For example, I need 100uF 60V capacitor for filtering in power supply. The DC source is about 40V, but I have 400uF 20V capacitors.
If I arrange four of them in series I got in total 100 uF and each capacitor has a voltage drop of 10 volts according DC source.
Thus, can I replace 100uF 60V capacitors with four 400uF 20V capacitors in series? Are 20V capacitors OK?
How can I design symmetrizing resistors for it?
You will have to include a parallel resistor-ladder to stabilize the node voltages. The resistor values must be high enough for the low-pass to be effective $$f_c = \frac{1}{2\pi RC} $$ and low enough to ensure a save operating point (smaller than the capacitors leakage). This will cost you some additional power.
Well, you have 4 400uF/20V capacitor. to make a 100uF capacitance, you could make a series circuit from them and for symmetrizing you have to make one 1Mohm resistor parallel with each 400uF capacitor. With this combination, you have made a circuit that is some how equivalent with a 100uF/80V capacitor that could tolerate 80V at most. For reliability issues, you can just use 80% of this therefore your circuit must not be under more than 0.8 * 80 == 64V. Due to your need that is a 100uF/60V capacitor it seems OK but be careful that reducing the number of component will increase the reliability and production costs and this solution is just good when you have strong reasons. For example, the 100uF/60V capacitor is too big for the system case or big for tolerating g-shocks. Moreover the capacitance and tolerated voltage of the capacitors have direct relation with ambient temperature and you have to support it in your design.
In the desktop PC switching power supplies, you can see two series 220uF~680uF/200V capacitors at its high voltage region (input == 220V AC). These capacitors are also symmetrized with two 1 Mega Ohm resistors and manufactured in very high volume with enough reliability. Desktop SPSS has used this combination because for reducing the 100Hz ripple of the DC output, it needs biggest capacitor that is able to be fitted in the case and tolerate 400V. Regulated value of the 220V AC input line voltage is around 308V DC and caps must work under it properly therefore the combination of caps in the desktop SPSS must be able to tolerate 400V (80% of it is 320V that is near enough to 308V DC)
Yes, as you say 4x 400uF caps in series gives 100uF and if they are rated at 20V each then total rating will be 80V, which is above your spec so it should be fine.
