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The arrangement of the converter has it referenced to the positive supply rail. The load as well. C28 is the typical position for a reservoir cap. However C30 also performs the same job even though it's referenced to 0v ground.
The designer could have been creating a safeguard by putting in two caps. The solenoid being an inductive load is liable to generate spikes at odd times. So depending on what polarity Is the spike, one or the other cap can absorb it, since one is referenced to supply plus, the other cap is referenced to supply minus.
I design a very similar circuit. My electronic circuit activates fan when processor heats up and then control rotation speed. The fan has a brushless motor with an internal motor controller - SUNON MF50100V1-1000U-A99, DC 5V
I calculated buck converter external components: L1 = 192uH, C1out = 80uF and C2in = 154uF.
I know that it is minimum value components. So, I'll use as: L1 = 330uH, C1out = 220uF, C2in = 220uF or 330uF.
I think that using capacitor C3 would be a good idea. But how to calculate its value?
Your approach is reasonable. C3 plays a lesser part in the action, and I think its value can be less than C1, or about the same as your formula yields, 80 uF.
I use Raspberry Pi to generate a PWM signal. Basic PWM generation on the Raspberry Pi only has two independent channels, which can be accessed via 4 pins: GPIOs 12 and 18 for channel 0, 13 and 19 for channel 1.
That's really interesting idea with all-in-one solution, Pavhek.
I just had an idea how to avoid high current peaks at the Mosfet. I could use dip switch, which will allow working circuit without L1, C1 and C3.
For fan which has a brushless motor: 1, 2, 3 pins are ON and 4 pin is OFF.
For fan which is compatible with PWM: 1, 2, 3 pins are OFF and 4 pin is ON.
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