Hi, I am working on an auto-ranging super fast ohm meter, mostly because all ohm meters in multimeters I have are incredibly slow and I have bags of unsorted resistors. It is based on a simple cascading voltage dividers.
I had 7 segment LED from an ardruino kit so I put together MPC 23017 interface for i2C.
I also made those little edgelight "displays" to show range. It reliably measure to about 10-20Mohm.
It has few modes of display: the Fluke 8050 mode where everything is displayed in kOhm all the time, auto-ranging like 3.3kOhm, 10Mohm etc... and also displaying a nominal value (closest to standard 5% resistor value)
As a bonus it also measure forward voltage of LED. The functions are selected with button where the LED briefly displays the function name. The sketch is rather pretty complex, where the entire functionality is based on timers and callbacks. It always take a median of multiple measurements and automatically find the most appropriate voltage divider (I have 5 cascades) that gives the best resolution.
So far it works rather incredibly well, maybe too well - it settles in stable correct measurement every time, nearly instantly. I am very pleased indeed.
An opinion: Would adding LM4040 to AREF (with the applicable changes to the calculation of external reference) give me a better precision or is that overkill.
Also any other opinions and useful tips or functionality is appreciated.
Here is a transparent version of my indicators (the previous had black background)
Congratulations on a successful project! 
Whether or not you need the LM4040 or not depends on 2 factors.
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Do you need more precision(actually accuracy)?
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Is AREF actually the limiting factor to obtaining higher accuracy?
The first only you can answer.
The second requires more information, schematic, code, tolerances and quality of the components currently used.
Hi Oscar,
GREAT project! Nice fusion of electronics knowledge and code. Are you publishing open-source schematic and code?? Huh? Huh???
I would be happy to feature this as a project on ArduinoInfo.Info if you are interested. I think this may be a good example of Arduino <-> Electronics.
YEARS ago I built 7-segment displays with edge-lit plastic segments embedded in Polyester Resin paste (Similar to "Bondo").. Then slices became individual numbers. OldSkool 1968 incandescent bulbs driven by 7447 chips and we were HighTech. I made timers for Radio Broadcast production that were synchronized to the reel tape and cartridge tape machines. Users KNEW when they came up on the 30 or 60 second standard commercial timings. But I digress, which does not surprise my wife 
Hmmm. How much current are you driving to do those milliohm measurements? Recently I tested some DC motors (locked rotor) and circuit breakers by putting 10 amps through them and reading the voltage. But that was brute force.
I LIKE the edge-lit K, M etc. Hmm.. another good reason to have an Arduino-driven CNC router!
I'm sure I could go out and get a meter costing more than $1000 and its auto ranging function would still be "slow". It actually has to be that way to get a useable meter. It's kind of one of those unsolvable problems like peace in the Middle East.
Cool transparent things! Love them. They don't change like a normal 7-segment, do they?
Oh, no my transparecies they don't change, but there is a way to make it sort of multi-changeable by gluing two thin ones together like a nixie numbers. The only problem is the etching on each layer has to be exclusive (not overlap or overlap very little, otherwise the top etching will block the light from bottom - unlike nixie). But for example you may make 3 layers of concentric circles, put 3mm leds on each layer and be able to lit up each circle separately or make a nice effect. Sort of DIY display. I want to put mine as a nixie tubes sticking from the top of the box.
Yes, I will publish it once it is sorted out, but I am a programmer first so of course I had to modify every piece of library I got my hands on....just to make it working exactly how I imagine it should... which means I have to note my changes in each library.
The main problem of project like this is of course that it has to be asynchronous (measuring sampled at intervals, evaluating and at the same time driving LEDs continuously), but that's why I used my kit LED with 23017 even it isn't ideal - to get some challenge.
I am still not quite sure about the LM4040. I do have one at hand, but then my thinking is that the way my circuit is wired, the variation in the arduino 5V will cancel itself out. I plugged the equations into online math solver and the input voltage did cancelled out, the final equation doesn't depend on the arduino input voltage.... so I don't know. Too tired to think now, but I think the LM will do absolutely nothing.
I realized that I can make capacitance mater as well by simply adjusting the code without any hw changes. Pretty accurate to single digits nano farad.
I finished that beauty, and I am pretty impressed by the arduino flexibility. I used the $3 ebay nano clone as the main brain and enclosed it all into a project box (which was the most expensive part of this journey, $10)
It measures resistance in pretty wide range 10 Ohm ~ 20M Ohm. It can display nominal value (from the 5% resistors scale). The display of the resistance is instantaneous and as accurate as my fluke.
It measures capacitance in range 1nF to 1000 uF. Again very accurately.
And I also added display of LED forward voltage just for fun.
It has beeper for continuity testing and some clicking sounds when measuring. And I added bunch of LEDs for show since there were still few empty outputs. And all is done with shockingly little components.
I will get my stuff together soon and post the schematic and the code.
I am rather proud of the code (just the main sketch is about 1000 lines) because it does a nice timer driven median averaging measurement and lot of other stuff (including driving the 7 segment display and leds through 23017).
I am totally convinced that arduino rules. Twenty years ago, this would be a pretty big task for me, today it was mostly sitting in my bed with keyboard and mouse....
Hi,
When you get everything together post it in Exhibition and Gallery section.
I have a multi component tester that is arduino based, it is slow but only because it does just about any component.
But most of the time I need resistance and capacitance, so this will do the trick sitting double sided tape to the front shelf of my bench.
Looking forward to the full docs.. Tom... 
I'm rather curious what the schematic looks like.
Looks like you have a popular project there! 
When you do get around to publishing it, please put a link to it in this thread.