I understand transformers only work with AC because there is electromagnetic induction only when the current going through is AC. In switch-mode power supplies, the pulse transformers are powered by high frequency signals generated by MOSFETs which means they can be smaller because the high frequency will compensate for the missing inductance.
I also learned that, when the output voltage drops (due to a load in the secondary), the PWM controller increases the duty cycle of the signal generated by the MOSFETs, in order to compensate and keep the voltage constant. However, the frequency of the signal is the same. Given that transformers only work with AC and that the frequency of ON/OFF switching of the MOSFETs (variation) is the same when the duty cycle is increased, how does that result in higher output power?