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RC time constant

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GerryR:
The first R-C group has a break frequency at 1/ 2pi R1C1 at 20 db / decade (1st order filter); the second R-C group has a break frequency at 1/2pi R2C2 at 20 db / decade (1st order filter).  Where the frequencies overlap, they roll off at 40 db / decade, a 2nd order filter.  :-//

Dave:

--- Quote from: GerryR on August 23, 2019, 12:25:36 am ---The first R-C group has a break frequency at 1/ 2pi R1C1 at 20 db / decade (1st order filter); the second R-C group has a break frequency at 1/2pi R2C2 at 20 db / decade (1st order filter).  Where the frequencies overlap, they roll off at 40 db / decade, a 2nd order filter.  :-//

--- End quote ---
Well, let's put this claim to the test.



Seems to hold up, -20 dB per decade after the first break frequency, -40 dB per decade after the second break frequency. So far so good.

Now let's switch their values.


Hmm... Weird, it suddenly behaves just like a 1st order LPF. The corner frequency seems to be closest to 1 / (2 * pi * R1 * C2).
It's almost as if the second pair of components is affecting the response of the first pair. ::)

Mattjd:

--- Quote from: rstofer on August 22, 2019, 02:48:12 pm ---
--- Quote from: Dave on August 22, 2019, 10:34:32 am ---If you do need an analytic solution, the URL I provided above has everything you need.

--- End quote ---

That's a great link!  You just know the thing is a second order differential equation and that Laplace Transforms are going to show up somewhere.  MATLAB can probably plot the equation for particular values.

LTspice is one way, Runge-Kutta and Fortran is another.

For a second order system, what does "time constant" even mean?  63% charge on the first capacitor or on the second capacitor?

--- End quote ---


there's a lot of heuristics, but for example, if you have a nth order system, depending on location of poles/zeros and what their residuals are (wrt to the dominate poles), you can ignore them and treat it as a 2nd order system. Same applies for a second order system

The Electrician:

--- Quote from: Dave on August 23, 2019, 01:03:10 pm ---
--- Quote from: GerryR on August 23, 2019, 12:25:36 am ---The first R-C group has a break frequency at 1/ 2pi R1C1 at 20 db / decade (1st order filter); the second R-C group has a break frequency at 1/2pi R2C2 at 20 db / decade (1st order filter).  Where the frequencies overlap, they roll off at 40 db / decade, a 2nd order filter.  :-//

--- End quote ---
Well, let's put this claim to the test.

(Attachment Link)

Seems to hold up, -20 dB per decade after the first break frequency, -40 dB per decade after the second break frequency. So far so good.

Now let's switch their values.
(Attachment Link)

Hmm... Weird, it suddenly behaves just like a 1st order LPF. The corner frequency seems to be closest to 1 / (2 * pi * R1 * C2).
It's almost as if the second pair of components is affecting the response of the first pair. ::)

--- End quote ---

You didn't plot the switched value version over a wide enough frequency range:

bson:

--- Quote from: GerryR on August 23, 2019, 12:25:36 am ---The first R-C group has a break frequency at 1/ 2pi R1C1 at 20 db / decade (1st order filter); the second R-C group has a break frequency at 1/2pi R2C2 at 20 db / decade (1st order filter).  Where the frequencies overlap, they roll off at 40 db / decade, a 2nd order filter.  :-//

--- End quote ---
Please don't do posters' homework for them here.  Hints are fine, but they need to do their own homework!

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