I would like to measure a High-Voltage pulse (20kV) with a duration of a few tens of nanoseconds using an oscilloscope and a simple 1000:1 Resistor Voltage divider.
Is it possible to do this without capacitors, considering that it is a simple pulse and not high-frequency?
A high resistor bridge would be fine, no capacitors needed. Make sure the 1000:1 attenuator is built from high voltage resistors (such as these) to ensure that arcing doesn't occur and destroy the scope. (most 'run of time mill' probes are only good to values like 600 VDC or 1000 VDC, check yours). The< problem that you might run into is the rise times might not be in the ns range because the parasitic inductance of the larger resistors is higher then something like an smt resistor. Using smaller attenuators would be better (like these 20 kV 1000:1 EBG resistors which tout a non-inductive design)
Another more expensive option would be to buy an HV probe for your scope instead of constructing something.
My intuition was way off.
I simulated resistors with leads, in my mind the inductance (I used 10 nH which would be in the range of a resistor with large leads) If there is inductance then it does create a pole and blocks high frequencies (vout1 has rolloff in the 1 kHz range). However with capacitance (just about everything has a few pF between it, the inductance does not matter and you should not have a problem with a resistor attenuation.
Apologize for the confusion
As others have said, 10's of nano seconds is high frequency. If you wanted a purely resistive divider and chose values of lets say \$R1 = 10 M\Omega\$ and \$R2 = 10k\Omega\$ which would create a ~1000:1 ratio. Unfortunately, even just a 1pF parallel capacitance which is well within the possibility of stray capacitance, would cause your Vin and Vout to look like this:
simulate this circuit – Schematic created using CircuitLab
(Note that C2 out to be 1pF NOT 1uF. The simulation was done with C2=1pF)
A better option, if you only need to measure a short pulse, would be a purely capacitive divider. Of course if you need to measure DC this would not be an option. Going this route you would be concerned with series inductance which would be hard to mitigate using discrete components. Measuring high voltage pulses this fast is far from trivial. That is why high voltage scope probes with 50-100Mhz bandwidth are so expensive. You could go the route of making a capacitive divider where the physical construction of your probe gives you the capacitance needed (see this paper). This makes minimizing the inductance much more feasible.
