A micromachined variable capacitor structure is used as a modulation mechanism for a differential parametric amplifier. The capacitance of the capacitor structure is modulated by a control signal while a differential signal is applied to the capacitor structure. Modulation of the capacitance produces a signal representative of the input differential voltage. This signal is provided to an amplifier. Once the signal is amplified, a demodulator demodulates the amplified signal to provide an amplified version of the differential signal. The variable capacitor structure also allows for internal feedback, which permits the parametric amplifier to be used as a galvanically isolated differential measurement amplifier. A number of techniques are used to remove common mode and other errors from the modulated difference signal, thereby eliminating them from the amplified output.