7th Order Butterworth Filter Help - Page 1
Forum section: electronics / projects

author: mbless
author_rank: Regular Contributor
timestamp: July 07, 2021, 02:45:28 pm
content: I have a black box data generator that outputs a differential signal from -3V to +3V (DC, sinewave, etc.) with 225kHz bandwidth. I use an opamp to convert the differential signal to single-ended with 3x gain for a final output of -9V to +9V. I found out there is up to 240mVpp noise at ~500kHz in the -9V to +9V output signal, which is above the device’s bandwidth, so my goal is to remove the noise from the amplified signal with a low-pass filter. My attempt at filtering resulted in slight noise reduction but caused other poles to show up, so I’m looking for help.Per The Art of Electronics, it is recommended to use a passive filter for frequencies >100kHz. I want the filter to be -3dB at 250kHz and < -34dB at 500kHz to reduce the noise to < 5mVpp. Using this online calculatorRF Tools | LC Filter Design Tool (rf-tools.com)to find common components, I need a 7th order Butterworth filter to get sufficient attenuation in short range between 250 and 500kHz. The “Filter design.png” image shows the calculator settings and determine components; the calculated filter attenuation is -2dB at 250kHz and -42dB at 500kHz.I simulated this using TINA TI since I’m using a TI OPA2991 for the amplification. The “TINA TI AC.png” image shows the circuit and AC transfer characteristic simulation. I simulated the data generator as single-ended sinewave, so the first opamp is the 3x amplifier and the 2nd is a 2x amplifier to recover the voltage halving of the filter. The simulation shows -3dB at 250kHz and -41.4dB at 500kHz. I chose the 550Ω to match the OPA2991 open-loop output impedance plot in its datasheet. I don’t know if I did this correctly, though.I implemented this circuit on a 4-layer PCB, but it’s not giving the results I expected. The “Pre-filter noise.png” image shows the noise out of the first opamp using a 16-bit PicoScope. In this particular image, the noise is 188mVpp at 511kHz. The “Post-filter noise.png” image then shows the output of the 2nd opamp. Instead of the noise being <5mVpp, it’s still 63mVpp with multiple frequencies. The lowest frequency is ~170kHz, but higher order stuff is visible.I used the PicoScope’s spectrum mode in an attempt to see the noise frequencies. The “Pre-filter spectrum.png” image shows the main offender at ~550kHz, while the “Post-filter spectrum.png” image shows the main frequency is 170kHz with residuals at 310, 450 and 500kHz. The post-filter spectrum indeed shows the filter works overall with noise reduction starting around 250kHz, but certain frequencies are still prominent, and in the case of 170kHz, are amplified.This is my first time trying a filter more complex than an RC filter, so I’m not sure how to proceed. I have formulated some questions.1. How do you decide on the filter input/output impedance? Does it need to match the OPA2991?2. Is there a way to tune the filter without a VNA that isn’t guessing/trial and error?3. Would it be better to convert the differential input signal to be single-ended with unity gain, filter, and then do all the gain in the 2nd op amp?

author: emece67
author_rank: Frequent Contributor
timestamp: July 07, 2021, 03:20:09 pm
content: .

author: TimFox
author_rank: Super Contributor
timestamp: July 07, 2021, 03:48:27 pm
content: For example, 10 pF of winding plus stray capacitance on a 680 uH coil gives a parallel resonance at 2 MHz.

author: mbless
author_rank: Regular Contributor
timestamp: July 07, 2021, 04:16:50 pm
content: Quote from: emece67 on July 07, 2021, 03:20:09 pmGood point! Here are the components I used.680uH: LB3218T681K, 2.1kΩ impedance at 500kHz, 3.6MHz self resonance470uH: CB2518T471K, 1.5kΩ impedance at 500kHz, 5MHz self resonance510pF: CC0603JRNPO9BN511, no characteristics plots but it's a 0603 NP0 MLCC2nF: GCM1885C1H202FA16J, again no characteristics plots but it's a 0603 C0G MLCC549Ω: RMCF0603FT549R, no characteristics plotsQuote from: emece67 on July 07, 2021, 03:20:09 pmThis is definitely getting above my hobbyist head. The two internal layers of the 4-layer PCB are all ground, and I ground fill the outer layers. All ground layer are via stitched, but I don't have it in a shielding box right now.

author: TimFox
author_rank: Super Contributor
timestamp: July 07, 2021, 04:24:37 pm
content: Of those components, only the coils look problematic (due to self-resonance).You can try a Spice simulation (.AC calculation), but you need to include the ESR of the inductors (which differs from that at DC) along with the parasitic capacitor that gives the self-resonance.The MLCC C0G capacitors and metal film resistors are much better, but Spice may want a small ESR on the capacitors (which have very high Q).

author: Kleinstein
author_rank: Super Contributor
timestamp: July 07, 2021, 05:39:20 pm
content: The filter response does not look that bad. Above some 400 kHz the output noise seems to be set by effects from behind the filter. So for better testing it would need a higher signal level at the input.The inductors may pic up some background signal, like a local AM radio station.Another point could be oscillation of the amplifier at the outout from too much capacitive loading. So some 50 or 100 Ohms in sereis to the output may be a good idea.The open loop ouput impedance is not really relevant for matching. Over much of the frequency range the relevant impedance would be the much lower closed loop ouput impedance. The 550 Ohms are still no that bad, though more on the high side.

author: Benta
author_rank: Super Contributor
timestamp: July 07, 2021, 05:54:55 pm
content: A well-known trick to minimize mutual inductance (coupling) between the inductors is to place them at right angles to each other.Like this:-- | --Only works with axial types, of course.

author: mbless
author_rank: Regular Contributor
timestamp: July 07, 2021, 10:10:37 pm
content: Quote from: TimFox on July 07, 2021, 04:24:37 pmAre you saying they are problematic because the self-resonance is close to the 2MHz you mentioned earlier for stray capacitance resonance? So the self-resonance should be higher, lower or just different?Quote from: Kleinstein on July 07, 2021, 05:39:20 pmOverall I would agree that the filter looks like it works based on the spectrums, but the few frequencies that survive or are induced still leave nontrivial noise. I'll try adding in series resistance at the output amp to see if that helps.Quote from: Kleinstein on July 07, 2021, 05:39:20 pmOk, using the "voltage swing from rail" and loads I was able to calculate an output resistance of 25-27Ω. In that case, does it make more sense to make the input/output filter impedance around 50Ω? At 50Ω, the inductances are reduced to 39uH and 68uH, so I can get inductors with higher self-resonance.Quote from: Benta on July 07, 2021, 05:54:55 pmI did that for inductor 1 and 2, but the 3rd one is inline with the 2nd. How are the capacitors typically arranged relative to the inductors?

author: TimFox
author_rank: Super Contributor
timestamp: July 07, 2021, 10:21:26 pm
content: Problematic coils: I said that since the self-resonating capacitance isn't trivial compared to the inductance at frequencies not too far above your cutoff.

author: jonpaul
author_rank: Super Contributor
timestamp: July 08, 2021, 07:46:56 am
content: Bonjour à tout et tous, salutations de Paris!Wonderful problem, I designed passive and active filters since 1970s, so very interesting to read the thread.1/ How are the noise and scope traces probed, eg 10X, diff probe, etc?2/ What is the requited spec of the filter: A Butterworth may not be the best choice: Does the OP need best transient and phase performance (Bessel), sharpest cutoff (Tchebychev) ?lease define exactly the objective.3/ How did OP choose passive LC en lieu of active filter ?4/ Passive LC term Zo is the choice of the filter design, and perhaps dictated by the load. Note that most passive LC filters have Zin=Zout.5/ See the Many excellent texts on passive LC and active filter design.6/ Off the shelf filters are available at low cost, Mini-Circuits has SMA/BNC/ LP inline filters.https://www.minicircuits.com/WebStore/RF-Filters.html7/ Can OP find the noise source: PSU, poor layout, probing, nearby digital circuits?Just the ramblings of an old retire EE!Enjoy, et bon chanceJon

author: mawyatt
author_rank: Super Contributor
timestamp: July 08, 2021, 12:29:41 pm
content: All good advise from Tim and Jon. One thing to add is the possible noise intrusion from the amplifier power supplies, the PSRR usually isn't very good above ~100KHz and has a rising slope (20dB/dec) with frequency.Best,

author: mbless
author_rank: Regular Contributor
timestamp: July 08, 2021, 02:03:56 pm
content: Quote from: TimFox on July 07, 2021, 10:21:26 pmSo then this specific filter doesn't work in the real world considering parasitics. If I change to 50Ω input/output impedance on the filter, the inductors change to 39uH and 68uH. Assuming the same 10pF, the parallel resonance is 8 and 6MHz, respectively. The self resonant frequency is >10MHz for those inductors. Do you think that will be sufficient?Quote from: jonpaul on July 08, 2021, 07:46:56 amThank you, Jon. Those are good questions.1. I use a 10x probe with the ground spring to minimize the loop.2. I want the filter to be -3dB at 250kHz and < -34dB at 500kHz. Bessel doesn't have sharp enough cutoff, and I not too concerned with the phase. I don't wany any passband ripple, so I eliminated Chebyshev and decided on Butterworth.3. The rule of thumb I have seen says to use passive filters for cutoff frequencies >100kHz since the recommended opamp bandwidth should be >50x the cutoff frequency. In my case the opamps for the active filter need to have >12MHz, which isn't unreasonable nowadays, but I wanted to reduce the IC count. Perhaps it would have been better to go the active route to avoid inductor issues.4. The filter is sandwiched between 2 opamps, so I am unclear on what to do for the impedance as I mentioned in earlier messages.6. I looked at those earlier. The lowest frequency filter available is <20dB attenuation at 500kHz, so that is not sufficient.7. I'll be looking into the power rails and layout.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 08, 2021, 02:43:17 pm
content: If you can get SPICE models for the components, a more accurate simulation can be made.The two components with characteristics, unfortunately do not provide enough detail to fit a model. The inductance plot is technically adequate, but subtle errors in the curve translate to large errors in Q factor or resistance, and better is a full complex (resistance and reactance/inductance) plot.If you like, models can be created here:https://www.seventransistorlabs.com/Calc/Coilcraft1.htmlthe resulting model can be imported into any SPICE-compatible simulator.The main impact of error in Q factor / resistance, is transition band attenuation (insertion loss). An ideal (lossless) filter has a sharp transition band (i.e., around Fc +/- a modest factor); the effect of resistance is to depress the transition band, so that it rolls off a bit sooner, and much slower, than intended. This can be compensated to some extent by adjusting L and C values, but only up to a limiting range determined by component Q. (How much depends on what the required component Q is -- sharper filters (Bessel < Butterworth < Chebyshev) require higher Q, as do higher order filters.)So basically, without reliable models, the transition band may be a bit high or low. The overall pass and stop bands should still be alright -- pass being limited by DCR, and stop limited by strays.Best practice is to go back and forth a bit, between the real filter and the simulated model, and adjust components and parasitics until they agree. In effect, measuring the elements in the filter by its frequency response.The effect of self-resonance is to add zeroes to the filter, worsening the stopband attenuation. It's actually improved at certain points (at each zero), but the worst-case value (between zeroes) is raised, so that it's no longer decreasing asymptotically, but lumpy instead.A similar effect is had from capacitor ESR and especially ESL, so make a tight layout with short component/lead/trace length to them. (Should be trivial with SMT chips at this frequency.)If you need strong attenuation at specific frequencies, such as for an anti-aliasing filter, you may consider adding zeroes intentionally. These aren't trivial to calculate (there are Cauer/Elliptic filter calculators; this type contains zeroes, but they are placed such that the worst case stopband attenuation is at least what's specified, you don't have any choice for specific frequencies), but are quite easy to place by small adjustment. (To do so, note that, for capacitance in parallel with any given inductor, its neighboring capacitors must be reduced by half the parallel capacitor's value; because, as seen by the inductor, those two capacitors act in series, and their series equivalent is in parallel with the parallel capacitor. So, reduce them by the difference, and the filter response is pretty much the same.)And yeah, as others have noted, the impedance is rather high for commercial components. Impedance relates to inductance and capacitance through their ratio: Zo = sqrt(L/C). So a lower Zo uses smaller inductors and larger capacitors. 50-200 ohms should be very reasonable here. Lower impedances run into issues with capacitor size, making ESR and ESL more troubling instead, and also need stronger drive (more current) for the same output voltage.Second for active filters. If you're already using op-amps, perhaps it's reasonable to upgrade to duals or quads, thus keeping the IC count low. They're easier to design than passive filters, which may prove attractive.Tim

author: jonpaul
author_rank: Super Contributor
timestamp: July 08, 2021, 04:25:32 pm
content: Rebonjour mbless,busy here, a few fast notes:0/ Is the noise common mode or normal (differential) mode?1/ Never use a 10X probe for such applications, just take a thin coax (RG198/U with a BNC, DIRECT WIRE to the signal point and keep shield VERY short and direct.ANY probe will increase pickup ground loop area to several sq inches and pickup noise.2/ With an opamp ckt, use ANY Zo the passive LC filter needs:A low Zo op amp out is in series with Zin - OP AMP Zo, the load is the Zload as opamp Zin is high Z3/ Active filter is much simpler, not even an opamp, just FET r BJT emitter follower can work.....4/ Inductor Fres and shunt C will be different for SMD vs axial vs radial and different sizes inductors.See CoilCraft for a wide selection!https://www.coilcraft.com/en-us/products/rf/Bon chanceJon

author: mawyatt
author_rank: Super Contributor
timestamp: July 08, 2021, 07:39:37 pm
content: One thing to watch is that Op-Amps have a rising closed loop output impedance vs frequency, inductive in nature. If your Op-Amp models are simple 1st order types, this may not show up in the simulations.On simple solution is to force the Op-Amp output class A/B stage to operate mostly class A, this can be accomplished by a small resistor from the output to the negative rail assuming the rails are clean. It's wasteful of current but lowers the closed loop output impedance at higher frequencies. Another solution is to place an emitter follower INSIDE the closed loop and drive the base with Op-AMP output and take the output signal for closing the loop and supplying the output from the emitter. Again bias the EF with a resistor to the negative rail. A typical 2N3904 or 2N2222 have a low emitter impedance ~(((kT/q)/Ic) + Re) well into the MHz region and will significantly improve stop band rejection. I wrote an EDN article about this ~40 years ago.A few other filter types which you might consider are the Elliptic (Cauer) and Inverse Chebyshevs.BTW what you are experiencing is sensitivity of the filter response to component variations, some filter types like the Elliptics are highly sensitive to certain components, while other filters like the Bessel are not nearly as sensitive.Best,

author: jonpaul
author_rank: Super Contributor
timestamp: July 08, 2021, 08:07:38 pm
content: Wow forgot the elliptic:The OP could study classic filter design:Specs are inband rippleOut of band rejectionRejection ratiocutoff freqFor example a +/-0.1 dB ripple can be achieved in an elliptic or tschybtchevEnjoyJon

author: mawyatt
author_rank: Super Contributor
timestamp: July 08, 2021, 08:14:53 pm
content: The Inverse Tschybtchev, I call them Chebyshev, not sure what is the proper translation, have an interesting property where the in-band ripple is inverted to the stop band, thus the name Inverse. These look like an Elliptic in the stop band.Best,

author: Benta
author_rank: Super Contributor
timestamp: July 08, 2021, 08:22:26 pm
content: Forget Cauer/elliptic for passive designs.I worked with those a lot and they have beautiful theoretical characteristics, but do not work well in practice. The company I worked for dropped them and went for a higher order Chebyschev LP instead (this was for local FM-radio transmitters in the 1...10 kW range).The problem with passive Cauers is, that you don't just get the desired notch, but also an undesired peak in the stop band.

author: mbless
author_rank: Regular Contributor
timestamp: July 08, 2021, 09:49:56 pm
content: Thank you, everyone!I'm going to tackle this in 2 steps. First I'll order parts for the lower impedance passive filter. If that doesn't show improvement then I'll do a small redesign with an active filter.

author: mawyatt
author_rank: Super Contributor
timestamp: July 08, 2021, 11:49:21 pm
content: An interesting thought experiment is to consider a passive filter design with ideal lossless inductors and capacitors. The design is specific for a given load and source impedance. Now ask where does the energy of the input waveform go when out of band? Well, very little should be dissipated in the real part of the load since the the imaginary part can't dissipate any energy, and if it's significant then the stop band attenuation is poor. So where does the input out of band energy go? The answer is it gets dissipated in the real part of the source impedance. This is why you can't directly cascade passively low loss high performance filters and expect the result to be the product of the two filter responses. Where is the second filter going to dissipate the out of band energy since it's "source" is the output of the first filter which can't absorb much energy, and how is the first filter going to behave when it's "load" is the input to the second filter, not exactly the design load impedanceHigh in-band loss filters can be cascaded and get a reasonable result since all the filter elements are lossy and contributing to the out of band energy loss, but not so with low in-band loss filters. This is why you see an attenuator between the two filter sections to help with a loss mechanism at the "source" for the second filter input and provide a real impedance "load" for the first filter section.Anyway, just one of the many nuances of filter design and why it's never as simple as it seems by just plugging in numbers into a Filter CAD program.Best,

author: TimFox
author_rank: Super Contributor
timestamp: July 09, 2021, 12:14:57 am
content: That filter is referred to as a “reflective” filter, as opposed to an “absorptive” filter, where the unwanted stuff is dissipated in internal resistance.

author: David Hess
author_rank: Super Contributor
timestamp: July 09, 2021, 03:38:04 am
content: Quote from: mbless on July 07, 2021, 02:45:28 pmIn practical active filter circuits impedances can be ignored, and operational amplifier input and output impedances have nothing to do with them.The output impedance of the operational amplifier is divided by gain in excess of the closed loop gain, and serves more to show how the open loop gain changes with load.QuoteWith appropriate component tolerances and topology, no tuning should be needed. If I did have to tune a filter of such high order, I would sure want to use a VNA or equivalent to do it.QuoteAll but EMI filtering should occur after the differential-to-single ended conversion to avoid corrupting the common mode rejection of the conversion state, and a 7th order filter would normally be made by 3 second order sections plus one extra RC section. High order differential filtering is possible but normally something to be avoided.I think what you are trying to accomplish can be done with an active filter like I described but with modern high frequency operational amplifiers. Take a look at Don Lancaster's "Active Filter Cookbook".

author: jonpaul
author_rank: Super Contributor
timestamp: July 09, 2021, 04:54:18 am
content: Rebonjour:1/ I am not convinced that the problem is defined, as the measurement of the interference may be picking up noise. The OP should use a better probing technique to verify.2/ May be easier to just build a simple circuit than to simulate .3/ Doubt if 7 th order is needed. Filter spec should be reexamined.4/ OP should let us know:Exact source of the signal (eg Digital Synthesizer, Arb Wave Gen, Calss D amp)Required specs for filter flatness/ripple, etc.5/ Don Lancasters Active Filter Cookbook is excellent, from 1970s.Enjoy,Jon

author: Kleinstein
author_rank: Super Contributor
timestamp: July 09, 2021, 08:54:11 am
content: Quote from: David Hess on July 09, 2021, 03:38:04 amA general filter can be divided in 2nd order parts and possibly 1 first order part. However one can not divide every 2nd order part in 2 x 1st order. So one can in general not seprate a 7th order filter in 3rd + 3rd + 1 st order. Active fitlers are usially 2nd order elements with sometimes a 1st order part usually at the front. Passive filters can be higher order as one string. Some forms like a series of RC elements may not be practical for higher order as they have the tendency to have an increasing impedance to the output. LC based fitlers can have the same ouput impedance as input impedance and thus no real problem as a long chain.Differential filters need more parts (e.g. twice the number of inductors), so they are less attractive. It can still help to fitler out the very high frequency part or large off band signals before the first amplifier.The dicrete frequenies are more like a signal pic up, not a question of the filter response curve. So more about the layout / shielding and not about the schematics.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 09, 2021, 11:22:45 am
content: Quote from: Kleinstein on July 09, 2021, 08:54:11 amTo be clear -- as in active filters, or passive filters with buffers between stages, or constant-resistance filters. (As mentioned earlier, passive, reflective filters can't be trivially cascaded, as the whole design depends on every other component value; as well as the input and output port impedances, one or both of which must be a resistance.)QuoteCommon mode filtering can also prove beneficial, especially to reduce the reliance on op-amp CMR (common mode range) and CMRR (rejection ratio; immunity).There is some merit to normal mode filtering, as well (that is, filtering each input by itself, without reference to the other line). Though probably not applicable to this case.The consideration is that, if you need filtering at frequencies where op-amp CMRR is poor, you can't do it after the op-amp -- it's already converted CM to DM there, and you're stuck.The tradeoff is, your CM filter won't be perfectly balanced, and will exhibit some mode conversion itself. This is especially critical near the transition band (where component reactances are comparable to signal impedance, so component tolerances are proportional to CM-DM conversion -- better than 5% capacitors are expensive, let alone inductors, so better than ~26dB balance is unlikely there). Deep into the stop band, CM is attenuated strongly and it's not an issue.So it works best when you don't need much CMRR (probably a trivial case where you aren't subject to much CM interference anyway!), or when (desired DM) signal bandwidth is much less than expected CMI and when op-amp performance is marginal given that CMI.A good example I think, is a thermocouple input, where the DM signal bandwidth is low (~Hz in this case), and the AFE (analog front end) is low voltage -- so the CMR is small. Let's say the analog supply is 0 to 3.3V, so the CMR is the same (we'll use a RRI opamp), and EMI testing is performed at 10V (conducted) and 10V/m (radiated). Such levels will easily exceed the CMR so either a boost converter is needed (at added expense, space, and possibly noise) say for a +/-15V input range, or we use filtering to chop down the EMI.To continue working the example, consider an EMI test with 150kHz-30MHz at 10Vrms applied (which is coming from a 50 ohm CDN (coupling-decoupling network) or cable clamp, and the EUT is grounded so the full voltage is applied to the input lines as such; also, these are unshielded connections). We need to knock that down to +/-1.65V peak (around a mean 1.65V bias set by the AFE circuit), or around 20dB attenuation at 150kHz. A 2nd order filter of say Zo = 100R and Fc = 15kHz should do well enough. This will use 1mH and 0.1uF, plus some damping RCs to ensure good behavior with unterminated cables as well as long cables or a grounded CDN.The 0.1uF will actually be a pair of 0.047uF, one from each line to GND. They add to a close enough parallel equivalent in the common mode, but will be somewhat imbalanced due to tolerance; say they're out by 5%. Now, at Fc (~15kHz), we expect about -26dB C-D mode conversion.If the final reading should have >80dB CMRR at all frequencies, then we must have our passband be -54dB at 15kHz. Which is easily obtained with a 2nd order filter cutting at ~50Hz, so we put that after the op-amp and we are done. This is still well in excess of the signal bandwidth, so no worries there. Or if we use a S-D ADC, simply choose a low enough sample rate; or a sampling ADC, oversample it a fair amount (some to 10s of kHz?) and average (and probably decimate) it down.Well, not quite done as we should model the DM filter as well (not just assume the CMC and caps will do their job), but that covers the CM design.Like I said, this probably wouldn't work here, as the signal bandwidth is relatively high, forcing the CM filter to cut very high (some to 10s of MHz?) and requiring the op-amp to fill in the rest (so, requiring a pretty high GBW amp, 10s of MHz).Although if you go with active filters, you'll need such amps anyway, so it's not a terrible tradeoff.The other side is CMR; to meet a 10V or 10V/m spec, you'd need +/-15V rails, at least. Susceptibility testing starts at 150kHz so if you can't filter that out, you have to handle the full range regardless. There is still value in filtering the highest stuff (10s of MHz, transitioning into RFI immunity 30-1000MHz) as that can skew op-amps (input RF rectification), you just don't get to save the CMR.Though there is some possibility with making an active, shunting mode CM filter, which relies on a single capacitor with precision resistors to obtain good balance, to get reasonable performance (if only 1st order, 2nd with a CMC in front) at such frequencies. I'd have to think about the design for such a thing (or look for examples), but I bet that's a possibility.Anyway, the point is, if you're receiving something general, differential, and about that bandwidth, you're probably pretty stuck on a wide supply range (if not full +/-15 or higher, then +/-5 for a commercial 3V conducted / 3V/m radiated immunity, for example), and a CM filter, down in the same bandwidth, won't provide a huge benefit.On a related note, mind signals that aren't actually differential. USB is a prime example: the J/K symbols are specifically unbalanced, so CM filtering cannot be used. The point-to-point link is also source terminated, so there's very little budget for a load termination to filter against. This is why USB is, and must always be, shielded.Tim

author: mawyatt
author_rank: Super Contributor
timestamp: July 09, 2021, 02:40:05 pm
content: An interesting active filter we did ~45 years ago and got published by EDN or Electronics Design (can't remember), then later Walter Jung of Analog Devices called to discuss this and use it in an ap note or one of his books (also can't remember, getting old sucksThis filter is a unique implementation of the 3rd Order Butterworth polynomial, which is S^3 + 2*S^2+2*S+1. This can be simply factored into S+1 times S^2 + S +1 which offers a implementation as a 1st Order followed by a 2nd Order, or the reverse. If the 2nd order is a Sallen-Key Low Pass type except with the junction of the feedback capacitor and input resistor is followed by a unity gain buffer to the second resistor. With this implementation the 3rd Order Butterworth can be created with all equal value resistors and all equal value capacitors, and the amplifiers are unity gain, all of which is a big advantage in implementation since as mentioned precision capacitors are difficult to find and expensive, but if all the same value then a little betterAnother interesting property is if the resistors and capacitors are exchanged the result is a 3rd Order Butterworth High Pass filter at the same corner frequency of 1/RC (radians/s).Once this filter implementation was discovered long ago we utilized this active filter in numerious applications over the years and it performed admirablyIf interested we can provide more details, but think this was posted here at sometime.Best,

author: T3sl4co1l
author_rank: Super Contributor
timestamp: July 09, 2021, 03:33:08 pm
content: Huh, wouldn't think that would be all that useful back in the day, opamps being much more expensive than resistors or capacitors? But yeah, other than that, buffering to isolate RC sections is nice, just as helpful as isolating LC sections but you may get to save a few BOM items.I'm fond of putting the real pole out in front, which works for Sallen-Key, MFB or other types -- see this for example:http://sim.okawa-denshi.jp/en/MultipleFB3Lowkeisan.htmAs usual, the added impedance in front [going from 2nd to 3rd order], affects all the other values, so you're again using a diversity of resistors, and you need a low impedance source (typically from a proceeding op-amp). Seems I can usually get reasonable results with common values (decades say) that are already in use, so it's not too big a deal on BOM size.Can also make an even higher order SK (or other type too, I suppose), by extending the RC from the feedback node to +in, with additional RC stages. Downside is, because there's an even higher order network inside the loop (more phase shift), it's even less stable (more sensitive to component values). For this reason, it's generally preferred to stick to 2nd and 3rd order sections, and cascade them.(Digital filters are the same way, you can do a higher order IIR filter but it's that much more sensitive to errors, requiring extra bits (in both the coefficients and accumulators) to preserve numerical stability. Better to cascade biquad sections for the same overall response.)Worthy of note, MFB is generally better than SK for a number of reasons:- Both are limited by amp output impedance and GBW; MFB's inverting op-amp performs slightly better.- Finite GBW (or less than unity gain for the follower, or less than infinite DC gain for op-amps in general) places a zero in the stopband. Which is to say, at high frequencies, the op-amp is no longer "able" to control the output, and feed-forward terms from the direct input-to-output path take over.- The 3rd order forms, both have a "hard" real pole (the input RC to GND). This ensures a decreasing stopband, even above GBW.- However, MFB has another: the node between R2, R3 and R4 is hard bypassed to ground by C2. This gives better asymptotic response.- MFB is less sensitive to component variation than SK. That is, the response is nearly 1:1 proportional to any given component value. Whereas ,SK has higher coefficients depending on filter type, meaning values need to be more precise.OTOH, nice thing about SK is it can be done with plain old emitter followers, or even FET or tube followers if you don't mind the slightly low gain. Here's one I did for an all-tube receiver:https://www.seventransistorlabs.com/Images/Rx_AF_Bandpass.pnghttps://www.seventransistorlabs.com/Images/Rx_AF_Bandpass_Response.png(6V6 being a pretty close SPICE model to the 5702 I actually used; or if you prefer, 2N3819 biased to around 3mS would do pretty much the same thing.)Note the pairs of RC feedback components; it's a bandpass. You can combine HP and LP filters in one circuit, each still being 2nd (or even 3rd?) order. At least if they're not too close together that their poles start overlapping (in which case you'll have something more of a tuned-resonator architecture, and a different topology may be preferable?). Beware, it may not be quite as easy as just superimpose both circuits and go; I recommend setting up in a simulator and adjusting values for best AC response. Good opportunity to select common values as well.Tim

author: mawyatt
author_rank: Super Contributor
timestamp: July 09, 2021, 04:22:20 pm
content: Quad package Op Amps were cheap even back then, so amp cost wasn't an issue. 1% caps were the overall cost driver since 1% resistors were also cheap. Agree that using the 1st order in front is best because this attenuates the higher frequencies passively before it "sees" the op amp. One of the weak issues with the Sallen-Key is the input signal can bypass the op-amp right to the output thru the feedback cap and totally depends on the op-amp output impedance to attenuate the signal. This is the limiting factor in stop band attenuation with SK configurations and why the methods of reducing the Op-Amp output impedance were mentioned earlier. We utilized both methods successfully and got text book filter responses even with general purpose Op-Amps.BTW some of the best passive filter designs I have seen were in the original Sony CD players before oversampling was employed, and the original Stanford Research function generators.Best,

author: TimFox
author_rank: Super Contributor
timestamp: July 09, 2021, 04:25:02 pm
content: I also recommend the passive network before the active-filter, for reasons you state.For hobbyist purposes, measuring the capacitors with a DE-5000 or similar LCR meter can easily sort capacitors to better than 1%. I do this often when matching capacitors.

author: mbless
author_rank: Regular Contributor
timestamp: July 09, 2021, 06:58:17 pm
content: I ordered parts to test the passive filter with lower impedance. I just realized the caps are only 5% tolerance, so I'll measure their capacitance before soldering them.I'm going to go ahead and design a board with an active filter while waiting for the passive parts. I found AD and TI both have active filter calculators, which have been helpful to ensure the selected opamp meets bandwidth requirements. It looks like they also tune the resistor and capacitors to the specific opamp, so perhaps they're using fairly accurate models... throwing caution into the wind.Quote from: jonpaul on July 09, 2021, 04:54:18 am7th order Butterworth is needed based on the values I gave earlier: 3dB at 250kHz and >34dB at 500kHz.The device is a black box, but I figured out how to feed in a voltage to test its functionality. Using a AAA alkaline battery, which from my understanding are essentially noise free, I checked the output voltage. The DC voltage was spot on, but it had an AC component which is the ~200mVpp, ~500kHz noise I'm trying to filter out. And to put the question of my probing to rest, I measured the battery voltage in-situ and got an AC component of 0.7mVrms and 6mVpp. So that's higher noise than I'd expect from a battery (likely scope noise floor and not perfect probing), but no, my probing is not causing the 200mVpp noise.

author: jonpaul
author_rank: Super Contributor
timestamp: July 10, 2021, 06:07:33 am
content: Hello we never used active filters above audio band.We used Sallen-Key three pole extensively.Also elliptic /Cauer passive.For a 500 kHz noise filter passive is the simplest.If you have electronics driving and receiving the filter signal, you are free to choose whatever Zo are convenient.Finally passive filters can have unequal Zin and Zout.Enjoy,Jon

author: Kleinstein
author_rank: Super Contributor
timestamp: July 10, 2021, 07:08:54 am
content: With passive fitlers the tolerance of the capacitors is usually less critical than with active fitlers. The more critical parts are the inductors: they can couple magnetically to other inductors and with a ferromagnetic core the inductance in temperature dependent and can change from mechanical stress. Core materials also are not perfectly linear, which can be a problem at higher amplitudes.Slight deviations in the capacitors would change the filter characteristics a little, but it would still be a good low pass filter. The relatively low Q Butterworth filter characteristics is not very sensitive. So 5% capacitiors should be nothing to worry about. The larger deviation is likely from the inductors, including the parasitic capacitance that causes the self resonance. One could at least include those parasitics in the simulation and if needed adjust the capacitors.There is no absolute need to use a Butterworth filter characteristics. A Chebychev type filter would give a sharper drop and may get away with lower order. Especially if this is about suppressing a known 500 kHz interference, a notch componenet (like in a Cauer filter) can be a good solution too. As a passive filter the Butterwirth type may still be good, as it has relativey low sensitivity to the component accuracy and higher order is not that much effort.

author: mawyatt
author_rank: Super Contributor
timestamp: July 10, 2021, 01:21:52 pm
content: Quote from: jonpaul on July 10, 2021, 06:07:33 amWe were able to use active filters into the 100s of KHz region back then, employing some of the techniques mentioned. Later when higher ft transistors became available we moved into the MHz region and more recently around ~2010 DARPA supported development of a ~100GHz Op-Amp which produced GHz region active filters. This Op-Amp was based around Cherry-Hooper circuit, a circuit we utilized often back then.Interesting you mention the unequal Zin and Out for passive filters, I remember way back in grad school Microwave Filters course we had a take home exam which required proof of Bartlett's Bi-Section Theorem which is used to modify the passive filter network components for unequal source and load impedances.Best,