How can I adapt a 3-pin PC fan connector to a 4-pin connector?

This solved my problem:

Cited from 3pin to 4pin fan adapter(Chinese)

Explanation:

• two fast-switch triodes (2N-2907 and 13003) utilize PWM control over 12v power.
• diode protects the fan from voltage higher than 12v
• 1K R gives a 12/1000=12mA ceiling to the current from 12v to ground, just in case 2N-2907 is damaged.
• 0.5K R does the same thing for 13003, limiting the max current approximately to 2.5/500=5mA

All these stuffs are easy and cheap to buy, enjoy..

You can just plug it in, the connectors are designed to be compatible. the fan will only run at full speed, that may or may not be a problem.

if you want variable speed that's obviously not a suitable solution.

using the PWM signal (which is is probably only 0-3.3V) to switch a mosfet probably won't work well, and if it does work the fan will tend to stick on some harmonic of the PWM frequency instead of following the PWM ratio.

a better approach is is to use the PWM signal to control the set-point of a voltage regulator and use the regulator output to power the fan, thus controlling it speed.

^{simulate this circuit – Schematic created using CircuitLab}

here I show the potentiometer on a typical adjustable lm2958 LM2956 buck converter module and then the same module with the potentiometer replaced with a PWM control circuit. it works by the PWM controlling the discharge speed of C2 and thus the bias given to feedback signal.

C1-R5 compensate for the low-pass formed by the presence of C2