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Why do I see more noise on my oscilloscope when a probe is connected?

The typical noise floor of a digitizing oscilloscope is a few millivolts peak-to-peak. You can measure the noise floor of your oscilloscope by disconnecting all cables and probes from the inputs and changing the volts per division setting to the lowest possible value. Set the scope to Auto trigger and you will see a baseline of the scope's internal noise.

All currently shipping Keysight scopes have an "Auto Probe" feature that automatically identifies connected probes. When a probe is connected, the scope changes its attenuation setting so that it correctly displays the voltage coming from the probe. For example, a typical passive probe has a 10:1 attenuation ratio, which means that the probe divides the signal by a factor of 10 before presenting it to the scope. The scope compensates for this attenuation by multiplying the input signal by a factor of 10.

Since the oscilloscope cannot distinguish between the external signal and the internal noise floor, the noise floor is also multiplied by the attenuation factor. Therefore with a 10:1 probe connected to a scope channel you can expect the noise floor to increase by a factor of 10. For this reason it is best to use a 1:1 probe, an active probe, or a simple coaxial cable to view low voltage signals.