## 3 Results and Discussions  
A three-port electrochemical sensor was modeled using a voltage controlled resistor, as shown in Figure 8[19; 20; 21]. The resistance between the RE and CE is modeled as a constant resistor at 10 k\(\Omega\). The typical voltage difference between the WE and RE was set to be 700 mV. In this circuit, the WE was forced by the VDD supply (1.8 V). The RE is typically indirectly biased to 1.1 V by the virtual short between the feedback amplifier input nodes. The current change due to the electrochemical reaction is modeled using a voltage-controlled resistor, which varies from 250 to 2250 k\(\Omega\), and is implemented using Verilog-A. Since the chip is under fabricate, post layout simulation was performed using parasitic extraction (PEX). Figure 9 shows the layout of the circuit. The circuit was implemented using a 0.18-um CMOS process with an active area of 1.073 mm\({}^{2}\). The overall current consumption was 287.9 uW. Figure 8: Configuration of the equivalent sensor model using a voltage-controlled resistor. Figure 7: Schematic of the fully-differential amplifier. Figure 9(a) shows the input-output characteristics of the proposed current mirror between the input current (\(I_{SEN\_IN}\)) and output current (\(I_{SEN\_OUT}\)). The maximum error from 0 to 4.5 \(\upmu\)A for the input current is 1.129%FSO (full scale output). Figure 9(b) shows the transimpedance of the TIA was simulated to be 300 k\(\Omega\) with a maximum nonlinearity of 0.793% in the current range of 3.83 \(\upmu\)A. Figure 10(b) shows the transimpedance of the TIA was simulated to be 300 k\(\Omega\) with a maximum nonlinearity of 0.793% in the current range of 3.83 \(\upmu\)A. Figure 11 shows the transient simulation results of the proposed potentiostat readout circuit. The resistance between the WE and RE varied from 250 to 2250 k\(\Omega\), and the \(V_{BIAS}\) was set to 500 mV. The transimpedance of the TIA was set to 300 k\(\Omega\) and feedback capacitance of 10 pF. Because the output current is inversely proportional to the sinusoidal input resistance change of the electrochemical sensor, the red line (\(I_{SEN}\)) and blue line (\(V_{OUT}\)) have the waveform shapes of \(1/[1+\sin\left(x\right)]\). Figure 11: Output voltage simulation results of the current mirror and TIA. Figure 10: (a) Linearity simulation result of the sensing current; (b) linearity simulation result of the TIA. Figure 9: Layout of proposed readout circuit. Figure 12 shows the stability simulation results of the TIA with the feedback transimpedance resistance of 300 k\(\Omega\) and feedback capacitance of 10 pF. The open-loop gain (OLG) is 117 dB, the unit gain bandwidth (UGBW) is 2.211 MHz, and the phase margin is 84.67 deg. This result shows stability at high-speed performance and can be setting the variable gain setup. The input referred noise simulation results are shown in Figure 13. The input referred current noise at 1 Hz is reduced from 13.2775 pA/\(\surd\)Hz to 936 fA/\(\surd\)Hz by the chopper operation. The input-referred noise density and the integrated input-referred noise from 0.1 Hz to 1 kHz are 21.7 pA\({}_{\text{RMS}}\), respectively. Table 1 shows noise contributors of readout circuit. When the chopper is disabled, the flicker noise components in the current mirror, \(M_{1,2}\), form about 72% of the total noise. When the chopper is enabled, the main contributors are changed to the thermal noise of \(M_{1,2}\). Figure 12: Stability simulation result of proposed TIA. Figure 13: Input-referred noise simulation results of the readout circuit. Figure 14 show the Monte-Carlo simulation results with N = 200. The input current, \(V_{BIAS}\) and \(R_{f}\), were fixed to 1 uA, 500 mV, and 300 k\(\Omega\), respectively. The desired nominal output of the TIA was 800 mV. In the simulation, the standard deviation of the TIA output was reduced from 2.49 to 0.12 mV by the DEM operation in Figure 14d. As shown in Figure 14b,c, the standard deviation of the TIA output was 0.75 to 0.68 mV.