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In this paper, advanced membrane designs are simulated in order to improve the sensitivity of micromachined silicon condenser microphones. Analytical analyzes and finite element simulations have been carried out to derive algebraic expressions for the mechanical compliance of corrugated membranes and membranes supported at spring elements. It is shown that the compliance of both types of membranes can be modeled with the help of an enhanced theory of circular membranes. For spring membranes, a numerically derived and design dependent constant takes into account the reduced suspension. The mechanical stress in corrugated membranes is calculated using a geometrical model and is confirmed by finite element simulations. A very good agreement between theory and experimental results is demonstrated for spring membranes of different shape and for membranes with varying number of corrugations. In a silicon microphone application, a high electro-acoustical sensitivity up to 8.2 mV/Pa/V is achieved with a membrane diameter of only 1 mm.