Decibel dB calculation amplification factor gain loss and damping factor ratio voltage power - sengpielaudio
 
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Calculation: amplification (gain) as factor ( ratio) ●
and damping (loss) as level in decibels (dB)
 
The amplification factor, also called gain, is the extent to which a device boosts the strength of a signal.
The damping factor, also called loss, is the extent to which a device reduces the strength of a signal.
 
Enter two values and press the right calculate bar in the line of the missing answer
 
Input: voltage power
 
Input   value 1
Output   value 2
 Level change   dB
 
In analog audio engineering we deal only with 'voltage' amplification (gain) and damping (loss).
gain and loss
V1 = Vin and V2 = Vout.
V2 > V1 or Vout > Vin means amplification. The dB value is positive. (+)
V2 < V
1 or Vout < Vin means damping. The dB value is negative. (−)
V2 / V1 or Vout / Vin means the ratio. The amplification or the damping in dB is:
L = 20 × log (voltage ratio V2 / V1) in dB.        V1 = Vin is the reference.

In physics, attenuation is regarded as a positive value.
This naturally leads to sign errors when entering numbers.

 3 dB ≡  1.414 times the voltage    (−)3 dB ≡  damping to the value 0.707
 6 dB ≡          2 times the voltage    (−)6 dB ≡  damping to the value 0.5
10 dB ≡  3.162 times the voltage    (−)10 dB ≡  damping to the value 0.316
20 dB ≡       10 times the voltage     (−)20 dB ≡  damping to the value 0.1

Using voltage we get: Level in dB: L = 20 × log (voltage ratio)

  +6 dB = twice the voltage
+12 dB = four times the voltage
+20 dB = ten times the voltage
+40 dB = hundred times the voltage

If we consider audio engineering, we are usually not interested in power.
Do not ask what the power amplification is.
Leave that to the telephone companies or the transmitting aerials (antennas).
Power gain is really not used in audio engineering.
We got no power (energy) amplification.
Read the text at the bottom.

 3 dB ≡  2 times the power    (−3) dB ≡  damping to the value 0.5
 6 dB ≡          4 times the power    (−6) dB ≡  damping to the value 0.25
10 dB ≡  10 times the power    (−10) dB ≡  damping to the value 0.1
20 dB ≡       100 times the power     (−20) dB ≡  damping to the value 0.01

Using power we get: Level in dB: L = 10 × log (power ratio)

   +3 dB = twice the power
   +6 dB = four times the power
 +10 dB = ten times the power
 +20 dB = hundred times the power 

If you search for the amplification ratio, given the dB value,
then go to the program dB calculation

Amplification (Gain) and Damping (Loss)

Gain ratio v = V2/V1:
for field quantities, e.g. voltage
 
 ↔  Amplification level L: 
voltage level
dB
Formula Factor   Formula Amplification
Voltage gain v = 1 ≡ 0 dB

In audio technique the following "power or energy amplification " is rather unusual.

Gain ratio v = P2/P1:
for energy quantities, e.g. power

 
 ↔  Amplification level L: 
power level

dB
Formula1   Formula2
Power gain v = 1 ≡ 0 dB
  Voltage/Pressure 
  amplification ratio  
  1  
 
 1.414 
= √2
  2  
 
 3.16
= √10
  4  
 
 10 
 
 20 
 
 40 
 
 100 
 
 1000 
 
  Increasing of x dB  0   3   6   10   12   20   26   32   40   60 

  Power/Intensity  
  amplification ratio  
  1  
 
 1.414 
= √2
  2  
 
 3.16
= √10
  4  
 
 10 
 
 20 
 
 40 
 
 100 
 
 1000 
 
  Increasing of y dB  0   1.5   3   5   6   10   13   16   20   30 

Aha!
 
At the cut-off frequency fc the dropped voltage is always fallen to the value of
1/√2 and the voltage level L is damped to 20 × log (1/√2) = (−)3,0103 dB.
 

Simply enter the value to the left or the right side.
The calculator works in both directions of the sign.

Voltage V: 
volts
 ↔  Voltage level LU:
dBV
Formula Volt   Formula Level
Reference voltage V0 = 1 Volt ≡ 0 dBV
Voltage V (Audio): 
volts
 ↔  Voltage level LU (Audio):
dBu
Formula Volt   Formula Level
Reference voltage V0 = 0.7746 Volt ≡ 0 dBu

The voltage is always given as RMS value - but that is not valid for electric power.

Electric power P: 
watts
 ↔  Electric power level LP
dB
Formula1   Formula2
Reference electric power P0 = 1 W ≡ 0 dB

There is also the reference power P0 = 1 milliwatt or 0.001 watt ≡ 0 dBm

Electric power P (Telephone): 
watts
 ↔  Electric power level LP:
dBm
Formel   Formel
Reference electric power P0 = 1 milliwatt = 0.001 watt ≡ 0 dBm

Level in psycho acoustics as subjectivly perceived loudness (volume)
The vague human feeling of the double loudness (volume) is specified
with about 6 to 10 dB. This personal feeling is not an exactly measurable value.

Conversion Factor, Ratio, or Gain to a Level Value (Decibels dB)
Amplifier conversion − Convert decibels to voltage gain / loss
Calculator Voltage Gain − Voltage Loss and Power Gain − Power Loss

Conversion: Gain G, Voltage ratio AV, and Power ratio AP
 
Gain G  dB    |    Voltage ratio (factor) AV    |    Power ratio (factor) AP 
    |     |  
         |            |       
    |     |  
 Voltage ratio (factor) AV    |   Voltage gain GV  dB    |  Power gain GP  dB 
Power ratio (factor) AP    |      |  
 
 
Voltage gain Amplification Factor Power and Decibels in dB
 
 
Power gain Amplification Factor Power and Decibels in dB
 
Voltage ratio Amplification Factor Power and Decibels = amplification factor (voltage)
Power ratio Amplification Factor Power and Decibels = amplification factor (power)
gain and loss
V1 = Vin and V2 = Vout.
V2 > V1 or Vout > Vin means amplification. The dB value is positive. (+)
V2 < V1 or Vout < Vin means damping. The dB value is negative. (−)
V2 / V1 or Vout / Vin means the ratio. The amplification or the damping in dB is: L = 20 × log (voltage ratio V2 / V1) in dB.        V1 = Vin is the reference.
 
Aha!
 
The word "power amplifier" is a misnomer. Power is not really something that can be "amplified". Voltage and current can be amplified. The term "power amplifier" although technically incorrect has become understood to mean an amplifier that is intended to drive a load such as a loudspeaker.
We call the product of current and voltage gain just "power amplification".
The total energy within a closed system due to the conservation of energy is neither increased nor decreased.

 
 
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