When Does Oscilloscope Probe's Capacitance and Resistance Matter?

 You may have noticed that almost every commercially available oscilloscope probes have their capacitance and resistance values marked down. Do you ever wonder what difference does that make to your readings?

Assume You have a signal source with 1mV and 0.1Ω series source resistance driving a load 1kOhm.

We can model that as follows.

As most of you know, Oscilloscopes sample the probes voltage. This is done as follows. Probes ground and signal terminal consists above mentioned capacitances and resistors. Refer the below model.

As you can see, oscilloscope sample the voltage above the resistance and capacitance. Lets connect the probe to our signal source. Refer the below model.

Now from your signals and systems knowledge, you know this creates an RC filter circuit. Essentially the R here is governed by the oscilloscopes R. 

For a moment if you neglect the capacitor, circuit forms a voltage divider. Therefore, you can observe an accurate result only if the oscilloscope probes resistance is much higher than the load resistance. Refer the below LTSpice model results for more clarification.

$$V_{Osc}  = \frac{R_{eq}}{R_{4}+R_{eq}}$$

Where $$R_{eq} = \frac{R_{6}R_{1}}{R_{6} + R_{1}}$$

Hence We can write $$V_{Osc}   = \frac{R_{6}R_{1}} {R_{4}(R_{6} + R_{1})+R_{6}R_{1}}= \frac{R_{6}} {R_{4}(\frac{R_{6}}{R_{1}} + 1)+R_{6}}$$  

From this equation you can see that low values for \( R_{1} \) decreases the \( V_{Osc} \) as the denominator increases with low \( R_{1} \) values. Following graphs depict the above theories.

As you can see, lower the probe's resistance, lower the readings from oscilloscope. Therefore, always try to get the highest resistance probes. 

Likewise, if you in crease the capacitance, cutoff frequency of the RC filter will be much smaller. Resulting in non sharp signal waveforms. 

You can see the sharp edges of the signal vanishes with the capacitance increase.

You might think that these slight deviations doesn't do a much impact on our developments. But when it comes to high speed low voltage measurements these thing matter!!