I don't think anyone mentioned this yet, but an advantage of a massively oversampled ADC is that you need only a simple analogue anti-aliasing filter.
Sigma-delta audio ADCs consist of a sigma-delta modulator that usually runs at a sample rate in the megahertz range followed by a digital decimation filter. The analogue anti-aliasing filter then only needs to suppress frequencies that are within the audio bandwidth from a multiple of the modulator sample rate, so its transition band can be wide.
Sigma-delta audio ADCs consist of a sigma-delta modulator that usually runs at a sample rate in the megahertz range followed by a digital decimation filter. The analogue anti-aliasing filter then only needs to suppress frequencies that are within the audio bandwidth from a multiple of the modulator sample rate, so its transition band can be wide.
So it's not the sampling rate that's on the spec? That and, if I recall, it's 4x your max sampling rate for nyquist right? So I would need 4x the sampling rate on a SAR then?
Example:
PCM4222:
PCM output sample rates from 8 kHz to 216 kHz, according to the first page of the datasheet ( see https://www.ti.com/product/PCM4222 )
Modulator output rate: 1.024 MHz to 6.912 MHz, according to the table on page 3 of the datasheet
The modulator sample rate is half the master clock frequency, which boils down to either 5.6448 MHz or 6.144 MHz for the usual PCM audio sample rates.
Suppose you want 192 kHz sample rate PCM (very suitable value for cats, whether it is useful for humans is the subject of long debates that never converge):
PCM sample rate (after decimation) 192 kHz
Nyquist frequency after decimation 96 kHz
Actual sigma-delta modulator sample rate 6.144 MHz
Lowest frequency that could alias into the band from 0 to 96 kHz in the modulator: 6.144 MHz - 96 kHz = 6.048 MHz
That is, when you have an analogue low-pass filter with a passband up to 96 kHz and a stopband starting at 6.048 MHz, that is enough to suppress anything that could alias into the 0 to 96 kHz band in the modulator. The extra aliasing that you get when the signal is decimated to 192 kHz PCM should be suppressed by the digital decimation filter chain. (Actually, ADC manufacturers usually cheat a bit and allow decimation chain aliases between 90 % and 100 % of the Nyquist frequency, because they can then use shorter and cheaper digital filters.)
When an analogue filter has a passband up to 96 kHz and a stopband starting at 6.048 MHz, there is a frequency ratio of 63 available for the transition band. That gives you roughly 36 dB of suppression for a simple first-order filter and 108 dB for a simple third-order Butterworth filter.
Another example:
SAR ADC running at 768 kHz (four times oversampling), aliases to be avoided up to 96 kHz:
Lowest frequency that could alias to below 96 kHz: 768 kHz - 96 kHz = 672 kHz
Ratio between 672 kHz and 96 kHz: 7
Suppression per filter order: about 17 dB
Compared to the PCM4222, you need about twice the analogue filter order for a given alias suppression, and you still need a decimation chain to get from 768 kHz to 192 kHz.
PCM4222:
PCM output sample rates from 8 kHz to 216 kHz, according to the first page of the datasheet ( see https://www.ti.com/product/PCM4222 )
Modulator output rate: 1.024 MHz to 6.912 MHz, according to the table on page 3 of the datasheet
The modulator sample rate is half the master clock frequency, which boils down to either 5.6448 MHz or 6.144 MHz for the usual PCM audio sample rates.
Suppose you want 192 kHz sample rate PCM (very suitable value for cats, whether it is useful for humans is the subject of long debates that never converge):
PCM sample rate (after decimation) 192 kHz
Nyquist frequency after decimation 96 kHz
Actual sigma-delta modulator sample rate 6.144 MHz
Lowest frequency that could alias into the band from 0 to 96 kHz in the modulator: 6.144 MHz - 96 kHz = 6.048 MHz
That is, when you have an analogue low-pass filter with a passband up to 96 kHz and a stopband starting at 6.048 MHz, that is enough to suppress anything that could alias into the 0 to 96 kHz band in the modulator. The extra aliasing that you get when the signal is decimated to 192 kHz PCM should be suppressed by the digital decimation filter chain. (Actually, ADC manufacturers usually cheat a bit and allow decimation chain aliases between 90 % and 100 % of the Nyquist frequency, because they can then use shorter and cheaper digital filters.)
When an analogue filter has a passband up to 96 kHz and a stopband starting at 6.048 MHz, there is a frequency ratio of 63 available for the transition band. That gives you roughly 36 dB of suppression for a simple first-order filter and 108 dB for a simple third-order Butterworth filter.
Another example:
SAR ADC running at 768 kHz (four times oversampling), aliases to be avoided up to 96 kHz:
Lowest frequency that could alias to below 96 kHz: 768 kHz - 96 kHz = 672 kHz
Ratio between 672 kHz and 96 kHz: 7
Suppression per filter order: about 17 dB
Compared to the PCM4222, you need about twice the analogue filter order for a given alias suppression, and you still need a decimation chain to get from 768 kHz to 192 kHz.
Ok so let me see if I have this right: So what you're saying @MarcelvdG is that in order to meet the same anti aliasing goal, a SAR of similar spec would have to work that much harder because it's modulator isn't nearly as fast. To do so, moving to a higher modulation rate, would also mean I would have to sacrifice performance in SINAD. What's more, SD also has the advantage because of digital filtering techniques. So then what it comes down to is better noise figures, or better response. I guess my next question would be, in the case of SAR, can any of this be done in the digital domain in order to compensate for those shortcomings enough to come closer to a SD of comparable spec (anti aliasing, decimation, low pass, etc)? Or is it I would need to add filtration before it even gets TO the ADC itself?
To prevent aliasing, you always need to make sure that the signal is band limited to less than half the sample rate before it reaches the ADC. Unless you know for sure that the signal cannot have any spectral content above half the sample rate, that means you always need an analogue low-pass filter before the ADC. The more oversampling, the wider the transition band of this filter can be, and the simpler the filter can be.
Sigma-delta ADCs can only work well with huge oversampling, so very simple analogue anti-aliasing filters suffice for them. They normally have built-in digital decimation filter chains to reduce the hugely oversampled modulator signal to a normal sample rate PCM signal.
SAR ADCs can be used with or without oversampling, but usually not with as much oversampling as sigma-delta ADCs, and as far as I know, they usually don't have a built-in digital decimation filter chain.
I'm quite sure sampling and aliasing are covered much clearer on Wikipedia.
Sigma-delta ADCs can only work well with huge oversampling, so very simple analogue anti-aliasing filters suffice for them. They normally have built-in digital decimation filter chains to reduce the hugely oversampled modulator signal to a normal sample rate PCM signal.
SAR ADCs can be used with or without oversampling, but usually not with as much oversampling as sigma-delta ADCs, and as far as I know, they usually don't have a built-in digital decimation filter chain.
I'm quite sure sampling and aliasing are covered much clearer on Wikipedia.
Yes a SAR ADC actually samples the voltage at distinct points in time. sigma-delta do not, they cleverly average a stream of crude samples coming in at a very high frequency (10's of MHz or so). A sigma-delta will synthesize an approximation to an abrupt voltage change with considerable time delay, but with a temporal resolution that's better than the output sample rate. In other words the output is automatically band-limited and will be clean spectrally.
An unfiltered SAR ADC will respond to an abrupt voltage change only on the next output sample, ie there will be jitter of +/-0.5 output sample times when fed a wide-band square wave, leading to lots of strong spurs in the spectrum.
The upshot is you need a very good anti-aliasing filter for a SAR ADC, and usually nothing for a sigma-delta ADC other than the usual RF-suppression. This is especially true if sampling from electronic signal sources like an analog synth which have wide band square waves.
An unfiltered SAR ADC will respond to an abrupt voltage change only on the next output sample, ie there will be jitter of +/-0.5 output sample times when fed a wide-band square wave, leading to lots of strong spurs in the spectrum.
The upshot is you need a very good anti-aliasing filter for a SAR ADC, and usually nothing for a sigma-delta ADC other than the usual RF-suppression. This is especially true if sampling from electronic signal sources like an analog synth which have wide band square waves.