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Transfer function of the circuit

user4090349
Intellectual 951 points
Other Parts Discussed in Thread: TINA-TI

Hello

I would like to understand the charge curve on C1. I would like a transfer function show the relationship of Vo(voltage on C1) and t.

And for this charge signal, is it possible to find a op amp to follow the signal.

Thanks!

  • Former Member
    0 Former Member

    Hello,

    Below is my solution.  Including every step would make things very long.  So, I have simplified down to an ordinary differential equation and then assumed a solution form.  You can search for solution forms online and come across the same format.

    As you can see, the equation has a similar form as the simple RC filter just with some more complicated coefficients.  This seems reasonable to me.  I have checked my work, but you may wish to double check it as well since it is long and involved.

    For your question about using an amp to follow the signal, I am not sure I completely understand your question.  Would you mind asking again in a different way?  Thanks!

    Regards,
    Daniel

  • Former Member
    0 Former Member in reply to Former Member

    To be clear, this is the final answer at the bottom of the work.  What I assumed is that we know the solution form for the differential equation.  This way, we don't have to solve the differential equations from scratch, which would make things more tedious.

    Regards,
    Daniel

  • 0 in reply to Former Member
    Intellectual 951 points

    Hello Daniel

    Thanks a lot for your support. After I check your paper. I think the function should be

    Could you check it? Thanks!

  • Former Member
    +1 Former Member in reply to user4090349

    Hi,

    Thank you for catching my mistake!  Yes, you are correct.  I got the same answer and it seems a bit more reasonable.

    Let me know if you have any follow up questions.

    Regards,
    Daniel

  • Former Member
    0 Former Member in reply to user4090349

    Hi,

    Also, please let me know if you still need an op amp suggestion for some aspect of your circuit.  I realize I may have marked this thread as resolved before potentially answering that question.

    Regards,
    Daniel

  • 0 in reply to Former Member
    Intellectual 951 points

    Hi Daniel

    Thanks! I do not have any more questions.

  • 0 in reply to user4090349
    Guru 140200 points

    This is a nice excercise for the Laplace-Transformation :-)

    Kai

  • Former Member
    0 Former Member in reply to kai klaas69

    Hi Kai,

    Yes, a good electrical engineer would not be so silly as to deal with the differential equation mess and would use his handy Laplace transformation table!  I am afraid I have been exposed.  Slight smile

    Thanks for confirming.  I think your answer with the simplified time constant is a bit more clean.  Have a nice weekend!

    Regards,
    Daniel

  • 0 in reply to Former Member
    Intellectual 951 points

    Thanks Daniel and Kai

    It is amazing to see the different method to solve the problem with same result. For me, no silly tool, only right tool.Grinning

    Thanks again for the support

  • 0 in reply to Former Member
    Guru 140200 points

    Hi Daniel, hi User,

    doing the Laplace-Transformation looks like overkill here and the approach Daniel shows leads to the solution much faster. But when the circuit becomes more and more extensive, doing the Laplace-Transformation is the far better way.

    Today my preferred method when only being interested in the final solution is using a simulator like TINA-TI, LTSpice, or else. So from to time I'm happy to have the opportunity to go the rocky road Relaxed

    Have a nice weekend too!

    Kai