Three identical cascaded amplifiers each feature a 50 voltage gain, 1 KΩ input resistance, and 250 output resistance. The composite open-circuit voltage gain is_________?
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Answer: C. 98dB
Explanation
Decibel voltage gains of identical cascaded amplifier stages add together directly in logarithmic scale calculations. Converting voltage gain ratios into decibels involves multiplying the common logarithm of the gain by twenty. Summing the decibel contributions of three individual amplifier stages yields the correct total composite gain value. Cascading multiple amplifier stages multiplies their individual linear voltage gains to achieve higher overall signal amplification. Decibel units simplify multiplicative gain chains into simple linear additions, easing complex system calculations. Standard logarithmic formulas define decibel voltage gain as twenty times the base-ten logarithm of the ratio.
Radio frequency communication chains cascade multiple low-noise amplifiers to boost extremely weak antenna signals. Audio mixing consoles combine numerous gain stages while tracking total signal level changes in decibels. Instrumentation systems use cascaded operational amplifiers to amplify microvolt sensor outputs to readable voltage levels. Forty-nine decibels is an incorrect mathematical calculation resulting from improper logarithmic conversion of stage gains. Fifty-one decibels miscalculates the cumulative logarithmic sum of the cascaded amplifier stages. One hundred and two decibels overestimates the combined decibel output by ignoring loading or conversion factors.
- Subject
- Engineering
- Category
- Electrical Engineering
- Topic
- —
- Difficulty
- medium
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