Why do differential signal traces on a PCB require a reference plane to have a controlled impedance? Whereas, in an unshielded twisted pair there is no reference, there are only the two conductors? Thank you for any answers that you can provide.
Why do differential signal traces on a PCB require a reference plane to have a controlled impedance?
They don't is the short and long answer. However, if you are wanting to fully utilize the space on your PCB for other components and other non-connected circuits you need to use ground planes to avoid upsetting the controlled impedance and avoiding unnecessary cross-talk or interference.
The coupling between differential pairs is different when differential traces are run over a ground (or power) plane on a PCB than when they are run using unshielded twisted pair (UTP) wires.
In the first case, assuming edge coupled traces on (or in) a PWB, each trace couples much more strongly to the ground plane than it does to the other trace. This is why in most cases the differential impedance of a pair of traces is a little less than twice the single ended impedance of each trace. For example, if you design a pwb with two traces, each one of which has a single ended impedance of 50 ohms, then the differential impedance of those two traces ends by being approximately 90 ohms. The ground plane in this case is used to establish the impedance of the traces, not upset them.
In the case of UTP wires, the wires couple to each other much more strongly than they do to anything else.