The carrier transport equations for a siliconp-i-nphotodiode have been linearized, and analytic solutions of the responsivity have been obtained for a step function of weakly absorbed radiation. These solutions have been used to calculate the responsivity toQ-switched pulses (tens of nanoseconds) from a Nd:YAG laser. Examples of the tradeoff between responsivity and electrical pulsewidth are given. Finally, the use ofp-i-nphotodiodes to detect mode locked (tens of picoseconds) pulses by taking advantage of the long period between pulses is shown to be feasible if the pulse shape does not have to be resolved. ©1997 American Institute of Physics.