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Subthreshold operation is emerging as an energy-saving approach to many new applications. This paper examines energy minimization for circuits operating in the subthreshold region. We show the dependence of the optimum VDD for a given technology on design characteristics and operating conditions. Solving equations for total energy provides an analytical solution for the Optimum VDD and VT to minimize energy for a given frequency in subthreshold operation. SPICE simulations of a 200K transistor FIR filter confirm the analytical solution and the dependence of the minimum energy operating point on important parameters.