## 3 Simulation Results and Discussion
### Gyrator Simulation and Optimization  
The input admittance magnitude of the gyrator chosen in this subsection is \(\mid\!Y_{\rm IN}\!\mid\) = 10 mS at 1 kHz, and the orders \(\alpha\) are 0.25, 0.5, 0.75, 1, i.e., three of them representing FO and one classic inductance simulator. Two sets of element parameters will be used for demonstration. The first set (labeled set 1) will be designed only to provide the required input admittance, regardless of the previously proposed recommendations concerning the wide frequency and magnitude range. Then, the elements of set 2 will be designed regarding these recommendations to demonstrate the optimization of admittance characteristics. The schematic of the gyrator in the OrCAD Capture editor is depicted in Figure 9. Unless otherwise noted, the circuit is considered without the compensation part indicated by the dashed box. Figure 8: A differential (floating) variant of the gyrator from Figure 2.  
Figure 9: OrCAD Capture schematic of the simulated gyrator. To show solely the influence of parasitic properties of the employed OTAs, ideal FO capacitors were used as gyrator load Y. These elements were modeled in OrCAD by GFREQ part representing voltage-controlled current source described by a table of frequency response in magnitude and phase domain [27]. Interpolation is performed between the entries; whereas, magnitude is interpolated logarithmically and phase linearly. By interconnecting the input and output of the GFREQ part as displayed in Figure 9, the resulting element admittance is described by a series of (input frequency in Hz, magnitude in dB, phase in degrees) triplets. The OTA transconductances are chosen \(g_{\text{m1}}=g_{\text{m2}}=1\) mS in the first set of circuit parameters. To obtain the required \(\mid\!Y_{\text{IN}}\!\mid\!=10\) mS at 1 kHz, the magnitude of loading admittance according to (4) is \(\mid\!Y\!\mid\!=0.1\) mS at 1 kHz. The orders of the loading admittance are \(\alpha=0.25\), \(0.5\), \(0.75\), \(1\), i.e., three of them FO and one classic capacitor. The summary of this first set of element parameters is given in Table 1, along with the expected lower and upper cut-off frequencies determined by the relations (8), (9), and (11). The second set of gyrator element parameters is designed following rules A from Section 2.3, which should provide optimization of both the frequency and dynamic range of the gyrator input admittance. The maximum transconductances of LT1228 OTA are chosen based on the datasheet \(g_{\text{m1}}=g_{\text{m2}}=20\) mS. To obtain the required \(\mid\!Y_{\text{IN}}\!\mid\!=10\) mS at 1 kHz, the magnitude of loading admittance is \(\mid\!Y\!\mid\!=40\) mS at 1 kHz. The summary of this second set of element parameters with the expected cut-off frequency values is given in Table 2.  
The values of lower cut-off frequency \(f_{\text{GP1}}\) for the second set are lower than for the first set, as expected. As seen in the last column of Table 2 (values that are not in parentheses), the upper cut-off frequencies decreased for \(\alpha=0.75\) and \(1\) compared with Table 1. This bandwidth degradation is caused by the parasitic conductance \(G_{\text{P2}}\), which raised from \(5\) uS for the first element set to \(100\) uS for the second set, due to increasing the transconductance \(g_{\text{m1}}\) (it holds \(G_{\text{P2}}=0.005g_{\text{m1}}\)). The parasitic conductance \(G_{\text{P2}}\) can be decreased as described in Section 2.2.2, resulting in an increase of the upper cut-off frequency. The compensation circuit with negative admittance utilized for this purpose is marked with the dashed box in Figure 9. The transconductance \(g_{\text{mC}}\) of the OTA in the compensation circuit was set to \(99.5\) uS, which leads to \(G_{\text{P2}}\approx 1\) uS and that is an even better value than for the first set of elements.