Ever since someone mentioned the use of dismantled Peltier element as cheap ceramic PCB, the thought stuck with me. Turns out, 0805 smd resistors fit quite well to the provided grid. The copper pads are big, thick and very firmly attached. Upsides seem obvious: Good thermal contact between elements; good match between ceramic material of PCB and resistors, yielding low force on resistors from thermal expansion; no humidity effect on PCB. Only downside is usually prohibitive price of such PCB. To insulate from environmental influence and aging effects on resistors (humidity, oxygen, etc.), special resistors or hermetic case is still needed though. So why not construct resistor divider of arbitrary ratio from equal elements to try idea? Resistor tempco should get better by statistical averaging in creating compounding resistors like this as well. But divider ratio will never be perfect, especially with cheap 0.5% resistors. Trimming by soldering elements afterwards is awkward on ceramic PCB and might introduce stress. But with 6 1/2 digit meter, resistors can be measured with quite high resolution - since all are close in value, measured at the same time and temperature, and in the end only division ratio is what counts; it seems like errors of offset, linearity, tempco of meter should cancel out? Sure, soldering will affect resistors, but hopefully in somewhat equal manner, especially on ceramic PCB when all are re-flowed at the same time.
A generalized python program was devised to find optimum arrangement and selection of resistors for divider, series and parallel connection (as shown below) are supported. It can just optimize the grouping of resistors, but if spare resistors are specified it will also make optimal selection. Program works by trying all combinations
Connection legend:
Integrated help:
Example prompt for hamon divider, with many spare resistors initial error can be virtually eliminated and other effects (measuring error, soldering shift, residual tempco, connection resistance, ...) should dominate:
Here is how ceramic divider looks:
Here is another example with case: