Question

An amplifier has a voltage gain $A_v=1000$. The voltage gain in $dB$ is

• A. $30dB$
• B. $60dB$
• C. $3dB$
• D. $20dB$

Answer 1

The correct option is B

$60dB$

Step 1. Given data

Voltage gain, $A_v=1000$

Voltage gain is a measure of the ability of two part circuit to increase the power or amplitude of a signal from the input to the output part by adding energy converted from some power supply to the signal voltage gain in decibel.

Step 2. Finding the voltage gain

Using formula for gain, $G$ in decibel we get,

$\begin{array}{rcl}G& =& 20{\log }_{10}\left(A_v\right)\\ & =& 20{\log }_{10}\left(1000\right)\\ & =& 20{\log }_{10}{\left(10\right)}^3\\ & =& 20x3{\log }_{10}\left(10\right)\\ & =& 60dB\end{array}$
Hence, option $\left(B\right)$ is correct.