I need to make a small PCB, this PCB is just for switching from one connector to another, it's just an adapter to change the pinout of the connector. So, there are no components, but only traces. The adapter is for an ethernet switch, so they are all ethernet signals, so all signals are differential pairs. My doubt arises from the fact that there is no ground reference on the connectors, but there are only the ethernet signals. At this point the question is: should I make the PCB without ground planes? How do I calculate trace impedance without reference plane? If I need to add a ground plane to control impedance, what should I connect the ground planes to? Anyone can help me?
Ethernet cables can be unshielded so obviously just two wires without a ground plane can work. In case your board only routes differential pairs between two connectors, you may not even have ground connected via cable shield to connector metal frame.
In many application notes how to make an Ethernet interface, the wiring between connector and the transformer is told to be routed without a ground plane, so you should look at available Ethernet application notes how to wire the connectors without a ground plane.
You can use a trace impedance calculator for stripline and just make the H (height above the ground plane) very large. But make sure you get the spacing between the diff pairs and their thickness (copper weight) correct.
But it's going to high, probably over 100 ohms. Note that starts to look like a twisted pair configuration, that has a Zo of approximately 120 ohms.
As to adding a ground plane, it should be connected to signal/power return. A picture of your connector and pin assignments would help.