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Track and hold circuit as a LPF (Read 5506 times)
HdrChopper
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Track and hold circuit as a LPF
Sep 23rd, 2008, 7:51pm
 
Hi,

I was wondering if a simple track and hold circuit could be used as a LPF by just increasing either the holding capacitor value or the switch Ron.
As for a deterministic input signal I imagine - as opposed to a conventional track and hold circuit where for each ON time the signal settles to its final value - it will take several clock cycles to reach the final input signal level. Therefore the LPF action will somehow take place.

However, what about the input white noise: is it going to be aliased back to the base band or the T&H circuit time constant will prevent such aliasing is properly sized according to the clock frequency?

I'm working on modeling this system but wanted to get some inputs as for how to look at this problem or what the best way is for modeling it.

Thanks in advance
Tosei
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vivkr
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Re: Track and hold circuit as a LPF
Reply #1 - Sep 23rd, 2008, 11:27pm
 
HdrChopper wrote on Sep 23rd, 2008, 7:51pm:
Hi,

I was wondering if a simple track and hold circuit could be used as a LPF by just increasing either the holding capacitor value or the switch Ron.
As for a deterministic input signal I imagine - as opposed to a conventional track and hold circuit where for each ON time the signal settles to its final value - it will take several clock cycles to reach the final input signal level. Therefore the LPF action will somehow take place.

However, what about the input white noise: is it going to be aliased back to the base band or the T&H circuit time constant will prevent such aliasing is properly sized according to the clock frequency?

I'm working on modeling this system but wanted to get some inputs as for how to look at this problem or what the best way is for modeling it.

Thanks in advance
Tosei


Hi Tosei,

In principle, this should function as a lowpass filter. I remember having had to build an analog moving average filter to reduce white noise in input samples, but cannot remember any details, as I was still a greenhorn then. However, we allowed good settling at each sample.

You will surely have plenty of distortion in your case, since you are sizing your switch in a such a way that it has too large an Ron, or to put it another way, your RC timeconstant is too large, and the R is nonlinear (since a switch is used).

Why not use a passive, linear R and a C for your filter. It would appear to me that the sampling part is anyway redundant since you are relying on averaging across multiple cycles.

As for white noise, the basic truth remains - total white noise power integrated = (kT/C).

Regards,

Vivek
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Tlaloc
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Re: Track and hold circuit as a LPF
Reply #2 - Sep 24th, 2008, 9:41am
 
Quote:
Why not use a passive, linear R and a C for your filter.

Or you could use a switched cap R into a C.  Then your pole would be more stable across process and you wouldn't have a DC voltage drop.

Quote:
I was wondering if a simple track and hold circuit could be used as a LPF by just increasing either the holding capacitor value or the switch Ron.

Why even turn off the switch in this case?  You could just have a weak switch that simplifies into an R--albiet, a highly varying R--for the passive filter that Vivek mentioned.

Adam
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HdrChopper
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Re: Track and hold circuit as a LPF
Reply #3 - Sep 24th, 2008, 6:59pm
 
Thanks vivek and Tlaloc for your answers...

vivkr wrote on Sep 23rd, 2008, 11:27pm:
In principle, this should function as a lowpass filter. I remember having had to build an analog moving average filter to reduce white noise in input samples, but cannot remember any details, as I was still a greenhorn then. However, we allowed good settling at each sample.



If in this case you allowed for good settling therefore the LPF action is very light, almost approaching the ideal T&H circuit where full settling is allowed. I'm actually looking for the opposite: a heavy filtering action.


vivkr wrote on Sep 23rd, 2008, 11:27pm:
You will surely have plenty of distortion in your case, since you are sizing your switch in a such a way that it has too large an Ron, or to put it another way, your RC time constant is too large, and the R is nonlinear (since a switch is used).

Why not use a passive, linear R and a C for your filter. It would appear to me that the sampling part is anyway redundant since you are relying on averaging across multiple cycles.



I'm actually thinking of using a very low Ron switch in series with a linear R and C (option 3 in the attached figure), in such a way the LPF time constant is set by linear components, and the switch just provides the holding action, which I require in my application.

In fact I´m looking to not increase the base band white noise power and at the same time hold the incoming signal every Tck. Therefore I need to provide some anti-aliasing means before sampling and I was wondering if merging the LPF (supposedly for preventing aliasing) and the sampling circuit would fulfill both requirements...

Obviously having a simple LPF and the T&H circuit with a buffer in the middle would do it (option 1 in the attached figure), but the whole point is about saving the buffer's area and merging both the filter and the T&H circuit....

vivkr wrote on Sep 23rd, 2008, 11:27pm:
As for white noise, the basic truth remains - total white noise power integrated = (kT/C).



I agree, but my problem is not the total integrated white noise, but rather how that power ends up distributed over frequency....


[/quote]

Or you could use a switched cap R into a C.  Then your pole would be more stable across process and you wouldn't have a DC voltage drop.

[/quote]

Tlaloc:

Using a switched cap is not an option since - as I described above - I 'd like to provide some antialiasing means and sample the signal in the same S&H circuit....if this were possible... that´s my question  :-/


Finally,
I think option 2 does provide antialiasing means before sampling the signal. Although the time constant of the filter changes during the sampling time (Ch in parallel with C1), the anti- aliasing action takes place....so, can this option also be reduced to option 3?

Many thanks
Tosei

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vivkr
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Re: Track and hold circuit as a LPF
Reply #4 - Sep 24th, 2008, 11:05pm
 
Hi Tosei,

If you cannot/don't want to use Option # 1, then I would go with # 2, make the cap in the lowpass filter much larger than the cap used in your T&H (to reduce ripple due to the switching action).

As for the noise, the final value you will see across the sampling cap will be (kT/Ch), and this will be spread uniformly over the band, and I would expect another noise component due to the noise from the linear resistor, which will be limited to the band defined by the RC timeconstant of that filter. So, you have a white noise component and a bandlimited noise (if I am right with my assumptions).

Regards,

Vivek
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ywguo
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Re: Track and hold circuit as a LPF
Reply #5 - Sep 25th, 2008, 2:53am
 
Hi Tosei,

The option 3 is not feasible becaue the input and white noise have already been aliased before they are low-pass filtered. That sampling occurs preceding the filter.


Yawei
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HdrChopper
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Re: Track and hold circuit as a LPF
Reply #6 - Sep 25th, 2008, 6:09am
 
Vivek,

I agree I should go with option 2, where anti-aliasing of the incoming noise is - at least intuitively - achieved by RC1 filter...

Therefore I also agree you will have a band limited white noise from RC1 (which will not be aliased given the time constant conditions) and the KT/C noise from the track and hold circuit. This second noise contributor I'm neglecting since I'm assuming a gain stage is placed before the RC1 filter.

Hi Yawei,

I agree that option 3 would generate white noise aliasing, although you could interchange the switch and R connections and then it would not be that clear the sampling occurs preceding the filter.
I find it difficult to represent such aliasing mathematically for option 3.

Many thanks for your comments
Tosei
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vivkr
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Re: Track and hold circuit as a LPF
Reply #7 - Sep 25th, 2008, 11:14pm
 
Hi Tosei,

From the relative values of the 2 resistors, I would also agree that there is no aliasing prior to sampling even with option # 3. Nonetheless, I fail to see why you would want to use it at all, since there appears to be no real advantage.

Your switch which is a nonlinear element is exposed to the largest possible signals, since there is no filtering preceding it, and so it will tend to worsen its nonlinear behavior.

Also you need to be careful if you want to neglect the kT/C noise from the smaller capacitor. Whether you can ignore it or not depends on its magnitude. Personally, I still do not see a significant advantage of this method but maybe you have found some use for it.

Regards,

Vivek

HdrChopper wrote on Sep 25th, 2008, 6:09am:
Vivek,

I agree I should go with option 2, where anti-aliasing of the incoming noise is - at least intuitively - achieved by RC1 filter...

Therefore I also agree you will have a band limited white noise from RC1 (which will not be aliased given the time constant conditions) and the KT/C noise from the track and hold circuit. This second noise contributor I'm neglecting since I'm assuming a gain stage is placed before the RC1 filter.

Hi Yawei,

I agree that option 3 would generate white noise aliasing, although you could interchange the switch and R connections and then it would not be that clear the sampling occurs preceding the filter.
I find it difficult to represent such aliasing mathematically for option 3.

Many thanks for your comments
Tosei

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HdrChopper
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Re: Track and hold circuit as a LPF
Reply #8 - Sep 27th, 2008, 11:25am
 
Hi Vivek,

I agree the switch non-linearity might be an issue in option 3 , but I´m not too concerned about that in my case. I was mainly concerned about the possiblilty of heavily aliasing the incoming white noise down to the base band, which was already amplified prior to this filtering stage. Such amplification  (abut 100x) makes the KT/C noise contribution negligible in my case.
I also agree there are no significant advantages between option 2 and 3, but at least it was clear to me option 2 does not fold back the incoming WN to the base band, while (assuming same time constants) I'm still not sure about option 3.
It seems Yawei thinks this might alias the incoming WN while you do not think the same. And I'm not sure of any of these two assumptions although I´m more inclined to think it will be some aliasing since there is a modulation process prior to the LP filtering....

This is more or less what I was trying to clarify in this post.

Thanks again for your comments.
Tosei
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