For an optimal design of a VDF/TrFE (vinylidene fluoride trifluoroethylene) copolymer-on-silicon pyroelectric sensor, the one-dimensional diffusion equation is solved for the pyroelectric multilayer structure. Output current and voltage of the sensor are calculated. Improvement of the sensor can be obtained by: (a) etching the silicon substrate under the sensor element and (b) an additional VDF/TrFE copolymer layer as thermal isolation. Different noise sources for a pyroelectric sensor have been calculated. The dielectric noise dominates the noise sources. This conclusion has been verified by measured values.