In a document Hiscocks et al. describes some basics of Oscilloscope probe theory. The document is very understandable and seems coherent. Notice in particular that for him, the bad guy is the parallel capacitance of the coaxial cable and of the oscilloscope that should be compensated by adding a capacitance in parallel to the tip of the probe (so, the capacitance of the tip is increased).
Then comes d. smith with his method to build a 1 GHz passive probe. First, it is not entirely clear why he terminates his probe by a 50 ohm resistance: to avoid reflections, isn't it sufficient that one side of the probe (that is the oscilloscope side) be terminated by a 50 ohm resistance? I presume that this is to kill even more the reflections. So, let it be. But what is strange for me is that he does not take into account the capacitance of the cable, nor the capacitance of the oscilloscope. In particular, for him, the beast that has to be killed is the tip capacitance (so he increases the parallel capacitance of the cable), the exact converse of what says Hiscoks in the document above. If this man were a newbie, I would say that he does not understand why his probe works, and that he actually increases the capacitance of the tip with his copper foil. But hey! this man is a guru of probes that published several articles in different journals.
And now the best of the best, The Art of Electronics, 12.2 p. 808: to do a high speed passive probe? very simple:
... and make your own by hooking a series resistor (we like 950 ohm) onto a length of skinny 50 ohm coax (we like RG-178); you temporarily solder the coax shield to a nearby ground, plug the other end into the scope (set for 50 ohm input) and voila - a high speed 20 x probe!.
If my understanding is right, the 950 ohm resistor with the 50 ohm characteristic impedance of the cable make a 1:20 resistor divider (up to now OK), but what about probe compensation etc.? uh!
Can someone tell me what is going on?