# VDGA-Based Resistorless Mixed-Mode Universal Filter and Dual-Mode Quadrature Oscillator
## 7 Simulation Verification
### Simulation Results of the Proposed Mixed-Mode Universal Biquad Filter in Figure 2  
The proposed resistorless mixed-mode universal biquad filter in Figure 2 was designed for the following frequency specifications: \(f_{p}=1.59\) MHz and \(Q=1\). The specified filter parameters yield component values of \(g_{mAi}=g_{mBi}=g_{mCi}=1\) mA/V (\(i=1\), \(2\)) and \(C_{1}=C_{2}=100\) pF. Figures 5 and 6, respectively, illustrate the simulation results of the time-domain and frequency-domain responses in VM and CM. A sinusoidal input signal with a peak amplitude of 40 mV at 1.59 MHz was applied to the proposed filter during time-domain response study. Similarly, Figures 7 and 8 present the simulated frequency characteristics for the TIM and TAM filters, respectively. There is significant agreement between the theory and simulation values. Additionally, the total power consumption of the circuit was determined to be 2.84 mW. Figure 4: Practical behavior model of the VDGA with its parasitic impedances. To demonstrate the electronic tunability of the proposed universal filter illustrated in Figure 2, the frequency responses of the VM BP filter for various pole frequencies \(f_{p}\) are plotted in Figure 9. To achieve this, the frequency \(f_{p}\) was adjusted for three different values, i.e., \(f_{p}\) = 0.62 MHz, 1.01 MHz, and 1.59 MHz, by changing the \(g_{mkl}\) value to 0.39 mA/V, 0.63 mA/V, and 1 mA/V, respectively. The findings indicated that the simulated \(f_{p}\) values were 0.616 MHz, 1.07 MHz, and 1.585 MHz, which correspond to the percentage absolute errors of 0.64%, 5.90%, and 0.31%, respectively. Figure 10 depicts the simulated  
Figure 5: Simulation results of the proposed VM filter in Figure 2. (**a**) LP; (**b**) BP; (**c**) HP. frequency responses of the VM BP filter for various \(Q\)-values. Table 3 tabulates the values of the active component corresponding to different \(Q\)-values based on the designs. The proposed circuit facilitates independent electronic adjustment of the \(f_{p}\) and \(Q\) values, as seen in Figures 9 and 10. Figure 6: Simulation results of the proposed CM filter in Figure 2. (**a**) LP\({}_{2}\) (**b**) BP; (**c**) HP. Figure 8: Simulated frequency responses of the proposed TAM filter in Figure 2.  
Figure 7: Simulated frequency responses of the proposed TIM filter in Figure 2.  
Figure 9.0 Simulated frequency responses of the VM BP filter in Figure 2 with tuning_f\({}_{p}\)_ value. Additionally, the sensitivity performance was examined for 100 runs using Monte Carlo statistical analysis, which considers both transconductances (\(g_{nki}\)) and capacitance values (\(C_{1}\) and \(C_{2}\)) with a 5% variation. Figure 11 shows the generated family histograms of \(f_{p}\). The mean and standard deviation were 1.63 MHz and 53.74 kHz, respectively, demonstrating that the scheme possesses sufficient sensitivity. Furthermore, to demonstrate the robustness of the proposed universal filter in Figure 2, the pole frequency \(f_{p}\) is analyzed at different process corner, voltage, and temperature (PVT) variations. Figure 12 presents the simulation results for the \(f_{p}\) of the VM BP filter response under PVT variations. The process corners were selected for the parameters nominal-nominal (NN), slow-slow (SS), fast-fast (FF), slow-fast (SF), and fast-slow (FS). We observe that the \(f_{p}\) increases as the supply voltage increases. As the temperature increases, the  
Figure 9.1 Monte Carlo statistical analysis results of the VM BP response with 5% deviation in transconductance and capacitor values. Figure 9.2 Simulated frequency responses of the VM BP filter in Figure 2 with tuning \(Q\) value. \begin{table}
\begin{tabular}{c c c} \hline \(g_{mB1}\) **(mA/V)** & \(g_{mC1}\) **(mA/V)** & \(Q\) \\ \hline
1 & 0.59 & 0.6 \\
1 & 1.00 & 1 \\
0.22 & 0.89 & 4 \\
0.17 & 1.73 & 10 \\ \hline \end{tabular}
\end{table} 
Table 3: Active component values of the proposed VM BP filter for tuning \(Q\) values at \(f_{p}=1.59\) MHz (\(g_{mA1}=g_{mA2}=g_{mB2}=g_{mC2}=1\) mA/V).