Decibel (dB)

• Decibel (dB) definition
• Power ratio to dB conversion
• dB to power ratio conversion
• Amplitude ratio to dB conversion
• dB to amplitude ratio conversion
• Absolute decibel units
• dB to ratio conversion table

Decibel (dB) definition

Decibel is a unit that describes logarithmic scale of ratio or gain. It is used to describe the level of waves and electronic signals. The logarithmic scale can describe very big or very small numbers with shorter notation. The dB level can be viewed as relative gain of one level vs. other level, or absolute logarithmic scale level for well known reference levels.

^{Power ratio to dB conversion}

The gain G_dB is equal to 10 times base 10 logarithm of the ratio of the power P₂ and the reference power P₁.

G_dB = 10 log₁₀(P₂ / P₁)

 

P₂ is the power level.

P₁ is the referenced power level.

G_dB is the power ratio or gain in dB.

 

Example

Find the gain in dB for a system with input power of 5W and output power of 10W.

G_dB = 10 log(P_out/ P_in) = 10 log(10W/5W) = 3.01dB

^{dB to power ratio conversion}

The power P₂ is equal to the reference power P₁ times 10 raised by the gain in G_dB divided by 10.

P₂ = P₁  · 10^(GdB ^{/ 10)}

 

P₂ is the power level.

P₁ is the referenced power level.

G_dB is the power ratio or gain in dB.

Amplitude ratio to dB conversion

For amplitude of waves like voltage, current and sound pressure level:

G_dB = 20 log₁₀(A₂ / A₁)

 

A₂ is the amplitude level.

A₁ is the referenced amplitude level.

G_dB is the amplitude ratio or gain in dB.

dB to amplitude ratio conversion

A₂ = A₁  · 10^(GdB ^{/ 20)}

A₂ is the amplitude level.

A₁ is the referenced amplitude level.

G_dB is the amplitude ratio or gain in dB.

 

Example

Find the output voltage for a system with input voltage of 5V and gain of 6dB.

V_out = V_in · 10 ^(GdB ^{/ 20)} = 5V · 10 ⁽⁶dB ^{/ 20)} = 9.976V ≈ 10V

 

Absolute decibel units

Unit	Name	Reference
dBm	decibel milliwatt	1mW
dBW	decibel watt	1W
dBV	decibel volt	1V
dBmV	decibel millivolt	1mV
dBu	decibel unloaded	0.775V
dB SPL	decibel sound pressure level	20μPa
dBHz	decibel hertz	1Hz

dB to ratio conversion table

dB	Amplitude ratio	Power ratio
-100 dB	10-5	10-10
-50 dB	0.00316	0.00001
-40 dB	0.01	0.0001
-30 dB	0.032	0.001
-20 dB	0.1	0.010
-10 dB	0.316	0.100
-6 dB	0.501	0.251
-3 dB	0.708	0.501
-2 dB	0.794	0.631
-1 dB	0.891	0.794
0 dB	1.000	1.000
1 dB	1.122	1.259
2 dB	1.259	1.585
3 dB	1.413	1.995 ≈ 2
6 dB	1.995 ≈ 2	3.981
10 dB	3.162	10.000
20 dB	10.000	100.000
30 dB	31.623	1000.000
40 dB	100.000	10000.000
50 dB	316.228	100000.000
100 dB	105	1010

 

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See also

• dBm
• Watt
• Volt
• Electrical units
• Logarithm
• Decibel - Wikipedia
• dB SPL (Sound Pressure Level) - Wikipedia