Signal signal to noise ratio

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The Decibel Scale

The decibel (dB) scale is logarithmic. Log scales have the advantage of representing a huge range of values with quite a small range of numbers.

Power Gain

The gain could be a loss called attenuation.

G_db = 10 log₁₀ ( P_OUT / P_IN )

Combined Gain of Several Stages

Voltage, current or power gains expressed as ratios multiply.
Gains expressed in dB add up.

Decibel Gains Add but Voltage or Power Gains Multiply

Signal to Noise Ratio

The signal is wanted. The unwanted electrical noise comes from external sources like lightning strikes, industrial machinery power switching, or warm components in sensitive electronics.

For Power SNR_db = 10 log₁₀ ( P_S / P_N )

For Voltage SNR_db = 20 log₁₀ ( V_S / V_N )

Conversions between Power Gain and dB

Ratio	dB
P_OUT/P_IN	10 log₁₀(P_OUT/P_IN)
10 000 000 000	100
1 000 000 000	90
100 000 000	80
10 000 000	70
1 000 000	60
100 000	50
10 000	40
1 000	30
100	20
10	10
4	6
2	3
1	0
0.5	−3
0.25	−6
0.1	−10
0.01	−20
0.001	−30
0.0001	−40
0.00001	−50
0.000001	−60
0.0000001	−70
0.00000001	−80
0.000000001	−90
0.0000000001	−100

Conversions between Voltage or Current Gain and dB

Ratio	dB
V_out / V_in I_out / I_in	20 log₁₀ ( V_out / V_in ) 20 log₁₀ ( I_out / I_in )
100 000	100
10 000	80
1 000	60
100	40
10	20
2	6
1.414	3
1	0
0.707	−3
0.5	−6
0.1	−20
0.01	−40
0.001	−60
0.0001	−80
0.00001	−100

The Universe with a Log Scale

Log Scale Universe from XKCD Thanks xkcd

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>|< nnn
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Pg Down
>> lll
End
>>>

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