Electronic – arduino – How short can an RF transmission line be

An interconnection should be considered a transmission line if reflections are detrimental to your application. As Leon Heller says, 1/10th wavelength is a good rule-of-thumb.

However, all this depends on the nature of the signal (1/10th of what wavelength?). With sine waves, the wavelength in the cable will be about $\frac{2 X 10^8}{f}$ where f is the frequency, but will vary according to the cable type. The effect of reflections on sine waves is to cause standing waves, so the amplitude will vary along the length of the cable but will always be sinusoidal. With square waves the situation is complicated by harmonics. Although the square-wave may have a low fundamental frequency, the harmonics introduced by the edges will be significant. The effect of reflections in this case is undershoot, overshoot or ringing depending on where the mismatches are (if both $R_S$ & $R_L$ are lower than $Z_0$ for example, you will get ringing).

So do you need to match the source? No. As long as the load is perfectly matched, the wavefront will travel down the transmission line and be fully absorbed by the load. Consider a digital system with 3.3V logic for example. If you terminated both source and load you would only get 1.65V swing at the load. Terminating only at the load is termed parallel termination.

There is also a technique known as series termination in which the source is terminated but the load is left open circuit. In this case, a half-amplitude edge propagates down the line and is reflected back to the source, lifting the voltage to full amplitude as it returns until it is absorbed by the source termination. Along the line, you would see a 'stepped' signal except right at the load where you would see a clean waveform.

Every wire is a transmission line when the frequency of the signal gets to the point where the physical size of the wire is comparable to the wavelength of the signal traveling down the line.

In normal circuit analysis, we make several assumption. First, we are using DC or low frequencies and we assume wires are perfect with no parasitics and no resistance to it. There are other assumptions such as no coupling between magnetic fields. I am talking about a first course in circuit analysis.

There is no hard and fast rule. Typically the rule of thumb is that if the wavelength of the signal is about 1/10th of the length of the wire, that you should consider it a transmission line.

In practice this really manifests itself in 300MHz+, but in some cases 100MHz can also require some attention.