RF Sampling Mixer


  • A simple passive sampling mixer is shown in Figure 1.

    RF Sampling Mixer

    Figure 1. RF sampling mixer

  • Sample RF signal at much lower frequency (LO frequency need not be near to RF)
  • RF sampling mixer can be modeled as sampler followed by a ZOH circuit as shown in Figure 2.
  • A continuous time signal(v_{RF}(t)) sampled at uniform sampling frequency(f_s) is given by

    (1)   \begin{equation*} v_{s,RF}(t) = v_{RF}(t)p(t) = \sum\limits_{n=-\infty}^{\infty} v_{RF}(nT_s) \delta(t-nT_s) \end{equation*}

    (2)   \begin{equation*} V_{RF}(\omega) = {1\over T_s}\sum\limits_{k=-\infty}^{\infty} V(\omega-k\omega_s) \end{equation*}

  • Hold circuit

    (3)   \begin{equation*} h(t) = \begin{cases} 1, & -T_h/2 < t < T_h/2 \\ 0, & \mbox{elsewhere} \end{cases} \end{equation*}

    Fourier transform is

    (4)   \begin{equation*} H(\omega) = T_h {\sin(\omega T_h/2) \over \omega T_h/2} \end{equation*}

  • The output after hold circuit is,

    (5)   \begin{eqnarray*} v_{o}(t) &=& v_{s,RF}(t)*h(t) \\ &=& (T_h f_s) {\sin(\omega T_h/2) \over \omega T_h/2} \underbrace{\sum\limits_{k=-\infty}^{\infty} V(\omega-k\omega_s)}_{\text{spectral images}} \end{eqnarray*}

    The spectral images of RF signal are suppressed by the sinc function
    At f_{IF}, Conversion gain = T_h f_s

Noise Figure

  • The capacitive load(C_L) of S/H circuit eliminate the noise due to R_L

[1]

References

[1] [doi] R. G. Vaughan, N. L. Scott, and D. R. White, “The Theory of Bandpass Sampling,” IEEE Transactions on Signal Processing, vol. 39, iss. 9, pp. 1973-1984, 1991.

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