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Design >> Analog Design >> Low frequency bandpass filter
https://designers-guide.org/forum/YaBB.pl?num=1376252674

Message started by harpoon on Aug 11^th, 2013, 1:24pm

Title: Low frequency bandpass filter
Post by harpoon on Aug 11^th, 2013, 1:24pm

Hi all,

I am about to design a low frequency bandpass filter, probably 2nd order. The passband is 0.2Hz to 100Hz.

My first thought is to use switched cap filters ... but maybe a gm-C filter will also be feasible ?

Can we safely rule out opamp-RC topologies ?

Any thoughts on the matter would be very much appreciated ...

Thanks ...

Title: Re: Low frequency bandpass filter
Post by buddypoor on Aug 18^th, 2013, 3:37am

Hi harpoon, I was absent for 8 days, therefore my late response.

I think, you shouldn`t rule out RC opamp filters from the beginning.
Based on a filter design program I arrived at a maximum capacitance of 3.5 µF and Rmax=10 kOhms.
The filter topology is based on integrators (two opamps for 2nd order).
Single-opamp topologies are possible but require larger capacitances (150 µF).

Title: Re: Low frequency bandpass filter
Post by loose-electron on Aug 18^th, 2013, 11:37am

Another possibility - if you are taking this signal into an ADC, digitally filter it after ADC - thus saving a lot of physical device space.

Title: Re: Low frequency bandpass filter
Post by harpoon on Aug 19^th, 2013, 2:22am

Hi buddypoor,

I should really have said that I am looking for an on-chip solution.

3.5uF cap on a chip is really too big ! For a 2fF/um^2 MIM cap, this equates to a cap area of ~42mm x 42mm ... much bigger than a standard wafer reticle size !

The filter is there to filter low f noise (drifts) and DC offsets, I was actually thinking of putting an amplifier in there as well to reduce the noise effect of the ADC downstream ... so pretty much have to be before the ADC.

So you can see where I am going with this ...

So far from literature searches ...

gm-c : Problematic generating a low enough gm (consistently over PVT) or a big enough C

switched-c : have to contend with very big C ratios

interesting real world challenge ! ... ;)

Title: Re: Low frequency bandpass filter
Post by buddypoor on Aug 19^th, 2013, 3:09am

harpoon wrote on Aug 19^th, 2013, 2:22am:

switched-c : have to contend with very big C ratios

OK - of course, for on-chip solutions there is no chance to realize RC filters.
Regarding S/C technique: I suppose you know that the time constant is set by a capacitor ratio AND the takt rate?
Thus, why do you expect "very big" ratios?

Title: Re: Low frequency bandpass filter
Post by harpoon on Aug 19^th, 2013, 7:11am

here are my first order back of envelope calc ...

at 0.2 Hz, the time constant needed is ~0.8s

tau = Cf/Cin * 1/fclk

fclk needs to be high-ish, at least an order higher than the 100Hz bandpass upper corner, say it is 2kHz

this means Cf/Cin is roughly 1600 !

if Cin is ~100fF, Cf needs to be ~160pF ... which is big on chip (but maybe not that unreasonable).

Maybe I should re-visit my cap-multiplier circuit again for this ...

Title: Re: Low frequency bandpass filter
Post by buddypoor on Aug 19^th, 2013, 7:21am

Yes - I see the problem.
I think, it is mainly caused by the large relative bandwidth.
Therefore: perhaps it is better to use a high pass (corner at 0.2 Hz) followed by a low pass (corner at 100 Hz)?
In this case, you must use two different clock frequencies.

Title: Re: Low frequency bandpass filter
Post by harpoon on Aug 20^th, 2013, 3:41am

hi buddypoor,

thanks for your comments ...

Title: Re: Low frequency bandpass filter
Post by Lex on Aug 21^st, 2013, 11:44pm

Any possibility to up convert the signal to a higher frequency band? E.g. chopping?

Title: Re: Low frequency bandpass filter
Post by harpoon on Aug 22^nd, 2013, 12:30am

Lex wrote on Aug 21^st, 2013, 11:44pm:

Any possibility to up convert the signal to a higher frequency band? E.g. chopping?

I am afraid not ... I am looking at an implementation suggested in this paper ...
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=34666

looks promising ...

Title: Re: Low frequency bandpass filter
Post by harpoon on Aug 22^nd, 2013, 5:45am

buddypoor wrote on Aug 18^th, 2013, 3:37am:

Based on a filter design program I arrived at a maximum capacitance of 3.5 µF and Rmax=10 kOhms.
The filter topology is based on integrators (two opamps for 2nd order).

Hi buddypoor,

I was just looking at these numbers you posted ... 3.5uF and 10kOhm to generate a 0.2Hz corner looks too good to be true, can you check if this is correct ? thanks ...

Title: Re: Low frequency bandpass filter
Post by buddypoor on Aug 22^nd, 2013, 6:25am

harpoon wrote on Aug 22^nd, 2013, 5:45am:

Hi buddypoor,

I was just looking at these numbers you posted ... 3.5uF and 10kOhm to generate a 0.2Hz corner looks too good to be true, can you check if this is correct ? thanks ...

It is a bandpass with a mid frequency of app. 4.5 Hz.
Corner frequencies (3 dB) at 0.2 Hz and 100 Hz.
Topology: Tow-Thomas (2 integrators) - that means: 2 capacitors.
The given values (10k, 3.5µF) are correct.

Please note that sometimes there is a confusion regarding the order of a bandpass.
Lowest possible order is n=2 (Denominator polynominal of 2nd order).
Some authors/programs claim that this would be first order (n=1).
However, this is not correct: The order is determined by the denominator.

For a higher order (n=4 with 4 capacitors) I get: Rmax=10k and Cmax=79 µF

Title: Re: Low frequency bandpass filter
Post by harpoon on Aug 23^rd, 2013, 5:53am

buddypoor wrote on Aug 22^nd, 2013, 6:25am:

thanks ...