Transfer function of a digital phase frequency detector
The pfd (with charge pump) generates current pulses of fixed amplitude ICPICP like it is described for example here. For small phase deviations the length of these current pulses is proportional to the phase difference of the input signals. So the pfd output current is clearly not proportional to the phase error.


Since the duty cycle is proportional to the phase error, and the amplitude of the pulses is fixed, when averaged over several cycles the output voltage or current is proportional to the phase error.

Since the control loop bandwidth is typically orders of magnitude lower than the clock frequency, this means the PFD output is proportional to the phase error when considering frequencies within the operating band of the control loop, which is what matters for modeling the control loop.