Well, that rule of thumb is flawed even for 60Hz. The equation for a capacitor charging / discharging is:
I = C dV/dT
So setting I to 1 A and C at 1000uF we find that dV/dT is 1000V / sec.
With a full bridge rectifier, the capacitor is going to have to supply the current for about 1/4 of the cycle or 1/4 * 1/60 = 4ms. This means the ripple in the voltage is 4V!
Simulation with LTSPICE shows that this is just about right for a 10V supply drawing 1 Amp with a 1000uF cap.
But, to answer your question. The time needed for the capacitor to supply current is inversely linear in the frequency, so at 20000 Hz you would need a capacitor 60/20000 = 0.003 as large as you would at 60 Hz.
Bob
I = C dV/dT
So setting I to 1 A and C at 1000uF we find that dV/dT is 1000V / sec.
With a full bridge rectifier, the capacitor is going to have to supply the current for about 1/4 of the cycle or 1/4 * 1/60 = 4ms. This means the ripple in the voltage is 4V!
Simulation with LTSPICE shows that this is just about right for a 10V supply drawing 1 Amp with a 1000uF cap.
But, to answer your question. The time needed for the capacitor to supply current is inversely linear in the frequency, so at 20000 Hz you would need a capacitor 60/20000 = 0.003 as large as you would at 60 Hz.
Bob