Regarding capacitance:
One possible conclusion, everything's always a lie. Perhaps it's measured at one particular frequency, and they don't care about it anywhere else.
Another possibility: there is a more general truth underlying it, which you're either assumed to know, or which almost everyone is ignorant of (the latter is more likely, but a bit of both really, I think).
The truth revealed: any impedance network can be approximated as an RLC lumped equivalent circuit. At low frequencies (below where transmission line properties of the internal components matter (1D fields), or let alone full 3D fields around them), especially when using lumped elements, this approximation can be done quite effectively, i.e. the accuracy of a curve fit improves rapidly as the number of elements used goes up.
So it's an accuracy thing, and there is an "order" parameter, meaning the order of the polynomial of the transfer function: the number of reactive elements used to model the network.
To summarize: if there is a lie, it's that an equivalent circuit only works over some frequency range; they might simply be leaving off further, extended details of that equivalent circuit -- whether because they don't care, or they don't know.
When a scope is advertised as "1M || 20pF", or a probe as "10M || 14pF" or whatever, they're giving the DC equivalent (a resistance), and the MF equivalent (shunt capacitance). They are not telling you anything about the HF equivalent, what happens to that xx pF as its reactance comes down ever closer to Zo. (And for various reasons, you can assume there's a Zo somewhere in the 50-200 ohm ballpark, depending on cable construction, trace geometry, wires through free space, whatever. Or a bit outside that if you really work at it, i.e., more severe geometry; hence 600 ohm ladder line exists, or you can put twisted pairs in parallel forever, or make an ever-wider parallel-plate transmission line, to make arbitrarily low impedances.)
There necessarily must be a loss element somewhere in the system, as you're reading a signal off the scope. That loss can be arbitrarily small, but most likely the front end levels off near 50 ohms, give or take a little peaking perhaps. Note a figure like 20pF has a cutoff with 50 ohms at 160MHz, so it wouldn't be very helpful for a 300MHz scope to have this much pure shunt capacitance and still be terminated into 50 ohms (say with a tee and terminator). It's perhaps possible that that capacitance gets switched out when the internal 50 ohm is switched on, but more likely it's always there, and just gets peaked out near cutoff; or it is itself the loss. In any case, the equivalent circuit will look more like 1M || (20pF + 50 ohm) up there, maybe with additional elements depending on peaking, front-end amplifier response, etc.
Likewise the probe, the 14pF or whatever isn't a pure capacitance, it just approximates that over the say 1kHz-20MHz range, but above there, it has significant ESR. You can imagine a probe constructed from ordinary 50 ohm transmission line, which therefore must have an equivalent circuit of a Low-Z Probe (say, 450 ohms dividing into the 50 ohm cable). And so above ~20MHz, the equivalent circuit looks like R+C rather than R||C. (Real probes aren't ordinary coax, but a special high impedance lossy kind, cut to just such a length that the loss along it gives the 10x attenuation for free; this improves response, and reduces compensation capacitance. The equivalent might look more like 1k + 14pF at HF.)
The probe tip impedance is further modified by its length, and that of the ground clip, which have inductance. The round trip of which might be 0.1-0.5uH depending on dimensions, so the probe further has a series RLC characteristic. This is generally made to peak at the probe's rated cutoff, introducing a zero to partially cancel out either the probe's own HF cutoff pole(s), or the scope's (in the hope that the scope's response is well behaved, which, it often isn't among DSOs..).
The ground clip inductance, also introduces a common-mode error between probe ground / cable, and circuit ground; an error not shared by the probe tip (which being high impedance, carries hardly any current in response to CM), thus CM voltage (that is, voltage between circuit and scope grounds), at high frequencies, manifests as the inverse signal superimposed on the probed signal. Hence why you also measure such signals when probing ground -- what you would naively assume to yield zero volts always, but doesn't when voltage is dropped across that ground wire.
Armed with this knowledge, you should be able to identify which poles are due to cable length, ground clip length, etc., and perhaps even compensate them further by adjusting those lengths -- or changing tack and using a coaxial adapter, rather than the probe tip/clip, to get the probe's internal response more simply.
Tim
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