For the complete period calculation of a pulse, the total resistance of the potentiometer (in parallel to R3 of course) is calculated. The duty cycle is changed according to the position of the potentiometer. The frequency is calculated from the capacitor itself ( C1 ) as well as from the total resistance of the potentiometer parallel to R3. Now the capacitor is charged from the output of the 555 when it is HIGH, and discharge the same way when the output is LOW. Usually the capacitor is charged through a resistor directly connected to the power supply, and discharged through pin 7 (discharging capacitor). This is the only point that needs of your attention. The output (pin 3) of the 555 timer will control the charging and the discharging of the capacitor.

Although the frequency is not very stable (come on it is just a 555 for crying out loud), it will never fall bellow 21KHz thus you will not hear a thing The circuit that i will present to you has all the advantages of the high frequency PWM controllers, but it uses only a 555 timer to generate the pulses. Moreover, PWM controllers can achieve very stable and low speeds without the possibility of a fan stall. A high frequency PWM controller usually operates above the 20KHz, thus the human ear cannot hear this sound. The PWM controllers usually generate acoustic noises, when the PWM frequency is within the acoustic spectrum (20Hz to 20KHz).

Yet, they tend to be difficult in construction when high frequency is required. The PWM fan controllers have many advantages against other rpm fan controllers.

4 pin fan controller