Suppose I have a BNC in connector, terminated in parallel with a 50 ohm resistor. The PCB trace extends for about 5-7cm before the signal is 'read' by a power amplifier.
Should I treat this PCB trace as a transmission line, and terminate it before the amp input again?
Should I treat this PCB trace as a transmission line
If your signal goes up to gigahertz range, then yes, your 5-7cm trace must be treated as a transmission line and meet your characteristic impedance requirement (looks like it is 50 ohm).
and terminate it before the amp input again?
Heck no, not "again"! Your R15 has to be removed and placed to R? spot. The connector impedance should match the trace impedance and the cable impedance so no R15 is necessary, then the cable->BNC->trace will act as a single hopefully uniform transmission line.
Whether a PCB trace is treated as a transmission line or not is purely based on the propagation delay of the trace and the rise time of the signal.
Please see this nice article from Altium. A summary from this article is given below.
when the travel time along this round-trip length is equal to or longer than the rise time of the signal, the integrity of that signal is in doubt and your design is now a high-speed design! The length of that route is referred to as the critical length - routes shorter than this should not experience signal integrity issues, whereas routes longer than this might.
As previously answered, if the length is long relative to the rise time of the signal, then yes, you should treat the trace as a transmission line. A complication is that the trace will probably NOT be a 50 ohm transmission line.
I don't have the formulas for determining the impedance of a trace at my fingertips, but they are googleable. Trace width, spacing from ground plane(s), and the material of the PCB all come into play.
As for how to deal with it, assuming that 1) the trace is long enough that you have to deal with it, and 2) you know the trace impedance, there are two cases:
Case 1: trace impedance higher than 50 ohms. For this example, I'll assume the trace is 150 ohms. Terminate the trace with its own characteristic impedance, in this case a 150 ohm resistor. So now the trace is good. Moving back to the connector, you have a 150 ohm trace and you want 50 ohms. So you need to add a resistor in parallel with the trace (from connector to ground) to make the total impedance be 50 ohms. Standard parallel resistor math applies here: 1/(1/50-1/150)=75, so you need a 75 ohm resistor.
Case 2: trace impedance lower than 50 ohms. For example, suppose the trace impedance is 30 ohms. Terminate it with a 30 ohm resistor. At the connector, you have 30 ohms and you want 50, so you need to add a 20 ohm resistor in SERIES with the trace.
In both cases, both the cable and the trace will be properly terminated.
