We characterize three different quenching circuits for InGaAs/InP single-photon avalanche diodes (SPADs) operated in gated mode: i) a simple passive quenching circuit; ii) an active quenching circuit; and iii) a fast active quenching circuit. For each of these, we acquire the shape of the avalanche current, at different excess biases, by reconstructing the waveform of the photons emitted from the detector during an avalanche and we simultaneously measure the afterpulsing probability and the dependence of dark count rate on gate period (to estimate the maximum count rate). We prove that the avalanche charge reduction is in agreement with the reduction of afterpulsing probability, giving a four-time decrease in afterpulsing when employing the...