You could just cut the capacitor by a factor of 10 or so and get the frequency high enough that the filament doesn't bounce as much. If you are going to add an inductor, raising the frequency will make it more effective. But adding a filter inductor, turns this into a switching regulator with potentially quite a bit higher efficiency. You put the inductor between the lamp and the drain. You also need a diode (should be a Schottky for its speed and low voltage drop) between the drain and the positive 12 volts, to carry the inductor current when the mosfet switches off. The cathode (banded end goes to
+12). This will lower the current in the mosfet to about the average lamp current, instead of the peak current it is carrying, now.The inductor needs to be a ferrite core type rated for lamp current, and the diode needs to be rated for almost lamp current, also.
Lets say the lamp draws up to 5 amperes and you raise the frequency to
30,000Hz (by making the cap .001uF). When the mosfet is on only half the time, the average voltage out will be about 6 volts, so the lamp current may fall to 4 amperes (lamps do not follow ohm's law when they change temperature). You want an inductor large enough to keep the current from changing drastically (lets say by not more than half) during the time the switch is off. So in half of 1/30,000 seconds the inductor with 6 volts across it must have its current fall from 5 to 3 amperes (the average being 4).The formula that relates voltage, current, inductance and time is: V=L*(di/dt) or voltage across the inductor in volts equals inductance in henries times the rate of change of current in amperes per second.
so 6V=L*(5-3)A/(1/(30000*2)) so L=50 micro henries, for this set of assumptions.
If you had a frequency of 3000Hz, L would need to be 500uHy and if you stay at 300Hz, it would have to be 5mHy to keep the current ripple the same. A 5mHy 5 ampere inductor is a lot bigger than a 50uHy one. but of course, by the time you have raised the frequency to an inaudible
30,000Hz, you noise problem has gone away (but your mosfet may be quite a bit warmer from the 100 times more switching loss).Whatever you do, do not add any inductor without also adding the diode to carry its current or the inductor will make large voltage spikes every time the mosfet turns off, and will probably destroy the mosfet.