Made some annotations on the basis of the original text
The concept analysis of decibel (dB)
dB (Decibel, decibel) is a pure counting unit, which is intended to express the ratio of two quantities, without a unit.
It is common to see definitions that appear to be different (just look different) in engineering applications. For power, dB= 10*lg(A/B). For
voltage or current, dB =20*lg(A/B). Here A and B represent the power value or the current and voltage values involved in the comparison. (The question of 10lg and 20lg will be discussed later)
The meaning of dB is actually very simple, that is, a very large (followed by a long string of 0's) or very small (a long string of 0's in front) numbers are expressed relatively briefly. Such as (here takes power as an example):
X = 100000 = 10^5
X(dB) = 10*lg(X) dB= 10*lg(10^5) dB= 50 dB
X = 0.000000000000001 = 10^ -15
X(dB) = 10*log(X) dB= 10*log(10^ -15) dB= -150 dB
Generally speaking, in engineering, there is only addition and subtraction between dB and dB, no multiplication and division. The most commonly used is subtraction: dBm minus dBm is actually the division of two powers, and the division of signal power and noise power is the signal-to-noise ratio (SNR). For example: 30dBm- 0dBm = 1000mW/1mW = 1000 = 30dB. dBm plus dBm is actually the multiplication of two powers and has no actual physical meaning.
In the field of electronic engineering, the amplifier gain is used in dB (decibel). The ratio of amplifier output to input is the magnification, the unit is "time", such as 10 times amplifier, 100 times amplifier. When the unit is changed to "decibel", the magnification is called gain, which are two names of a concept.
The conversion relationship between decibel and magnification in electricity is:
A(V)(dB)=20lg(Vo/Vi); voltage gain
A(I)(dB)=20lg(Io/Ii); current gain
Ap(dB)= 10lg(Po/Pi);
The formulas of voltage (current) gain and power gain are different when the power gain decibel is defined, but we all know that the relationship between power and voltage and current is P=V^2/R=I^2*R. After using this formula, the gain value of the two is the same:
10lg[Po/Pi]=10lg[(Vo^2/R)/(Vi^2/R)]=20lg(Vo/Vi).
There are three main advantages to using decibels as units.
(1) The value becomes smaller and the reading and writing are convenient. The total magnification of the electronic system is often several thousand, tens of thousands or even hundreds of thousands. A radio needs to amplify about 20,000 times in total from the signal received from the antenna to the output of the speaker. In decibels, take a logarithm first, and the value is much smaller.
(2) The operation is convenient. When the amplifiers are cascaded, the total magnification is multiplied by the stages. When measured in decibels, the total gain is additive. 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 is 100×20=2000 times, and the total gain is 20dB+13dB=33dB.
(3) It conforms to the sense of hearing and is easy to estimate. The loudness of the sound heard by humans is positively correlated with the relative increase in power. For example, when the electrical power is increased from 0.1 watts to 1.1 watts, the sound is much louder; when boosted from 1 watt to 2 watts, the loudness is not too much; when boosted from 10 watts to 11 watts, there is no sound. Humans can hear the difference in loudness. If the absolute value of the power is expressed as 1 watt, and the gain is expressed as 10.4dB, 3dB and 0.4dB, it can more consistently reflect the difference in loudness heard by the human ear. If you pay attention, you will find that the scale of the volume knob on the Hi-Fi amplifier is marked with decibels, which makes it more intuitive when you change the volume.
In the decibel value, -3dB and 0dB are two points that must be understood. -3dB is also called the half power point or cutoff frequency point. At this time, the power is half of normal
[ -3=10lg(pi/po) , pi/po = 10^-0.3 = 1/1.99526 ] The voltage or current is 0.707 when it is normal. In electroacoustic systems, a difference of ±3dB is not considered to affect the overall characteristics. Therefore, various equipment indicators, such as frequency range, output level, etc., may have a difference of ±3dB without explanation. 0dB means that the output is as large as the input or both comparison signals. The decibel is a relative quantity, there is no absolute value. But you can also see the measured value in dB on a level meter or a noise meter on the road, because people have set a benchmark for 0dB. For example, the 0dB of the sound level meter is 2 × 10-4μb (microbar), so that the noise on the road is 50dB, 60dB, there is an absolute concept of soft sound. Commonly used 0dB benchmarks are as follows:
dBFS——The value of full scale is 0dB, which is often used on various characteristic curves;dBm——1mW power (or 0.775V voltage) generated on a 600Ω load is 0dBm, which is often used in AC level measuring instruments;
dBV—— 1 volt is 0dB;
dBW - 1 watt is 0dB.
Generally, after reading how many dB, there is no need to convert it into physical quantities such as voltage and sound pressure. Professionals can understand. Folding is only required on rare occasions. At this time, you only need to substitute the formula: 10A/20 (or A/10) × D0 for calculation. A is the decibel value read, D0 is the reference value at 0dB, A/20 is used for voltage, current or sound pressure, and A/10 is used for electric power, sound power or sound intensity.
Appendix:
Concept Analysis: dBm, dBi, dBd, dB, dBc, dBuV
1. dBm (the teacher asks for the definition in class)
dBm is a value that evaluates the absolute value of power, and the calculation formula is: 10lgP (power value/1mw).
[Example 1] If the transmit power P is 1mw, it is 0dBm after converting to dBm.
[Example 2] For a power of 40W, the converted value in dBm should be:
10lg(40W/1mw)=10lg(40000)=10lg4+10lg10+10lg1000=46dBm.
dBm is a unit of power;
dBm is defined as miliwatt. 0 dBm = 10log1 mw;
dBw defines watt. 0 dBw = 10log1 W = 10log1000 mw = 30dBm.
2. dBi and dBd
dBi and dBd are the values of the test gain (power gain), both are relative values, but the reference benchmarks are different. The reference reference of dBi is an omnidirectional antenna, and the reference reference of dBd is a dipole, so the two are slightly different. It is generally believed that the same gain expressed in dBi is 2.15 larger than that expressed in dBd.
[Example 3] For an antenna with a gain of 16dBd, when its gain is converted into a unit of dBi, it is 18.15dBi (generally ignoring the decimal place, it is 18dBi).
[Example 4] 0dBd=2.15dBi.
[Example 5] GSM900 antenna gain can be 13dBd (15dBi), GSM1800 antenna gain can be 15dBd (17dBi).
3、dB
dB is a value that characterizes the relative value. When considering how many dB the power of A is larger or smaller than the power of B, the following formula is used: 10lg (power of A/power of B)
[Example 6] The power of A is larger than the power of B Double, then 10lg (A power / B power) = 10lg2 = 3dB. That is, A's power is 3dB greater than B's power.
[Example 7] The 100-meter transmission loss of a 7/8-inch GSM900 feeder is about 3.9dB.
[Example 8] If A's power is 46dBm and B's power is 40dBm, then it can be said that A is 6dB larger than B.
[Example 9] If antenna A is 12dBd and antenna B is 14dBd, it can be said that A is 2dB smaller than B.
4、dBc
Sometimes you will also see dBc, which is also a unit that expresses the relative value of power, and is calculated in exactly the same way as dB. Generally speaking, dBc is relative to the carrier power. In many cases, it is used to measure the relative value of the carrier power, such as to measure interference (co-channel interference, intermodulation interference, intermodulation interference, band external interference, etc.) and the relative magnitude of coupling, spurious, etc. Where dBc is used, dB can in principle also be used instead.
5、dBuV
According to the basic formula V^2=P*R between power and level, it can be known that dBuV=90+dBm+10*log(R), R is the resistance value.
The correct value in the PHS system should be dBm=dBuv-107, because its antenna feed impedance is 50 ohms.
6. dBuVemf and dBuV
emf: electromotive force (electromotive force)
For a signal source, dBuVemf refers to the port voltage when the circuit is open, and dBuV is the port voltage when the matched load is connected.