In a typical position detection system for optical tweezers, laser light impinges on a quadrant photodiode, and the signal from the four quadrants of the diode is used to determine the position of a trapped object. A widely used position detection system consists of a Si-PIN photodiode and an infrared laser. In previous work we have demonstrated with two distinct experimental methods how such a system may act as an unintended low-pass filter and we modeled its physical origin mathematically. Here we demonstrate that the general solution to this model can account precisely for the "parasitic" filter's effects up to as large frequencies as we can measure, approximately 100 kHz. Thus we increase the useful bandwidth of tweezers experiments by nearly two decades. This opens for investigations of phenomena in biophysics, soft matter, and polymer science at much higher frequencies than before.