Oh, thank you for pointing me at the resistor "not seeing" this capacitance. I completely forgot that RC filter relies on R "knowing" the voltage across C in real time
This being said, I know this capacitance simply must have some bad effect on performance Flattened edges in one-shot transitions? Inverted reflections causing FR ripple? I think somebody reported the latter, blaming it on bad terminating resistor.
Theoretically there 'should' be no reflection to worry about. In practice nothing is perfect, I use a through-terminator, which is much better than a T connector and BNC terminator, but
hopefully worse than a scope with internal 50R termination (not sure if this is actually the case on modern low cost ones). There will always be some slight discontinuity in practice, but there is on a normal passive probe too. Remember at this point, the time constant you're talking about with the scope input capacitance is against 50R, not 1k (<1ns). There is no time constant associated with the cable distributed capacitance as this, coupled with distributed inductance is what makes up its characteristic impedance.
The other imperfect area of course is the probe tip, where the resistor must couple into the end of the 50R coax. Parasitics both capacitive and inductive of the resistor and coupling. It is these factors that are the reason that joeqsmith and others (see the linked articles early in the tread) have measured ripple at high frequency, and tend to limit its use to 1-2GHz (where everything struggles anyway apart from a direct 50R connection).
All that said, it still tends to work better than a passive probe at high frequencies. True, it has lower input impedance at low frequency, but at 100MHz the 8pF capacitance of the Tek P6139A (a 'good' 500MHz probe) brings its input impedance down to 200R, while the Zo probe is still up at nearly 1k.
I tried both probes (the Zo and the Tek) at the same time on the output of a Williams type avalanche pulse generator, both give similar traces but if I disconnect one or the other, the P6129A tip is clearly distorting the pulse generator output a lot more than the Zo one, the same applies to logic outputs. As I say, I make no claims about the flatness of the ones that I built (others have certainly built and characterized better ones).
Time for a question from me... In Douglas Smith's implementation,
http://www.emcesd.com/1ghzprob.htm why does he include 50R termination (the 4x200R smd resistors) at the probe end of the cable? I realize it's a double parallel termination of the cable (presumably there's 50R termination at the scope end too), but what benefit does it give in this application, given that it seems to work pretty well without? One downside is obviously the increased attenuation for any given tip resistor. Confused.