How would you measure the characteristic impedance of a differential pair (stripline) if you don't have access to a Vector Network analyzer? I have access to an oscilloscope and a signal generator.
Most of the traces are buried, but I can desolder parts at both ends of the traces to have access to the pads connecting to the traces.
A: The VNA (and/or Spectrum Analyzer) is designed to show impedance over frequency, while the oscilloscope is designed to show voltage over time. These are fundamentally different, yet also the flip-side of the same proverbial coin. So an oscilloscope will not give you the same type of information that a VNA would.
But it can give you enough information to make a partial impedance match, provided the 'scope and function generator are fast enough, and only through trial-and-error.
Desolder parts at the ends. Connect the function generator (with a matching stripline impedance; 50Ω/100Ω whatever), to the input pair. Terminate the pair at the other end with similar resistors. Probe using the oscilloscope at the injection point and start injecting squarewave pulses. If the termination resistors are too high or low, there will be reflections visible. Change the termination resistor values and try again. When the termination resistors match the line impedance, those reflections will disappear. The value of those resistors is the characteristic impedance of the line.
Note, this will not work so well for high frequencies due to parasitic inductance and capacitance, which add two more dimensions to the problem.
If you have a pulse generator with short rise time (several times shorter than transmission line length) and high speed oscilloscope, you can make time domain reflectometry (TDR) measurement and calculate characteristic impedance. TDR setup is quite simple for single ended transmission lines, but for differential lines it is not so straightforward. Read for example this application note http://hparchive.com/seminar_notes/a-210.pdf .
Measurements to useful accuracy will be difficult with your equipment. You could make a Jim Williams pulse generator AN-47 (see Appendix D), but producing a balanced output with good accuracy seems difficult.
Do you have a microscope? If so, butcher one board and make a cross-section where you can measure the dimensions (ground plane spacing, track width and spacing), and use the known mathematical approximations. If you have only one board and cannot risk damaging it, you need serious equipment.
You may have enough track for static capacitance measurements to be useful, but I guess the issue will be whether you can measure the coupling capacitance accurately or whether end strays will dominate.
