## 3 Simulation Results
### Post-Layout Simulation  
The layout of the entire schematic was done using cadence's virtuoso tool. Figures 13 and 14 show the overall chip layout and the detail layout of the filter core, respectively. The layout floorplan is shown in Figure 15 which explains element placement. The component values of Figures 13 and 14 were given by g\({}_{\rm m}\) = 100 \(\mu\)S, R\({}_{\rm X}\) = 10 k\(\Omega\) and C\({}_{1}\) = C\({}_{2}\) = 5 pF, leading to a center frequency f\({}_{\rm o}\) = 3.183 MHz. A design rules check (DRC) and a layout versus schematic (LVS) comparison were performed on the layout. The DRC checks for potential errors in the layout. The LVS checks the layout against the schematic and verifies that all the nets are matching. After the DRC and LVS were completed successfully, layout extraction was done. The extraction gives an overall idea about the parasities of the design. All these processes are carried out using a cadence virtuoso schematic and layout editor tool for TSMC 0.18-\(\mu\)m CMOS process technology. The post-layout simulations were carried out to check the functionality of the design. Figure 16 represents the post-layout simulated frequency responses for the HP (I\({}_{01}\)), BP (I\({}_{02}\)), LP (I\({}_{03}\)) and BP (I\({}_{04}\)) filters in the CM. The post-layout simulation results show the CM simulated natural frequency as 3.10 MHz, that is, an approximately 2.52% error with the theoretical value. Figure 17 represents the post-layout simulated frequency responses for the LP (V\({}_{01}\)), BP (V\({}_{02}\)), HP (V\({}_{03}\)) and BS (V\({}_{04}\)) filter in the VM. The post-layout simulation results show the VM simulated natural frequency as 3.08 MHz, that is, an approximately 3.14% error with the theoretical value. Figure 18 represents the post-layout simulated frequency responses for the HP (I\({}_{01}\)), BP (I\({}_{02}\)), LP (I\({}_{03}\)) and BS (I\({}_{04}\)) filter in the TAM. The post-layout simulation results show the TAM simulated  
Figure 12: Time-domain results of VM bandpass filter at the output V\({}_{\rm o2}\) of Figure 2 (**a**) input (blue line) and output (red line) waveforms; (**b**) total harmonic distortion (THD) analysis results on input voltage at 3.183 MHz. \begin{table}
\begin{tabular}{c c c c c} \hline
**Bias Currents I\({}_{\rm B1}\)** & **Bias Currents** & **Capacitances** & **Calculated** & **Simulated** & **Frequency** \\ = **18\({}_{\rm B2}\)** = **18\({}_{\rm B3}\)** & **18\({}_{\rm B2}\)** = 18\({}_{\rm S3}\)** & **C\({}_{1}\) = C\({}_{2}\)** & **Value of f\({}_{\rm o}\)** & **Value of f\({}_{\rm o}\)** & **Error** \\ \hline
10.726 \(\mu\)A (g\({}_{\rm m}\) = 66.67 \(\mu\)S) & 0.79 \(\mu\)A (R\({}_{\rm X}\) = 15 k\(\Omega\)) & 5 pF & 2.122 MHz & 2.13 MHz & 0.3\% \\ \hline
24.135 \(\mu\)A (g\({}_{\rm m}\) = 100 \(\mu\)S) & 1.7782 \(\mu\)A (R\({}_{\rm X}\) = 10 k\(\Omega\)) & 5 pF & 3.183 MHz & 3.22 MHz & 1.62\% \\ \hline
42.902 \(\mu\)A (g\({}_{\rm m}\) = 133.33 \(\mu\)S) & 3.161 \(\mu\)A (R\({}_{\rm X}\) = 7.5 k\(\Omega\)) & 5 pF & 4.244 MHz & 4.32 MHz & 1.79\% \\ \hline
96.5 \(\mu\)A (g\({}_{\rm m}\) = 200 \(\mu\)S) & 7.113 \(\mu\)A (R\({}_{\rm X}\) = 5 k\(\Omega\)) & 5 pF & 6.366 MHz & 6.48 MHz & 1.79\% \\ \hline \end{tabular}
\end{table} 
Table 8: Component values used to obtain a specified f\({}_{\rm o}\). natural frequency as 3.10 MHz, that is, an approximately 2.52% error with the theoretical value. Figure 19 represents the post-layout simulated frequency responses for the LP (V\({}_{\text{o1}}\)), BP (V\({}_{\text{o2}}\)), HP (V\({}_{\text{o3}}\)) and BP (V\({}_{\text{o4}}\)) filter in the TIM. The post-layout simulation results show the TIM simulated natural frequency as 3.09 MHz, that is, an approximately 2.83% error with the theoretical value. It appears from Figures 16-19 that the filter post-layout simulation performs all the filter functions well, but the small departures filter responses mainly stems from the parasitic impedance effects and non-ideal gains of the CCCCTA. The total power dissipation is found to be 0.593 mW.