I know that an integrator is an example of a low pass filter. Does this mean that all low pass filters are integrators?
low pass filter is always integrator?
Started by ●August 21, 2007
Reply by ●August 21, 20072007-08-21
On Aug 21, 1:49 pm, "dtsao" <tsaod...@yahoo.ca> wrote:> I know that an integrator is an example of a low pass filter. Does this > mean that all low pass filters are integrators?No. Jason
Reply by ●August 21, 20072007-08-21
dtsao wrote:> I know that an integrator is an example of a low pass filter. Does this > mean that all low pass filters are integrators?No. An integrator has a gain that goes as 1/f; at DC (f = 0) an integrator's gain is infinity. A low-pass filter has a gain that goes as 1/sqrt((f/f_o)^2+1), i.e. the gain is more or less level from DC to more or less f = f_o, then it starts decreasing at approximately 1/f. All low pass filters _contain_ integrators, but they aren't integrators. And all integrators are _sort of_ low pass filters, but they're not quite really low pass filters. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" gives you just what it says. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●August 21, 20072007-08-21
I think I am confused about the wording. If as you say "All low pass filters _contain_ integrators", that is what I thought we call "integrator": meaning the act of integrating somewhere in the circuit makes it an integrator. If "at DC (f = 0) an integrator's gain is infinity", then do you not consider an inverting integrator (opamp circuit with RC in the feedback whose DC gain is R2/R1) to be an "integrator". Sorry, I guess I just have some confusion on the terminology of "integrator". Is it so specific? Thanks.>dtsao wrote: >> I know that an integrator is an example of a low pass filter. Doesthis>> mean that all low pass filters are integrators? > >No. > >An integrator has a gain that goes as 1/f; at DC (f = 0) an integrator's>gain is infinity. A low-pass filter has a gain that goes as >1/sqrt((f/f_o)^2+1), i.e. the gain is more or less level from DC to more>or less f = f_o, then it starts decreasing at approximately 1/f. > >All low pass filters _contain_ integrators, but they aren't integrators.> And all integrators are _sort of_ low pass filters, but they're not >quite really low pass filters. > >-- > >Tim Wescott >Wescott Design Services >http://www.wescottdesign.com > >Do you need to implement control loops in software? >"Applied Control Theory for Embedded Systems" gives you just what itsays.>See details at http://www.wescottdesign.com/actfes/actfes.html >
Reply by ●August 21, 20072007-08-21
On Tue, 21 Aug 2007 11:00:42 -0700, Tim Wescott <tim@seemywebsite.com> wrote:>dtsao wrote: >> I know that an integrator is an example of a low pass filter. Does this >> mean that all low pass filters are integrators? > >No. > >An integrator has a gain that goes as 1/f; at DC (f = 0) an integrator's >gain is infinity. A low-pass filter has a gain that goes as >1/sqrt((f/f_o)^2+1), i.e. the gain is more or less level from DC to more >or less f = f_o, then it starts decreasing at approximately 1/f. > >All low pass filters _contain_ integrators, but they aren't integrators. > And all integrators are _sort of_ low pass filters, but they're not >quite really low pass filters.Would it be OK to say if the "leakiness" of the integrator reaches to a certain level it behaves as a low pass filter ?
Reply by ●August 21, 20072007-08-21
dtsao wrote: (top posting fixed)>> dtsao wrote: >>> I know that an integrator is an example of a low pass filter. Does > this >>> mean that all low pass filters are integrators? >> No. >> >> An integrator has a gain that goes as 1/f; at DC (f = 0) an integrator's > >> gain is infinity. A low-pass filter has a gain that goes as >> 1/sqrt((f/f_o)^2+1), i.e. the gain is more or less level from DC to more > >> or less f = f_o, then it starts decreasing at approximately 1/f. >> >> All low pass filters _contain_ integrators, but they aren't integrators. > >> And all integrators are _sort of_ low pass filters, but they're not >> quite really low pass filters. >> >> -- >> >> Tim Wescott >> Wescott Design Services >> http://www.wescottdesign.com >> >> Do you need to implement control loops in software? >> "Applied Control Theory for Embedded Systems" gives you just what it > says. >> See details at http://www.wescottdesign.com/actfes/actfes.html >>> > I think I am confused about the wording. If as you say "All low pass > filters _contain_ integrators", that is what I thought we call > "integrator": meaning the act of integrating somewhere in the circuit > makes it an integrator. All (working) cars contain motors, but at lunch time you don't say to the hot babe "let's jump in my motor and get some food." > If "at DC (f = 0) an integrator's gain is infinity", then do you not > consider an inverting integrator (opamp circuit with RC in the feedback > whose DC gain is R2/R1) to be an "integrator". If the DC gain is finite then it is, ipso facto, not an integrator (except in the case of a "leaky" integrator where the intended function is an integrator, but you intentionally make it less than perfect for other practical reasons). As with cars and motors, you can open the hood and point to the integrator, or at least point out where integration is happening. > Sorry, I guess I just have > some confusion on the terminology of "integrator". Is it so specific? It is in this office! > Thanks. > -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" gives you just what it says. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●August 21, 20072007-08-21
mk wrote:> On Tue, 21 Aug 2007 11:00:42 -0700, Tim Wescott <tim@seemywebsite.com> > wrote: > >> dtsao wrote: >>> I know that an integrator is an example of a low pass filter. Does this >>> mean that all low pass filters are integrators? >> No. >> >> An integrator has a gain that goes as 1/f; at DC (f = 0) an integrator's >> gain is infinity. A low-pass filter has a gain that goes as >> 1/sqrt((f/f_o)^2+1), i.e. the gain is more or less level from DC to more >> or less f = f_o, then it starts decreasing at approximately 1/f. >> >> All low pass filters _contain_ integrators, but they aren't integrators. >> And all integrators are _sort of_ low pass filters, but they're not >> quite really low pass filters. > > Would it be OK to say if the "leakiness" of the integrator reaches to > a certain level it behaves as a low pass filter ?"Leaky integrator" vs. "low pass filter" is more a difference in intent rather than design. If you are primarily interested in the behavior of the device at the frequencies where the gain is dropping at 20dB/decade and the phase is -90 degrees then it is an integrator, leaky or not. If you are primarily interested in the behavior of the device at the frequencies where the gain is quite close to the DC gain and the phase isn't shifted that much, then it is a low-pass filter. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" gives you just what it says. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●August 21, 20072007-08-21
dtsao wrote:> I know that an integrator is an example of a low pass filter. Does this > mean that all low pass filters are integrators?At least a little bit. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●August 21, 20072007-08-21
Ok, since an "integrator" is not exactly interchangeable with "low pass filter", does that mean when designing a 2nd order (or Nth order) sigma-delta ADC, I must use a series of first order integrators? Meaning, these integrators cannot be replaced by any kind of Nth order low pass filter design?
Reply by ●August 21, 20072007-08-21
dtsao wrote:> I think I am confused about the wording. If as you say "All low pass > filters _contain_ integrators", that is what I thought we call > "integrator": meaning the act of integrating somewhere in the circuit > makes it an integrator. > If "at DC (f = 0) an integrator's gain is infinity", then do you not > consider an inverting integrator (opamp circuit with RC in the feedback > whose DC gain is R2/R1) to be an "integrator". Sorry, I guess I just have > some confusion on the terminology of "integrator". Is it so specific? > Thanks.Consider a simple R-C lowpass, the R providing a source resistance, and the C, connected across the load, bypassing high frequencies around it. The magnitude transfer function of such a filter is h = 1/sqrt[1+(f/f_0^2)], where f is the frequency of interest, and f_0 is the "corner" frequency -- the half-power frequency -- and equals 1/(2piRC.) At very low frequencies, f/f_0 is small enough for its square to be neglected, and h equals one. This constant response is nothing like an integrator's. I think it may be misleading to say that a low-pass filter "contains" an integrator. Certainly is does not in the same sense that a can in my larder contains baked beans. What it does have is a term f/f_0 in the denominator. (In this case, 1/sqrt(f/f_0^2), but no matter.) That is the hallmark (and the transfer function) of an integrator. Its integration character is manifest in its property that the filtered signal is influenced by its past, the more recent the signal, the more the influence. The distant past is "forgotten". We call this a "leaky integrator". Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
