Keep in mind I will find out soon what the next generation of the design will be. But I'm interested in learning about the rest of this design.
Context. The experience difference between a 20-year designer and a 50-year designer breeds a healthy respect for context. I'm a big fan of answering the question that was asked, but over 50% of the time it turns out that that isn't the real question.
I have noticed that. One reason why I'm not usually the first responder.
What are the switches driving the ladder inputs? Electronic or mechanical?
They were mechanical. Either relay or rotary switch.
How solid/stable are the 8 V and 20 V sources? Accuracy? Drift? Noise? Output impedance over temperature?
How accurate and stable? I hope enough.
Resistance/impedance? Constant with voltage and/or temperature?
Should be, indoor lab use only.
What is the input impedance of whatever the ladders drive? Does the ladder impedance have to be kept low to swamp out local noise sources?
opamps, so high impedance.
How fast are the inputs changing?
VERY VERY Slowly. manually input setting.
Are the resistors thru-hole or SMT? What is the power rating?
I was taught/told years ago to select resistor power based on 5x the typical design power rating. Under the premise, the higher the difference in power rating (actual vs design) the more temperature stable the value will be. Obviously there is a trade off of stability vs size. You don't see 10W resistors on every board.
For the same resistor values in both ladders, there is a 6.25x difference in power dissipation. Is this important?
Not unless it effects the how/why of the resistor value(s) selected.
What is the power budget? Is this battery operated? If so, what are the expected circuit current and operating time?
Wall powered, lots of juice available.
In post #7 you said "I need very specific 1.00v increments." That implies at least 8-bit accuracy so you can tell the difference between 0.99, 1.00, and 1.01. If you mean to extend this to differentiate between 19.00 and 19.01, that is 12 bit accuracy, requiring 0.02% tolerance resistors.
My point there was that I needed 1.0V increments, only 1.0V increments, and not some binary DAC represesentation close to a 1V increment.
I was looking for the best to get 1.00V increments, in the least number of components with values closest to 1.00V. The other options I was considering had substantial error in the required vs realized voltages. A 12 bit 0-5V DAC amplified 4x resulted in some values off by more than 50mV with a lot of options I didn't need (only 20 of 4096 values would be used). My thought was I could select a set of resistors in a R2R ladder that would give me exactly only the values needed. The combination of the two ladders produces only the 20 1.00V options required.
AND - what is with the two voltages and combining the outputs of the two ladders? Approximately zero percent of that is clear? Does this mean that the impedances of the two ladders interact? Does one ladder have to be at least 10 times the impedance of the other to minimize loading?
I did not feel that was relevant. Why does it matter what I'm doing with them? I have found I have to keep the post short and isolated to the point on hand. Otherwise the thread devolves into design by committee (see above) or I never get an answer to the question at hand (example present). I am looking for the methodology on selecting the value of R best suited for an R-2R ladder that will be used to breakdown a 20V input and an 8V input. Furthermore, each ladder was to be opamp buffered due to the difference in source and, possible, output impedances.