It's the duty cycle not the frequency that determines the output voltage.For an inductor
V = L di/dt
With PWM, you switch the cycle on and off. So, when di/dt increases (your PWM goes faster), V becomes bigger to compensate.
Every time the transistor switches off, the energy stored in the inductor is "pumped" into the capacitor - increasing the voltage on the capacitor.It's the duty cycle not the frequency that determines the output voltage.
The ON time may be less than, equal to, or greater than the OFF time. A boost converter functions with PWM duty cycles from 0% to 100%. When the input voltage is only slightly less than the output voltage, i.e. 12V input w/ 15V output, the duty cycle is well under 50%. The ON time is less than the OFF time.---In any boost converter the transistor ON time is longer than the OFF time. This is because it takes longer to store the energy in the inductor than it does to release it. This is because the voltage when storing is less than the voltage when discharging.
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