## 3 Simulation and Experimental Measurements
### First Proposed Isomorphic Circuit Simulation and Experimental Results
The figure of merit (FoM) of the filter can be defined as [28]  
Figure 2.5  
According the NBPF frequency spectrum measured in Figure 15, the dynamic range between the fundamental tone and the largest spurious of the spurious-free dynamic range was approximately 40.79 dB. Thus, the FoM of the proposed VM NBPF at the voltage output of V\({}_{\text{BP2}}\) was approximately computed to be 3.07 \(\times\) 10\({}^{6}\). Figure 2.6 The measured phase noise performance of the NBPF at V\({}_{\text{BP2}}\). Figure 2.7 The NBPF at the V\({}_{\text{BP2}}\) output spectrum for a two-tone intermodulation distortion test. Figure 2.8 The measured P1 dB of the NBPF at V\({}_{\text{BP2}}\) with the input power when f\({}_{\text{o}}\) was 165.8 kHz. To investigate the VM fully uncoupled QSO in Figure 2b, Figure 20 shows the measured waveforms of the quadrature voltage outputs V\({}_{\rm o1}\) and V\({}_{\rm o2}\) in the time domain. The component values used in Figure 20 were C\({}_{1}\) = C\({}_{2}\) = 0.96 nF, g\({}_{\rm m1}\) = g\({}_{\rm m2}\) = g\({}_{\rm m3}\) = 1 mS and R\({}_{1}\) = R\({}_{2}\) = R\({}_{3}\) = 1 k\(\Omega\) for the theoretical value of f\({}_{\rm o}\) = 165.8 kHz. The measured FO in Figure 20 was 162.3 kHz, which was close to the theoretical value of 165.8 kHz. Figure 21 shows the spectrum of the VM fully uncoupled QSO at the V\({}_{\rm o2}\) output terminal. The measured FO was 160.95 kHz, which was close to the theoretical value of 165.8 kHz. The difference between the amplitudes of the fundamental and second harmonics was 41.87 dB, and the calculated THD was about 0.81%. As shown in Figure 21, the third harmonic and subsequent harmonics were not visible in the spectrum because these harmonics were lower than the noise floor. This means that the THD of the first proposed VM fully uncoupled QSO was small. Figure 22 shows the phase noise performance of the QSO measured at the output of V\({}_{\rm o2}\). The measured value of the phase noise of V\({}_{\rm o2}\) was less than \(-\)40.18 dBc/Hz at a 30-Hz offset. Figure 23 shows the FO tuning range of the measured output voltage V\({}_{\rm o2}\), where C\({}_{1}\) = C\({}_{2}\) = 0.96 nF, g\({}_{\rm m2}\) = 1 mS and R\({}_{1}\) = R\({}_{2}\) = R\({}_{3}\) = 1 k\(\Omega\), and only g\({}_{\rm m1}\) = g\({}_{\rm m3}\) were varied from the values of 0.5-10 mS. As is shown in Figure 23, the measured oscillation frequency was electronically and linearly varied from 82.15 kHz to 1629 kHz. In Figures 20-23, the g\({}_{\rm m2}\) value should have been slightly adjusted to satisfy the CO as depicted in Equation (19). Figure 24 shows the relationship between the measured amplitude ratio of the quadrature output voltages V\({}_{\rm o1}\) and V\({}_{\rm o2}\) and the FO as depicted in Equation (23). Figure 25 shows the relationship between the measured phase difference of the quadrature output voltages V\({}_{\rm o1}\) and V\({}_{\rm o2}\) and the FO as depicted in Equation (24). Figure 26 shows the experimental results of the voltage gain of V\({}_{\rm o3}\) when only R\({}_{2}\) was changed while maintaining C\({}_{1}\) = C\({}_{2}\) = 0.96 nF, g\({}_{\rm m1}\) = g\({}_{\rm m2}\) = g\({}_{\rm m3}\) = 1 mS, g\({}_{\rm m2}\) = 1.05 mS and R\({}_{1}\) = R\({}_{3}\) = 1 k\(\Omega\). As is shown in Figure 26, the proposed VM fully uncoupled QSO (Figure 2b) exhibited a wide range of independent amplitude adjustable V\({}_{\rm o3}\) voltage gains. The measured operating amplitude control range could be adjusted from 1.51 to 24.05. Table 4 summarizes the performance of the first proposed isomorphic circuit. Figure 2.9 The frequency spectrum results of the VM fully uncoupled QSO at the V\({}_{\rm o2}\) output terminal. Figure 5:0 The measured waveforms of the quadrature voltage outputs V\({}_{\rm o1}\) and V\({}_{\rm o2}\) in the time domain. Figure 5:1 The experimental results of \(\rm V_{\rm o2}\) for \(\rm g_{\rm m1}=\rm g_{\rm m3}\). Figure 5:2 The measured amplitude ratio of the quadrature output voltages \(\rm V_{\rm o1}\) and \(\rm V_{\rm o2}\) versus the tuning FO.