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Homework Help: Signal to noise ratio for thermal and shot noise

  1. Jan 10, 2014 #1
    1. The problem statement, all variables and given/known data
    The output of a sensor which produces 10000 electrons is connected to parallel RC circuit with Resistance= 50 ohm, and the capacitance=10pF.
    Calculate the signal to noise ratio at temperature 300K.

    2. Relevant equations
    SNR= 10 log (power of signal/ power of noise)
    Or SNR = 20log ( voltage signal / voltage noise)

    3. The attempt at a solution
    Power of signal= voltage square / resistance= 7791.2 J
    But how to calculate power of noise? The thermal noise = 4kTf, where k is boltzman constant, f is frequency bandwidth. Yet not given , but I can only think of these formula for thermal noise and 10000 electron need to include shot noise?

    Please help
  2. jcsd
  3. Jan 11, 2014 #2


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    Science Advisor
    Gold Member

    Check your equation for the voltage on a capacitor--it's not quite right. Then use this hint: the noise bandwidth is determined by the RC filter.
  4. Jan 11, 2014 #3

    rude man

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    Homework Helper
    Gold Member

    Is that 10,000 electrons or 10,000 electrons per second?
  5. Jan 11, 2014 #4
    Yup, V =Q/C , and f=1/(2∏RC)
    But why is this the Bandwidth? The impedance of capacitor is same as resistance so we get maximum power for?
    And 10000 electrons need to consider shot noise? If I consider, so I just add thermal noise voltage and shot noise together to get the total voltage noise?
  6. Jan 11, 2014 #5
    10000 electrons without telling time, but even telling time, I still can calculate the thermal and shot noise.
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