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ADC input referred noise

  1. Jun 12, 2015 #1
    1. The problem statement, all variables and given/known data

    A simplified model of ADC noise refers the noise to a noisy source resistance Rn while assuming the rest of the signal path to be noiseless. Figure 3 represents a particular 18-bit ADC that has a 10 V input voltage range. The ADC has a bandwidth of 1 MHz.

    Calculate the maximum value of Rn if the resolution of the ADC is not to be adversely affected by thermal noise. Assume the ADC operates at 25 degrees C.

    [N.b. The voltage resolution of an ADC is equal to its overall voltage measurement range divided by the number of discrete values possible on its output.] ADC.png FIG. 3

    2. Relevant equations

    3. The attempt at a solution

    The issue of resolution has totally thrown me off but here is what I'm thinking.

    Rn = (Vn \ 4kTRB), where k is the Boltzmann constant.

    Vn = ? I'm not sure whether Vn = resolution or full scale voltage.

    It's all I got for now, please help!

    Last edited by a moderator: Jun 12, 2015
  2. jcsd
  3. Jun 12, 2015 #2


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    Staff: Mentor

    That equation does not look correct. What is the equation for the thermal noise voltage in terms of of k and T and R and B?
  4. Jun 12, 2015 #3
    Thanks, Yea my mistake

    Vn = sqrt(4kTBR)


    R = (Vn^2 / 4kTB)
  5. Jun 12, 2015 #4


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    Staff: Mentor

    Ah, much better. I was getting vertigo trying to decipher what you wrote. :smile:

    So now you're pretty much done. Take the input voltage range and divide by the total resolution (18 bits is how many steps?). Then apply the formula...
  6. Jun 12, 2015 #5


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    Staff: Mentor

    Oh, and remember that T is absolute temperature...
  7. Jun 12, 2015 #6
    Input voltage resolution

    18bits = 2^18 steps = 262144

    Voltage range / steps = (10 / 262144)

    Vn = 38.14697 x 10^-6 V

    Is that correct?
  8. Jun 12, 2015 #7


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    Staff: Mentor

    Yes, I get 38.15uV as well. So what is the equivalent resistance to make that noise voltage at (absolute) room temperature?
  9. Jun 12, 2015 #8
    Converting Celsius to Kelvin

    25degrees = 298.15 K

    Plugging numbers into equation

    Rn = (38.15 x 10^-6)^2 / (4 x (1.38 x 10^-23) x 298.15 x 1000000)

    = 88433.17

    Rn = 88.4 kOhms
  10. Jun 12, 2015 #9


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    Staff: Mentor

    Looks like a reasonable value. Do you know if it's correct?
  11. Jun 12, 2015 #10
    I hope it is correct, will send it for marking. Thanks for your help, much appreciated.
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