This paper proposes a new readout method for a sensor to detect minute variations into the capacitance. A sensor is based on the weakly coupled electrical resonators that use an amplitude ratio (AR) as an output signal. A new readout scheme with a relatively higher output sensitivity is proposed to measure the relative changes in the input capacitor. A mathematical model is derived to express the readout output as a function of change into the capacitance. To validate the theoretical model, a system is modeled and designed using an industry-standard electronic circuit design environment. A SPICE simulation results are presented for a wide range of design parameters, such as varying coupling factors between the two electrical resonators. A sensitivity comparison between the existing and the proposed AR readout is presented to show the effectiveness of the method of detection proposed in this work.