it is impossible to construct an attenuator to the following specifications:
1) constructed from an arbitrary number of resistors and potentiometers where the potentiometers are ganged together on a simple shaft2) attenuator driven by a voltage source
3) output voltage varies with shaft position4) the output impedance of the network is constant with shaft position
Proof:
I believe it's possible to construct an attenuator of this type with a constant input impedance? But not output. It's possible to do the above if negative resistors are allowed but I have none handy.
The proof is from the IEEE Transactions on Circuit Theory from June of
1964, a lot of interesting papers in that one. Wish I could get hardcopies of those at reasonable price