The circuit goes all the way back to that link I provided a couple of posts back
https://www.eevblog.com/forum/testgear/starter-scope/50/ Starting at Reply 52
Basically, there are just two components: a 10k resistor and a 0.1 ufd capacitor. I do 4 experiments in that thread starting at Reply 52
The signal goes into a 10k resistor in series with a 0.1 ufd capacitor to ground. The output is measured across the capacitor.
The point of the 3 sets of values is that the charge/discharge would look like my plot above only in the case of the 10k/0.1 ufd setup because, as the resistor gets larger, the voltage divider effect of the scope probe in series with the resistor drops the voltage to the capacitor.
Draw 2 1M resistors in series between, say, 1V and ground. What is the voltage at the junction where the capacitor would be connected? Well, it would be exactly 1/2 of 1V because the first resistor drops 0.5V and the 2d resistor (emulating the scope impedance) drops the other half.
Now, replace the first resistor with 10k but leave the 1M to ground. Now the voltage at the junction will be 0.99V and that is within 1% of the applied voltage.
Here is a better explanation of the voltage divider than I can provide. Using the early examples, R1 is 10k and R2 is 1M, calculate Vout. Then make R1 = 1M with R2 (the scope impedance) still 1M and see what happens. The voltage will be cut in half.
Then change R2 (the scope impedance) to 10M and recalculate the two values as above. In all cases, use 1V for Vin.
https://www.elprocus.com/voltage-divider-rule-with-examples/Nothing, even using a scope, is as easy as it seems. Ohm's Law jumps up and bites us from time to time. BTW, Ohm's Law really is a Law, not simply a suggestion like speed limits.
The point of this long-winded explanation is just this: Don't believe everything you see on your scope. If the trace shows 0.5V, is it because the point being probed is low impedance and the voltage actually IS 0.5V or is it because your 1x probe is upsetting the measurement by creating a voltage divider? In 10x you still have the voltage divider, it's just not as noticeable. 100x just might be necessary for some high impedance circuits.
Where this comes up, for me, is with my analog computers. I want Tau=1 second and I use 1 ufd capacitors. Therefore, the resistor is 1M and it's important to remember what is being probed.