Power gain and Voltage gain in dB
Suppose the input power is Pi and output power is Po.
Power gain, Ap (linear) = Po/Pi [W/W]; Power gain, Ap (dB) = 10*log10(Po/Pi).
[Why do we express dB as above? Because, dB (decibel) is defined as one tenth of a
B (Bel) or 1 dB = (1/10) B or 1 B = 10 dB. Note that log10 (ratio) has a unit of bel. In
order to express in dB, we multiply them by factor of 10. So, Ap=log10(Po/Pi) B or
Ap=10*log(Po/Pi) dB].
Voltage gain (linear) = Vo/Vi [V/V], Voltage gain (dB) = 20*log10 (Vo/Vi)
[Why is voltage gain defined as 20*log10 (Vo/Vi)? Because if you have same input
and output resistance, say R, then Po=Vo2/R and Pi=Vi2/R. Now, Po/Pi= Vo2/ Vi2. In
dB it would be, 10*log10(Vo2/ Vi2)=20*log10 (Vo/Vi)].
Note that for an order of magnitude increase (x10) , we have 10 dB increase in power
and 20 dB increase in voltage. For an order of magnitude decrease (/10), we have 10
dB decrease in power and 20 dB decrease in voltage. A decade is same as an order of
magnitude (usually log10 (numbers) are plotted as x axis).
Remember the following:
Power ratio, P(dB) => 10*log10 (P1/P2);
Voltage ratio, V(dB)=20*log10(V1/V2);
Current ratio, I(dB)=20*log10(I1/I2);
Impedance ratio, Z(dB) = 20*log10(Z1/Z2)
Use the following table for quick conversion:
Linear Value
dB Value [10*log10 (Linear)]
0.001 (=10-3)
-30 dB
0.01 (10-2)
-20 dB
0.1 (10-1)
-10 dB
0.5
-3 dB
1
0 dB
5
3 dB
10
10 dB
100 (102)
20 dB
1000 (103)
30 dB