Third order filters with a single opamp are possible after all? - Page 1
Forum section: electronics / projects

author: rs20
author_rank: Super Contributor
timestamp: October 03, 2014, 10:10:35 am
content: Obviously I missed a memo....I was reading random datasheets (as you do) when I came across page 15 ofthe LTC1968 datasheet, which presents a 3rd order Sallen-Key active-RC filter using a single op-amp. My immediate reaction was "haha! a mistake! I'm going to put that circuit into LTSPICE and see a 40dB/octave rolloff!". But lo, I got 60dB/octave:And sure enough, there arepages about designing this sort of thing. Am I the only one surprised to hear that this is possible?So why is it that when you want to build a 6th order Chebyshev, you use 3 2nd-order stages instead of 2 3rd-order stages? That page I linked above hints that component tolerance sensitivity has something to do with it. But I'd be curious to hear all your thoughts on this.

author: Christe4nM
author_rank: Unknown
timestamp: October 03, 2014, 10:19:26 am
content: Cascading single pole filter stages without opamps or any buffering is always a possibility. But in that case you have to be aware that every subsequent stage is loading the previous. That will alter the stage's filter characteristics a bit and you need to compensate by taking the loading into account when calculating the component values.In this example that is true also in that R3/C3 is loaded by the rest of the circuit. (The opamp provides buffering for the other two stages.)

author: c4757p
author_rank: Super Contributor
timestamp: October 03, 2014, 11:09:50 am
content: They're more complicated to design - though who cares, the computer can do it! I had a little .exe floating around here somewhere that did fourth-order. No idea where that disappeared to

author: David Hess
author_rank: Super Contributor
timestamp: October 03, 2014, 01:25:44 pm
content: The single pole RC filter stages have fixed Q so you only have two instead of three stages with adjustable Q.

author: tggzzz
author_rank: Super Contributor
timestamp: October 03, 2014, 02:34:23 pm
content: Quote from: rs20 on October 03, 2014, 10:10:35 amAh, youngsters! Once upon a time there weren't any opamps, and "computer" was a job title. Books were written about how to make Nth order filters.For amusement, here's a current data sheet that shows a 7th order elliptical low pass filter without any opamps; see figure 24 inhttp://www.analog.com/static/imported-files/data_sheets/AD9851.pdfIf you go to higher frequencies, to achieve the same effect you merely change the geometry of your PCB tracks(An exaggeration to make the point, but there's more than a little truth in it!)

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: October 03, 2014, 06:27:45 pm
content: There was an old Burr-Brown book that showed some 3rd order and 4th order single opamp filters. My favorite is the 4th order filter and I've got a design programhttp://conradhoffman.com/chsw.htm, fourth item down. If I remember right, it uses brute force numeric methods to solve the equations. People worry about component sensitivity with these designs, but I've had little trouble. The 4th order filter is an extremely effective filter for out of band noise.

author: jimmc
author_rank: Frequent Contributor
timestamp: October 03, 2014, 06:47:13 pm
content: Zverev used to be the 'Bible' for filter designhttp://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471749427.htmlJim

author: SArepairman
author_rank: Frequent Contributor
timestamp: October 03, 2014, 09:49:14 pm
content: I think they have pretty evil drift parameters if you are looking at bits

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: October 05, 2014, 04:14:47 pm
content: If you're operating on the roll-off curve, drift will be a serious issue with any high order filter. You need to choose part types carefully and select for value. If operating well in-band and just rejecting noise and the like, they're as good as any other design, assuming the opamp is up to the task to begin with, i.e., with or without the filter components.

author: CRPaul
author_rank: Newbie
timestamp: September 12, 2017, 09:28:57 pm
content: Hi folks, sorry to be so late, but yes there is a way to make precise low sensitivity 3rd order low pass filters with a single op amp. You'll find out how by visiting this URL:http://www.edn.com/design/analog/4363970/Design-second-and-third-order-Sallen-Key-filters-with-one-op-amp.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: September 12, 2017, 09:42:21 pm
content: Quote from: CRPaul on September 12, 2017, 09:28:57 pmThat's literally in the OP.A good set of calculators is here:http://sim.okawa-denshi.jp/en/Fkeisan.htmTim

author: MasterT
author_rank: Frequent Contributor
timestamp: September 12, 2017, 10:19:56 pm
content: Quote from: rs20 on October 03, 2014, 10:10:35 amShouldn't it be 60 dB/decade?

author: Audioguru
author_rank: Super Contributor
timestamp: September 12, 2017, 11:23:49 pm
content: Quote from: MasterT on September 12, 2017, 10:19:56 pmYou are correct.An octave is double or half a frequency. A decade is 10 times or 1/10th a frequency.This simple circuit has 3 RC networks and one RC produces 6dB per octave which is 20dB per decade. Then its 3 RC networks produces 60dB per decade.

author: GK
author_rank: Super Contributor
timestamp: September 12, 2017, 11:45:55 pm
content: Tables for Bessel/Cheb/Butter up to 10 pole where all of the odd orders from 3-pole up save an op-amp. IIRC these internal University-produced tables date back to the 60ies or so.https://www.eevblog.com/forum/projects/ultimate-active-filter-design-tables/msg602311/#msg602311

author: b_force
author_rank: Super Contributor
timestamp: September 13, 2017, 12:56:16 am
content: Guess what, even a 4th order is possible!Only the math is a little bit of a pain.edit; need to read better, was already mentioned.Well, to add something useful.Can someone show/explain the math behind the 4th order one?Are these gain resistors always needed for example?The reason why asking, is that I ones made a very simple excel sheet for 2nd order filters.It works great for backwards engineering of filters for example (to modify certain circuits)It would be awesome to add 3rd and 4th as well (I can share this if people are interested)

author: dmills
author_rank: Super Contributor
timestamp: September 13, 2017, 11:34:20 am
content: Quote from: jimmc on October 03, 2014, 06:47:13 pmThe "Handbook of filter synthesis" is still the bible for when you cannot use opamps (RF Power, LC networks, applications like that).Regards, Dan.

author: b_force
author_rank: Super Contributor
timestamp: September 13, 2017, 01:11:40 pm
content: Quote from: Conrad Hoffman on October 05, 2014, 04:14:47 pmI just did a worst-case analyses and it's not so bad.The gain resistors are the most critical part, and the caps of course.Also really depends what Q-factor you would like to choose of course.In general I use a Q of 0.5 (Linkwitz-riley) for things that are not so critical.Overshoot can be much worse than over-damping.This little circuit works great as a PWM output filter for example.With a 4th order you can choice a much lower carrier frequency.

author: duak
author_rank: Super Contributor
timestamp: September 14, 2017, 12:19:32 am
content: I'm rusty on filters and s-plane terminology so forgive me if I get it wrong.I've understood that when one designs a 3rd order filter using one op-amp as in the first posting, the RC network on the input realizes the pole that is located on the x or real axis, ie. the real pole. The other two poles are complex and require either an amplifier or an inductor in addition to a capacitor to be realized. A 6th order filter has no real poles as all the poles are complex, ie. none of the poles are on the real axis. I would think that three amplifiers (or inductors) would be needed. I could envisage doing some reflex stuff where an amplifier does two things at once, but it'd be fiddly.If one duplicated a 3rd order and put two in series it would be two cascaded 3rd order filters, not one 6th order filter. Even if the component values were adjusted it wouldn't quite be the same as the 6th order because two of poles are real. It might be good enough to get the job done though. As a friend said once "there's a big difference between two 6 oz steaks and one 12 oz steak". But it's the results that matter.Cheers,

author: T3sl4co1l
author_rank: Super Contributor
timestamp: September 14, 2017, 11:48:28 am
content: Careful -- a 6th order filter is a 6th order filter!What you wouldn't get, is a standard filter prototype that's optimal for whatever the given constraints are (Butterworth for flatness, Chebyshev for sharpness, etc.).For example, you could make a composite Chebyshev filter, where the second filter section is made with a higher Q than the first: its poles are spread further apart (in the imaginary direction). When combined with the first section (which is made with less Q), the result is a 5th order Chebyshev filter with an extra real pole.That extra real pole will give slower settling, and not much improvement to the close-in stopband attenuation, but will nonetheless improve the asymptotic attenuation.For the op-amp implementation, you have the double bonus that the real pole is passive, so it provides attenuation well into, and beyond, the point where the op-amp gain is poor. That is, an active filter exhibits poor stopband attenuation on account of the op-amp's finite GBW, and further, exhibits feed-forward because its output impedance is nonzero. A real passive pole provides attenuation, whether the op-amps are working at that frequency, or not.An example application might be: a Bessel or Butterworth prototype, for reasonably flat time or frequency response, requiring just a little bit more asymptotic attenuation than a 5th order filter can do. Let's say the application is an ADC, so the asymptote has to hit an attenuation(frequency) point that ensures aliased signals are in the noise floor.It would still be pretty odd, to need a 5th or 6th order filter, in a sampling application, but still having F_cutoff well below Fs (by two decades, maybe), where the extra passive pole would be able to shine. (That filter order suggests needing BW ~= Fs/20 or thereabouts, which won't benefit much from the passive pole.)Tim

author: tszaboo
author_rank: Super Contributor
timestamp: September 14, 2017, 12:07:30 pm
content: Yes, you can create a whatever order filter, even without an opamp. Just place a bunch of RC one after another, and done. All this snobbery with the passband gain flatness and linear phase response, or group delay, is there just to confuse you. And Q factor. It does not even have a dimension, sure it is not gonna do anything with the signal. I demand simple and dumb filters for simple and dump people, like me.

author: Someone
author_rank: Super Contributor
timestamp: September 22, 2017, 11:31:49 pm
content: Quote from: Conrad Hoffman on October 03, 2014, 06:27:45 pmDid you have a reference for that Burr Brown book? TI have migrated some of the older documents and it would be good to have a look if its still available. There is an old article on this topic in Elektor Electronics July/August 1993 where a T. Giesberts presented the transfer function for a multiple feedback "Fourth Order Single Chip Filter" where single chip actually refers to single opamp stage.

author: Wimberleytech
author_rank: Super Contributor
timestamp: September 23, 2017, 08:48:14 pm
content: Quote from: tggzzz on October 03, 2014, 02:34:23 pmLOL True that! Though I am an old fart, I at least started my education in the opamp era. But, I did not have the benefit of "computers" for my early filter designs. Zverev was my go-to reference!

author: technogeeky
author_rank: Frequent Contributor
timestamp: September 24, 2017, 06:42:52 am
content: Quote from: tggzzz on October 03, 2014, 02:34:23 pmI'm one of them youngsters with one of them computers, so I quickly used a filter simulator to look at the circuit in that datasheet.it is.

author: b_force
author_rank: Super Contributor
timestamp: September 24, 2017, 02:59:18 pm
content: Depending on the circuit and the system, but there are many reasons to go for an opamp instead.In general the tolerance of most inudctors is pretty high, plus you will have a little bit more trouble with EMI.Also inductors are big!But again in some other circuits passive elements are the only way to go.

author: David Hess
author_rank: Super Contributor
timestamp: September 24, 2017, 03:19:05 pm
content: Quote from: b_force on September 24, 2017, 02:59:18 pmAnother reason to use operational amplifiers is that they allow synthesizing unreal parts like frequency dependent negative resistors or impractically sized parts.

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: May 20, 2018, 02:31:26 pm
content: I finally got around to updating my4-polesingle opampfilter program to make it a bit more friendly-http://conradhoffman.com/chsw.htm, fifth item down. If anybody tries it, let me know if everything formats and displays correctly, as I've only got one machine handy to test it on.

author: b_force
author_rank: Super Contributor
timestamp: May 20, 2018, 06:53:28 pm
content: Quote from: Conrad Hoffman on May 20, 2018, 02:31:26 pmAwesome!Looks pretty good to me.Maybe an idea, but can you also let the user choice the total Q factor, as well as changing it to highpass filter ?

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: May 20, 2018, 07:32:20 pm
content: One can enter any numbers they like in the parameters, and AF1 and AF2 are just 1/Q, so you can do it, but without using the various tables of F0 & Q for the various filter types, I think one would be lost. It's not hard to transform the filter into the matching high pass, so I'll think about doing that in the next go-around. Since I'd never build a filter without checking the response and sensitivity in LTSpice, I wonder if generating an LTSpice .asc file right from the program would be useful?

author: CopperCone
author_rank: Super Contributor
timestamp: May 22, 2018, 02:00:44 am
content: When I experimented with this and motecarlo analysis, I found that high order filters tend to get the 'unstable' result in nu-hertz filter solutions. I was getting problems with like 20ppm parts on 4th order SK filters that had combined stages.I don't remember if it said oscillates or unstable or what, but it was enough of a warning that I stopped messing with them.

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: May 22, 2018, 02:17:00 am
content: No question things can go wonky as the orders go up. Probably the reason for no higher single opamp filters. It's probably dependent on the type of filter, but instead of a warning, I take it as another interesting thing to investigate!

author: b_force
author_rank: Super Contributor
timestamp: May 22, 2018, 05:35:07 pm
content: Quote from: CopperCone on May 22, 2018, 02:00:44 amI personally never seen an unstable sallenkey filter, unless you go for an high gain or high Q solution (at high frequencies).The biggest issue I have found with this type of one opamp, 4th order circuit is to keep the tolerances tights.(more difficult than cascading two 2nd order filters)

author: CopperCone
author_rank: Super Contributor
timestamp: May 22, 2018, 06:45:55 pm
content: oh yes my Q was tightother filter typologies managed the same Q without instability but you use a hell of a lot more op-amps for gyrators then sk filtersI know you can make less then ideal gyrators using less op-amps but I never investigated it.If you gotta build a damn analog filter you might as well go balls out unless its for production. I just see like zero benefit towards doing it yourself and the amount of work that you put into it would only benefit mass production, even with expensive IC's, unless you are just curious like Conrad.And if noise is not an issue and you need higher orders then its likely much easier to go for a LTC/Maxim filter block like the lt14somethingThough the combined ones might have less noise right? Since you have less stages. Noise analysis is kinda painful

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: May 22, 2018, 07:41:39 pm
content: There's an interesting article on component sensitivity here-https://www.maximintegrated.com/en/app-notes/index.mvp/id/738I can't apply it to the method used for the single opamp 4-pole, but it's worth considering in any application. FWIW, I'm not sure anybody rolls their own in commercial products anymore. I view playing with analog filters mostly a hobbyist's game these days.I recently did some noise analysis and found most of the work had already been done and compiled in this TI spreadsheet-http://www.ti.com/tool/OPAMP-NOISECALCIt does the common opamp circuits, but not filters specifically.

author: b_force
author_rank: Super Contributor
timestamp: May 22, 2018, 08:52:23 pm
content: 4th order filters are very common in audio related stuff, or for something like a PWM output filter.This circuit is perfect for a PWM filter, since the exact Q and Fs are not really critical.So if you just choice a Q around 0.5-0.6 that will be just fine (and always stable).Unity gain would only be easier.

author: CopperCone
author_rank: Super Contributor
timestamp: May 23, 2018, 12:07:28 am
content: analog filter with high rails can protect saturation of a gain stage or ADC, imo they are still rather useful for certain things but I never sold some kind of equipment like that, I can imagine it being made though.Probably best would be to switch em in if noise is detected or suspected like the fluke 6.5 digit meters that have the option to add in the analog filter, i suspect for this very reason. For unknown source you can compare analog, digital, no filter and both filters to get a better idea of the signal properties.if you have +-15V rails on a 5V adc, 30/5 = 6, 6 times is like 17dBV right? IMO anything over a 10dB gain in SNR is pretty significant. I would imagine that it can save alot of grief from near band interference sources, especially at high orders.

author: Zero999
author_rank: Super Contributor
timestamp: May 23, 2018, 09:44:13 am
content: Quote from: tggzzz on October 03, 2014, 02:34:23 pmVery good, but I presume the original poster is talking about only using resistors and capacitors, no inductors!

author: blackdog
author_rank: Frequent Contributor
timestamp: May 30, 2018, 10:07:26 pm
content: Hi Gentlemen,I've been playing with Conrad Hoffman's 4th Order Low Pass software, and naturally my first filter didn't work...I thought I was handy and didn't think I needed a gain for my test circuit.So I connected the opamp output to the inverting input, well... the frequency characteristic wasn't right at all.Everything checked at least three times, replacing opamp, putting the parts back on the breadboard again...So I didn't think any further when building and that the passive section " attenuates " and that this must be compensated by the gain of the opamp.So, after also configuring the software several times and I always got the same values for the components, I placed two equal values of the feedback resistors, TADA!Now I had a filter that was almost perfect...The setup is that it becomes a filter for measuring noise from power supply's and voltage references and that I want to keep the consumption as low as possible,because the whole thing will be powered from batteries, but more about this later.Testing filters at low frequencies is usually more difficult, so I always take a frequency that allows me to measure and scale the whole thing to the final frequency.The filter shown on the picture is for 10KHz low pass filter.It is set up so that I only need to adjust the capacitors to 4.7uF for the 10Hz for which I want to use this filter.The opamp I use here is probably not the opamp that comes in the final circuit, great chance that this will be an OPA140 or one of his brothers.One more comment, the feedback resistance, so that of the output of the opamp to the inverting input is quite sensitive.I mean that deviations in the indicated value of Conrad's Software must be accurately checked for flat frequency characteristics.That is why in this schematic two resistors are drawn in series, R7 and R8.For noise measurements this is not such a problem, but in other applications I would take it into account.Tomorrow I will show a drawn version of the frquence characteristic.I need some sleep now, I had a long flight today that lasted 12 hours and my battery is empty....Kind regards,BramPS,Thanks Conrad!

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: May 30, 2018, 11:35:22 pm
content: Yes, the gain is a critical parameter. It can actually be used as a tuning tool- if you put a trimpot on one of the gain resistors, you can compensate for small errors in other parts because it changes the Q. When doing this sort of filter, always run a simulation to check for component value sensitivity. I haven't found it to be a huge issue, but with the sharper filters it can bite you. The intrepid filter designer should probably own an LCR meter! There are various ways to scale the filter with the software. In this case, entering 47 uF for the starting value makes setting the FSF and ISF easier. Then set the feedback resistor to 4750 and you'll get very close to the values shown here. Glad somebody gave it a shot!

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 31, 2018, 02:05:08 am
content: Is op-amp gain and phase simulated?That's going to be extremely critical, easily moreso than the gain alone.Tim

author: blackdog
author_rank: Frequent Contributor
timestamp: May 31, 2018, 08:06:02 am
content: Hi,Conrad, of course I have RCL meters.All components were measured, the resistors in the test circuit are within 1% and the capacitors within 1.5% equal to each other.A simple circuit and then so many measuring cables...As I indicated earlier, later today I will draw the frequency plot and if I feel like it I will also draw the phase plot.Kind regards,Bram

author: b_force
author_rank: Super Contributor
timestamp: May 31, 2018, 10:20:11 am
content: Sallen-Key filters with gain can always be very tricky, even 2nd order filters.In this case that issue is only being amplified (lol pun)edit:Looking at the schematic, proper decoupling with some 100nF would also fix issues.

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: May 31, 2018, 02:14:59 pm
content: The program doesn't know anything about your choice of opamp, making simulation even more important. It used to be that it was hard to find opamps with sufficient GBP for some applications, but unless you're designing a very high frequency filter, there are lots of choices today that will minimize the contribution of the opamp. This is the best of times for opamps!edit/add- This fellow did a really nice spreadsheet for passive networks you might like:http://axotron.se/blog/tool-for-designing-butterworth-and-chebyshev-filters/I thought about automatically doing an LTSpice file, but he actually did it!

author: blackdog
author_rank: Frequent Contributor
timestamp: May 31, 2018, 10:16:06 pm
content: Hi,I had promised a plot of the 4 pole Low Pass filter and here it is.Because my Log paper was running out, I started looking if I could buy it again.But the Dutch product I have is no longer made.After having tried various programs and many websites I came up with this website.http://customgraph.com/piart.php?art=415Usually I use on the X-axis, 4 decades Log.And that's pretty easy with this program to setup.With my PDF editor, I placed text and created two scales.Below is my version of the used log paper as pdf, this for everyone who also like "Old School".www.bramcam.nl/Diversen/4-Decaden-10Hz-100KHz-Log.pdfThere is quite a lot of work in it, I have to put the text neatly in and I want to have several versions of this log paper.b_forceThis test setup is well decoupledThere are three decoupling capacitors, there is also a yellow capacitor (0. 47uF) over pin 4 and pin 7, see the picture.ConradThe first glance at the excel file shows only CLC filters and I usually use Elsie for that.Kind regards,Bram

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: May 31, 2018, 11:20:37 pm
content: Yes, that spreadsheet I linked to is for passive networks. Still useful, especially for higher frequencies. It also shows how to calculate the parameters from scratch, rather than using look-up tables, plus the LTSpice feature.Today's engineers wouldn't be caught dead using graph paper, but I still do sometimes. I've quite a lot purchased at flea markets, plus I use that website or even draw it up in CAD.

author: b_force
author_rank: Super Contributor
timestamp: June 01, 2018, 09:34:03 am
content: Log-paper!!!! Wow that is vintage!For the record, there are plenty of computer programs nowadays.I mostly use ARTA (there is a free version), but there are others out there.

author: blackdog
author_rank: Frequent Contributor
timestamp: June 01, 2018, 10:06:24 am
content: Hi b_force,I have a measuring computer with a good soundcard (M-Audio Delta) and several pieces of software like ARTA and Virtins, TrueRTA enz.But il like to use Log paper for some documentation end my opiniom is that it gives me more fucus on the results.Also i like the my Audio Precision:Portable One Plusfore al my measurements below 100KHz.This measuring instrument was bought by me almost 18 years ago to make measurements on studio equipment, such as mixers and Studer tape recorders.And now I use it for testing filters below 100KHz, noise measurements on voltage references and power supplies and some other things, I really like AP.So because I am not good at programming the GPIB bus of this measuring instrument I often use Log paper for documentation to record the measured values.And of course I can also show a picture of the phase behavior on the AP itself as below.But not as beautiful as that I drew it on Log paper.The center is preciesly on the -3dB pointThe phase reversal is exactly 10.145KHz and that is of course also the -3dB point of this filter.Furthermore, I am very satisfied with the result of the software of Conrad and I have learned some more about the construction of this type of filters.And now design the rest of the circuit, 80 or 100dB gain and the 0.1Hz filter.Kind regards,Bram

author: Conrad Hoffman
author_rank: Super Contributor
timestamp: June 01, 2018, 12:20:06 pm
content: I also program many things using the GPIB on various instruments I've got, but when all else fails, I've still got a Mossler 7000A analog X-Y pen plotter in the garage- the one that holds the sheet of paper down with a high voltage static charge! I think HP may have sold the same one. It's so old I couldn't find a photo of it, but it worked ten or so years ago when I put it in storage.