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| Modified second-order low pass filter (third order?) |
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| hatte:
I have been looking at ways of improving the response of a low pass filter while keeping component count and costs to a minimum. The filter will be used to remove noise at frequencies above +/- 10 kHz, and phase changes and distortions are not important. I have considered modifying a standard OpAmp-based second order filter: Would adding a capacitor to the feedback not improve the frequency response (effectiveness) of the filter, turning it into a third-order filter? I guess I could try to SPICE the filter, but I would like to hear, if you guys have other suggestions to achieve my objective. |
| Wimberleytech:
Yes, it appears to add another pole in the transfer function. It complicates the math somewhat...and thus the design procedure. If you are driving into another high-impedance stage, you could follow the Sallen-Key architecture with another RC. <<Update>> As noted by the Wizard, indeed it does not add another pole although it would appear to by affecting the gain term. The effect is really to reduce the Q |
| SiliconWizard:
Adding a cap in parallel to the negative feedback resistor won't change the order of the filter. You'll still get basically a second-order filter (-40 dB/decade), with a lowered cut-off frequency. The Q factor will also be lowered. With a properly choosen capacitance, you can actually limit the "peaking" effect of this basic sallen-key filter at the cut-off frequency. But it's still second-order. A classic way of getting an higher-order filter is to cascade filters. Going from the above sallen-key design, you could either add a passive RC filter in front of, or following it, depending on your constraints on input and output impedance. You'll get a 3-rd order filter with just 2 added passives. If you don't much care about phase response, it should do. (With the base sallen-key filter, you get a phase reversal beyond the cut-off frequency. With this added low-pass stage, it's slightly different.) |
| T3sl4co1l:
Put an RC out in front. Calculator: http://sim.okawa-denshi.jp/en/Sallenkey3Lowkeisan.htm --- Quote from: SiliconWizard on February 02, 2020, 03:34:34 pm ---Adding a cap in parallel to the negative feedback resistor won't change the order of the filter. You'll still get basically a second-order filter (-40 dB/decade), with a lowered cut-off frequency. The Q factor will also be lowered. With a properly choosen capacitance, you can actually limit the "peaking" effect of this basic sallen-key filter at the cut-off frequency. But it's still second-order. --- End quote --- It's interesting because at a glance it might seem to work, but because it's controlling the amp's gain itself, it's just making the feedback cap work less. So it cancels out. There will still be a pole-zero left over, I think? The change in gain over that region being relatively tiny, due to the amp's relatively high gain. Incidentally, it's good design practice to work on the assumption that your amps have limited bandwidth -- the standard S-K analysis omits this I believe, which can make for unfortunate problems when implementing a sharper, higher frequency design (you need fT >= Fc * Q for each stage in the filter, or thereabouts). If you don't need noninverting operation, the multiple-feedback configuration: http://sim.okawa-denshi.jp/en/MultipleFB3Lowkeisan.htm is not just less sensitive to component values, but also accounts for amp bandwidth (because there's an intentional capacitor in that very location -- its value can be adjusted for amp fT). --- Quote ---Going from the above sallen-key design, you could either add a passive RC filter in front of, or following it, depending on your constraints on input and output impedance. You'll get a 3-rd order filter with just 2 added passives. If you don't much care about phase response, it should do. (With the base sallen-key filter, you get a phase reversal beyond the cut-off frequency. With this added low-pass stage, it's slightly different.) --- End quote --- Yup, in fact the phase reversal is due to feed-forward through the filter RCs, into the amp's output. The output is not actually an ideal voltage source, but has some impedance all its own (typically 100s ohms). There's also a zero, out in the cutoff band, due to limited amp gain. The filter depends on feedback to work, and with finite gain, the feedback can't totally cancel the signal, in the stopband. Typically stop band gain below -40dB from a single stage is reasonable. Since a 2nd order filter is supposed to have a 180 degree phase shift well above cutoff, the introduction of un-shifted signal means it flips back, with a notch or null at some intermediate frequency where they briefly cancel. The total stopband gain might still be ca. -40dB, but it'll be lumpy because of stuff like this. The passive RC in front of the 3rd order helps a lot, as its performance can be better than the opamp's, at high frequencies (at and beyond fT). Tim |
| hatte:
--- Quote from: SiliconWizard on February 02, 2020, 03:34:34 pm ---You'll still get basically a second-order filter (-40 dB/decade), with a lowered cut-off frequency. --- End quote --- Of course! However, choosing RgCf to match the filter corner frequency it would increase the attenuation, thus increasing the efficiency of the filter a little. Obviously, the effect is limited, if the gain of the circuit is small (as in the example: 2). Or am I still missing something? |
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