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> Question About Active, Second-order Filter
ohio_rifleman
Posted: July 15, 2011 01:07 am
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I am looking at someone's design of an active, second-order filter. Here it is:

http://i1103.photobucket.com/albums/g471/o...orderfilter.jpg

I find this design unusual, in that it is simply two, passive, first-order filters connected in series followed by an op amp buffer. I have never seen this before; in my experience, active, second-order filters always have a Sallen-Key or multiple feedback topology.

Why would someone use this filter in lieu of a Sallen-Key or multiple feedback topology? Are there any advantages to this design? Are there disadvantages to this design? If so, what are they?


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GPG
Posted: July 15, 2011 05:04 am
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cdstahl
Posted: July 15, 2011 02:06 pm
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In this case, the RCRC network is the filter, and the opamp only serves as a buffer. The RCRC network shown is significantly affected by loading. The result would be to make R1,R2 small and C1,C2 large. This is impractical, so an opamp can be added. This allows the RCRC circuit to see a high impedance load, while allowing the actual load to see a low impedance source.

The above is how the circuit could come into being -- an attempt at a simple passive filter that requires a buffer. The RCRC filter is also easier to analyze. The circuit itself is limited to real poles, and must be overdamped. This gives a very large transition band, possibly to the point where the filter is effectively a first order design.

Other opamp-based, or LC based filters allow for complex poles. This allows for common filter types, like Butterworth, Bessel, and Chebychev to be employed. Each of which solves a slightly different set of design requirement, and none of which are necessarily optimal in a given design.

It is possible that these filter poles are desirable for some reason, though I suspect the ease of design/analysis was probably the reason it was chosen.
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ohio_rifleman
Posted: July 15, 2011 04:15 pm
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Thanks. So if I understand correctly, the major disadvantage is an over-damped response? So this design might actually be less susceptible to instability, ringing, oscillations, etc.?
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crutschow
Posted: July 15, 2011 04:35 pm
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QUOTE (ohio_rifleman @ July 15, 2011 09:15 am)
Thanks. So if I understand correctly, the major disadvantage is an over-damped response? So this design might actually be less susceptible to instability, ringing, oscillations, etc.?

Yes it would have less chance of instability, but that is not normally a problem with a properly designed Sallen-Key or multiple feedback active filter.

The big disadvantage of such an overdamped filter is that the roll-off corner is very broad and slow as compared to a critically damped filter. Normally your want as sharp a roll off as possible from a filter (the brick-wall ideal). If you need a multiple-pole filter I recommend you use a standard active filter circuit. Texas Instrument has a free download for its Filter Pro software (http://focus.ti.com/docs/toolsw/folders/print/filterpro.html) which makes it easy to design optimized active filters with various architectures and number of poles.

This post has been edited by crutschow on July 16, 2011 05:17 am


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cdstahl
Posted: July 16, 2011 12:23 am
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QUOTE (ohio_rifleman @ July 15, 2011 04:15 pm)
Thanks. So if I understand correctly, the major disadvantage is an over-damped response? So this design might actually be less susceptible to instability, ringing, oscillations, etc.?

the filter itself will be stable. The opamp itself may be unstable for unrelated reasons. Obviously if it is not unity-gain stable there will be some issues. In short, the RC-RC circuit would do nothing to stabilize an unstable opamp. However, if the opamp itself is stable, the RC-RC circuit will not make the circuit unstable.
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Sch3mat1c
Posted: July 18, 2011 07:12 pm
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Actually, the maximum Q achievable is only 1/3, i.e. it takes a long range in frequency between passband and stopband. Generally you want it as sharp as possible, given other constraints such as phase shift, flatness, etc.

A very high Q filter can be very sharp, but is prone to oscillation (overshoot, in both frequency response and waveform response), nonlinear phase shift, etc.

There are several analytical filter types which offer compromises between these extremes.

The main reason you might select a low Q (RC) filter is because you don't need much filtering (a wide band between signals of interest and noise you don't care about, such as, for instance, a pulse width modulator, where the signal might be <1kHz while the switching frequency is >100kHz), or the parts are very cheap and noncritical (common resistor and capacitor values are more than suitable).

For purposes where the waveform or time delay is important (an oscilloscope or ADC filter, a control loop where excessive delay cannot be tolerated, etc.), a Bessel filter is used. This has a very gradual drop-off with frequency, but the waveform looks the best. It still has better performance than an RC filter, because the Q is higher, but not so much that it distorts things.

For general purposes, a Butterworth filter is typical. This has "maximally flat" response, which means the gain is constant in the passband, then it drops off gradually after the cutoff point. These filters do exhibit overshoot on the waveform, though it's usually not too much (Q ~ 1).

For heavy filtering applications, like radio, a more aggressive filter can be used to separate adjacent channels. Examples are Chebyshev type I, II and Elliptical type filters (among others). The latter has the most aggressive response (even for a low-order filter, frequency response drops precipitously, allowing tightly controlled channel spacings and such), but all of these types exhibit uneven gain, either in the passband, stopband or both.

Tim


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analogbeginer
Posted: March 07, 2012 10:03 am
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Hi Tim,

It seems that you are an expert in this field. But one small query. Generally the butterworth filter co-effiecint are chosen such that 60 degree of pahse margin is achieved, which corresponds to 1/sqrt(2) as the damping factor. So, I didnt really get how even slight overshoot happens...atleast theoritically.
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Sch3mat1c
Posted: March 08, 2012 12:10 am
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Damping is not the critical factor, nor is it a necessary condition with respect to overshoot. Even a minimum-phase filter (Bessel, see http://www.dspguide.com/ch3/4.htm ) exhibits a miniscule degree of overshoot and settling. The damping coefficients on the high frequency poles in a high order Bessel are fairly large (i.e., underdamped), which effectively says they are used to "speed up" the slow, lower frequency poles which dominate in rise time.

RC filters can even be designed which exhibit gain peaking, though the effect is very small (under 10% I believe). I don't know if these exhibit overshoot in the step response as well.

Tim


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Answering questions is a tricky subject to practice. Not due to the difficulty of formulating or locating answers, but due to the human inability of asking the right questions; a skill that, were one to possess, would put them in the "answering" category.
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