## 3 Simulation and Experimental Measurements
### First Proposed Isomorphic Circuit Simulation and Experimental Results  
The theoretical, simulated and measured NBPF responses of \(\mathrm{V_{BP2}}\) and \(\mathrm{V_{BP3}}\) (Figure 2a) are shown in Figures 6 and 7, respectively, as depicted in Equations (11) and (12). In Figure 6, the NBPF voltage gain at the voltage output of \(\mathrm{V_{BP2}}\) could be adjusted independently by \(\mathrm{g_{m2}}\) without affecting parameters \(\mathrm{f_{o}}\) and \(\mathrm{Q}\), as depicted in Equations (13)-(15). In Figure 7, the wide range of independent amplitude adjustable NBPF voltage gain at the voltage output of \(\mathrm{V_{BP3}}\) could also be independently adjusted by \(\mathrm{R_{2}}\) without affecting the NBPF parameters \(\mathrm{f_{o}}\) and \(\mathrm{Q}\), as depicted in Equations (13), (14) and (16). The component values used in Figure 6 were \(\mathrm{C_{1}}=\mathrm{C_{2}}=0.96\) nF, \(\mathrm{g_{m1}}=\mathrm{g_{m3}}=1\) ms and \(\mathrm{R_{1}}=\mathrm{R_{2}}=\mathrm{R_{3}}=1\) k\(\Omega\)  
Figure 4: The (**a**) top view and (**b**) bottom view of the measured prototype from Figure 2.  
Figure 5: The (**a**) top view and (**b**) bottom view of the measured prototype from Figure 3.  
for the theoretical value of \(f_{0}\) = 165.8 kHz, and only \(g_{m2}\) changed, with different values of 1, 1.5, 2 and 3 mS. This resulted in an NBPF at a voltage output of \(V_{\text{BP2}}\) with voltage gains of 0, 3.52, 6.02 and 9.54 dB. Figure 8 shows the measurement results of the \(V_{\text{BP2}}\) gain response. The component values used in Figure 7 were C1 = C2 = 0.96 nF, \(g_{m1}\) = \(g_{m2}\) = \(g_{m3}\) = 1 mS and R1 = R3 = 1 k\(\Omega\) for a theoretical value of \(f_{0}\) = 165.8 kHz, and only R2 changed, with different values of 1, 4, 11 and 19 k\(\Omega\). This resulted in an NBPF at a voltage output of \(V_{\text{BP3}}\) with voltage gains of 6.02, 13.98, 21.58 and 26 dB. Figure 9 shows the measurement results of the \(V_{\text{BP3}}\) gain response. To display the independent electronically adjusted passband gains from Figure 2a, the value of \(g_{m2}\) was changed from 1 mS to 4 mS, and the NBPF voltage gain at the voltage output of \(V_{\text{BP2}}\) could be changed from 0 dB to 12.04 dB. As shown in Figure 10, the proposed NBPF in Figure 2a exhibited independent electronic adjustment of passband gains at the voltage output of \(V_{\text{BP2}}\). To display the maximum operating passband gains of Figure 2a, the value of R2 was changed from 1 k\(\Omega\) to 25 k\(\Omega\), and the NBPF voltage gain at the voltage output of \(V_{\text{BP3}}\) could be changed from 6.02 dB to 28.3 dB. As is shown in Figure 11, the proposed NBPF from Figure 2a exhibited a wide range of independent amplitude adjustable passbands at a voltage output of \(V_{\text{BP3}}\). Figure 12 shows the theoretical, simulated and measured NBPF responses on the \(V_{\text{BP2}}\) output terminal with different values of R1 when C1 = C2 = 0.96 nF, R2 = R3 = 1 k\(\Omega\) and \(g_{m1}\) = \(g_{m2}\) = \(g_{m3}\) = 1 mS. Figure 13 shows the measurement results of the \(V_{\text{BP2}}\) gain response with different Q values. In this case, the four values of R1 were changed to 1, 1.5, 2 and 3 k\(\Omega\), and the measured values of Q were 1.17, 1.53, 2.08 and 3. As shown in Figures 12 and 13, the Q parameter of the NBPF could be independently controlled by adjusting the different values of R1 without affecting the parameters of \(f_{0}\), as depicted in Equations (13) and (14). For an experimental test, Figure 14 shows the input and output voltage waveforms of the NBPF response at the \(V_{\text{BP2}}\) output terminal, which could be extended to an amplitude of 120 mVpp without signification distortion. As shown in Figure 14, the input voltage waveform was a 165.8-kHz sinusoidal waveform, and the output voltage waveform was measured to be a 161.7-kHz sinusoidal waveform with a phase difference of 0.23\({}^{\circ}\).