There is a wide variety of probes available – passive, active, current-measurement, optical, high voltage and differential. But let's narrow discussion to probes that are used to measure signals with wide bandwidth and short rise times. There are also many variations on what probe is proper. As probes are potential load to measured circuit, it is important to know its sensitivity to resistive, capacitive or inductive loading. Incorrectly chosen probe (like high capacitance) can distort fast rising signal. Some circuits may not tolerate probes at all (high speed amplifiers).

Sp first of all use two signal parameters for selecting probe – bandwidth and rise time. Generally speaking – scope and probe bandwidth should be three to five times wider than signal's being measured. Select a probe that is at least the same frequency range as the oscilloscope being used. When using a 100MHz oscilloscope, select a minimum of 100 MHz probe. To achieve the optimum performance, choose a probe with more than twice the bandwidth of the oscilloscope.
Probe Bandwidth

It doesn't matter what type of signal is measured it is always important that scope have enough bandwidth to reproduce signal correctly. For analog signals highest frequency will determine the scope bandwidth while in digital signal measurements there is signal rise time important. Like usually bandwidth is determined at -3dB level or 70.7% signal drop level:

20·log(Vout/Vin)=20·log(0.707)=-3dB

To avoid significant measurement errors measurements should never be performed near -3dB bandwidth level. Other wise it may produce up to 30%amplitude error for sine wave. So if 100MHz signal is measured with scope where bandwidth is 100MHz then signal will have about 30% error. So with 100MHz oscilloscope measured signal frequency shouldn't exceed 0.3·100MHz=33.3MHz. For 100MHz signal there is 300MHz bandwidth oscilloscope needed. Probe bandwidth should be at least twice as oscilloscope. This would be 600MHz. Then you should achieve less than 3% error.

For digital signals rise time is important. Rise time determines probe bandwidth. Let's say we use simple RC network probe:

Input signal is voltage step, and then output voltage will be calculated as follows:

Vout=Vin(1-e-t/RC)

Rise time is a time which is taken by signal to go from 10% (0.1RC) to 90%(2.3RC) of its level. So the difference is equal to 2.2RC. -3dB bandwidth is equal to 1/(2Ï€RC). Then

RC=1/(2Ï€f)=tr/2.2

And bandwidth is dF=0.35/tr.

According to formula if signal rise time is 2ns, then probe bandwidth would be PdF=0.35/2ns=175MHz. And to ensure less than 3% error we should use three times bigger probe bandwidth so about 600 MHz.
Inside the Probe

Probes are simple devices but may have significant impact to measured signal. Usually probe consists of:

- Probe tip;

- Parallel RC network;

- Shielded wire;

- A compensation RC network;

- Ground clip.

Main requirement for probes is that they didn't provide any invasive effect to measured circuit. Te meat this requirement one of factor is high impedance so it wouldn't load the circuit. Most popular probes are 1X and 10X probes. For instance 10X probe attenuates signal by factor 10. it has 10MΩ input impedance and 10pF tip capacitance while 1X probes have 1MΩ input impedance and 100pF tip capacitance. For accurate measurements probe tip resistance Rp and capacitance Cp must be equal to oscilloscope input resistance RIN and capacitance CIN. To ensure they are equal scope has to be calibrated.
Probe calibration

Calibrating probe isn't hard task especially when oscilloscope has necessary tools built in. This is a signal generator used for calibration. Turn on signal generator on oscilloscope and put tip to it and ground clip to oscilloscope ground. There should be some sort screw for adjustments in the compensation box of probe. By inspecting signals in oscilloscope you can compensate probe.

Overcompensated or under-compensated probes may produce significant errors in rise time and amplitude.