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In this paper, we present the design and the analysis of an electrochemical circuit for measuring the concentrations of therapeutic drugs using structure-switching aptamers. Aptamers are single-stranded nucleic acids, whose sequence is selected to exhibit high affinity and specificity toward a molecular target, and change its conformation upon binding. This property, when coupled with a redox reporter and electrochemical detection, enables reagent-free biosensing with a sub-minute temporal resolution for in vivo therapeutic drug monitoring. Specifically, we design a chronoamperometry-based electrochemical circuit that measures the direct changes in the electron transfer (ET) kinetics of a methylene blue reporter conjugated at the distal-end of the aptamer. To overcome the high-frequency noise amplification issue when interfacing with a large-size (> 0.25 mm2) implantable electrode, we present a sample-and-hold (S/H) circuit technique in which the desired electrode potentials are held onto noiseless capacitors during the recording of the redox currents. This allows disconnecting the feedback amplifiers to avoid its noise injection while reducing the total power consumption. A prototype circuit implemented in 65-nm CMOS demonstrates a cell-capacitance-insensitive input-referred noise (IRN) current of 15.2 pArms at a 2.5-kHz filtering bandwidth. Tested in human whole blood samples, changes in the ET kinetics from the redox-labeled aminoglycoside aptamers at different kanamycin concentrations are measured from the recorded current waveforms. By employing principal component analysis (PCA) to compensate for the sampling errors, a detection limit (SNR = 1) of 3.1 uM under 1-sec acquisition is achieved at 0.22-mW power consumption.