D/A converter help plze

Discussion in 'General Electronics Chat' started by kaznov, Apr 18, 2012.

  1. kaznov

    Thread Starter Member

    Mar 10, 2012
    30
    0
    the attached circuit is the 4-bit resistor ladder D/A with digital input of 0001 . for the simplcity we assume all values of R is the same . I didnt really get how the analoug output voltage came to be -(1/16)Vs . I did combine 2R with 2R which they located in the farthest right so they are in parellel and I know that the gain (V out/V in ) for this inverting circuit is -R(feedback) / R but I still didnt get Vout = - 1/16 Vs

    any help please
     
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  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
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    A simple approach is to assume a current Io flows via the 2R resistor via the bo active switch and into the Op-Amp feedback resistor R.

    This gives a Vout=-Io*R

    The Op-Amp feedback will force the (switched) bo switch node to ground potential. Hence if Io is flowing via the 2R resistor & bo switch then the rightmost 2R resistor in the R-2R ladder network will also have an equal current Io flowing to the rightmost ground terminal.

    The potential at the top-line rightmost ladder network node will then be Io*2R volts.

    The rightmost R resistor in the ladder network will therefore be carrying a current of (Io+Io)=2*Io amps. The voltage drop across this resistor will be 2*Io*R volts, meaning the potential at the next left node of the ladder network will be 4*Io*R volts.

    The current in the 2R resistor at the grounded (un-switched) b1 switch position will then be 2*Io amps. This means the current in the next left R resistor in the R-2R will be 4*Io amps. This will give a potential at the next left node in the ladder network of 8*Io*R volts.

    The current in the 2R resistor at the grounded b2 switch position will then be 4*Io amps. This means the current in the next left R resistor in the ladder network will be 8*Io amps, giving a potential at the next left-hand node in the R-2R network of 16*Io*R volts. This will in fact be the same potential as Vs.

    That is, Vs=16*Io*R volts.

    One should note in passing that the (un-switched) grounded b3 switch condition has no bearing on the output voltage.

    We know from the initial assumptions above that Vout=-Io*R

    In addition knowing Vs=16*Io*R we may eliminate the unknown Io and conclude that Vout=-Vs/16 volts
     
  3. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Posting a rough image of the annotated schematic to 'match' with the previous verbose post.
     
  4. kaznov

    Thread Starter Member

    Mar 10, 2012
    30
    0
    thanks alot guys that helpes a lot :)
     
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