Need help designing 32 bit ADC

I want to use a ultra low noise 32 bit adc with Arduino or ESP32 module.

Can someone recommend a schematic and ADC chip?

The odds that you have an analog front end that's sufficiently low noise to even approximate the needs of a 32bit ADC are virtually zero. You'll be very, very hard pressed to approximate 16 bit actual measurement resolution in a real-world, DIY setting. Very hard pressed indeed. 32 bit? Hell no.

Please describe the application and why you think you need a 32 bit ADC; perhaps it's possible to suggest a more realistic course of action.

I have a sensor which detects minor changes in pulsatile blood flow in arteries. I am able to use it with a 8 bit adc and about 1000 times amplification, but not happily. Also, I'd love to get rid of the amplification (more parts more noise).

Also, I just want to try a 32 bit ADC and see what it looks like, what all it picks up.

Just use a 16 bit ADC like the ADS1115.

How are you amplifying the signal currently?
You'll trade one error for another. You'll have to work out which is worse - analog amplification or an ADC error.

Think about your 32bit ADC idea for a second. Suppose you have a signal with a maximum of 5V that you want to measure. A 32bit step size is 1.16nV - nanoVolts! At 16 bits, you're looking at a 76uV step size. It's already plenty difficult enough to get noise down that far.

It'll pick up a truckload of noise and will give you absolutely nothing more than a 16 bit ADC will give you.
Even with a 16 bit ADC in order to get a decent s/n ratio you'll have to work hard in terms of system design and physical layout. If you're working with a breadboard and dupont cables, you're not going to get there, ever. It'll take a custom PCB with very careful layout, component choice and of course conceptual design that fits your specific application.

I get it that noise management is going to be a task in 32 bit ADCs, but then why are all EEG, ECG machines using 32 bit ADCs and not less?

It's not just going to be a "task". It's going to be nigh impossible to design any analog front end that will give 32bit resolution with a living human body in the same room - let alone measuring anything on that body.

They're probably not. They will probably use 32 bit data width computing. Not 32 bit ADC's. It's likely you're mixing things up.
Read this for instance: https://www.acns.org/UserFiles/file/EEGGuideline4Digital.pdf
16-24 bits, it says. 32 bits is simply unrealistic. Even if a system uses a 32 bit ADC, it'll struggle to get close to 24 bits actual resolution, essentially binning the remaining data.

I have indeed heard that human body heat radiation can create noise with a 32 bit ADC. The theory is not completely within my domain of expertise to understand.

I did read somewhere that a polygraph used to measure ECG and EEG was using 32 bit ADC. Let me recheck and come back.

I am curious, why do 32 bit ADC exist? What applications demand them?

I think you're going to poke around in fundamental physics labs, places like CERN, IMEC and in the semiconductor industry, you may find a few applications for 32 bit ADC's.

In the hands of mere mortals like you and me, in a home or small business setting, a 32 bit ADC is, as someone much funnier than myself once said, "as useful as a cat flap in an elephant house."

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I used to work as an electroencephalographer.
The signals you are looking at have a low bandwidth - like EEG signals.
The FIRST step in working with signals like this then was to change them from DC - with all the drift and offset issues - to an AC signal.
You can then amplify as much as you want, filter, and detect the signal envelope.
Trying to do this with DC and a 32 bit ADC is not appropriate.
Have you thought about what the characteristics of the signal are? IE the bandwidth, the range and the resolution you actually need? (as explained here)

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Apparently on a ecommerce website it is claimed that one device has a 32 bit ADC, but on their own web page for specifications although they do not use the term ADC, they are using the term Data Resolution (which is 16 bit). Is Data Resolution the same as ADC?

Not necessarily, no. Data resolution just means that this is the resolution the device puts out or uses somewhere in its processing path. The actual acquisition resolution can deviate from this. It's for instance entirely possible that they use a 12 bit ADC and interpolate to 16 bit resolution e.g. to linearize or normalize readings. Not saying that this is certainly the case, but just illustrating how a vague term like 'data resolution' does not necessarily say anything about an ADC.

Here's the link to the specifications page. Can you go through it and tell what ADC they are using? I am not good at reading technicals.

No. It's not specified. (And you didn't specify which device we're looking at, but they seem similar.)
They probably use 16 bit ADC's.

Thank you for the guidance. I think I'll also work with 16 bit, and play with 24 bit just for knowledge sake.

Note that 1000 time more sensitive than 8bits is about 18bits…

Digikey has some 32bit ADC chips that are not too expensive. I suggest you check out their manufacturer’s web sites for app notes decribing recommendations for actuallly using them…

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Start with 16 bit and see if you can get 14 bits of actual resolution from it. By the time you got that under your belt, you know how to design a decent analog front end, lay out a PCB, understand shielding, etc. etc. and at that point it will make sense to start thinking about higher resolutions.

I suspect you've not yet realized that going from 16 to 24 or 32 bits isn't a linear increase. It's exponential. To get a feeling for this, read this page: Wheat and chessboard problem - Wikipedia

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That is because it is utter rubbish.

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About 5 years ago I have seen the following signature on the amplifier box of the electronic guitar of my son:

Noting to loose -- here is 32-bit digitization!

Can you present the approximate shape of the signal (mV vs time) that is avialable at the output of the above sensor. If possible, please provide a link to that sensor.

I am confused, please expand.