The inductor needs to be rated to carry higher current than your load. That is, the saturation parameter. The amount might be from 110% to 200%, depending on the peak level of your Ampere waveform.
Usually some frequency and duty cycle can be found so that you get desired output from the inductor. This assumes it can carry sufficient current for your load.
20 kHz is a reasonable frequency. It is above the range of human hearing. It does not need unusually fast components.