What are the resistors in digital pots?
I think anything called a digi-pot will have to use cascaded resistors.  An R/2R topology has the effect of yielding a constant output impedance when driven with a low-impedance source, but its input impedance will vary depending upon the value selected.  The circuit below illustrates a 4-bit R/2R DAC with source and load impedance switched between 1K and zero/infinite (it runs a 0-15 cycle with each combination of source/load impedance).







simulate this circuit &ndash; Schematic created using CircuitLab

When source impedance is zero and load impedance is infinite, the output ramps 0 to 15/16 volts.  Adding a 1K load (closing RLY6) cuts the output voltage, but it still ramps nicely.  When the source resistance is increased to 1K (RLY5 opens), however, the ramp becomes not only non-linear, but non-monotonic.

While it would probably be possible to construct a digipot with two sets of eight switched resistors in a 1:2:4:8:16:32:64:128 sequence, I'm not sure that would be particularly helpful from a cost perspective since ensuring that the 128:1 ratio remains 128:1 over various temperature conditions would likely mean that the larger resistor had to be constructed out of 128 smaller ones wired in series.

An approach that might be somewhat workable would be to have e.g. 65 unit resistors and a circuit which connects between two spots two-resistors apart a series of four pairs of two parallel resistors.  The smaller network would have a series resistance of 2R, and it would sit across two resistors totalling 2R, thus yielding a net resistance of 1R.  Moving the taps would cause slight momentary increase or decrease in the outer resistance (depending upon make or break behavior) but not nearly as disastrous as with R/2R DAC.  I don't know if anyone uses such an approach, however.