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A simple 2-resistor voltage divider can function as a fixed attenuator to reduce a signal level that is too large.
Given the input voltage Vi and the two resistors R1 and R2, the output voltage Vo is:
Vo = Vi * R2 / (R1 + R2)
The fractional voltage reduction K is:
K = Vo / Vi = R2 / (R1 + R2)
To get a specified output voltage from a known input voltage, pick one of the resistor values and solve for the other:
R2 = Vo * R1 / (Vi - Vo)
R1 = R2 * (Vi - Vo) / Vo
Or, if you know the desired fraction K and want to find the resistors:
R2 = K * R1 / (1 - K)
R1 = R2 * (1 - K) / K
The ratio of the two resistors needed for a given reduction is:
R2/R1 = K / (1 - K)
R2/R1 = Vo / (Vi - Vo)
To determine the input voltage that produces a given output voltage from a known divider:
Vi = Vo * (R1 + R2) / R2
The reduction ratio K is normally used for range changes, such as 0.10 for a 10-to-1 reduction. However, for audio work you may want to obtain a specific reduction in dB. (See dB From Voltages and Working With dB.)
The dB corresponding to a given voltage ratio is:
dB = 20 * log10(Vo / Vi)
dB = 20 * log10(K)
where log is the base-10 (common) logarithm. For voltage dividers, note that K is always less than 1, so the dB value will always be negative.
To find the ratio K corresponding to a given dB value, use the following formula. Remember to use a negative value for dB:
K = 10^(dB/20)
Typical dB values and corresponding voltage ratios:
-1 = 0.891251 -2 = 0.794328 -3 = 0.707946 -6 = 0.501187 -10 = 0.316228 -20 = 0.100000 -30 = 0.031623 -40 = 0.010000 -60 = 0.001000 -80 = 0.000100 -100 = 0.000010 -120 = 0.000001
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