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SAR adc oversampling SQNR

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Hello,In sigma delta we have SQNR based On OSR.
In SAR ADC I need to find the link between the number of bits(number of switches of SAR) and Its potential OSR and SQNR.
The only thing i have in SAR is the convertion time formula belloa
SAR_time_convertion=T_sampling+N*T_switch .
How do i derive from its the F_sample (sampling rate) and signal frequenct Fd?
giving me OSR by fb/(fs*0.5)
I know that the input has some frequency and the sampler of the SAR has frequency too but we have the switches too in there ,how it going to affect it?
Thanks.
 

This is not that straight forward. It is easy to have the sampling time. and then your sampling frequency is just 1/T_sampling. But can you fit all N*T_switch between two samples. In T_switch you have to account for the time needed for the CDAC to settle, the time for the comparator to make a decision and the time for the SAR logic to process the comparator decision and produce the switch signals. Add to this the fact that the comparator decision time needs to take into account also its dependence on its input difference. If your SAR is asynchronous, you can't come with a closed form expression. You only know the boundaries, which is T_sampling.
 

Hello, i saw the following case where 1000 in numerator is sampling frequency (normalised by some f0)
and in the denominator we see an expression of time B*Tswitch+3*Tswitch ,so i think F_switch=1/f0
I am just gusting the meaning of this .
what you think the definition of SAR adc OSR expression shown bellow?
1601482275696.png
 

I can't guess, because I don't know the context of this formula.
Oversampling means sampling fast, way faster than the Nyquist rate. So, it boils down to can you fit all bit tests within the sampling period with given probability of error.
 

so convertion time which is sampling and switches time must met the sampling rate.
and signal frquency is the fb
so the OSR of SAR
OSR=(1/(full convertion time) ) / 2*frequency of the input ?
Is this a correct idia?
Thanks
 

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