At what cable length does matching the impedance at the ends of the cable become important?
The rule of thumb I use is that anything exceeding 1/20 of the wavelength is to be considered a transmission line. And bad terminated transmission lines have reflections that distort the signal.
To get a fast approximation of the wavelength, I consider that the speed of a signal is half the speed of light (based on experience with PCBs) and that the speed in a cable is similar. Hence, the signal travels 15 centimeters every nanosecond.
One period of 5MHz is 200ns, so the wavelength of the electrical signal is about 30 meters. One twentieth of that is 1.5 meters. The difference with Dave Tweed's calculation is that:
- I use 1/20th which is a factor of two smaller than Dave's rule of thumb;
- I consider that the speed is half the speed of light, which is another factor of two.
Therefore I find 1.5 meters in stead of 6.
Checking the dielectric constants of PVCs, I see that there is a great variance for commonly used materials. The dielectric constant of a PCB using FR4 for its material is just above 4 (with the square root being 2). I'ld say that the highest value you'll use in practice is 4 while it may be about 3 for cables.
The rule of thumb that an electrical signal travels at half the speed of light is a bit pessimistic for cables but ok - it impacts the length estimation by about 15%. Regarding the main part of the rule (1/10th or 1/20th) - it depends on how much distortion you allow. I do not remember how much it is for 1/20th but there is a theory behind it (as there is for 1/10th) and I prefer to be on the safe side.
As a general rule of thumb, you should begin taking transmission line effects into consideration when the cable length approaches λ/10 — i.e., 1/10 of the wavelength of the highest frequency in the signal.
For example, if you have pulse rise/fall times on the order of 100 ns, you need to have good fidelity at 5 MHz, so cables longer than 6 meters should be impedance-matched.