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

[Conrad Hoffman]

I finally got around to updating my 4-pole single opamp filter 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.

[b_force]

I finally got around to updating my 4-pole single opamp filter 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.

Awesome!
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 ?

[Conrad Hoffman]

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?

[CopperCone]

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.

[Conrad Hoffman]

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!

[b_force]

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.

I 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)

[CopperCone]

oh yes my Q was tight

other filter typologies managed the same Q without instability but you use a hell of a lot more op-amps for gyrators then sk filters

I 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 lt14something

Though the combined ones might have less noise right? Since you have less stages. Noise analysis is kinda painful

[Conrad Hoffman]

There's an interesting article on component sensitivity here- https://www.maximintegrated.com/en/app-notes/index.mvp/id/738
I 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-NOISECALC It does the common opamp circuits, but not filters specifically.

[b_force]

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.

[CopperCone]

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.

[Zero999]

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!)

Very good, but I presume the original poster is talking about only using resistors and capacitors, no inductors!

[blackdog]

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,
Bram

PS,
Thanks Conrad!

[Conrad Hoffman]

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!

[T3sl4co1l]

Is op-amp gain and phase simulated?

That's going to be extremely critical, easily moreso than the gain alone.

Tim

[blackdog]

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

[b_force]

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.

[Conrad Hoffman]

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!

[blackdog]

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=415

Usually 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.pdf

There 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_force
This test setup is well decoupled 
There are three decoupling capacitors, there is also a yellow capacitor (0. 47uF) over pin 4 and pin 7, see the picture.

Conrad
The first glance at the excel file shows only CLC filters and I usually use Elsie for that.

Kind regards,
Bram

[Conrad Hoffman]

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.

[b_force]

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.

[blackdog]

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 Plus fore 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 point



The 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

[Conrad Hoffman]

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.