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A micromechanical resonator with eigenfrequencies in the megahertz-range is excited by signals having frequencies from tens of megahertz to gigahertz. The high-frequency excitation voltage is downconverted to mechanical force at the lower resonance frequency by the second-order force-voltage nonlinearity. The conversion is either assisted by additional local-oscillator signal or it is intrinsic due to an amplitude-modulated (AM) input signal. A circuit-simulator model is tested against measurements and an excellent agreement and thorough interpretation of the results is found. The third-order intercept point is measured and simulated to study the strength of the capacitive third-order nonlinearity. Finally, various nonlinear contributions are compared and further improvements for the device are suggested based on the simulations.