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The authors develop a device model for a resonant detector of modulated terahertz radiation based on a micromachined high-electron-mobility transistor with the microcantilever serving as the gate. The device model accounts for mechanical motion of the microcantilever and plasma effects of the two-dimensional electron channel. It is demonstrated that at a combined resonance when the carrier terahertz frequency and the modulation frequency coincide with the plasma resonant frequency and the mechanical resonant frequency, respectively, the amplitude of the output gate and drain ac currents and, hence, the detector resonsivity exhibit sharp and high maximum.