Thread: 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

Gus could you post your work and the results you would expect?

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!!

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?

I let mathcad do it.