# reduction in the SNR after output passed through CIC filter

1. ## reduction in the SNR after output passed through CIC filter

I am studying the use of decimation filters in Sigma Delta modulators. While simulating I came across an unusual result.

i) I have an ideal 2nd order 1-bit (OSR=2048) sigma delta modulator. The SNR of its output is 145dB.

ii) I passed the modulators output through the first CIC filter (decimation factor = 64, no. of sections=3, wordlength of the cic output=19). The SNR of the output of the this CIC filter is 120dB.

Is it right that the SNR of the CIC output is less than the SNR of the modulators output? What might be the reason?

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2. ## Re: reduction in the SNR after output passed through CIC filter

I have an ideal 2nd order 1-bit (OSR=2048) sigma delta modulator. The SNR of its output is 145dB
Unlikely.

How do you determine SNR? My SD books don't grant 145 dB SNR for 2nd order and OSR 2048.
If the ADC had this SNR, it won't reproduced by 19 bit output length.

3. ## Re: reduction in the SNR after output passed through CIC filter

Originally Posted by FvM
Unlikely.

How do you determine SNR? My SD books don't grant 145 dB SNR for 2nd order and OSR 2048.
If the ADC had this SNR, it won't reproduced by 19 bit output length.

I am getting a high SNR since its an ideal SDM. Moreover, the theoretical formula for SNR calculation of the SDM also gives a SNR of ≈154dB.

can you explain why SNR of 145dB, it won't reproduced by 19 bit output length??

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4. ## Re: reduction in the SNR after output passed through CIC filter

because ideal ADC SNR is equall to 6.02N+1.76 dB and for N=19 u can achieve max 116,14 dB.
if u dont bealive u can calculate yourself 20*log10(2^19).

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5. ## Re: reduction in the SNR after output passed through CIC filter

Originally Posted by axcdd
because ideal ADC SNR is equall to 6.02N+1.76 dB and for N=19 u can achieve max 116,14 dB.
if u dont bealive u can calculate yourself 20*log10(2^19).
I am working in Simulink (matlab). I am passing the sigma delta modulator's output(1-bit) through a CIC decimation block. The specifications for this CIC decimation are as follows:
Decimation ratio=R= 64
no. of sections=N=3 (which is one more than my modulators order)
differential delays=M=1
word and fraction lengths of the filter sections and outputs =19 [wordlength=ceil(N*log2(M*R))+input wordlength]

The SNR of my modulators output is 145dB. The SNR of output of CIC decimation block is 120dB ( less than 145dB).

What could be reason for this? Can you help me with the simulation ? what simulink blocks to use after the modulator? any reference which gives the complete design flow with parameters' values?

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6. ## Re: reduction in the SNR after output passed through CIC filter

Now things start to make sense.

How do you achieve 2048 OSR with a decimation ratio of only 64? There must be additional decimation stages after the CIC to achieve the specified ratio.