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Design procedure for integrated MFB low pass filter

Junus2012

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Dear friends,

I would like to ask you about text book or good material to study the design of integrated fully differential anti-aliasing filter (AAF),
I am intending to use Multi-feedback topology which is suitable most for the fully differential amplifier, as I read from Texas Instruments.

I also heard about MOS_C filter, but I couldn't find the difference from the above one, is it just a name ?

What about the design with Gm_C filter, is it also possible ?,

The upper frequency of the AFF is 5 MHz,

I am looking for your suggestions as well

Best Regards
 

sutapanaki

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Gm-C filter for 5MHz is hardly justified. But apart from frequency, you should also know what order of a filter you need, what resolution do you target, which will define distortion and noise spec of the filter. Not lastly, what process technology do you intend to use.
 

Junus2012

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Thank you Suta for your reply

I am intending to design 2nd order or 4th order filter (or the required higher order which I don't know yet)
Resolution is 12 bit
Technology 0.35 µm CMS
 

sutapanaki

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12 bit would suggest a distortion going into the ADC of at least 72dB, better - 78dB. You don't have much choice here but use opamp-RC filters. Gm-C will not give you that kind of distortion because it uses open loop integrators. If you want 2nd order you may go by with Sallen-Key filter but it becomes too sensitive to component variations for higher orders. If it is 4th order, then you'd be better off with a cascade of biquads. If you need more than 4-th order, then you should better use ladder filter architecture.
In any case you will have to design opamps with UGBW of around 100MHz. I would suggest before even starting the transistor level design, create a model for the opamp, that would have a first pole at low frequencies and a second pole at above UGBW - 3-4x higher than UGBW. Would also need to have of course DC gain modeled as well as noise (very important). Then, build your filter, whichever one you decide to use, with this amplifier model. You can change all parameters of the model and study how they influence the overall filter characteristic. You will not be able to see distortion with that model, though, unless some distortion comes from the resistors/capacitors you use, but it is not going to be the whole picture.
 

Dominik Przyborowski

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Find answers for following questions:
1. What is sampling frequency?
2. What is required image rejection?
3. What is required settling time?
4. What is minimum input impedance?
5. What is maximum noise floor?
6. What is In-Band and Out-of-Band linearity requirements
7. What is stop-band attenuation requirements?
8. What is maximum recovery time after saturation?

Potential other questions are possible as well.

MFB filters are realized usually on OPAMPs and uses passive RC elements to define filtering, Gm-C (known also as OTA-C) is an abbreviation for transconductor based filters. The difference is meaningful between both.

In OPAMP based filters you can achieve very good noise performance (as long as input impedance is not bottom limited - usually is), perfect linearity and "infinite" stop-band attenuation (excluding Chebyshev filter which has limited attenuation by definition). However, the problem is to design OPAMP which will be able to drive it all in wide bandwidth without large signal distortions and with reasonable current consumption.

On the other hand, Gm-C has high input impedance (transistor gates), poles are defined by OTA's Gm and drived capacitors (so can be whatever - or by use low caps or low currents), it allows wide tunability. Gm-C are also nicely configurable and might be compact with low current consumption. However, linearity is creepy, achieved by linearization of diff-pairs with cost of noises. Attenuation is limited usually to 40-50dB. There might be also a lot of other pros'n'cons.

Literature is wide.
A few books, like:
1. K. Su "Analog Filters"
2. B. Nauta "Analog Filters for Very High Freqs"
3. Another classic
4. And much more

Also tons of papers/thesis are in the web.
 

Junus2012

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Dear Suta and Dominik

Thank you very much for your nice explanation

My supervisor asked me to design 2nd order filter for the beginning, and he suggested me later to cascaded it to achieve 4th order or six order, he suggested me the MFB filter, but when I searched in literature I found many people are using Biquad filter topology like commonly saw the Tow-Tomas scheme, as also suggested by Suta to go for Biquad filter but didn't mention the reason. By the way Suta, Sallen-Key filters are more difficult to implement than MFB since they require a diffierential-difference amplifier (4-input differential amplifier).

Texas Instruments always advise for MFB, but their documentation is about the discrete filter, not integrated as my case.

Dear Dominik,

I see you didn't cancel the option of the Gm-C filter completely as our friend Suta did. You emphasized on a good point of Gm-C filter, that is tunability, since my task is to design tunable low pass filter with tunable fc vary from tens of hertz up to 5 MHz.

I have one question about the Gm-C filter, it is basically open loop OTA where the fc is defined from the open-loop characteristics, which means that the input signal will be amplified by the open-loop gain of the Gm-C filter. The open-loop gain is usually high even if we try to decrease still can drive the signal to the saturation, besides dealing with the open-loop amplifier is not reliable as a closed-loop amplifier.

By the way, I don't need amplification since I already have an amplifier before the filter.

If the main feature of the Gm-C filter is regarding the tunability, the MFB filter, for example, can also be tuned by using Mosfet-resistors and which can be tuned to by changing the gate voltage.

Thank you, Dominik, for the books

Thank you once again guys
 

KlausST

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Hi,

Post#6 is totally confusing to me, because it mixes just a bunch if technical terms.

For example:
* 2nd order, 4th order, cascading...
It seems you try to use a 2nd order ... then add another 2nd order ... but ignore that cascading shifts the cutoff frequency

* MFB tecnology is mixed with biquad topology.
But MFB is an analog filter ... while a biquad is a digital filter (which can't be used as anti aliasing filter, for example)

* and other issues

It's urgent to first define the requirements for yourself.

Klaus
 

Junus2012

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Hi,

Post#6 is totally confusing to me, because it mixes just a bunch if technical terms.

For example:
* 2nd order, 4th order, cascading...
It seems you try to use a 2nd order ... then add another 2nd order ... but ignore that cascading shifts the cutoff frequency

You mean to say that cascading two 2nd order filters with cutoff frequency = fc for each result in 4th order filter but with different fc ?


* MFB tecnology is mixed with biquad topology.
But MFB is an analog filter ... while a biquad is a digital filter (which can't be used as anti aliasing filter, for example)

* and other issues
biquad can be digital and can be analog, an example of the analog is the Two-Thomas filter, the latter one which I am comparing to MFB or Sallen-key or Gm-C filter
Klaus
 

sutapanaki

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Biquad filters, of course, are analog and could also have digital counterparts.

Junus, building a filter, especially going up to 6 order is not as simple as cascading individual second order stages. There is a lot more to it. For example, a cascade of bi-quads has more variation in their Q and pole locations when you take into account the variation and mismatches in the components. This is because each bi-quad is by itself and doesn't talk to the poles coming from the next/previous bi-quad in the cascade. In contrast, in ladder filters the poles are all inter-coupled and change in one of them changes the rest to a certain extend and this helps with preserving the filter transfer characteristic shape in the presence of variations. I would assume that in the case of MFB topology we have a similar situation as with Sallen-Key, when it comes to the stability of the filter shape, which is not great. It comes from the fact that it builds the entire 2nd order function around only one opamp. You will have to investigate this if you decide to use it. But as a general rule, when you try to build higher order functions, you also build high-Q biquads and high Q means more variation in the filter transfer function when it is based on cascading stages.
Gm-C filters can not get you the level of linearity that you would need for 12 bit ADC. They are well tuned, that's true but it is not the only thing that you require from a filter. In the Gm-C filter the integrators are open loop, but the filter you build with them is not open loop, so you can't say that because the Gm-C integrator has large DC gain, so does your overall filter. You filter will have a gain of 1 or maybe 1/2, depending on the topology.
 

Dominik Przyborowski

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I see you didn't cancel the option of the Gm-C filter completely as our friend Suta did.
You are a designer, so you decide - I am not going to decide for yourself, only gives answer for question ;-)

Biquad is short for bi-quadratic means two poles and two zeros.

You mentioned, you have 12bit ADC following filter stage. The most likely you need nice Butterworth low-pass with good stop-band attenuation.
As I mentioned early, with Gm-C you get no more than 40-50dB, what is sufficient for 7 maybe 8 bits but not for 12.
Sallen-Key is bad idea, not because of fully-differential implementation (IMO it doesn't need FDDA) but because strict requirements for low output impedance of OPAMP.

You emphasized on a good point of Gm-C filter, that is tunability, since my task is to design tunable low pass filter with tunable fc vary from tens of hertz up to 5 MHz.
7 orders of magnitude of tunability?
You don't want to do it. Believe me.
If we take some numbers for 5MHz and MFB topology we get for example 66kΩ and 260kΩ (already high values for noise performance) for resistors and 750pF and 75fF capacitance. 500kHz is achievable by multiplying caps by 10×, what gives 7.5pF and 0.75pF. And this is close to limit in IC implementation (reasonable).
In contrary, for Gm-C, with 1pF cap, Gm has to be varied from 30µS (5MHz) to 3pS. With 100fF lower value is 30pS. Designing an OTA with so low transconductance and still reasonable other parameters is another challenge.

If the main feature of the Gm-C filter is regarding the tunability, the MFB filter, for example, can also be tuned by using Mosfet-resistors and which can be tuned to by changing the gate voltage.
As long as your signal swing is higher than few mV it will not work. Linear pseudoresistor is challenging, and you will need to have a few of them matched together. People were trying this in past, but with no big success.

As sutapanaki said earlier - start with defining spec and build model to check what is feasible to achieve.
 

KlausST

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Hi,

Biquad filters, of course, are analog and could also have digital counterparts.
Thanks for clarifying this. I wonder why I never realized this terminology for analog filters.
Dominik's explanation makes sense, too.

Thanks both of you.

Klaus
 

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Junus2012, you are writing about designing an integrated 4th or 6th order filter, possibly tunable. I'm not aware of having seen a similar filter in a commercial IC, I think for a good reason. Since decades, high perfromance ADC are build with oversampling, simple first or second order analog filter and precise digital decimation filters. If higher data rate than achievable by oversampling and steep analog anti-alias filters are required, they are typically build discretely.

Did you estimate the achievable pole/zero accuracy in your available IC technology? Is it sufficient for the intended filter characteristic?
 

sutapanaki

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It is quite true that if one uses/designs oversampled A2D, with a lot of oversampling, the anti-aliasing filter becomes a no issue. because the filter has a lot of room in the frequency domain to develop attenuation. However, not all ADCs are oversampled and these are not a small percentage of all all ADC build on chip. For example, ADC going into wireless products are rarely oversampled but still require resolutions of 10 to 12 bit. DSL products also employ ADC of high frequency and resolution.
Oversampled ADCs are not suitable in control systems. They are very good, though, for DC measurements, audio, sensors i.e. relatively low frequencies.

In Junus's case frequency is not that high, 5MHz, but we don't know the application. Also, we don't know what is the max signal frequency component with respect to Fs/2 because this will define the needed order of the filter. But we can assume that whatever filter it is, it doesn't need attenuation in stop-band, that is, it doesn't need zeroes in stop band, because they will also introduce finite attenuation. This will leave Butterworth or maybe Chebishev type 1, or some customized shape filter as choices. In any case going from 2nd to 4th, to 6th order is not a simple task.
 

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Can't follow exactly your considerations about not using zeros in transfer function, high performance analog AAF are typically of the elliptical type. Butterworth/Chebyshev would be used if you decide for limited filter effort.

But as said, my basic doubt is about achievable filter precision in IC implementation. We didn't yet hear the requirements.
 

sutapanaki

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My considerations were that when you put zeros in the stop band that usually limits the attenuation for frequencies other than the zero frequency( in the case the zero is placed on the jw axis).
Elliptic filters have terrible phase response and may not be always suitable if signal shape is to be preserved. That's why people often opt for Butterworth filters as a compromise between Bessel filters with much more linear phase response and filters like Chebishev or Elliptic which have steeper response but very non-linear phase.
 

Junus2012

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Dear friends,

Thank you very much for your reply

I have discussed with my team leader about the points you addressed.

After discussion, he said to me it is true that gm-C filter can not fit into our ADC requirement of 12 bit resolution. Hence RC based integrated filter is mandatory.

Now he defined the task for me more clearly as below

1. The filter has to drive a pipelined ADC with 12 bit resolution.
2. The Samling frequency of the ADC is 10 MHz (means the sampling of the sample and hold circuit), hence my supervisor suggested me to design a filter with an fc = 5 MHz.
3. The required attenuation of the stop-band is 80 dB, which means 4th order filter (this is good for me to avoid higher older complication).
4. The filter has to tune the fc down to low-frequency sensor signal, in principle, he wants to use the filter as more generic interface circuit to cover wide range of frequency varying from few tens of hertz up to 5 MHz
5. Toward tunning, he suggested me to use bank of selectable capacitors and resistors, however, for the low frequencies these resistors will be very big crossing the limit of our chip size. Therefore, he asked me to implement it using a tunable MOS Pseudo resistor.
Yes it is right as you already said, the pseudo-MOS resistor is not great for linearity, but he said we can add some in series to improve the linearity. He shared with me some papers from IEEE about an enormous filter design using Pseudo resistor.


Now the only thing lift is to choose between MFB topology or Two-Tomas biquad topology. Please sugget me which one should be better for IC implementation.

Thank you very much for your help, your previous comments were very useful to me in my last meeting, I do appreciate that from you

Best Regards
 

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Saying fc=5MHz is far from a complete filter specification. A full specification involves pass and stop band corners, max. pass band and min. stop band attenuation. If you want 80 dB stop band attenuation with only 4th order, you have to accept a much lower pass band corner, e.g. 1 MHz.
 

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If your corner frequency is 5MHz and the sampling frequency is 10MHz, then with a 4th order filter roll-off you only get 24dB attenuation at 10MHz. What actually is important here is to know the spectrum of your intended input signal. That will help you decide how much you will have to attenuate the unwanted frequency components around Fs before they alias back into the signal bandwidth.
Also important consideration is what you want your tuning step to be. I would guess you don't have to do linear tuning steps in the whole range from low frequencies to 5MHz.

Whether to use MFB or Tow-Thomas is something you will have to investigate perhaps with the way I suggested previously by building a model of the amplifiers and then using it to build a filter and see how it behaves under different non-idealities. I think Tow -Tomas is abetter choice, more opamps, but you'll have to check both out.
 

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Hi,

That will help you decide how much you will have to attenuate the unwanted frequency components around Fs before they alias back into the signal bandwidth.
With a sampling frequency of 10MHz .... alias frequencies occur beginning from 5MHz.

Example:
6MHz input will become 4MHz alias..

Thus a 5MHz filter will attenuate alias frequencies just by 3dB worst case.

If you want an anti alias filter then the cutoff frequency needs to be (far) below 5MHz.
Audio anti aliasing filters (without oversampling technique) were optimized to get about 20kHz upper frequency with a sampling frequency of 44100Hz ... in early CD era.

Klaus
 

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Hi,


With a sampling frequency of 10MHz .... alias frequencies occur beginning from 5MHz.

Example:
6MHz input will become 4MHz alias..

Thus a 5MHz filter will attenuate alias frequencies just by 3dB worst case.
That is correct and is also common knowledge. We talk about Fs and Fs/2 here but we don't talk about the bandwidth of the input signal. For example, if the BW of the input spectrum is limited to 1MHz and Fs=10MHz, then the least attenuated aliasing frequency is at 9MHz. All frequencies 9MHz<f<10MHz will be attenuated even more. And all frequencies between 5MHz and 9MHz will alias outside the bandwidth of the input signal.
 
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