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?
Best Answer
For 100 MHz and slower probes, the wavelength of the signals in question is long enough that the cable doesn't really act like a transmission line and the probe tip pretty much directly 'sees' the input impedance of the scope. Also, the probe impedance and scope input impedance do not match the cable characteristic impedance. In this case, the capacitance is really the main thing that needs to be controlled and compensated for. This is described in the Hiscocks et al. document.
At high frequencies, the cable acts like a transmission line and the probe tip doesn't see the scope input impedance directly. Instead, the probe tip sees the cable's characteristic impedance. Usually for high frequency probes, standard 50 ohm RF design techniques are used. Everything just gets matched to 50 ohms - both the scope input and the probe tip.
As for the difference between d. smith and art of electronics, they're basically trying to do more or less the same thing. d. smith adds a parallel resistance to ground to form one side of a voltage divider to produce a ~40:1 probe. That 50 ohm resistance appears in parallel with the 50 ohm cable for an equivalent 25 ohm resistance. This then forms a voltage divider with the 976 ohm series resistor. Apparently the tip capacitance of his probe is high enough that extra compensation was required to get a flat frequency response. Note that this resistor isn't really necessary as a termination resistor--presuming the other end of the line (at the scope) is properly terminated into 50 ohms, then there should be no reflections coming back up the cable that could reflect off of an impedance mismatch at the probe head.
The art of electronics design does the same thing, but only uses the cable's characteristic impedance as one side of the voltage divider. In combination with a 950 ohm series resistor, this produces a 20:1 probe. This probably works 'well enough' up to reasonably high frequencies without additional compensation if the right resistor is used, but I presume you could do a little better if you add a properly-sized capacitor to ground between the 950 ohm resistor and the coax cable. The attenuation of the art of electronics design is also lower than the d. smith design, which likely makes the mismatch in capacitance less of a problem. In general, I think the art of electronics design is really intended to be a quick-and-dirty technique that works well enough for debugging but could be improved upon if more accuracy is required.