Electronics > Beginners

RC time constant

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Nitrousoxide:
A good exercise would be to derive the transfer functions for a fully passive second-order network and a cascade of 1'st order networks with an intermediate buffer.

You will (or should) see that the "center" frequency will remain the same (Hint: the 0th order term in the denominator when simplifying), Whilst the 1st order term will vary. The first-order term contains information about the system damping and thus can lead you to an answer about the system settling time.

As mentioned before the "time-constant" is not really applicable to second-order systems. However, if the system is critically damped (zeta = 1), both the poles of the system will be purely real and exist on the same point (repeated root), thus it can be seen as two identical networks charging (Note: This is only for the buffered case). Think for what values of R and C this would occur.

Dave:

--- Quote from: The Electrician on August 23, 2019, 04:11:39 pm ---You didn't plot the switched value version over a wide enough frequency range:

--- End quote ---
The point stands, you can't evaluate a second order system by simplifying it to a combined response of two first order systems, because without an intermediate buffer, they affect each other.

GerryR:
Your point is well taken, but why would anyone, or should I say for what reason would anyone, put the higher break frequency of a low-pass filter ahead of the the one with the lower break frequency in a stacked filter like that?  Maybe just to prove a point??

Nitrousoxide:

--- Quote from: GerryR on August 23, 2019, 11:31:54 pm ---Your point is well taken, but why would anyone, or should I say for what reason would anyone, put the higher break frequency of a low-pass filter ahead of the the one with the lower break frequency in a stacked filter like that?  Maybe just to prove a point??

--- End quote ---

Time domain and phase response. This is could be potentially critically important for system compensation. Say for maximising time-domain performance whilst ensuring stability. (i.e. say you want an underdamped response versus a critically damped response)

rstofer:

--- Quote from: The Electrician on August 23, 2019, 04:11:39 pm ---You didn't plot the switched value version over a wide enough frequency range:

--- End quote ---

What math package did you use for that plot?  It looks like something I should be playing with.
Thanks!

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