https://zh.wikipedia.org/wiki/%E5%88%86%E8%B2%9D
分貝（decibel）是量度兩個相同單位之數量比例的單位，主要用於度量聲音強度，常用dB表示。
“分”（deci-）指十分之一，個位是“貝”或“貝爾”（bel），但一般只採用分貝。
分貝(dB)是十分之一貝爾(B): 1B = 10dB。
功率量
考慮功率或者強度（intensity）時, 其比值可以表示為分貝，這是通過把測量值與參考量值之比計算基於10的對數，再乘以10。
因此功率值P1與另一個功率值P0之比用分貝表示為LdB：
兩個功率值的比值基於10的對數，就是貝爾（bel）值。
兩個功率值之比的分貝值是貝爾值的10倍（或者說，1個分貝是十分之一貝爾）。
P1 與P0必須度量同一個數值型別，具有相同的單位。
如果在上式中P1 = P0，那麼LdB = 0。
如果P1大於P0，那麼LdB是正的；
如果P1小於P0，那麼LdB是負的。
重新安排上式可得到計算P1的公式，依據P0與LdB:
因為貝爾是10倍的分貝，對應的使用貝爾(LB)的公式為
所有例子都是無量綱的分貝表示的值，因為它們是同量綱的兩個數量的比值的分貝表示。
"dBW"表示參考值是1瓦特，"dBm"表示參考值是1毫瓦。
注意到
，
解釋了上述
的定義具有相同的值——
不論是用功率值還是電壓幅值計算出來的，只要在特定系統中功率之比正比於幅值之比的平方。
使用分貝有很多便利之處：
- 分貝實際上是對數值，因此可以用常用的數量來表示非常大的比值，可以清楚地表示非常大的數量變化。
- 多部件系統的整體增益（如級聯的放大器）可以直接用各部件的增益分貝相加而求得。
不必把這些增益值相乘（例如log(A × B × C) = log(A) + log(B) + log(C)）。 - 人對強度的感知，如聲音或者光照，更接近與強度的對數成正比而不是強度值本身，
依據韋伯定理，因此分貝值可用於描述感知級別或級差。
電子學中，通常用分貝表示功率或幅值之比（增益），而不常用算術比或者百分比。
一項好處是一些列部件組成的系統的總增益是各部件增益之和。
dB與字尾的組合，指出計算比值時的參考值。例如dBm指示功率值與1毫瓦的比值的分貝數。
如果計算分貝時的參考值明確、確切地給出，那麼分貝數值可以作為絕對量，
如同被測量的功率量或者場量。例如，2 dBm即為10毫瓦。
由於分貝是依據功率而定義的，因此把電壓比值轉化為分貝，必須採用20倍對數。
在分貝計前大叫得震耳欲聾，可能也不如輕輕對準探測器一吹的分貝讀數來得大。
這可能是因為尖叫只帶來空氣中能量的傳送，但吹風帶動空氣粒子直接撞擊分貝計的探測器，
引起額外的“零距離”聲波，取得更大的正增長引數數值
增益
增益在電子學上，通常為一個系統的訊號輸出與訊號輸入的比率。
如5倍的增益，即是指系統令電壓或功率增加了5倍。
增益主要應用於放大電路中。
對數單位與分貝
電子學上常使用對數單位量度增益，並以貝（bel）作為單位：
- Gain = log10(P2/P1) bel
其中P1與P2分別為輸入及輸出的功率。
由於增益的數值通常都很大，因此一般都使用分貝（dB，貝的10分之1）來表示：
- Gain = 10×log10(P2/P1) dB
一個類似的單位使用自然對數，稱為neper。
當增益以電壓而非功率計算時，使用焦耳定律 （Joule's law，P=V2/R），其公式為：
- 增益 =10×log10 ((V22/R) /(V12/R) )dB
=10×log10((V2/V1)2)dB
=20×log10(V2/V1) dB
此公式只有在負載阻抗相等（阻抗匹配）時才為正確。
在不少現代電子裝置中，由於輸出阻抗較低，而輸入阻抗則較高，令負載可被忽略而不明顯地影響計算結果。
舉例
如一個放大器輸出1伏特至1歐姆的負載，提供的輸出功率為1瓦特。
如放大器被調節至輸出10伏特至同一負載，它提供的輸出功率則為100瓦特（P=V2/R）。
因此：電壓增益 = 100/10 = 10倍
P = V²/R
功率增益 = (100²/R) / (10²/R) = 100倍
根據定義，其功率增益為 10Log100 = 20 dB
如果增益為1或0 dB，即輸出電壓等於輸入電壓，這個增益也稱為單位增益。
功率增益（英語：Power gain）是指一個電路里輸出功率和輸入功率的比例。
不像其他的訊號增益，例如電壓增益和電流增益，功率增益由於“輸入功率”和“輸出功率”本身有著相對模糊的定義，因此有時顯得有點混淆。
三種重要的功率增益包括：
- 運算功率增益（英語：operating power gain）、
- 轉換功率增益（transducer power gain）和
- 有效功率增益（available power gain）。
值得注意的是，上述三種增益的定義均基於功率的平均效果，而非瞬時功率，不過“平均”二字經常被省略，在有的情況會引起混淆。
The amplification factor, also called gain , is the extent to which an analog amplifier boosts the strength of a signal .
Amplification factors are usually expressed in terms of power .
The decibel (dB), a logarithmic unit, is the most common way of quantifying the gain of an amplifier.
For power, If the output-to-input signal power ratio is 1:1, then the amplification factor is 0 dB.
a doubling the signal strength (an output-to-input power ratio of 2:1) translates into a gain of 3 dB;
a tenfold increase in power (output-to-input ratio of 10:1) equals a gain of 10 dB;
a hundredfold increase in power (output-to-input ratio of 100:1) represents 20 dB gain.
If the output power is less than the input power, the amplification factor in decibels is negative.
Power amplifiers typically have gain figures from a few decibels up to about 20 dB.
Sensitive amplifiers used in wireless communications equipment can show gain of up to about 30 dB.
If higher gain is needed, amplifiers can be cascaded, that is, hooked up one after another.
But there is a limit to the amplification that can be attained this way.
When amplifiers are cascaded, the later circuits receive noise at their inputs along with the signals.
This noise can cause distortion.
Also, if the amplification factor is too high, the slightest feedback can trigger oscillation,
rendering an amplifier system inoperative.
Amplifier Gain & Decibels
Voltage Amplification
The Voltage Amplification (Av) or Gain of a voltage amplifier is given by:
With both voltages measured in the same way (i.e. both RMS, both Peak, or both Peak to Peak),
Av is a ratio of how much bigger is the output than the input, and so has no units.
It is a basic measure of the Gain or effectiveness of the amplifier.
Because the output of an amplifier varies at different signal frequencies,
measurements of output power, or often voltage, which is easier to measure than power,
are plotted against frequency on a graph (response curve)
to show comparative output across the working frequency band of the amplifier.
Logarithmic Scales
Response curves normally use a logarithmic scale of frequency, plotted along the horizontal x-axis.
This allows for a wider range of frequency to be accommodated than if a linear scale were used.
The vertical y-axis is marked in linear divisions but using the logarithmic units of decibels
allowing for a much greater range within the same distance.
The logarithmic unit used is the decibel, which is one tenth of a Bel,
a unit originally designed for measuring losses of telephone cables,
but as the Bel is generally too large for most electronic uses, the decibel (dB) is the unit of choice.
Apart from providing a more convenient scale the decibel has another advantage in displaying audio information,
the human ear also responds to the loudness of sounds in a manner similar to a logarithmic scale,
so using a decibel scale gives a more meaningful representation of audio levels.
Power Gain in dBs
To describe a change in output power over the whole frequency range of the amplifier,
a response curve, plotted in decibels is used to show variations in output.
The powers at various frequencies throughout the range are compared to
a particular reference frequency, (the mid band frequency).
The difference in power at the mid band frequency and the power at any other frequency being measured,
is given as so many decibels greater (+dB) or less (-dB) than the mid band frequency,
which is given a value of 0dB.
Notice that, on the logarithmic frequency scale in Fig 1.3.1 the middle of the 10Hz to 100kHz band is 1kHz
and frequencies around this figure (where the output is usually at its maximum)
are normally chosen as the reference frequency.
Converting a power gain ratio to dBs is calculated by multiplying the log of the ratio by 10:
Where P1 is the power at mid band and P2 is the power being measured.
Note: When using this formula in a calculator the use of brackets is important,
so that 10 x the log of (P1/P2) is used, rather than 10 x the log of P1, divided by P2.
e.g. if P1 = 6 and P2 =3
10 x log(6/3) =3dB (right answer), but 10 x log 6/3 = 2.6dB (wrong answer).
Voltage Gain in dBs
Although it is common to describe the voltage gain of an amplifier as so many decibels,
this is not really an accurate use for the unit.
It is OK to use decibels to compare the output of an amplifier at different frequencies,
since all the measurements of output power or voltage are taken across the same impedance (the amplifier load),
but when describing the voltage gain (between input and output) of an amplifier,
the input and output voltages are being developed across quite different impedances.
However it is quite widely accepted to also describe voltage gain in decibels.
When voltage gain(Av) or current gain (Ai) is plotted against frequency the −3dB points are where the gain falls to 0.707 of the maximum (mid band) gain.
Notice that converting voltage ratios to dBs uses 20 log(Vout/Vin)
Describing the voltage gain of an amplifier that produces an output voltage of 3.5V for an input of 35mV as being 40dB,
is equivalent to saying that the output voltage is 100 times greater than the input voltage.
To reverse the process, and convert dBs to a voltage ratios for example, use:
Note that the brackets are important and antilog may be shown on calculator keypads as 10x or 10^
and is also usually Shift +log.
Use the same formula for dBs to Current gain ratio, and to convert dBs to a power ratio, simply replace the 20 in the formula with 10.
An advantage of using dBs to indicate the gain of amplifiers is that in multi stage amplifiers,
the total gain of a series of amplifiers expressed in simple ratios, would be the product of the individual gains:
Av1 x Av2 x Av3 x Av4 ...etc.
This can produce some very large numbers,
but the total of individual gains expressed in dBs would be the sum of the individual gains:
Av1 + Av2 + Av3 + Av4 ...etc.
Likewise losses due to circuits such as filters, attenuators etc. are subtracted to give the total loss.
Commonly Encountered dB Values
0dB The reference level to which all +dB and −dB figures refer.
±1dB The least noticeable change in audio levels, also used for the limits of bandwidth on high quality audio amplifiers.
−3dB Commonly used for limits of bandwidth in amplifiers, indicating the points where:
a. The output voltage has fallen to 0.707 of the maximum (mid band) output.
b. The output power has fallen to half the maximum or mid band power.
(Half the VOLTAGE amplitude is −6dB)
Figures often quoted on attenuators designed to reduce the outputs on signal generators by measured amounts.
−20 dB Signal voltage amplitude divided by 10
−40dB Signal voltage amplitude divided by 100
Converting Between dBs and Power or Voltage gain
