The pyroelectric response and NEP of pyroelectric detectors with and without a substrate are calculated as functions of detector thickness and working frequency, using the one-dimensional diffusion theory. It is found that in order for a thin pyroelectric film detector to have better low frequency performance, it is essential that the substrate should be effectively free-bearing and very thin, preferably less than 0.1μ thick. The pyroelectric layer should also be thin, preferably as thin as the substrate. As concerns the substrate material, the product of its specific heat and density should be as small as possible.