When you see a Vgs(th) for a FET. You will need at least 2 to 3x Vgs(th) (threshold) conduct fully.
**Change **to** R = 500 Ohms or less depending on LED string current such that input current is 5~10% of switched output current.**
IRFxxx FETs are Vgs(th)=3V +/-1 tolerance This is the threshold for 500uA not Amps !!
So you need >4.5V for Vgs or this IRFxxx family of FETs and preferably 10V for rated RdsOn as shown in specs.
You ONLY get 10% of hFE = Beta as a saturated switch.
We want to ensure base current = >5% of LED current. Preferably 10%. *(never use Vgs(th)2~4V FETS on 3.3V logic. It needs >5V.)* All IRFxxx's I think are this way, Now they make Logic level FETS with a different prefix in P/N.
Your design was (3.3V-0.6Vbe)/5k=Ib= 540 uA.
**Change Rb to >= 100 Ohms** and it will work off any 3.3V logic and NPN open collector. Iout=(3.3-Vbe)/(Rcmos+Rs)= (3.3-0.7)/(33+100)=20 mA so it can drive 200mA to 350mA on collector with low Vce(sat)
Adjust series Rs as required.
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