# How to calculate SNR in sigma delta modulator?

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#### jn_mohit

##### Newbie level 4 SNR in sigma delta

I am trying to find SNR of a sigma delta modultor, I have tried a lot but not able to come to conclusion as different writers use different procedure to calculate it.

I have simulated the system in simulink, I dump the input and output in the workspace. I take the fft and find abs(fft), what do i do now.
Let
fb: be max frequency of input,
fn = 2fb i.e. Nyquist frequency
fs: be the smapling frequency.
N = no. of points generated in input/output (2^13 is what i usually choose)

can anyone guide me how do i calculate SNR.

Thanks

#### Buriedcode

##### Full Member level 6 Re: SNR in sigma delta

Well, it really depends on what 'order' of SD adc you have.
The SNR is related to the resolution of the convertor and the amount of quantization noise.

Here's the way of calculating it:

I was always told in university that whenever you double the samping frequency, its like adding another bit and a half to the resolution.
But thats only for first order, where, if you want 16-bits, then 15/1.5 = 10. So its 2^10 = 1024, stupid number :x .

The equation, off the top of my head :roll: is (L+0.5) bits added to the resolution for every doubling of the sampling frequency, where L is the order of the convertor. Most people nowadays use 2nd to 4th order. Say for now, you want a second order SD convertor, resolution 16 bits, and a sampling rate of 48Khz.

16 bits needed, how many added bits do we need = 16-1 = 15.

L is 2 (2nd order), so for every doubling of the sampling frequency = 2.5 bits.

So 15/2.5 = 6.

2^6 = 64. (For sampling rate of 48Khz, 48 *64 = 3.072Mhz Ouch 8O)
In your terms, thats Fs = 64 * Fn.

Well, I know that doesn't really help you, but at least theres something on SD convertors for you For experimental readings, I'm not too up on fft. I found this ages ago when doing research into convertors:

Hope this isn't a waste of your time regards,

BuriedCode.

• tdf

### tdf

Points: 2

#### bamboo

##### Junior Member level 2 Re: SNR in sigma delta

hi jn_mohit,

Let
fin: input frequency,
fs: max input Nyquest frequency. (48kHz for Buriedcode's case)
OSR : Oversampling Ratio (64 for Buriedcode's case)
N : no. of points generated in input/output
M : prime Number

You may try the equation below:
fin = M * (fs*OSR)/N

You can get output and take the fft to find its SNR.

#### dinolin

##### Member level 1 Re: SNR in sigma delta

I think it depends on the noise shaper design and required bandwidth.

#### bernd

##### Newbie level 1 Re: SNR in sigma delta

hello guys,

I'm looking for a calculation to estimate the SNR for SD-Converter

I found different kinds of formulas,

like SNR=6.02*(bit+(order+0.5)*log2(OSR))

OSR,Order,BIT are the paramters

could someone give me a validation?

I have to programm a Matlab GUI to estimate the SNR which depends on the given parameters

thx
lg Bernd

#### yaxazaa Re: SNR in sigma delta

Basically increase your over-sample-rate by 2, SNR improves 9.03, which is 1.5 bit for 1st-order SDM, for 2nd-order SDM, SNR improves 15.05, which 2.5 bits, etc.

The same reason you can conclude for the improvement of SNR due to increase of OSR

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