An injector driver module includes: a first node that is connected to a first terminal of a fuel injector; a first switch configured to, when closed, connect a first potential of a battery to the first node; a second switch configured to, when closed, connect a second potential that is greater than the first potential to the first node; a second node that is connected to a second terminal of the fuel injector; and a third switch configured to, when closed, connect a ground potential to the second node. A switch control module is configured to, starting at a target injecting timing for a fuel injection event of the fuel injector: maintain the third switch closed; and switch the second switch using a pulse width modulated (PWM) signal having (i) a duty cycle that is less than 100 percent and (ii) a predetermined frequency.