# 3.13: Exercises

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1. A superheterodyne receiver has, in order, an antenna, a low-noise amplifier, a bandpass filter, a mixer, a second bandpass filter, a second mixer, a lowpass filter, an ADC, and a DSP that will implement quadrature demodulation. Develop the frequency plan of the receiver if the RF input is at $$2\text{ GHz}$$ and has a $$200\text{ kHz}$$ single-channel bandwidth. The final signal applied to the ADC must be between DC and $$400\text{ kHz}$$ so that $$I/Q$$ demodulation can be done in the DSP unit. Noise considerations mandate that the LO of the first mixer must be more than $$10\text{ MHz}$$ away from the input RF. Also, for a bandpass filter to have minimum size, the center frequency of the filter should be as high as possible. It has been determined that the appropriate trade-off of physical size and cost is to have a $$100\text{ MHz}$$ bandpass filter between the two mixers. (Note: $$100\text{ MHz}$$ is the center frequency of the bandpass filter.)
1. Draw a block diagram of the receiver and annotate it with symbols for the frequencies of the LOs and the RF and IF signals.
2. What is the LO frequency $$f_{\text{LO1}}$$ of the first mixer?
3. What is the LO frequency $$f_{\text{LO2}}$$ of the second mixer?
4. Specify the cutoff frequency of the lowpass filter following the second mixer.
5. Discuss in less than $$\frac{1}{2}$$ a page other design considerations relating to frequency plan, filter size, and filter specification.
2. Short answer questions. Each part requires a short paragraph of about five lines and a figure where appropriate to illustrate your understanding.
1. Explain the operation of a superheterodyne receiver.
2. Compare zero-IF and low-IF receivers.

This page titled 3.13: Exercises is shared under a CC BY-NC license and was authored, remixed, and/or curated by Michael Steer.