Question

Three identical amplifiers with each one having a voltage gain of 50, input resistance of 1 kΩ and output resistance of 250 Ω are cascaded. The open circuit voltage gain of the combined amplifier is

• A. 49 dB
• B. 102 dB
• C. 98 dB
• D. 51 dB

Hint:

For cascaded amplifiers, the total gain is the product of the individual gains, and the total dB gain is calculated using \( 20 \log_{10}(\text{Total Gain}) \).

Answer 1

The Correct Option is C

When amplifiers are cascaded, the total voltage gain is the product of the individual gains. The voltage gain in dB is given by: \[ A_{dB} = 20 \log_{10} \left( \text{Total Voltage Gain} \right) \] For three amplifiers with individual gains of 50, the total voltage gain is: \[ \text{Total Voltage Gain} = 50 \times 50 \times 50 = 125000 \] Now, converting this to dB: \[ A_{dB} = 20 \log_{10}(125000) \approx 98 \, \text{dB} \] Thus, the correct answer is option (3).