[SOLVED] Chebyshev for anti-aliasing filter

[Junus2012]

Dear friends,

Although I am not intending to use the chebyshev LPF, but it came to mind how the ripple in the passband is accepted by the ADC converter,

If I am not wrong the ripple should be below the ADCE sensitivity, in other words it should be less than 1/2 LSB error. if I take 12 bit as anexample then error should be greater than 1 mdB while mostly we employ chebyshevwith at least 0.5 dB ripple.

Thank you

Regards

 

[sutapanaki]

How about regular Butterworth filter where you have -3dB at the pole frequency? Is this unacceptable? Or if we turn the question around - does the ripple in the Chebyshev filter cause new frequencies to appear in the spectrum i.e. does it distort?

 

[KlausST]

Hi,

If I am not wrong the ripple should be below the ADCE sensitivity, in other words it should be less than 1/2 LSB error.

I assume you misinterprete a "ripple in the frequency domain" as "ripple in the time domain" (which could be interpreted as noise).
A passband ripple in a chebychev LPF just says that - close to cutoff frequency - one frequency has different gain as another frequency.

Example:
Let´s say there is a passband ripple of +/-2dB...and the cutoff frequency is 10kHz.
Then ideally all frequencies in the passband should have a gain of 1 (0dB, let´s consider it is 1V RMS)
But in reality there may be a sine frequency (let´s say 9400 Hz) has a gain of 0.794 (-2dB, or 0.794 V RMS)
and another sine frequency (let´s say 9700 Hz) has a gain of 1,259 (+2dB, or 1,259 V RMS)

But each sine will still remain an undistorted clean sine.

For sure the error in sine amplitude is an error you may consider it or not... it depends on your application.

Klaus

 

[Junus2012]

Dear Suat
Dear Klaus

Thank you very much for your nice explanation,

How about regular Butterworth filter where you have -3dB at the pole frequency? Is this unacceptable? Or if we turn the question around - does the ripple in the Chebyshev filter cause new frequencies to appear in the spectrum i.e. does it distort?

The -3dB we shouldn't work at it, that is why fc > 10 maximum input signal, by this way we will not have a drop below the ADC resolution

please have a look on the following article, where he explained it in the section " Determine maximum signal frequency (fSIGNAL, fLSB) and acceptable gain error "

https://www.ti.com/lit/an/slyt626/slyt626.pdf?ts=1598372466100&ref_url=https%253A%252F%252Fwww.google.com%252F

I assume you misinterprete a "ripple in the frequency domain" as "ripple in the time domain" (which could be interpreted as noise).
A passband ripple in a chebychev LPF just says that - close to cutoff frequency - one frequency has different gain as another frequency.

Pleasse also read the above article,

also if you read in the TexasInstrument book given below, in the top page 335 (section 16-51), you will read that he didn't accept a ripple of 0.35 dB and he commennted that such ripple is barely enough for 4 bit resolution.

https://web.mit.edu/6.101/www/reference/op_amps_everyone.pdf

I understand your explanation regarding clean output, but you see the same input amplitude with different frequeny will result in different output amplitude, does this not mean different ADC output code ?

So for me it is also new concept since in my all basic study I learned that input signal frequency is defined limited to the filter cuttoff frequency, but after reading these two article I got different idea (mostly wrong) that for LPF for example it has to be very less the fc to get flat pass band with an error less than ADC resolution

Once again I am thankful to your explanation and help

 

[FvM]

Some applications set strict constraints on the passband gain error, in this case you would also restrict the ripple to a low value. The backside is that the passband corner is fixed to a low gain drop. The transition band of a low order filter becomes respectively wide.

The low gain error approach is feasible for high order filters, e.g. the digital filter of a oversampling ADC. I don't believe that it makes sense for your project.

 

[Junus2012]

Dear friends,

Thank you very much for your response to my post

I have double read and check the documents from Texas Instrument I have posted in #4, and it is misleading

If I follow that procedure to have fc > 10 fsignal with passband ripple less than 1 lsb error, it will not be practical at all

The standard bandwidth of a filter should accept signal drop-3 dB at fc (as Suta noticed that), it means that I should design fc equal to the maximum input signal information frequency, maybe a little bigger if we want less drop but not 10 times as they are suggesting in the first document.

The filter stop band frequency at (f= fs/2 )should have attenuation gain equal to the half LSB of the intended ADC. By this way, the aliasing is avoided.


If I take an example of commercial audio signal anti-aliasing filter used in CDs and audio equipment, they use standard sampling frequency of 44.1KHz, and fc = 20 kHz leaving 2 kHz space between fs/2 and fc.

However, I have here a question, with 3 kHz space that will be used as stop band range of the filter, how many orders required to have 8 bit of resolution (filter stop band gain at fs/2 = 51 dB) ??

Thank you once again
Regards

 

[sutapanaki]

If you know the max frequency fmax in your input signal spectrum, you can place your fc close to it, maybe somewhat higher. Usually fmax is lower than fs/2 because you need to leave some space for the filter transfer function to roll off down to the desired attenuation at fs-fmax. From that desired attenuation and from the frequency range over which it has to develop, you can decide the filter order.
By the way, I think in audio systems, the 2KHz drop is for the digital filter. Usually audio systems are oversampled a lot because they use sigma-delta converters and in this case the AAF is quite relaxed.

 

[KlausST]

Hi,

If I take an example of commercial audio signal anti-aliasing filter

With audio the anti aliasing filters are somehow very optimized.
I can't say what order the filter is.
In early CD days it was hard to achieve. But later they used oversampling techniques which made the anti aliasing relatively simple. At first they used 2-times, then 4-times, 8-times oversampling now they often use delta sigma ADCs with more than 64, 128 or 256 times oversampling.
The analog anti aliasing filter becomes a simple RC, the rest is done on the digital side...usully within the ADC itself.

Klaus