Question

If each stage of a three-stage amplifier has a gain of \(10\), the overall gain in dB is

• A. \(10\,\text{dB}\)
• B. \(20\,\text{dB}\)
• C. \(30\,\text{dB}\)
• D. \(60\,\text{dB}\)

Hint:

For cascaded amplifiers, \[ \boxed{ A_{\text{total}}=A_1A_2A_3\cdots } \] and \[ \boxed{ G_{dB}=20\log_{10}(A_v). } \]

Answer 1

The Correct Option is D

Step 1: Calculate the overall voltage gain. Each stage has a gain of \[ A_v=10. \] For three cascaded stages, \[ A_{v(\text{total})} = 10\times10\times10 = 1000. \]

Step 2: Convert the gain into decibels. Voltage gain in decibels is \[ G_{dB} = 20\log_{10}(A_v). \] Therefore, \[ G_{dB} = 20\log_{10}(1000) = 20\times3 = 60\,\text{dB}. \] Hence, \[ \boxed{60\,\text{dB}} \] Therefore, \[ \boxed{(D)} \] is the correct answer.