32 10k pots in parallel have a combined resistance of about 313 Ohms.
For a regulated voltage of 2.048V, the pots will use about 6.6mA.
If you’re using a 3.3V supply, the upstream resistor will have 3.3V - 2.048V = 1.252V across it.
If you put 1.252V across a 60 Ohm resistor, you get about 21mA through the resistor. Subtracting the 6.6mA for the 32 10k pots leaves about 14.4mA for the LM4040 to absorb.
The LM4040 can do that, but its upper limit is 15mA. You can’t remove too many 10k pots before hitting the 15mA limit.
A more effective approach is to figure the current for a single 10k pot with 2.048V across it: 204.8uA.
Then we set a couple ground rules: the LM4040 will always have at least 1mA flowing through it, but will never have more than 14mA flowing through it. Both of those numbers are comfortably inside the LM4040’s limits.
14mA - 1mA = 13mA, which means we never want more than 13mA flowing through a bunch of 10k pots in parallel.
13mA / 204.8uA = = 63.5. So the LM4040 can handle any number between 1 and 63 10k pots in parallel without breaking the ground rules.. there will always be at least 1mA through the LM4040, and there will never be more than 14mA through it.
Then we find the value for the resistor above the LM4040 by choosing the amount of voltage that will be across it.. 5V - 2.048V = 2.952V for a 5V supply, and 3.3V - 2.048V = 1.252V for a 3.3V supply.. and finding the resistor whose current will be 14mA at that voltage.
For a 5V supply, 2.952V / 14mA = 211 Ohms.
For a 3.3V supply, 1.252V / 14mA = 89 Ohms.
Then we do a reality check: you can get resistors in lots of values, but the values aren’t arbitrary. There’s a mathematical sequence where each value is a fixed multiple of the previous one. If each value is about 1.5X the previous one, you get what’s known as the E6 Series: 10, 15, 22, 33, 47, 68, 100, … If each value is 1.2X the previous one, we get the E12 Series: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82. If you look carefully, every other value of the E12 Series is a value from the E6 Series. Then every other value of the E24 Series is a member of the E12 Series, every other member of the E48 Series is a member of the E24 Series, and so on.
Collectively they’re known as the Preferred Numbers.
In general, you want to stick to values from the E12 Series unless you have a good reason to go to a higher series.
The nearest E12 value to 211 Ohms is 220 Ohms. If you put 2.952V across a 220 Ohm resistor, you get 13.4 mA. Taking 1mA out for the LM4040 leaves 12.4mA for the 10k pots, and 12.4mA / 204.8uA = 60.5. Instead of being able to put 63 10k pots in parallel, you can only have 60.. not a huge difference.
The nearest E12 value to 89 Ohms is 82 Ohms. If you put 1.252V across an 82 Ohm resistor you get 15.26mA.. a little too much for the LM4040 to handle, and about 1.25mA more than our 14mA ground rule.
We can work around that by saying 1.25mA / 204.8uA = 6.1, and adding another rule to say there must always be at least 6 10k pots in parallel with the LM4040, making the working range 6 to 69 pots.
We can also play it safe and go to the next E12 value above 82: 100. That will give us 12.52mA at 1.252V. Subtracting 1mA for the LM4040 leaves 11.52mA, which is enough for 11.52mA / 204.8uA = 56 10k pots.
We can also go up to the E24 Series and choose 91 Ohms. At 1.252V the current through a 91 Ohm resistor will be 13.8mA, which is about 200uA less that our 14mA target, and about the same as the current through a 10k pot. So instead of getting 1-to-63 pots, we get 1-to-62.
alexdry wrote:but what sort of information should I be looking for in the ADS1115 datasheet to extract the value similar to the 409.6uA, which is the current each 10K pot is taking?
That won’t be in the LM4040 datasheet.. it’s a value you calculate based on the LM4040’s regulated voltage and a resistor value you’ve chosen yourself.
The only trick in all this is to do the Ohm’s Law calculations enough to get comfortable with them, so you can think of a bunch of 10k pots in parallel as ‘so much current per pot, multiplied by the number of pots’.
The chain of reasoning always gives you two values, and makes you look for the third. There’s also some logic on the order of, “I don’t want more than 14mA here, so how do I create that limit?” And some of it is just familiarity.. a handful of common approaches like, “set an upper limt, take a certain amount for this piece, then figure out what to do with the rest” tend to show up over and over. Once you’ve gone through them a few times you’ll start to recognize the places to use them.