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HF probe

The most simpele HF probe contains just a resistor and a variable capacitor:

RIN and CIN make the input impedance of the scope. RP and CP make the probe.

For DC voltages VRIN/VRP = RIN/RP. For high frequency voltages VRIN/VRP = XCIN/XCP = CP/CIN. To make the voltage devider frequency-independant RIN/RP must be equal to CP/CIN. So: CP = CIN∙RIN/RP.

In our case CP must be adjusted to 30p∙1M/9M = 3.33pF.

If you own a scope and HF probe, you already know that the probe has a little 'screw' that needs to be adjusted. That screw is capacitor CP. CP can be adjusted properly by connecting the probe to a square wave voltage. A square wave signal contains many sinusoidal signals. E.g. a 1kHz square wave contains sinusoidal voltages of 1kHz, 3kHz, 5kHz, 7kHz, etcetera. If CP has been adjusted properly, a square wave will appear on the scope's screen (left). All frequencies the square wave consists of will be attentuated equally. If CP is too low, the higher frequencies will be attenuated too much (middle); if CP is set too high, the higher frequencies will not be attenuated enough (right).

RP and RIN are in series, so the input resistance is 1M+9M=10M. CP and CIN are also in series, so: 1/C = 1/CP+1/CIN = 1/3.33p+1/30p. Thus, the input capacity is 3pF. So the input impedance of the probe is 10M//3pF.