Is the reflection phenomenon common in RF work with unmatched source/load pairs also present at low frequencies? Or are the wavelengths so much longer than the physical conductor lengths that reflections do not matter? I.e, are reflections strictly a function of wavelength relative to the conductors lengths?
Say for example I have a square wave fed into a pi-filter whose purpose is to extract a 100kHz fundamental (1/4 λ = about half a mile). The source and the pi-filter (and load) are unmatched. Does the power reflect back to the source? The wavelength of the signal is much, much greater than the length of the conductors (about 10,000 times, for example, for 3" traces on a PCB). So I'm not sure how that would interfere with the source signal. Perhaps the wavelengths of the higher harmonics would eventually be of "meaningful" lengths, but they should be at much lower power levels.
Would I see a distorted signal at the source due to a reflection from the pi-filter? Could the reflection damage the source? If the power is not reflected, is it absorbed by the filter? Where does it go?
Since we can often "get away" without terminating signals in low frequency designs, I hardly ever worry about reflections. I've typically only worried about them at at high MHz signals (and higher), and when interfacing signals across backplanes, or long board interconnects. But, it occurs to me that there should be reflections all the time. How is it that they don't typically matter (in low frequency designs)? How is it that sources driving unmatched loads are not "blown up" more often due to these reflections?
Best Answer
The equation shown below describes the input impedance to a transmission line in terms of length, terminating impedance and characteristic impedance: -
So, if \$\ell\$ is zero then: -
$$Z_{IN} = Z_L$$
Do the math, plug some numbers in.
And of course for very long lines, any reflections are more highly attenuated by the return journey to the source so it's not usually a big deal except in power AC analysis.
So, as the line extends from zero length it starts to alter the impedance presented to the source but, for short lines and long wavelength this is pretty much all that it manifests as; it just looks like a slightly odd-ball impedance.