Why the \$F_{knee} = 0.5 / T_{r}\$?

If you take a random digital signal with Tr as rise/fall time and plot the power versus frequency, you will see that the power falls off by 20dB/decade until about Fknee, where the power drops off by 40 dB/decade.

If you use 10%-90% rise/fall time definition, at Fknee you will have 6.8dB additional loss compared to the 20db/decade.

If you go for 3dB additional loss, the magic constant "0.5" becomes the more often used "0.35", so Fknee = 0.35/Tr.

If you go for 3dB additional loss and use the 20%-80% risetime definition, the constant becomes "0.22" instead.

Great if someone can find a Matlab/Scilab script to plot and show this :-)