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R-2R ladder D/A converter problem

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  1. Dec 27, 2015 #1
    1. The problem statement, all variables and given/known data
    R-2R ladder question.png
    Simplify in order to find voltage output.

    2. Relevant equations
    Vout= -Vref x (A + B/2 + C/4 + D/8)

    3. The attempt at a solution
    R-2R ladder Q attempt.png
    Firstly is this even correct?
    Secondly, I have 2 voltages (2.5V and 5V), what should I do now? what is my Vref?
     
  2. jcsd
  3. Dec 27, 2015 #2

    Hesch

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    Gold Member

    Vref = 0V

    I think that what is meant is that you must form a Thevenin equivalent from R1, R2:
    Vth12 = 0V , Rth12 = R1 || R2 = 1Ω.
    Now, this equivalent is connected in series with R3, giving Rth123 = 2Ω , Vth123 = 0V.

    In this way you successive form new equivalents from left to right, until you have an equivalent for R1 . . R8 and VD . . VA.
    Then you can calculate Vout.
     
    Last edited: Dec 27, 2015
  4. Dec 28, 2015 #3
    Hi, I don't understand why Vref = 0. I have 2 inputs; 5V and 2.5V. I thought one or both of those would be Vref. Also if Vref is zero, wouldn't Vout also be zero?
     
  5. Dec 28, 2015 #4

    Hesch

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    Gold Member

    The 2.5V is not an input, but ( I assume ) an internal analog voltage you have calculated. I don't know how.

    The ⊥ - symbol is Vref = 0V, and the terminals: A . . D are inputs ( something like TTL-level logic ( 0V = low level, 5V = high level ) ).

    Vout will be a negative voltage, due to an inverting amplifier. Don't care about that, just calculate :smile:.
     
  6. Dec 29, 2015 #5

    gneill

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    Staff: Mentor

    If you are looking for the ##V_{ref}## that fits your relevant equation, then set voltages B,C, and D to zero and then find the output due to voltage A alone. Then set ##V_{ref}## to a value that satisfies the reference equation for that scenario.
     
  7. Dec 29, 2015 #6
    The problem is only C and D are 0V (A and B are both 5V), so I don't know how to do this problem. I've only been taught binary inputs where there is only one input.
     
  8. Dec 29, 2015 #7

    gneill

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    Staff: Mentor

    Just set B,C, and D to zero volts for purposes of finding your Vref. It should be clear that A,B,C,and D are inputs for this circuit, and apparently the logic levels are 0V and 5V.

    After you determine Vref you can find the output given any combination of inputs by using your relevant equation.
     
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