If an amplifier has a 30 dB voltage gain, what voltage ratio does the gain represent?

Question

I can't figure out this homework problem:

If an amplifier has a 30 dB voltage gain, what voltage ratio does the gain represent?

I think the formula is V in divided by V out. ?

Answer 1

Voltage dB are calculated as
dB = 20 log(v/V) where log is the common (base 10) log, v is output, and V is input. So
30 = 20 log(v/V)
3/2 = log(v/V)
10^(3/2) = v/V = √1000 = 31.622 so
v = 31.622*V

HTH ☺


Doug

Answer 2

Since this is voltage, dB is calulated using V(dB) = 20*log(V) Now gain = -6 dB so lets convert that to decimal ---> g = 10^(-6/20) = 0.501 Now Vout = g*Vin so Vin = Vout/g = 3.99 mV ~ 4 mV