Third order filters with a single opamp are possible after all?

[rs20]

Obviously I missed a memo....

I was reading random datasheets (as you do) when I came across page 15 of the 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 are pages 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.

[Christe4nM]

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.)

[c4757p]

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

[David Hess]

The single pole RC filter stages have fixed Q so you only have two instead of three stages with adjustable Q.

[tggzzz]

I was reading random datasheets (as you do) when I came across page 15 of the 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: ....... Am I the only one surprised to hear that this is possible?

Ah, 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 in http://www.analog.com/static/imported-files/data_sheets/AD9851.pdf If 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!)

[Conrad Hoffman]

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 program http://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.

[jimmc]

Zverev used to be the 'Bible' for filter design http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471749427.html

Jim

[SArepairman]

I think they have pretty evil drift parameters if you are looking at bits

[Conrad Hoffman]

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.

[CRPaul]

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 .

[T3sl4co1l]

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 .

That's literally in the OP.

A good set of calculators is here:
http://sim.okawa-denshi.jp/en/Fkeisan.htm

Tim

[MasterT]

I'm going to put that circuit into LTSPICE and see a 40dB/octave rolloff!". But lo, I got 60dB/octave:

Shouldn't it be 60 dB/decade?

[Audioguru]

I'm going to put that circuit into LTSPICE and see a 40dB/octave rolloff!". But lo, I got 60dB/octave:

Shouldn't it be 60 dB/decade?

You 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.

[GK]

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

[b_force]

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)

[dmills]

Zverev used to be the 'Bible' for filter design http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471749427.html

The "Handbook of filter synthesis"  is still the bible for when you cannot use opamps (RF Power, LC networks, applications like that).

Regards, Dan.

[b_force]

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.

I 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.

[duak]

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,

[T3sl4co1l]

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

[tszaboo]

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.

[Someone]

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 program http://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.

Did 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.

[Wimberleytech]

I was reading random datasheets (as you do) when I came across page 15 of the 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: ....... Am I the only one surprised to hear that this is possible?

Ah, 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 in http://www.analog.com/static/imported-files/data_sheets/AD9851.pdf If 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!)

LOL 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!

[technogeeky]

I was reading random datasheets (as you do) when I came across page 15 of the 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: ....... Am I the only one surprised to hear that this is possible?

Ah, 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 in http://www.analog.com/static/imported-files/data_sheets/AD9851.pdf If 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!)

I'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.

[b_force]

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.

[David Hess]

Depending on the circuit and the system, but there are many reasons to go for an opamp instead.
In general the tolerance of most inductors is pretty high, plus you will have a little bit more trouble with EMI.

Another reason to use operational amplifiers is that they allow synthesizing unreal parts like frequency dependent negative resistors or impractically sized parts.