## 3 Simulation Results and Discussion
### Gyrator Simulation and Optimization
It should be taken into account that the compensation circuit causes a doubling of the parasitic capacitance \(C_{\text{P2}}\), therefore, the results after compensation have improved, but still do not reach the values as for the first set, see the frequencies in the last column of Table 2 in parentheses. \begin{table}
\begin{tabular}{c c c c c c} \hline \(g_{\text{m1}}=g_{\text{m2}}\) & \(\alpha\) & \(F\) & \(GFREQ TABLE\) & \(f_{\text{GP1}}\) & \(\text{min}\{f_{\text{GP2}},f_{\text{CP2}}\}\) \\ (**mS**) & **(F-sec\({}^{*-1}\))** & **(F-sec\({}^{*-1}\))** & **(GFREQ TABLE\)** & **(Hz)** & **(Hz)** \\ \hline
1 & 0.25 & 11.23 u & (10m,-105,22.5) (100 meg-,55,22.5) & 6.25 m & 24.5 M \\
1 & 0.5 & 1.262 u & (10m,-130,45) (100 meg-,30,45) & 2.5 & 4.54 M \\
1 & 0.75 & 141.7 n & (10m,-155,67.5) (100 meg-,5,67.5) & 18.4 & 1.36 M \\
1 & 1 & 15.92 n & Classic capacitor 15.92 nF instead of GFREQ & 50 & 553 k \\ \hline \end{tabular}
\end{table} 
Table 1: First set of element parameters for simulation of the circuit in Figure 9 and its expected cut-off frequencies. \begin{table}
\begin{tabular}{c c c c c c} \hline \(g_{\text{m1}}=g_{\text{m2}}\) & \(\alpha\) & \(F\) & \(GFREQ TABLE\) & \(f_{\text{GP1}}\) & \(\text{min}\{f_{\text{GP2}},f_{\text{CP2}}\}\) \\ (**mS**) & **(F-sec\({}^{*-1}\))** & **(GFREQ TABLE\)** & **(Hz)** & **(Hz)** \\ \hline
20 & 0.25 & 4.493 m & (10m,-52.96,22.5) (100 meg-,2.96,22.5) & 39.1 n & 24.5 M \\
20 & 0.5 & 504.6 u & (10m,-77.96,45) (100 meg-,22.04,45) & 6.25 m & 4.54 M \\
20 & 0.75 & 56.68 u & (10m,-102.96,67.5) (100 meg-,47.04,67.5) & 339 m & 464 k (918 k) \\
20 & 1 & 6.366 u & Classic capacitor 6.366 uF instead of GFREQ & 2.5 & 100 k (391 k) \\ \hline \end{tabular}
\end{table} 
Table 2: The second set of element parameters for simulation of the circuit in Figure 9 and its expected cut-off frequencies. The simulated magnitude and phase-frequency characteristics of the gyrator input admittance are depicted in Figures 10-13 for the \(\alpha\) values 0.25, 0.5, 0.75, 1, respectively. The solid black lines are valid for the first set of circuit parameters, the dotted green lines for the second set, and the dashed blue lines indicate ideal results. It is worth to mention again that the simulations in this subsection are performed with ideal FO capacitor loading the gyrator to solely illustrate the effect of OTA non-ideal properties. Common FO capacitors emulated by RC structures of reasonable complexity have limited accuracy in a limited frequency band [28], which would unnecessarily degrade the results, and it would not be clear whether the distortion is caused by non-idealities of OTA or FO capacitor. The simulated admittance characteristics in Figures 10-13 are in accordance with the Bode plots in Figure 5, and the important asymptotic magnitude and phase values are confirmed. The limited frequency band of the correct functionality of the gyrator can be observed, and the simulated magnitude cut-off frequencies correspond to the expected values from Tables 1 and 2. Considering the maximum phase error \(\pm 2\) degrees, the useful frequency ranges for the designed FO inductance simulators are listed in Table 3.  
Furthermore, the simulations confirm that the admittance magnitude at low frequencies is limited to the value \(g_{\text{m1}}g_{\text{m2}}/G_{\text{P1}}\), which is 200 mS for the first set of elements and 4 S for the second one. The constant magnitude section between \(\omega_{\text{GP2}}\) and \(\omega_{\text{CP2}}\) is not apparent in the simulations as the value \(G_{\text{P2}}\) is too low to take effect. This section would be visible for the set 2 magnitudes with \(\alpha\) values 0.75 and 1 if no \(G_{\text{P2}}\) compensation were applied. The effect of the additional capacitance of the compensation circuit is demonstrated in Figures 12a and 13a by increasing the magnitude at high frequencies compared to set 1 results. The simulated results also confirm that the bandwidth of correct gyrator operation increases as \(\alpha\) decreases.