Skip to main content
Engineering LibreTexts

3.13: Exercises

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    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.

    • Was this article helpful?