op amp differentiator

Discussion in 'Homework Help' started by rafeekrs, Aug 20, 2010.

  1. rafeekrs

    Thread Starter New Member

    Aug 20, 2010
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    i had found in a text book(gaykwad) that for proper differenciation the condition to be satisfied is T lessthan or equal to Rf*c1.what is the theoretical concept behind this
     
  2. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469

    It's helpful to have the circuit schematic to be sure, but my guess is that you have some type of high pass filter with a cutoff frequency set by Rf*c1. However, if this is the case, you have stated it backward. The period T must be much greater than the Rf*c1.

    If this is correct, the theoretical concept is that the low frequency range of a simple high pass filter looks similar to a differentiator in the frequency domain. Note the transfer function of a simple high pass filter is as follows.

    {{V_o}\over{V_i}}={{s}\over{s + {{{1}/{RC}}} }}

    in the limit as T=1/f goes to infinity, the transfer function looks like ...

    {{V_o}\over{V_i}}\approx{{s}\over{0+ {{{1}/{RC}}} }}=sRC

    Remember that a differentiator has a transfer function of s, so the high pass filter is a scaled version of a differentiator in the limit as frequency gets small (or period T gets large).

    If it turns out that you are correct and T must be less than Rf*c1 then it means you have a more complicated circuit, and we would need to see it. However, any circuit you have will have to operate in a frequency range where the transfer function approximately looks like a scaled differentiator.
     
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