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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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