Op-Amps

Modern operational amplifiers are a marvel of analog design. They enable circuits on the razor edge of the analog and digital domains, like the multislope ADC described in this project. Right from the uA741 released in the late 1960s with a measly 7.5mV offset voltage, to the modern OPA140 (released by TI in 2010) with a 150μV offset voltage (and a 1μV/C drift to go with it), the analog semiconductor industry has seen astounding growth. CMOS processes for analog design have enabled "hybrid" chopper amplifiers like theADA4523 with single-digit microvolt offsets and 10s of nanovolts of temperature dependence. Going into the future, further developments in silicon processes and thoughtful mixed-signal design might facilitate the performance needed to unlock the 10th digit in DMMs. 

Of course, there is no "all-rounder" op-amp. The limitations of one op-amp can be overcome by using a composite configuration as described. There is a lot of theory behind composite amplifiers and their stability, on which I will have to do more research to fully understand and implement to achieve better performance.

Calibration

The multislope ADC can easily be configured to self-calibrate drift of the reference amplifiers and zero error, with the addition of a multiplexer on the input. If the reference voltage is fed into the multislope ADC, it can compare the reading with a previous reading of the reference, which would indicate how much the reference amplifiers have drifted since the last calibration, since it is assumed that the reference is the most stable voltage in the circuit. By connecting the input multiplexer to ground, zero error can be measured. 

Another trick here is to connect the input multiplexer before the input buffer op-amp. The high input impedance of the op-amp means there is little to no input current, so the multiplexer's on-state resistance errors are eliminated. 

Code

When this project started, my coding expertise was limited to Arduino C++. Of course, the AVR-based Arduino boards were not ideally suited to running a demanding application like the multislope ADC. I was introduced to both the Raspberry Pi Pico with the remarkable PIO peripheral and Dmytro, who is now probably one of the world's leading Pi Pico experts. Without their assistance, this project would not have reached the stage it is in today. 

Falstad

Falstad is an incredibly convenient and intuitive way to simulate circuits. I have encountered criticism for using it to simulate precision circuits like the multislope, since it does not account for a lot of real world non-idealities. To that, I will have to say that the goal of a Falstad simulation is not to accurately model the real world, but to quickly get a circuit up and running to do an "idiot check". Its real-time simulation also helps in understanding circuit functionality, with sliders being used to change parameters on the fly. 

Have other people tried to make multislope ADCs?

Yes! One of the most brilliant examples is Jaromir's Nanovoltmeter, which uses a DIY multislope ADC not very different from the one described here, exhibiting +/-0.25ppm non-linearity. Several others have been built and characterized, details can be found buried in various EEVBlog Forum threads.