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cascading filter after a 2 poles sallenkey

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The circuit in post #1 doesn't implement a Bessel filter, it's roughly a critically damped (Q = 0.5) filter, very droopy as already stated. Looking primarily for a sharper corner and higher stop band attenuation, you would use Butterworth or Chebyshev filter of e.g. 4 to 8th order.

Ok, this is the reason. The signals are generated by a DAC at 100kHz S/s, and they are synthesized, not sampled. Therefore there is no energy over Nyquist.
However I see after the filter the signal mirrored, i.e. if I output 23kHz I see energy at the mirrored frequency 100-23kHz. I want to eliminate this.
The filter that I described looks insufficient. I am trying to make it sharper by adding more stages after. I have to make sure I do not change the phase till 25-30kHz. Since signals are generated at 100kHz the best frequency for the cutoff is 40kHz.
To start with a simple point, the specification doesn't particularly suggest a cut-off frequency of 40 kHz. You should better specify the maximum signal frequency and acceptable affection.

The really problematic point is "not change the phase", which can't be strictly achieved with an analog filter. There's another simple point here, instead of absolute phase, you'll better look for relative phase respectively the group delay. To achieve almost constant group delay within the pass band, you'll probably go for a Bessel filter, although the magnitude response is less sharp.

For a detailed discussion you should fix your requirements quantitatively.

See below a comparison of Bessel and Chebyshev 5th order filters:

Bessel 5th.png Bessel 5th circuit.png

Chebyshev 5th.png Chebyshev 5th circuit.png

- - - Updated - - -

A point I forgot to mention. A probably much simpler way to implement an almost ideal digital-analog conversion with 100 kHz sampling rate is to use an oversampling audio DAC. It has a perfect built-in digital linear phase interpolation filter and only requires a simple RC filter for the oversampling rate (e.g. x64).
 

Here's the LT spice simulation with an added 2-pole Sallen-Key filer.
I Increased the value of the feedback capacitor C4 to reduce the damping factor of the second filter and sharpen the overall rolloff.
Capture.PNG
 

Hi,

A point I forgot to mention. A probably much simpler way to implement an almost ideal digital-analog conversion with 100 kHz sampling rate is to use an oversampling audio DAC. It has a perfect built-in digital linear phase interpolation filter and only requires a simple RC filter for the oversampling rate (e.g. x64).
Good point. I fully agree.
Additionally they are very cheap and very low distortion.

Klaus
 

Here's a simulation with a 3-pole Sallen-Key LP Butterworth filter added to the output of the original filter.

Capture.PNG
 

Hi,


Good point. I fully agree.
Additionally they are very cheap and very low distortion.

Klaus

Any example? Could you please give a part number?
 


Hi,

Just go to a dustributor and do a search for "audio dac".
Like this: https://uk.farnell.com/w/c/semicond...ers-dac/prl/results?st=Audio dac&sort=P_PRICE

Then go through the results and check the datasheets.

One if the cheapest is: PCM5100APWR
Even at 8x oversampling it has an impressive reconstruction filter.

Klaus

Very nice toy! Now I understand how they work. In general they have a second clock for the oversampled frequency, and the samples in between 2 samples are interpolated.
In practice you have your data sampled at 100kHz but they are sent out as if they were sampled at higher rate.
Unfortunately, I could not find such a dac's with more than 8 channels.
 

Is "an oversampling audio DAC" the same as a switched capacitor lowpass filter IC like a Maxim MAX295 Butterworth 8th-order? Years ago I used a National Semi switched capacitor IC to make an extremely low distortion audio frequency generator with it and the original signal was a digitally stepped sinewave.
 

Is "an oversampling audio DAC" the same as a switched capacitor lowpass filter IC like a Maxim MAX295 Butterworth 8th-order? Years ago I used a National Semi switched capacitor IC to make an extremely low distortion audio frequency generator with it and the original signal was a digitally stepped sinewave.

No. The oversampling audio dac uses digital algorithm to reconstruct the signal at higher frequency, therefore is more similar to a DSP.
I do not want to use switched capacitors because I do not want to have too many clocks. I have high number of channels.
 

The MAX295 switched capacitor lowpass filter IC has an internal clock, or one external clock can drive hundreds of them because it is low power Cmos. It is filtered by using oversampling.
 

The MAX295 switched capacitor lowpass filter IC has an internal clock, or one external clock can drive hundreds of them because it is low power Cmos. It is filtered by using oversampling.

My initial question was about adding 2 or more stages to an existing filter. I cannot do that. Separate circuits for each channel, unfortunately.
Still looking for a tool that allows designing a filter and modifying first stage. Webench does not allow that.
 

So - you are allowed to modify the existing filter with respect to cutoff and pole-Q ?
In that case - where is the problem? Modify the existing stage according to 4-pole parameters and add a second stage.
 

So - you are allowed to modify the existing filter with respect to cutoff and pole-Q ?
In that case - where is the problem? Modify the existing stage according to 4-pole parameters and add a second stage.

If I were allowed to modify it I wouldn't have asked!
As I said in my initial post, and I remarked in post#12, I cannot modify the first stage in the PCB.
When I said "modify first stage" in post #31 I meant in the software, or simulation tool, whatever you want to call it.
In other words: if I simulate 6 poles with webench, for example, I get 3 sallen-key stages but the first stage does not match with the one I already have on the pcb, and that I cannot modify.
Therefore I have to use a tool where I can change values of the first stage (on the software, not on my PCB), in order to match them with my PCB.
 

Sorry - but in post #31 I can read:

Still looking for a tool that allows designing a filter and modifying first stage

So - you have caused the misunderstanding.
 

Sorry - but in post #31 I can read:

Still looking for a tool that allows designing a filter and modifying first stage

So - you have caused the misunderstanding.

Very useful clarification, congratulations!
 

Here is what I would do, at least to start (not saying this is the best):
1) Use one of the mentioned tools to design the filter you want, like 4th order bessel
2) Simulate this along side the filter you currently have (and can't modify) with more stages added after it.
3) Manually experiment with Q's and cutoffs of those new stages until the entire filter matches the filter you want in LTSpice's AC sim.
4) You could probably speed up this experimentation by parameterizing the component values based on equations for the relevant filter so you just need to modify a Q and cutoff parameter and the components follow.

I consider this LTSpice eyeball test good enough since real life component tolerances are going to slightly alter the filter parameters anyway.
 

Besides ambiguous phrasing, I don't get the idea behind reusing the post #1 bi-quad block in a higher order filter. The specific complex pole pair either fits the intended overall characteristic or it doesn't. At best it you get a similar pole pattern that's not too far from the designed filter.

I'm not aware of a free filter tool that allows such manipulations. You can do it with commercial tools like Nuhertz Filter Solutions.
 

According to your link, and also the one I have used originally:
http://sim.okawa-denshi.jp/en/OPseikiLowkeisan.htm
the filter I posted is correct, in fact the 39k, 39k, 100p, 100p give a cutoff at 40kHz.

However, I simulated this filter with LTSPICE and it seems that the cutoff is at 27kHz, while at 40kHz I have exactly -6dB.
I do not understand why.

Then I used this calculator
http://www.calculatoredge.com/electronics/sk low pass.htm
which, with 39k and 39k, provides 144p and 72p as capacitor values. With these LTSPICE is happy and I have -3dB at 40kHz.

If the Q<0.707 the roll-of happens before the cut-off frequency, this is why you have seen bigger attenuation, but the calculators are correct. Only for higher Q values you will get exact 3dB relative attenuation. (If C1,C2 is 100pF the Q is 0.5, with C1=144pF and C2=72pF the Q is exatly 0.707. See page 11 http://www.analog.com/media/en/training-seminars/design-handbooks/Basic-Linear-Design/Chapter8.pdf)
So I am not sure your filter on the PCB has exactly 3dB attenuation at 40kHz. But it could be designed to F0=40kHz, and you could extend it I think to 6th order butterworth with 40kHz cutoff, because that has a stage with Q=0.5176 by the table I post, it is pretty close to your existing stage.
 

Yes, the f0=40 kHz, Q=0.5 block can work well for 6th order Butterworh with 40 kHz cut-off. But Butterworth doesn't meet the linear phase requirement in post #18. A 40 kHz Bessel filter would, but it needs f0=60 kHz Q=0.5.

I think, all options are on the table, it's up to you to decide about the solution.
 

Very useful clarification, congratulations!

(As a questioner you shouldn`t be too ironic - if you need help).

I rather think that YOU should try to clarify things....a good answer requires a good and clear question.
Why didn`t you tell us about the properties of the existing two-pole stage (which approximation, pole-Q) ?
What are your requirements for the whole filter chain? To speak about a "stronger" filter is by far not sufficient.
Which approximation? Which order? Still 40 kHz cut-off? Is this an absolut requirement?
In general, it is not a problem to add 2 or 4 poles - however, what are your final requirements for the complete filter?

Example: A 4th-order Chebyshev lowpass (0.5 dB ripple) needs a first stage with a pole-Q of 0.7051 (which is rather close to 0.7071).
Hence, if the existing stage has a Butterworth response (Qp=0.7071) , it shouldn?´t be a problem to add a 2nd-stage with Qp=2.9 - and you have a 4th-order Chebyshev filter
 

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