I only have a vague idea of what characteristic impedance
Characteristic impedance is the ratio of voltage to current (thus, an impedance) for signals propagating along the trace, which is determined by the balance of capacitance and inductance along the trace.
It should be dependent on the length and the frequency, how come it isn't?
Characteristic impedance depends on the ratio of inductance to capacitance. Since both inductance and capacitance increase linearly when the trace length increases, their ratio doesn't depend on the trace length.
Also, within limits, these parameters also don't change much with frequency, so again the ratio doesn't depend on frequency and the characteristic impedance doesn't depend on frequency.
Intuitively I should calculate the characteristic impedance of each pad-to-pad trace and make sure it is always 50Ohm. Is that the case?
If the driving circuits are designed to drive 50 ohm loads, then generally yes. You also want to provide matched termination at at least one end of the trace, and possibly both, depending on the details of your circuit.
Generally you don't have to make a separate calculation for each connection. You just look at your board stack-up and find a trace width that achieves 50-ohm characteristic impedance, and make all of your traces that width. You might use microstrip, stripline, or coplanar waveguide geometry depending on the circumstances of your layout. You would do a separate calculation for each signal layer on your PCB, and maybe for the different types of geometry (microstrip and coplanar, single-ended and differential) if you need to use all those combinations.
If the trace length is less than about 1/10 of a wavelength at your operating frequency, then you can often get away with using an unmatched trace.
Unless you want to do your own S-Parameter de-embedding mathematics, you must fit a 50\$\Omega\$ connector to at least one end of the trace. You can either fit a connector to the other end, or a good quality 50\$\Omega\$ resistor. I tend to use 2 x 100\$\Omega\$ resistors in parallel for lower ground inductance.
There are many connector styles to choose from, you just haven't looked hard enough yet. If you are only going to 1GHz, then the tolerances will be fairly pedestrian.
If you have a pattern of vias at the end of the trace, you should be able to find a connector with a through hole spill pattern that fits. If not, drill holes adjacent to the signal via through the ground plane to take the grounding spills of such a connector.
If you only want to measure the trace, and not the via, then you have more options. There are many connectors designed to fit a board edge. Cut the via off the board, and fit the connector to the end of the trace at the board edge.
You can solder 50\$\Omega\$ coax to the end of the strip, but you will need to be careful of excess lengths, same pedestrian tolerances but easier to get wrong with cable. Don't tell my boss, but often I would cut a lab 50\$\Omega\$ connectered cable in half, and solder each bit to my test board, saves fitting connectors to cable!
Equipment. A Time Domain Reflectometer (TDR) will give you a nice graphical display of impedance versus distance. A Network Analyser will give you traces of S-Parameters versus frequency, which you would need to analyse to determine the impedances you have. Hint, in the bad old days, a TDR did actually throw a pulse down the track and listened for the reflections. These days a TDR is simply a Network Analyser with an FFT function to synthesise the effect of such a pulse. Both of these types of equipment are very expensive, even to hire for short periods.
There are plenty of ways you can rig cheaper equipment, and some thought, into making measurements of impedance, even if not to 1GHz. A good logic source and a fast digital 'scope will get you a 'poor man's TDR'. A signal generator, a measuring receiver (a 'scope, a power meter, a spectrum analyser), and several tapping points for resistors and a bit more thought will allow good impedance measurements over the frequency range of your source and receiver.
Best Answer
DRAM will NEVER work with transmission lines and terminations because the termination (50 ohms) will kill the digital signal.
The whole point about memory and micro slumming it in the same place (or very close) is that you can get away with teminations because the length of the trace is so short.
25mm of trace represents a signal delay of about 150p seconds and a rule of thumb is that you invert the 150ps to get a frequency of 6.7 GHz then divide that by ten to get an acceptable top limit speed for clk and data i.e. 670 MHz.
Is this too low?