# 0.5-V High-Order Universal Filter for Bio-Signal Processing Applications
## 3 Simulation Results  
The MI-OTA circuit and filter applications were designed and simulated in Cadence using 0.18 \(\upmu\)m CMOS technology from TSMC. The supply voltage was 0.5 V (\(\pm\)0.25 V). The transistor aspect ratios in Figure 2 are listed in Table 4. Note that the ratio of the aspect ratios for M\({}_{1,3}\) and M\({}_{2,A}\) meets the requirement \(m=2+\sqrt{3}\). The power consumption of the MI-OTA at \(I_{set}=625\) pA was 937 pW. Figure 9 shows the DC characteristics of the output current and small-signal transconductance of the OTA with and without MI for \(I_{set}=625\) pA when the output terminal is grounded. As can be seen, the linearity and input voltage range are expanding thanks to the MI technique. Figure 10 shows the frequency characteristic of the MI-OTA output impedance for \(I_{set}=625\) pA with and without SC. While \(Z_{o}\) shows 2.56 G\(\Omega\) for the structure without SC, it shows 4.08 G\(\Omega\) for the structure with SC, so the improvement in impedance is obvious. \begin{table}
\begin{tabular}{l c} \hline \hline
**Component** & **W/L (\(\upmu\)m/\(\upmu\)m)** \\ \hline M\({}_{1}\), M\({}_{3}\) & 37.5/1 \\ \hline M\({}_{2}\), M\({}_{4}\) & 10/1 \\ \hline M\({}_{7}\), M\({}_{7C}\), M\({}_{8}\), M\({}_{8C}\) & 30/1 \\ \hline M\({}_{b}\), M\({}_{5}\), M\({}_{6}\) & 15/1 \\ \hline M\({}_{R}\) & 4/5 \\ \hline C\({}_{B}=0.5\) pF \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Component values of the proposed MI-OTA. Figure 9: DC transfer characteristics of the OTA with and without MI for \(I_{set}=625\) pA; (**a**) output currents \(I_{o}\), and (**b**) small-signal transconductance \(g_{m}\). The transient response of the MI-OTA with applied input sine wave \(V_{in-amp}\) = 250 mV@1 kHz for \(I_{set}\) = 625 pA is shown in Figure 11. The total harmonic distortion (THD) was around 1.2%. Figure 12 shows the DC characteristics of the output current and transconductance characteristics of the MI-OTA for different values of \(I_{set}\) = (0.625, 1.25, 2.5, 5) nA, where wide tunability is achieved. For the filter application, the value of capacitors C\({}_{1}\) = C\({}_{2}\) = 25 pF was selected for the second-order universal filter. The frequency responses of the LP, HP, BP, BS, and AP gains and phases with setting current \(I_{set1-3}\) = 625 pA with 4 pF load capacitance are shown in Figure 13. The cutoff frequency was 11 Hz while the power consumption was 2.8 nW. Figure 11: Transient response of the MI-OTA with 250 mV input amplitudes and 1 kHz frequency. Figure 12: DC characteristics of the MI-OTA for different \(I_{set}\); (**a**) output currents \(I_{o}\) and (**b**) small-signal transconductance \(g_{m}\). Figure 10: Frequency characteristic of the output impedance of the MI-OTA for \(I_{set}\) = 625 pA with and without SC. Obviously, the filter can reach very low cutoff frequencies, making it suitable for biomedical signal processing. The frequency characteristics of gains (lines) and phases (dots) with different \(I_{set}\) for the: LPF (a), HPF (b), BPF (c), BSF (d), and APF (e) are shown in Figure 14. The wide tunability of the filter was achieved by varying the setting current \(I_{set1-3}\) = (0.625, 1.25, 2.5, 5) nA. The cutoff frequency was (11, 21, 39.8, 75) Hz, respectively. Figure 13: Frequency characteristics of gains (lines) and phases (dots) with \(I_{set}\) = 625 pA for the LPF (a), HPF (b), BPF (c), BSF (d), and APF (e). Figure 15 shows the results of the process and mismatch Monte Carlo (MC) analysis with 200 runs and the process, voltage, and temperature (PVT) corners of the second-order LPF. As can be seen, the curves almost overlap for the MC, process, and power supply voltage corners, with small deviations in the case of the temperature corners due to the sensitivity of the circuit operating in the subthreshold region to temperature changes. Figure 14: Frequency characteristics of gains (lines) and phases (dots) with different \(I_{\text{set}}\) for the LPF (**a**), HPF (**b**), BPF (**c**), BSF (**d**), and APF (**e**).