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Most of the ADCs I see are designed for a single sensor voltage.

I have read that this is not a problem for something like an acoustic sensor like a hydrophone because the ADC can be multiplexed so fast that it easily samples the sound.

So, for example, if you want to sample at 10 kHz, which is sufficient for underwater situations, and you have a 100 element array, then you would just need for the ADC to be able to sample at 10 kHz * 100 = 1 MHz which an ADC can do no problem.

Is that analysis correct, or are there multichannel ADCs that accept 100 or 1000 analog inputs and have an advantage over multiplexing? If so, what is that advantage?

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  • \$\begingroup\$ If you want to measure phase shift you may need simultaneous sampling. You can find (for example) 8 precision ADCs on a single chip. \$\endgroup\$ Jan 18 '17 at 18:25
  • \$\begingroup\$ The highest number of channels I've ever seen in an ADC was 256 channels (and 64 independent ADCs), but that was for a charge integrating ADC and that's really aimed at a specific use case (photodiode imaging detectors) \$\endgroup\$
    – Sam
    Jan 19 '17 at 2:23
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Most of the ADCs I see are designed for a single sensor voltage.

Hm, well, that depends on where you look, and what you look at. So I'd say that presumption is wrong, in general.

are there multichannel ADCs that accept 100 or 1000 analog inputs and have an advantage over multiplexing? If so, what is that advantage?

There certainly are systems that have a whole lot of coherent ADC channels – not necessarily inside the same silicon chip, but distributed across multiple synchroniced ADC ICs.

Very simply because your assumption "My single channel is much narrower than what technically feasible ADCs can do" breaks down for other channels.

Assume you're doing digital beamforming with 128 channels of 40 MHz each – typical 5G research. Where's your single ADC that can cover that bandwidth by multiplexing now?

The fact that ADCs exist that have a far higher bandwidth than your signal is not because someone wanted to do hundreds of your signals at once, but because they needed to capture a wider signal. For that wider signal, at the time the ADC that could cover that was developed, there inherently existed no ADC that could do multiples of them. So, your question seems to be a little too focussed on your own problem, ignoring other signals that exist.

So, for example, if you want to sample at 10 kHz, which is sufficient for underwater situations, and you have a 100 element array, then you would just need for the ADC to be able to sample at 10 kHz * 100 = 1 MHz which an ADC can do no problem.

Well, add in the fact that a switchover takes time, too, so you'll have additional signal distortions, as well.

Notice that if your switching frequency is \$f_M\$, your signal will invariantly need to contain a component at that frequency, three times that, five, seven, nine times..., because what you're effectively doing is taking $N$ signals \$s_n\$, and multiplying each with a periodic rectangular signal \$r(t)\$ of \$\frac1{f_M}\$ width, shifted by their individual position in the multiplex sequence. So what you get as sum signal going to the ADC is

$$ s_\Sigma(t) = \sum\limits_{n=0}^{N-1}{s_n(t) \cdot r\left(t-\frac n{f_M}\right)} $$

which in frequency domain becomes

$$ S_\Sigma(f) = \sum\limits_{n=0}^{N-1}{S_n(f) * \left(R(f)\cdot e^{j2\pi\frac 2{f_M} f}\right)} $$

(\$*\$ is the convolution operator)

\$R(f) = \mathcal F\left\{r(t)\right\}(f)\$ is known – it's a comb of diracs with descending amplitude, at every odd multiple of \$f_M\$, and convolution with a comb of diracs leads to spectral repetitions.

Luckily, we defined the bandwidth of the input signals \$b_{in}\ll f_M\$, so that these repetitions don't alias into each other, but it means that your system needs to look like

input signals –> filter to \$b_{in}\$ –> multiplex at rate \$f_M\$ –> filter \$\ge f_M + b_{in}\$ -> ADC

The question of how fast your ADC needs to be is hence answered by how steep your filter will cut off after the minimum it needs to pass; it's usually easier to just make your ADC a bit faster and not use an overly complex analog filter. The first repetition happens at \$3f_M\$, and so you effectively have nearly \$2f_M\$ of maximum transition band (due to switching imperfection, you'd want to stay significantly below that).

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  • \$\begingroup\$ Ok, so the multiplexing is pretty complicated. Do ADCs exist that have built-in multiplexing so you can just wire 1000 hydrophones directly to the ADC, or will a designer have to create a custom board with multiple chips to do this? \$\endgroup\$ Jan 18 '17 at 16:09
  • \$\begingroup\$ @TylerDurden I'm not aware of such an IC. The classical use case – underwater operation – would probably call for sensors being distributed across a wide (>50m) range (>wavelength of audio), so I'd doubt the usefulness of having that in a single IC, anyway. However, since this is something that would, if someone was crazy enough to want this on a single die, be asked for by the military, I doubt we'd find out easily. \$\endgroup\$ Jan 18 '17 at 16:11
  • \$\begingroup\$ @TylerDurden also, making multiple ADCs coherent at 100 MHz rates is technically challenging. At rates of 100 kHz – 10 MHz, not that much. \$\endgroup\$ Jan 18 '17 at 16:12
  • \$\begingroup\$ Well, acoustic arrays are a common need. For example, ultrasound machines have accoustic arrays. Also, any underwater vehicle, will have a sonar array, and there are other automated vehicles that could potentially use sensor arrays with hundreds of antennas or sonic transducers. \$\endgroup\$ Jan 18 '17 at 16:26
  • \$\begingroup\$ well, you said it yourself, a developer just needs to coordinate mutliple ADCs to get more channels. At some point, I just don't see the advantage of having more channels in a single IC. And that point is reached before I reach 1000 channels, simply because you can't sensibly put 1000 microphones close to a single ADC. My reasing is That Simple<sup>TM</sup>. Please don't argue with me over whether or not I've heard of a device that I believe doesn't exist. \$\endgroup\$ Jan 18 '17 at 16:27

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