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Math Help - Average value of a decaying exponetial

  1. #1
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    Average value of a decaying exponetial

    Hi all… I’m new to the forum and I’m here because I’m in need of HELP!!!! It’s been more than 30 years since I’ve seen the inside of a classroom and my “math skills” are beyond “rusty”… they’re more like “seized” and hopefully someone can point me in the right direction.

    My problem is electrical in nature… I have a capacitor that is discharging through a resistor and I would like to know the average value of the exponential discharge current over a period that is much, much greater than 6 time constants of the RC circuit. What is the proper way to calculate the “average” value of that decaying exponential? I tried taking the integral of “the function” divided by difference of the limits which is the period of time I’m interested in… I did not get the correct answer, as it doesn’t agree with the circuit’s actual performance.

    Any help would be appreciated!!!

    Thanks
    Gus
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  2. #2
    MHF Contributor Calculus26's Avatar
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    rc circuit

    Gus could you post your work and the results you would expect?
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  3. #3
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    Hi Calculus26... thanks for the reply... see the attachment

    The output of the 555 drives the RC. All of the circuit isn't here, but there is a diode from Vcc that charges the "unknown cap" (1µF was chosen for the math) while the 555 output is low, and another diode from the same node in series with a 50µA ammeter back to Vcc that discharges the cap. It's basically a voltage doubler. A simulation and an actual circuit show that the correct answer should be a full scale reading of 50µA... my answer isn't even close!!
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  4. #4
    MHF Contributor Calculus26's Avatar
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    The integral

    Gus

    Using your data I get 1.149*10^-4 roughly twice your expected value.

    Did you do the integral by hand or did you let mathcad do it?
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  5. #5
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    I let mathcad do it.
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