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A pair has a differential gain of \( 200 \) and a common-mode gain of \( 0.02 \). Its rejection ratio is

  • A.20 dB
  • B.80 dB
  • C.40 dB
  • D.10000 dB

Answer: B

Taking the ratio and converting:

\[ \begin{aligned} \text{CMRR} &= \tfrac{200}{0.02} = 10^{4} \\ &= 20\log_{10}10^{4} = 80 \ \mathrm{dB} \end{aligned} \]

giving 80 dB. The value 10000 is the ratio itself rather than its decibel form, and forty decibels would follow from the power convention, which does not apply to a ratio of voltage gains. Establishing whether a quantity is a power or an amplitude before converting is what settles the factor of two. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

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