Electronics > Beginners
RC time constant
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Wimberleytech:

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But now with the availability of software like Mathematica with built-in Inverse Laplace transforms, and fast computers to go along with the software, it's quicker to get the analytical expression for the time response than to calculate the Elmore delay.


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To be fair, I think Pileggi's work was not simply to analyze an RC network.  IMHO, his work was to develop a fast method to calculate delays in large-scale timing analyzers (for integrated circuit design).
schratterulrich:
In general for second order systems there exists three cases:
Critically damped
Underdamped
Overdamped

if we assume that this circuit always generates an overdamped case, there is a simpler analytic solution in the time domain:

proof:


I have derived the formula using this document:
https://www.eal.ei.tum.de/fileadmin/tueieal/www/courses/AESACA/5__Responce_first_and_second.pdf


ledtester:

--- Quote from: schratterulrich on August 31, 2019, 04:02:47 pm ---if we assume that this circuit always generates an overdamped case, there is a simpler analytic solution in the time domain:

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This condition always holds.

It follows from the inequality a^2 + b^2 >= 2*a*b. Use a = sqrt(R1*C1), b = sqrt(R2*C2).

It follows from the inequality \$a^2 + b^2 \ge 2ab\$. Use \$a = \sqrt{R_1C_1}\$, \$b = \sqrt{R_2C_2}\$.

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