Discussion
If differential amplifier has a differential gain of 20,000. CMRR = 80 dB, then common mode gain is
Answer: A
The common mode gain is 2, option (A). The CMRR in decibels is \(20\log_{10}(A_{d}/A_{c})\), so 80 dB means a ratio of \(10^{4}\).
\[ \text{CMRR} = 10^{80/20} = 10^{4} \]
\[ A_{c} = \frac{A_{d}}{\text{CMRR}} \]
\[ = \frac{20{,}000}{10{,}000} = 2 \]
Option (B), 1, would need a CMRR of 20,000. Option (C), one half, would need a CMRR of 40,000. Option (D), 0, is the common mode gain of an ideal amplifier with an infinite CMRR, which a real one with 80 dB does not have.
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