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Question no. 26696

If a three-stage electronic amplifier features individual stage gains of 10 dB, 5 dB, and 12 dB, what is the total cumulative gain in dB____________?

Select your answer for: If a three-stage electronic amplifier features individual stage gains of 10 dB, 5 dB, and 12 dB, what is the total cumulative gain in dB____________?
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Answer: D. 27 db

Explanation

Total gain in decibels for cascaded amplifier stages is found by taking the direct algebraic sum of the individual stage decibel gains. Decibel units represent logarithmic power ratios, allowing engineers to add stage gains together rather than multiplying linear voltage ratios. Summing the individual decibel values of ten, five, and twelve yields a cumulative total gain of exactly twenty-seven decibels. Cascaded electronic amplifiers connect multiple stages in series to achieve higher overall signal gain than any single stage provides. The decibel scale compresses large multiplication factors into manageable additive numbers, simplifying cascade system analysis and design. Logarithmic math rules dictate that multiplying linear gains corresponds directly to adding their logarithmic decibel equivalents together.

Six hundred decibels is mathematically incorrect and represents an extreme exaggeration resulting from improper multiplication instead of addition. Twenty-four decibels is an incorrect arithmetic sum of the provided stage values due to calculation errors in addition. Fourteen decibels fails to account for the correct cumulative addition of all three positive amplifier stage gain values.

Subject
Engineering
Topic
—
Difficulty
medium

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