Electronics > Beginners
RC time constant
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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