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I'm wondering why an oscilloscope's Attenuation switch is placed on the probe not on the oscilloscope's body (like the AC/DC Coupling switch that's placed on the scope body not on the probe)?

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The reason for putting an attenutator at the probe is to reduce the loading presented by the probe to the circuit under test. For a high-impedance probe (most probes) the cable looks like a capacitor, so it doesn't present much load at low frequencies but as the frequency goes up the loading can be significant.

The only real reason for using a probe in x1 mode is if your signals are very small and the scopes input noise is becoming a problem.

Most high end probes don't bother with the switch at all and are just permanently in x10 mode.

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    \$\begingroup\$ I've never liked the term "attenuator" for this function. The x10 is foremost to increase the impedance of the probe, thereby reducing its loading effects on the device under measurement. The scheme it uses is to insert an attenuator, but the attenuation, per se, is not the main purpose. \$\endgroup\$ – mike65535 May 23 '18 at 15:59

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