The effects of charge carrier trapping (i.e. incomplete charge collection) on the detective quantum efficiency (DQE) of a photoconductive detector are studied by using a cascaded linear system model. The model includes signal and noise propagations in the following stages: (1) x-ray attenuation, (2) conversion gain, (3) charge collection, (4) the addition of electronic noise. We examine the DQE(0) of a-Se for fluoroscopy application as a function of photoconductor thickness with varying amounts of electronic noise under (a) constant field, and (b) constant voltage operating conditions. We show that there is an optimum photoconductor thickness, which maximizes the DQE(0) under a constant voltage operation. The optimum thickness depends on the added electronic noise, x-ray exposure, bias voltage and polarity. The actual broad x-ray spectrum emitted from a typical x-ray tube is used in the calculation. The DQE for the negative bias is significantly lower than that of the positive bias, and the diversity in DQE, as expected, increases with the photoconductor thickness because of the asymmetric transport properties of holes and electrons in a-Se. The present results show that the DQE generally does not continue to improve with greater photoconductor thickness in the presence of added electronic noise because of charge transport and trapping effects.