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Bell(B)
Bell (B) was originally used to represent the ratio of volume power 10 to 1, named after Alexander Graham Bell. 1B represents a power ratio of 10:1, so this is a logarithmic relationship with a base of 10, 100:1=2B, 1000:1=3B. The mathematical relationship is as follows, where P 2 /P 1 represents the power ratio.
lg(P 2 /P 1 )
Decibel (dB)
5B is 100,000 times larger, so it can be seen that Bel is a relatively large unit and is inconvenient to use. Usually, a smaller unit is used, which is also common to us: decibel (dB), where d stands for "one tenth (deci-)", 1B=10dB, 2B=20dB, and the calculation method is as follows:
10*lg(P 2 /P 1 )
In the field of acoustics, decibel refers to the logarithm of the ratio of the sound source to the reference sound power multiplied by 10. It is used to indicate the intensity of the sound. For example, 1 decibel is a sound that can just be heard, the sound of a normal conversation is 60 decibels, and exceeding 110 decibels may cause permanent damage to our hearing.
In addition to the field of acoustics, decibels have been widely used in many fields such as radio, electrical engineering, mechanics, etc.
Bel and decibel do not refer to power itself, but to the ratio of two power values. If you need to express a fixed power value, you need a power as a reference, and then express the absolute power level in decibels. The most commonly used power references are mW and W.
dBm represents the power decibel value relative to the reference power of 1 milliwatt (mW). The conversion formula is as follows:
1W = 1000mW = 30dBm = 0dBW
A more general logarithmic relationship
In the field of radar communications and electronic warfare, you will often see or hear these words, such as antenna gain, amplifier gain, cable attenuation, propagation loss, etc. So what are the connections and differences between them?
Gain and Attenuation (dB)
First, let's look at the amplifier gain or cable attenuation. Everyone knows at a glance that it represents a power ratio, using the output power to divide the input power. If it is greater than 1, it is a positive dB value, which means amplification; if it is less than 1, it is a negative dB value, which means attenuation or loss. It is easy to understand.
Antenna gain (dB) and dBi/dBd/dBc
The ability of an antenna to transmit or receive signals is usually expressed in decibels (dBi) relative to an omnidirectional antenna. For example, if the antenna gain is 10 dBi, it does not mean that the antenna can amplify the signal power 10 times, but rather that the power is concentrated in a certain direction by controlling the angle of signal transmission.
When the input power is equal, the antenna gain refers to the ratio of the power density of the actual antenna and the omnidirectional antenna at the same point in space. It describes the degree to which the antenna radiates power in a concentrated manner, and is therefore closely related to the antenna pattern. Generally speaking, the narrower the main lobe of the antenna pattern and the smaller the side lobe, the higher the gain.
When talking about antenna gain, there is a distinction between directional gain and power gain, which are related to each other through radiation efficiency. Directional gain is always greater than power gain and is closely related to the antenna beam width.
The antenna pattern shows that there are different gains in different directions in space. The "antenna gain" we often refer to usually refers to the gain in the direction of maximum gain, and the unit is dBi or dBd . The reference bases of these two units are different. The former is based on the isotropic antenna, and the latter is based on the dipole antenna. The gain of the dipole antenna is:
0dBd=2.15dBi
The " 3dB beamwidth " of an antenna that we often refer to is the angle between the two gain values when the antenna gain drops to half of the boresight gain, that is, when the maximum gain is attenuated by 3dB.
dBc
Sometimes we also see the unit of dBc, which is generally relative to the carrier power and is used to measure the relative value of the carrier power, such as co-frequency/intermodulation/cross-band/out-of-band interference or spurious.
Calculation example:
To generate a signal of a certain size at a certain point at a certain distance, using an ideal omnidirectional antenna, it is assumed that an input power of 100W is required. However, if a directional antenna with a gain of G=20dBi is used as the transmitting antenna, the input power is only 100/10 20/10 =1W.
If you often hear people say that the antenna gain is x dB, this is actually not rigorous, and usually dBi is used as the default. But you should know that this is a completely different concept from saying that the amplifier gain is x dB.
Since the numbers expressed in dB are logarithmic, it is more convenient to change the existing equations into equations in dB form. A common example is the spreading loss equation in radio propagation, which is very convenient to express in dB form.
10lg(.) and 20lg(.)
The logarithmic characteristic of decibels makes it very convenient to express power and power ratios. We know that power is proportional to the square of voltage or current, so when converting voltage or current, we need to use 20lg(.), for example:
1mV=1000uV=(20*lg(1000))dBuV=60dBuV
However, it should be noted that this is the absolute value of the voltage expressed in decibels, but if the voltage ratio is expressed in dB and the power ratio is expressed in dB, it is consistent and both represent ratios.
Common conversion value: 10lg(.)
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