## 2 Methods
### Guidelines for Setting of Gyrator Parameters  
Practical guidelines for gyrator parameter design were compiled based on the above observations. By following these rules, in addition to the correct input admittance, we also ensure its highest possible frequency and magnitude range and prevent the active elements from non-linear operation and overloading. The starting point of the design is the required value of input admittance \(Y_{\text{IN}}\) specified, e.g., by \(F_{\text{IN}}\) and \(\alpha\), or magnitude at specific frequency and phase, see (5) and (6). The first set of guidelines (labeled A) can be used if there is available any value of the fractance \(F\) of the FO capacitor loading the gyrator.  
1. Choose the same \(g_{\text{m1}}\) and \(g_{\text{m2}}\) as the highest possible values for the correct functionality of the selected OTAs. The maximum transconductance values can be found in OTA documentation and are usually several hundreds of \(\upmu\)S for CMOS and several tens of mS for BIT implementations. The choice of maximal trans conductances extends the operating band to low frequencies. If this is not a priority, choose the transconductances equal to the required input admittance magnitude at the commonly used frequency, e.g., at the geometric mean of the operating band.
2. Calculate the value of fractance \(F\) from the magnitude part of (6). If the value of \(F\) turns out too high for implementation, then it is possible to use the next set of rules labeled B, where a lower value of \(F\) can be set at the beginning. If \(F\) turns out too small, the only solution is to choose OTAs with higher maximum trans conductances.
3. Check the frequency range of the correct functionality of the gyrator, according to (8), (9), or (11). If the range is not sufficient, consider reducing parasitic conductance(s) by the compensation described in Section 2.2.2.
4. To prevent the OTAs from the non-linear operation, ensure that the magnitude of the gyrator input voltage \(V_{\text{IN}}\) meets both the conditions (13) and (14) simultaneously in the operating frequency band.  
The next set of rules (labeled B) is applicable if a specific value of the fractance \(F\) should be set at the beginning.  
1. Set a specific value of the fractance \(F\). If a cut-off frequency \(\omega_{\text{GP1}}\) should be reached without compensation of parasitic conductance \(G_{\text{P1}}\), the selected value \(F\) must be at least as determined from (8).
2. Determine the required product \(g_{\text{m1}}g_{\text{m2}}\) for the selected \(F\) and given \(F_{\text{IN}}\) from the magnitude part of (6). Evaluate whether the product is achievable by the selected OTAs. If not, \(F\) must be reduced for the design to continue (regardless of fulfilling (8) in the previous step).
3. Choose \(g_{\text{m2}}\) as the highest possible value for the proper functionality of the selected OTA\({}_{2}\).
4. Calculate \(g_{\text{m1}}\) from the magnitude part of (6). If the ratio \(g_{\text{m1}}/g_{\text{m2}}\) turns out excessively low, then it is possible to decrease \(g_{\text{m2}}\) and an increase \(g_{\text{m1}}\) such that their product remains the same. However, keep in mind that decreasing \(g_{\text{m2}}\) may decrease the allowed gyrator input voltage, according to (14).  
* Check the frequency range of the correct functionality of the gyrator, according to (8), (9), or (11). If the range is not sufficient, consider reducing parasitic conductance(s) by the compensation described in Section 2.2.2.
* To prevent the OTAs from the non-linear operation, ensure that the magnitude of the gyrator input voltage \(V_{\text{IN}}\) meets both the conditions (13) and (14) simultaneously in the operating frequency band.  
To add more clarity, a flowchart of the above guidelines for the setting of gyrator parameters is enclosed in Figure 7.