Discussion
A receiver has an intermediate frequency of \( 455 \ \mathrm{kHz} \) and a preselector quality factor of \( 50 \) at \( 1000 \ \mathrm{kHz} \). Its image rejection ratio is roughly
Answer: B
The image is \( 910 \ \mathrm{kHz} \) away, so the detuning ratio is large:
\[ \begin{aligned} \rho &= \tfrac{1910}{1000} - \tfrac{1000}{1910} \approx 1.39 \\ \text{ratio} &\approx \sqrt{1 + (50 \times 1.39)^{2}} \approx 70 \end{aligned} \]
which is about 37 dB, so about 40 dB. The rejection depends on the quality factor and on how far out the image lies, which is why both the preselector and the choice of intermediate frequency appear in the answer.
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