dB calculator for amplification (gain) and damping (loss) of an audio amplifier calculation decibel dB

Calculation: amplification (gain) and damping (loss)
as level in decibels or dB

Enter two values and press the right calculate bar in the line of the missing answer

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In analog audio engineering we deal only with 'voltage' amplification (gain) and damping (loss).
gain and loss - sengpielaudio

V₂ > V₁ means amplification. The dB value is positive.
V₂ < V₁ means damping. The dB value is negative.
V₂ / V₁ means the ratio. The amplification or the damping in dB is:
L = 20 × log (voltage ratio V₂ / V₁)         V₁ is the reference.

3 dB ≡ 1.414 fold the voltage    (−3) dB ≡ damping to the value 0.707

6 dB ≡          2 fold the voltage    (−6) dB ≡ damping to the value 0.5

10 dB ≡ 3.162 fold the voltage    (−10) dB ≡ damping to the value 0.316

20 dB ≡       10 fold the voltage     (−20) dB ≡ damping to the value 0.1

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

  +6 dB = twofold the voltage
+12 dB = fourfold the voltage
+20 dB = tenfold the voltage
+40 dB = hundredfold the voltage

Not often one is interested in power, if we consider audio engineering.
Do not ask what the power amplification is.
Leave that to the telephone company.

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

+3 dB = twofold the power
+6 dB = fourfold the power
+10 dB = tenfold the power
+20 dB = hundredfold the power

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

At the cut-off frequency f_c 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.

Enter a value in the left or right box, then press the TAB bar or make
a mouse click at an empty space at the side, to get the solution.
The calculator works in both directions of the ↔ sign.

The voltage is always given as RMS value - but not the electric power.

There is also the reference power P₀ = 1 milliwatt or 0,001 watt ≡ 0 dB_m

Amplification and Damping

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

Voltage/Pressure amplification factor	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 factor	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

Level in psycho acoustics as subjectivly perceived loudness (volume)

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.

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Voltage V: volts	↔	Voltage level L_U: dBV
$V = V_0 \cdot 10^\frac{L_V}{20} \ \mbox{volts}$		$L_V = 20\, \log_{10}\left(\frac{V}{V_0}\right) \ \mbox{dBV}$
Reference voltage V₀ = 1 Volt ≡ 0 dBV

Voltage V (Audio): volts	↔	Voltage level L_U (Audio) : dBu
$V = V_0 \cdot 10^\frac{L_V}{20} \ \mbox{volts}$		$L_V = 20\, \log_{10}\left(\frac{V}{V_0}\right) \ \mbox{dBu}$
Reference voltage V₀ = 0.7746 Volt ≡ 0 dBu

Electric Power P: watts	↔	Electric Power level L_P dB

Reference electric power P₀ = 1 W ≡ 0 dB

Electric power (telephone) P: watts	↔	Electric Power level (phone) L_P dB_m

Reference power P₀ = 1 milliwatt (mW) = 0.001 W ≡ 0 dB_m

gain factor v = V₂/V₁: for field quantities, e.g. voltage	↔	amplification level L: voltage level dB

Voltage gain v = 1 ≡ 0 dB

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

gain factor v = P₂/P₁: for energy quantities, e.g. power	↔	amplification level L: power level dB

Power gain v = 1 ≡ 0 dB