Today I messed around with building the ADC described in AN008. Despite reading everywhere that it wouldn't work on a breadboard, I figured I'd be stubborn and try it anyway. I got it working fairly well by oversampling at 12 bits and reading off the top 10. The key difference between the given design and mine is that I used 51K resistors and no caps. I got decent results, plots of scaled input voltage and measured values and error are below. While I wouldn't use it for reading precise sensors, something like potentiometers and other basic analog inputs would work great.
My main question is this: is there any analysis available describing the details of the design in AN008 and choice of capacitor/resistor values? For the capacitor/resistor to behave like an integrator, the RC constant must be large. But I found that the larger the capacitance, the larger the peak-peak voltage on the summing node, which we want to remain constant at Vdd/2. With no capacitance, it would remain very steadily around Vdd/2, while with a 1nF the circuit would not function at all (as described for breadboard designs). Surely the capacitance of the breadboard isn't enough to make the RC large, right? Why did removing the caps work?
I have a good understanding of circuits, feel free to give complicated answers :)