relative loudness of sounds. Originally in the field of telephone engineering, dB was defined to represent the ratio of two powers. It is the ratio of P1/P0 and then takes the logarithm of base 10 and multiplies it by 10. The mathematical formula is:
dB is a ratio, a numerical value, a pure counting method without any unit label. Since it has different names in different fields, it also represents different practical meanings. Common fields include: sound, signal, gain, etc.
3. Application of dB
1. The volume of the sound
In daily life, notice boards in residential areas indicate that the noise should be less than 60 decibels, that is, less than 60 dB. Here dB (decibel) is defined as the logarithm of the ratio of the noise source power to the reference sound power multiplied by 10. It is not a unit, but a numerical value used to describe the size of the sound.
2. Signal strength
In the field of wireless communications, measuring the communication signal strength of a certain wireless base station in a location can also be expressed in dB. For example, the measured communication signal strength of No. 1 wireless base station in Room 402 of a hotel is -90dBm. It is defined here as the ratio of the useful signal strength of the room to all signals (including interference signals).
3. Gain
In terms of antenna technology, dB is a parameter that measures antenna performance, and its name is gain. It refers to the ratio of the power density of the signal generated by the actual antenna and the ideal antenna at the same point in space under the condition that the input power is equal.
dB is a pure counting unit and is defined in different ways in engineering (it just looks different). For power, dB=10*log(). For voltage or current, dB=20*log().
The meaning of dB could not be simpler. It is to express a large number (followed by a long string of 0s) or a small number (followed by a long string of 0s) relatively briefly. For example (take power as an example here):
X=100000=10*log(10^5)=50dB
X=0.000000000000001=10*log(10^-15)=-150dB
dBm defines miliwatt. 0dBm=10log(1)mW=1mW.
dBw defines watt. 0dBw=10log1W=10*log(1000)mw=30dBm.
dB always defines the power unit by default, calculated as 10*log. Of course, in some cases, signal strength (Amplitude) can be used to describe work and power. In this case, 20log is used as the calculation. This is true whether it is in the field of control or signal processing. For example, sometimes you can see the expression of dBmV.
In the calculation of dB, dBm and dBw, pay attention to the basic concepts. For example, as mentioned earlier, 0dBw=10log1W=10log1000mw=30dBm; for another example, when one dBm is subtracted from another dBm, the result is dB. For example: 30dBm-0dBm=30dB.
Generally speaking, in engineering, there are only additions and subtractions between dB and dB, but no multiplication or division. The most commonly used method is subtraction: dBm minus dBm is actually the division of two powers. The division of signal power and noise power is the signal-to-noise ratio (SNR). dBm plus dBm is actually the multiplication of two powers, which is rare (I only know of such applications in power spectrum convolution calculations).
Simply put, decibels are the unit of amplifier gain. The ratio of the amplifier output to the input is the amplification factor, and the unit is "times", such as a 10x amplifier and a 100x amplifier. When "decibels" is used as the unit, the amplification factor is called gain, which are two names for the same concept. The conversion relationship between decibels and amplification in electricity is: AV(I)(dB)=20lg[Vo/Vi(Io/Ii)]; Ap(dB)=10lg(Po/Pi) voltage (current) gain when decibel is defined It is different from the formula of power gain, but we all know that the relationship between power, voltage and current is P=V2/R=I2R. After using this set of formulas, the gain values of the two are the same: 10lg[Po/Pi]=10lg(V2o/R)/(V2i/R)=20lg(Vo/Vi). The main reasons for using decibel as a unit are: the numerical value becomes smaller and it is easier to read and write. The total amplification factor of an electronic system is often thousands, tens of thousands or even hundreds of thousands. A radio needs to amplify a total of about 20,000 times from the signal received by the antenna to the speaker output. Expressed in decibels, take the logarithm first, and the value will be much smaller. The attached table shows the corresponding relationship between amplification factor and gain; it is easy to calculate. When amplifiers are cascaded, the total amplification factor is the multiplication of each stage. When using decibels as the unit, the total gain is the sum. If the front stage of a power amplifier is 100 times (20dB) and the rear stage is 20 times (13dB), then the total power amplification factor is 100×20=2000 times, and the total gain is 20dB+13dB=33dB.
4. dBA
dBA refers to the A-weighting of sound. Usually the result of A weighting is expressed in the unit dBA or dB(A).
The sound that can be heard by the human ear has a certain frequency range (20-20KHz) and a certain sound pressure level range (0-130dB), as shown in the figure below.
The human ear is not equally sensitive to all frequencies. The most sensitive frequency band of normal human ears is 3000Hz-6000Hz, and its frequency response will change with the change of sound volume. Generally, the sound perception ability of low-frequency and high-frequency bands is not as good as that of mid-frequency bands. The effect is more obvious at low sound pressure levels and will be flattened at high sound pressure levels. As shown in the curves (equal loudness curves) in the figure, the sound The smaller the pressure level, the steeper the curve, and the larger the sound pressure level, the flatter the curve.
It is precisely because the human ear has different sensitivities to different frequencies that even if the sound pressure level is the same, it will sound different. Therefore, the actually heard sound pressure level needs to be corrected by the gain factor, and the most commonly used is A weighting, and of course B, C, and D weighting. A-weighting corresponds to the 40-cubic equal-noise curve, which is the curve represented by the red line in the figure above. The B and C weightings correspond to the equal loudness curves of 70 and 100 square meters. The four weighting curves are shown in the figure below.
Using different weighting methods for the same signal will result in different sound pressure levels. As shown in the figure below, when calculating the 1/3 octave curve of a random signal without weighting and A-weighting, it can be seen that the difference between the two is obvious. Therefore, when the weighting is different, the results are also different.
In addition to dBA and other three weightings, there are dBm, dBW, dBu, dBv, dBi, dBd, dBc, etc. in other fields, but dBA is the most commonly used in the NVH field.
5. dB superposition
Can dB be added arbitrarily? How to add them up? For example, is 70dB+60dB equal to 130dB? If it were that simple, the world would be quiet, there wouldn't be so many debates, and no one would say NVH is "metaphysics."
This is explained using the superposition of sound pressure levels. SPLresult=SPL1+SPL2+SPL3+…+SPLn? The synthesis operation of sound pressure levels is not a simple addition and subtraction operation. Sound pressure levels cannot be added directly and must be calculated in the form of energy. Therefore, the synthetic formula for sound pressure level is as follows
If the two sound pressure levels SPL1=SPL2=60dB, but the two sound sources are related and in phase, then the synthesized sound pressure level SPL is 66dB, because 60dB corresponds to 0.02Pa, and the sum of the two is 0.04Pa, corresponding to 66dB. Is reality so beautiful? There are rarely two sound sources that are related and in phase, so this is a waste of time. Are you going to chop my heart out? If any two sound pressure levels SPL1=SPL2, then the synthesized sound pressure level is
That is to say, if the two sound pressure levels are the same, the combined sound pressure level will be 3dB greater than before. It can also be represented by the following figure. The horizontal axis represents the difference between the two sound pressure levels, and the vertical axis represents how many dB should be increased on the original basis. When the difference between the two is 0dB, the synthesis is 3dB larger; when the difference between the two sound pressure levels is more than 15dB, the impact of the sound pressure level with a small value can be ignored. The synthesized sound pressure level can also be obtained by querying the figure below.
Back to the question mentioned at the beginning of this section: What is 70dB+60dB? We can calculate according to the first formula in this section or compare it with the picture above to get the result to be 70.4dB. Remember, it is not 130dB.
After talking about the synthesis of sound pressure level, let’s talk about the decomposition of sound pressure level. The decomposition of sound pressure level is usually used to correct the influence of background noise. For example, the noise measurement value Lmeasured corrects the influence of background noise LBGN. It is not simply Lsource=Lmeasured-LBGN, but
The correction principles for background noise in international standards are shown in the figure below. When the difference between the sound pressure level of the background noise and the sound source is less than 6dB, the measurement is invalid; when the difference between the two is between 6 and 15dB, it needs to be corrected. The correction should be made according to the above formula; when the difference between the two is greater than 15dB, it can be corrected. Ignore the influence of background noise on the measurement results.
6. dB calculation
1. The unit DB can actually be said to have no unit, because it actually represents a proportional relationship. The calculation formula is given:
SPL=20 x log10[ p(e) / p(ref) ]
SPL is what we usually call decibels, p(e) is the sound pressure to be measured, and p(ref) is the reference sound pressure.
Calculation:
A). The calibrated sound source produces a 1000Hz, 94dB sound signal. The recording equipment collects the audio signal in an absolutely quiet environment (the gain defaults to 1). Decode and normalize the audio signal, perform DFT transformation, and obtain the corresponding amplitude A at 1000Hz. Then we can get the conversion coefficient α=Δp/ΔA between audio amplitude and sound signal, 94 = 20lg(Δp).
B) Convert the audio signal into a sound signal
Assume that the audio signal is f(t), and f(t) is the decoded and normalized function of the audio signal. Assume that the sound signal is g(t), then g(t) = f(t) * α
C). Perform DFT transformation on the sound signal.
Perform Fourier transform on g(t) and turn it into spectrum G(k). k represents the frequency point.
D), calculate DB_K at each frequency on the spectrum
dB_k = 20lg|G(k)|, generally, the spectrum range is 0-10KHz
E), calculate the final value (average value) DB
dB = 1/N*Σ(dB_k)
7. Calculation of dB A
dB = 1/N*Σ(dB_k - W'_k)
dBA defines volume from the perspective of the human ear, and has an additional weighting coefficient W compared to dB. That is to say, a weighting coefficient is added to the calculation formula from dB_k to dB. The coefficient is as shown below:
2. Conversion relationship between decibels dB and amplification
Gain (dB) Introduction
1. Decibel is the unit of amplifier gain --- dB. The ratio of amplifier output to input is the amplification factor, and the unit is "times", such as a 10x amplifier and a 100x amplifier. When "decibels" is used as the unit, the amplification factor is called gain, which are two names for the same concept.
2. Decibel in electricity is defined as the logarithm of signal amplification. The definitions of voltage (current) and power amplification are different;
Two definitions of dB
1. The definition of the voltage (current) amplification factor in decibels: K=20lg(Vo/Vi), where K is the decibel factor of the amplification factor, Vo is the amplified signal output, and Vi is the signal input;
2. The definition of power amplification decibels: K=10lg (Po/Pi), where K is the amplification decibels, Po is the amplified signal output, and Pi is the signal input;
4.K>0 means the signal is amplified, K=0 means the signal is passed through, K<0 means the signal is attenuated;
5. Take voltage (current) decibels as an example (corresponding to the image signal gain of the camera):
(1) When the gain is 0dB, the signal is passed through without amplification.
(2) When the gain is 3dB, the actual amplification factor is about 1.4.
Calculation method: = (lg1.4)*20 = 0.146*20 = 2.92 (DB)
(3) When the gain is 6dB, the actual amplification factor is about 2.
Calculation method: = (lg2)*20 = 0.301*20 = 6.020 (DB)
(4) When the gain is 9dB, the actual amplification factor is about 2.8.
Calculation method: = (lg2.8)*20 = 0.447*20 = 8.943 (DB)
(5) When the gain is 12dB, the actual amplification factor is about 4.
Calculation method: = (lg4)*20 = 0.602*20 = 12.040 (DB)
(6) When the gain is 18dB, the actual amplification factor is about 8
Calculation method: =(lg8)*20 = 0.903*20 = 18.061(DB)
In the decibel value, there are two points -3dB and 0dB that must be understood.
About -3dB bandwidth
-3dB is also called the half power point or cutoff frequency point. At this time, the power is half of the normal value, and the voltage or current is 0.707 of the normal value. In electroacoustic systems, a difference of ±3dB is considered not to affect the overall characteristics. Therefore, various equipment indicators, such as frequency range, output level, etc., may vary by ±3dB without explanation.
As the input frequency increases, the voltage amplification factor of the amplifier circuit will decrease. The position when the voltage amplitude drops to 0.707 times the maximum value is the cut-off frequency. At this time, the power value is exactly half of the maximum power, so it is also called the half power point. It is expressed in decibels that it has dropped by exactly 3dB (calculated according to the voltage amplitude: 20log (0.707) = -3dB, calculated according to the power: 10log (0.5) = -3dB). The corresponding frequency is called the upper cut-off frequency, also often called -3dB bandwidth .
About 0dB
0dB means the output is as loud as the input or both comparison signals. Decibel is a relative quantity and has no absolute value. But you can also see the measured dB value on a level meter or a noise meter on the road. This is because people have set a benchmark for 0dB.
For example, the 0dB of a sound meter is 2×10-4μb (microbar), so if the noise on the road is 50dB or 60dB, there is an absolute concept of light noise. Commonly used 0dB benchmarks include the following: dBFS - the full scale value is 0dB, commonly used in various characteristic curves; dBm - generating 1mW power (or 0.775V voltage) on a 600Ω load is 0dB, commonly used in On the AC level measuring instrument; dBV - 1 volt is 0dB; dBW - 1 watt is 0dB.
Regardless of whether it is the amplitude type or the square term, their magnitudes are the same after being converted into decibels, and they can be directly compared and calculated. When amplifiers are cascaded, the total amplification factor is the multiplication of each stage. When measured in decibels, the total gain of the cascaded amplifiers is the sum.
reference:
1. What is the unit of sound in dB? - Zhihu (zhihu.com)
2. Calculation methods of sound signal dB and dBA - Huixin.com (software development blog aggregation) (freesion.com)
3. dB (decibel) definition and application (qq.com)