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Design >> Analog Design >> Biquad types
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Message started by rfmagic on Dec 30^th, 2010, 1:19pm

Title: Biquad types
Post by rfmagic on Dec 30^th, 2010, 1:19pm

Hi,
I am designing a 5th order Butterworth filter using casceded biquads. I have seen many topologies to implement a biquad but I am not sure I got the main advantages of each type.
I appreciate is someone could tell me the main advantages and disadvantages of the following biquad types:
1. Sallen_Key
2. MFB
3. Tow-Thomas

Thanks

Title: Re: Biquad types
Post by buddypoor on Dec 31^st, 2010, 1:49am

rfmagic wrote on Dec 30^th, 2010, 1:19pm:

At first, I wouln't call S+K and MFB a "Biquad" since both cannot create a biquadratic transfer function - but that's not too important.
In particular:
* S+K is rather sensitive to parts tolerances, but less sensitive to opamps GBW.
* Just the opposite is true for MFB
* The TT-biquad also is not suited for rather high frequencies (because of sensitivity to the GBW). More than that, it uses more than one opamp (as both other alternatives, S+K, MFB).
*One additional hint: The cascade approach (several stages in series) is not the best from the sensitivity point of view. What about active realization of a passive ladder structure (FDNR technique)?

Title: Re: Biquad types
Post by ssahl on Dec 31^st, 2010, 1:52am

Hi!

One difference between Sallen Key and MFB is that you can easily build a fully differential filter with the MFB, which is tricky with the Sallen Key.

Tow-Thomas can give you a bandpass filter if you need it.

Have you looked into a leapfrog architecture? It is a robust architechture and I believe that you get better SNR performance per current consumption. But it requires some theory to calculate the RC values.

Title: Re: Biquad types
Post by rfmagic on Dec 31^st, 2010, 4:15am

Thanks for your reply...

Buddypoor,

is it possible to design a filter with such a minimal sensitivity to parts and GBW so that it will eliminate the need for calibration?. the tolerance for CMOS 0.18u technology is pretty large (+/- 15%).

I saw some designs that actually use TT stages in cascade for WLAN zero IF frequencies (<20MHz BW) can you think of a possible advantage of the TT over other configurations even though it uses 2 opamps?.

Which configuration has the best noise performance?

Thanks in advance

I

Title: Re: Biquad types
Post by rfmagic on Dec 31^st, 2010, 4:59am

ssahl,

I am not familiar with the the leapfrog implementation but I will look into that as it has better noise performance according to your reply.

At first I wanted to used the cascaded Biquads architecture as it is very simple implement.

Thanks

Title: Re: Biquad types
Post by ssahl on Jan 2^nd, 2011, 7:06am

rfmagic wrote on Dec 31^st, 2010, 4:59am:

Yeah, the biquads are much simpler to understand. But for high orders you get vary high Q-value for some of the biquads and you need low-resistors to get the noise performance. I think it is worth the extra theoretical effort of the leapfrog. I found some simple presentation how to make it work.

http://amesp02.tamu.edu/~sanchez/458-Leapfrog.PDF

/ssahl

Title: Re: Biquad types
Post by rfmagic on Jan 2^nd, 2011, 10:12am

Thanks for the presentation ssahl, i

I am not sure I that I get your point, in order to get good noise performance I would expect to have high Q circuit so that the resistive components will be low, right? but you say just the opposite...
If my argument is correct then it will be better to use a cascaded biquads.

Title: Re: Biquad types
Post by ssahl on Jan 2^nd, 2011, 12:46pm

rfmagic wrote on Jan 2^nd, 2011, 10:12am:

Hi,

what I meant my high Q circuits is the Q-value of the pole that the active filter is implementing, not the Q value of the components itself.

For the biquad implementation all poles needs to be placed in a specific biquad. Placing the ones with high Q early will make the filter to peak internally. This generates large voltage swing. To handle that you probably need to lower the gain to that point. Keeping the SNR you need to lower the resistor values and increasing the capacitor values, which cost you current in the opamps.

If you try out the leapfrog structure it looks like there is less peaking internally in the filter. (I have no theoretical proof for this but it is my experiance.) This lower peaking means that you can keep a larger signal swing in the filter and therefor keeping the SNR high without going for low resistor values.

I hope this explaination makes sense.

/ssahl

Title: Re: Biquad types
Post by buddypoor on Jan 3^rd, 2011, 1:48am

Yes, I agree with ssahl concerning trade-off between leapfrog and cascade design.
One additional recommendation: Why not use - at least to gather some information about circuit alternatives - some filter design programs?
There are several different design programs available for free via download.
I tend to remember that there is even a program containing the leapfrog topology (filter_solutions).

Title: Re: Biquad types
Post by rfmagic on Jan 3^rd, 2011, 4:58am

buddypoor,

That's a very good idea, following your input and ssahl inputs, I started to wonder how to compare the different alternatives quickly, and without making this project to complicated. I am working with ADS and the "Filter Design Guide" only synthesises lumped elements ladder networks so I suppose that this is not the right tool as it still leaves me too much work to transform the passive ladder into an active one.

It will be very nice to use a program that can generate diffrent Active filter architectures in order to compare their performance. Is the program that you recommend (filter_solutions) can do that?

Title: Re: Biquad types
Post by buddypoor on Jan 3^rd, 2011, 7:15am

Here are some useful links for active filters:

*www.filter-solutions.com (filter_free)
*www.microchip.com (Filterlab)
*www.ti.com (FilterPro)
*www.schematica.com (FilWizPro)

All have working demo versions for free

Regards

Title: Re: Biquad types
Post by ssahl on Jan 3^rd, 2011, 7:27am

buddypoor wrote on Jan 3^rd, 2011, 7:15am:

Hi,

I have found a simple program from Linear by which you can get the poles and zeros from a filter. I have found it useful.

http://www.linear.com/designtools/software/filtercad.jsp

Title: Re: Biquad types
Post by rfmagic on Jan 3^rd, 2011, 7:36am

Thanks guys,

I will take a look at the links and update you on the results

Title: Re: Biquad types
Post by buddypoor on Jan 3^rd, 2011, 9:15am

Hi ssahl, I know the program from LTC - and, indeed, it is very useful to find the pole parameter for different approximations.
However, it gives parts values only for the design of filter modules from LTC. Thus, it cannot help by designing other structures.

Title: Re: Biquad types
Post by ssahl on Jan 3^rd, 2011, 11:55am

Hi Buddy!

Yes, the only use I have of it is the poles and zeros. It's lika a filter table. Thanks for the tips of the other softwares, I will have a look at them next time I run into a filter problem.

Cheers

Title: Re: Biquad types
Post by rfmagic on Jan 10^th, 2011, 5:50am

Hi,

Back again with some interesting results of the biquads that we have been discussing on the previous posts.

I have downloaded the Filter Solutions software trial and produced 4 3rd order active Butterworth LPFs. I have to admit that Filter Solution is great and can save a lot of time in the process of filter configuration research. I then simulated the ferquency response and noise of the filters and it seems that theh Sallen-Key filter has the best noise performance even over the LeapFrog filter (any idea why, ssahl??). I then wanted to see the sensitivity of the different configurations to component variations and the opamp GBW, so I set all the component values to vary +/-3 std and also the opamps GBW was varied by +/- 3std (using MC simulation). as you can see also here (in the attached plot) the Sallen-Key configuration has least sensitivity.

It seems that these results does not support the laepfrog configuration as havin gthe best noise and sensitivity performance.

Title: Re: Biquad types
Post by ssahl on Jan 10^th, 2011, 7:51am

Thank's for sharing the pictures and also the review of Filter Solutions. Some comments about your curves.

You have very low sensitivity for the SC filter. I think that has to do with that you have an ideal unity-gain block, without any mismatch. If you put in an opamp based unity-gain amplifier with two feedback resistors you will see some gain-variation. The other topologies has that gain stage build into them.

If you look at the noise plots you see that the leapfrom has the lowest peak around the band edge, which is good. This has to do with that the internal Q-values in that topology is low.

It is always possible to generate a low noise value, it is only to use small resistors and large capacitors. Before you make any conclusions you should have a look at how much signal currents each opamp must deliver into the RC networks. (You can do that with a simple AC analysis.) Also have a look at how high voltage amplitudes you have at the opamp outputs inside the filters. It is easy to have very large signal swings at internal nodes that will saturate you opamp.

Title: Re: Biquad types
Post by rfmagic on Jan 10^th, 2011, 10:52am

Hi ssahl,

I agree about the peak at the band edge but still, an integration of the noise on the entire frequency range ends up with the SK a little better than leapfrog. My design criterion was maximum capacitor value of no more than 4.5pF (for area considerations) and the resistors value were set accordingly.

I still think that the leapfrog and MFB advantages are not evident in this simulation and it might got to do with the fact that it is a relatively low order filter (3rd order Butterworth), maybe if I repeat this simulation for a 5th order filter the results will be different. I think it worth the effort.

Anyway, thanks for the tips regarding the current consumption and maximum voltage peaks at the opamps, I will take that into consideration

Title: Re: Biquad types
Post by ssahl on Jan 10^th, 2011, 12:29pm

I see your point and understand that you need to put your foot down! As you pointed out the conclusions for an 5'th order filter can be different, such filter has higher Q values. Different conclusions can also be drawn if you consider integrated noise or spot noise.

If you are going to check the signals currents, do not forget the amplifier driving the filter. A RC network at the filter input will load preceeding stage. If it is possible, please keep us updated. It has been an interesting discussion.

Title: Re: Biquad types
Post by buddypoor on Jan 11^th, 2011, 1:54am

Hi rfmagic,

in your evaluation of the filter software simulation results you shouldn't forget that all simulations assume ideal opamp properties - as far as input and output impedances are concerned.
Because of this, you did not detect the following disadvantage of the S+K topology:
Above a certain frequency the attenuation will again decrease (the filter transfer curve is rising).
This effect is due to the feedback capacitor:
For higher frequencies there is a remarkable and rising portion of the input signal that reaches the opamp output DIRECTLY (not via the internal amplifier chain). This portion creates at the finite opamp output a signal voltage that increases with frequency. You can observe this effect via circuit simulation based on real amplifier macro models.
Example: opamp type LM741, second order lowpass with Qp=1 and 3-dB frequency 50 kHz. As a result, the attenuation will be not better than -35 dB (at app. 400 kHz) and then will decrease again.

Regarding Monte Carlo simulation: May be you didn't get the right picture because - in some cases - tolerance variations can cancel or reduce each other. The worst case for S+K topology is variation of one of the gain fixing resistors alone! Try it - it's really bad!
(Obviously, this is not the case for unity gain design - however, this alternative has other disadvantages).

Title: Re: Biquad types
Post by rfmagic on Jan 11^th, 2011, 2:23am

Hi buddypoor,

Actually I used an opamp model with a finite GBW of 1GHz and output impedance of 100Ohm. I also compared this model to a real opamp implementation and the only difference that I saw was the 1/f noise due to the transistors that was not acounted for with the opamp model. so, I think that to that point I am pretty much simulating a real scenario.

Regarding Monte Carlo simulation, it is clear that some of the scenarios created by the MC generator will end up in canceling devastating effects but this is also true for the opposite case where some scenarios are very bad.

I agree that for a unity gain S+K topology the mismatch is low, I will repeat the simulations for S+K that has some gain , I expect to see more mismatch effect as you noted. What are the disadvantages that you mentioned regarding a unity gain S+K?

Thanks

Title: Re: Biquad types
Post by buddypoor on Jan 11^th, 2011, 3:07am

rfmagic, for clarification I enclose a pdf-picture with a comparison of some different approaches.
Regarding your question: For a unity gain S+K topology you will have a relatively large component spread for resistors as well as capacitors (in the order of 10 or something similar). In some cases (IC technology) this is not wanted.

Title: Re: Biquad types
Post by vp1953 on Jan 12^th, 2011, 4:24pm

Hi Buddypoor,

Thank you very much for your detailed explanation and the example you illustrated.

Question for you : your curve 3 (in the pdf) has a substantial rising portion (just before the rolloff) - almost seems like it has an additional low frequency zero. What is the reason for this and is it a consequence of op amp nonideality?

Title: Re: Biquad types
Post by buddypoor on Jan 13^th, 2011, 2:44am

Yes, you are right. The peaking of No. 3 is a consequence of the additional phase shift - introduced by the non-ideal opamp which in this case (negative feedback topology) gas a rather large gain of app (-20).
Because of the relatively high pole frequency (app. 50 kHz) and this gain requirement, the non-idealities have a remarkable influence and cause a pole Q enhancement.
This is a disadvantage of this structure (for high pole frequencies). The advantage is a much better (lower) sensitivity to parts tolerances.
This is a general rule: negative feedback topologies always have smaller sensitivities to tolerances - if compared with positive feedback structures.
However, they are more sensible to opamp non-idealities.
Another general rule: Each circuit alternative is a compromize between several - mostly conflicting - requirements.
Regards