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Working With dB
When a voltage is reduced by half, it is -6 dB. When it's doubled, it's +6 dB. Every halving or doubling changes the result by 6 dB, so 1/4 is -12 dB, 1/8 is -18 dB, and so on.
When a voltage is changed by a factor of 10, there is a 20 dB change. So if the output is 60 dB less than the input, the voltage is 1/1000.
A 10 dB change represents a factor of 3.16 voltage change. This value has the magical property that the reciprocal has the same digits, so -10 dB is a factor of 0.316 voltage change.
A 1 dB change represents about 11% voltage change.
Putting all these little rules of thumb together, you can make approximate conversions between dB and voltage in your head. Since adding or subtracting dB is the same as multiplying or dividing by the ratios, you can break an oddball value into separate steps.
For example, if an output signal is -56 dB relative to the input, you can break it into -40, -10, and -6 dB. You know that every -20 dB is a factor of 10 (one decimal place) smaller, so -40 dB is 0.01. The -10 dB will make that 0.316 smaller, down to 0.00316. And since -6 dB is just 1/2, the overall output must be 0.00158 of the input.
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