The figure is shows the first stage of a superheterodyne receiver. The desired input signal is at a frequency of $700 \; \mathrm{MHz}$. The local oscillator $\text{(L.O)}$ frequency is $1 \; \mathrm{GHz}$. The mixer is an ideal multiplier with a gain independent of frequency. A band-pass filter $\text{(BPF)}$ is used to select the Intermediate Frequency $\text{(IF)}$ output at $300 \; \mathrm{MHz}$.
- What is the image frequency of the desired input?
- A Low Pass Filter $\text{(LPF)}$ can be used before the mixer to reject the image frequency. If a perfect rejection (zero transmission) of the image is desired, what type of $\text{(LPF)}$ should be employed?
- The input in the figure is corrupted by an undesired $750 \; \mathrm{MHz}$ signal which has the same amplitude as that of the desired signal at $700 \; \mathrm{MHz}$. Let the $\text{(BPF)}$ be of second order. At the $\text{(BPF)}$ output, the undesired signal should be $20 \mathrm{~dB}$ below the desired signal. Calculate the $Q$ required for the $\text{(BPF)}$.