In electronics, the decibel is often used to express power or amplitude ratios (as for gains) in preference to arithmetic ratios or percentages. For example, the cutoff frequency is usually defined as the point at which the gain falls off −3 dB. When we use decibel to compare the power, we use therefore the log(Pout/Pin) Because The formula to calculate the power gain is therefore Gain=log(Pout/Pin)=20log(Uout/Uin) At -3dB point, the Uout/Uin=0.707, which means the amplitude of the input signal is damped to about 70%.
If the input signal has to be damped to 5%, the Gain=20log(0.05)=-26dB.
