OSCILLOSCOPES, PLUG-INS, PROBES
AND SYSTEM BANDWIDTH
Many folks have the misconception that if they have an oscilloscope with a 50MHz bandwidth (upper frequency limit), a probe with a 50MHz bandwidth is a good match, as long as the probe can be compensated to the scope's input capacitance.
Probe Compensation
Yes, probe compensation is important. A feature of all attenuator probes (not non-attenuating 1x probes) is that they have a compensation adjustment to match the probe's attenuating capacitance to the input capacitance of the scope. A properly made adjustment will keep the system's frequency response flat throughout the system bandwidth. An improperly compensated probe will cause an erroneous fall in amplitude or increase in amplitude as the frequency is increased.
Poor compensation is often noticed with poor waveshape on square waves have a frequency in the 100Hz to 2kHz area. Unfortunately, most non-rectangular waveforms will not show any problems at all because only the amplitude is affected, not the waveshape.
The best way to compensate a probe is to simply use the probe compensation signal available on the front panel of every* scope. It's usually a square wave of around 1kHz and the probe is adjusted (see probe manual) for the flattest-topped** square wave possible.
Selecting a new probe for your scope must include the determination that the range of capacitance to which it can compensate will include the input capacitance of your scope. Beware of older and lower-bandwidth scopes. They sometimes have higher input capacitances. I've seen as high as 33pF and 47pF and many probes, especially high-bandwidth probes in the 200- and 300MHz area, will only compensate between 10pF and 30pF. 20pF has become pretty much the standard input capacitance for most oscilloscopes.
System Bandwidth
Risetime of a system is directly related to bandwidth. The standard equation for this is:
risetime = 350/bandwidth,
where risetime is in nanoseconds and bandwidth is in megahertz
If you have an oscilloscope mainframe with a risetime of 2ns and a plug-in with a risetime of 2ns, the system risetime (input to CRT) will be the square root of the sum of the squares of the individual risetimes. So the square root of 2² + 2² = the square root of 8 or 2.8ns. A 2ns risetime computes to a 175MHz bandwidth. This means that a 175MHz plug-in installed in a 175MHz mainframe will not have a system bandwidth of 175MHz, but will be 350/2.8 or 125MHz! If you add a probe, it gets even worse.
Let's assume you have a 100MHz mainframe, a 250MHz plug-in and a 200MHz probe. The risetimes of those three will be 3.5ns, 1.4ns and 1.75ns respectively. This calculates to a system risetime of the squareroot of 3.5² + 1.4² + 1.75² or 4.15ns which calculates to a bandwidth of about 84MHz.
If you're using a portable scope with a 50MHz bandwidth, you'll have a system bandwidth of 35MHz with a 50MHz probe, 45MHz with a 100MHz probe and 48.5MHz with a 200MHz probe. If you can outfit your scope with a probe with a bandwidth of at least twice the scope bandwidth, you'll be doing pretty good with system bandwidth.
Don't forget that the better brands of scopes (Tektronix, Hewlett-Packard/Agilent) are pretty lax in their bandwidth specifications. A 100MHz Tektronix 465 can usually be counted on to have an actual bandwidth of around 130MHz or more. If it actually is 130Mhz, a 200MHz probe will give you a system bandwidth of 109MHz, better than the scope's catalog bandwidth specification!
For a "fast" system bandwidth calculation, the equation is "the inverse of the square root of the sums of the inverse bandwidths".
OK. If you have a 500MHz mainframe, a 250MHz plug-in and a 350MHz probe, here's the calculator steps for system bandwidth:
500 [1/X] [X²] + 250 [1/X] [X²] + 350 [1/X] [X²] = [1/X] [SQR X]
which should get you about 188MHz.
* I say "every" here because you don't have much of a worthwhile scope if it doesn't have that signal available. Some lab-grade scopes have it available in several amplitudes and at a fairly accurate frequency.
**Don't quote me or make fun of my term here.