I read in many forums that one can use a probe with a higher bandwidth than oscilloscope's bandwidth.
If it is right why it is not a problem? What is the theoretical explanation?
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That is right. Not a problem in doing that. Think of it as a filter between your oscilloscope and the point you are probing.
The bandwidth of the oscilloscope will determine the overall bandwidth of your "measuring system", since it is the most restrictive one.
For instance, if you are using a 150MHz probe with a 100MHz Oscilloscope, then the probe will attenuate the signals over 150MHz, and that input (with a 150MHz bandwidth) will enter your oscilloscope, which will then attenuate the signals over 100MHz. So your probe will pass the signals between 100MHz and 150MHz, but they will be filtered out by the oscilloscope input circuitry. In the end, you will have filtered the signals over 100MHz anyway, so no big diference with using a 100MHz probe.
In the other hand, if you use a probe with lower bandwidth, then it will determine the bandwidth of your input filter, and you will have less bandwidth in your input filter.
OP, I don't have the reputation needed yet to reply to comments, but to answer your questions regarding probes, there are passive and active types, to divide voltage probes into two broad categories.
Passive probes are probably what you are most familiar with -- they present a high impedance and some capacitance to the signal you probe (10pF to 20pF or so). These commonly have bandwidths of 200MHz to 500MHz. As the name suggests, they don't consume power to run / do active filtering. These are relatively inexpensive (especially used) and the bread and butter.
Active probes range from simple 1GHz active FET probes to several thousand dollar 16GHz differential probes. An active FET probe presents a very low capacitance (<1pF), which can be useful in certain applications; I often use it to measure gate drive signals in switching power supplies as 12pF from a passive probe can perturb my measurement. The differential model would be something you solder onto say (yes, solder) a PCI Express link to check eye diagrams and such.