## 3 Simulation and Experimental Measurements
### Second Proposed Isomorphic Circuit Simulation and Experimental Results  
The theoretical, simulated and measured NBPF responses of the VBP5 and VBP6 (Figure 3a) are shown in Figures 27 and 28, respectively, as depicted in Equations (26) and (27). In Figure 27, the NBPF voltage gain at the voltage output of VBP5 could be adjusted independently by gm2 without affecting the parameters f0 and Q as depicted in Equations (28)-(30). In Figure 28, the wide range of the independent amplitude adjustable NBPF voltage gain at the voltage output of VBP6 could also be independently adjusted by R5 without affecting the NBPF parameters f0 and Q as depicted in Equations (28), (29) and (31). The component values used in Figure 27 were C3 = C4 = 0.96 nF, gm1 = gm3 = 1 mS and R4 = R5 = R6 = 1 k\(\Omega\) for the theoretical value of f0 = 165.8 kHz, and only gm2 changed, with different values of 1, 1.5, 2 and 3 mS. This resulted in an NBPF at a voltage output of VBP5 with voltage gains of 0, 3.52, 6.02 and 9.54 dB. Figure 29 shows the measurement results of the VBP5 gain response. The component values used in Figure 28 were C3 = C4 = 0.96 nF, gm1 = gm2 = gm3 = 1 mS and R4 = R6 = 1 k\(\Omega\) for a theoretical value of f0 = 165.8 kHz, and only R5 changed, with different values of 1, 4, 11 and 19 k\(\Omega\). This resulted in an NBPF at a voltage output of VBP6 with voltage gains of 6.12, 13.9, 21.3 and 25.52 dB. Figure 30 shows the measurement results of the VBP6 gain response. To display the independent electronically adjusted passband gains from Figure 3a, the value of gm2 was changed from 1 mS to 4 mS, and the NBPF voltage gain at the voltage output of VBP5 could be changed from 0 dB to 12.04 dB. As is shown in Figure 31, the proposed NBPF from Figure 3a exhibited independent electronic adjustment of the passband gains at a voltage output of VBP5. To display the maximum operating passband gains from Figure 3a, the value of R5 was changed from 1 k\(\Omega\) to 25 k\(\Omega\), and the NBPF voltage gain at the voltage output of VBP6 could be changed from 6.02 dB to 28.3 dB. As is shown in Figure 32, the proposed NBPF from Figure 3a exhibited a wide range of independent amplitude adjustable passbands at the voltage output of VBP6. Figure 33 shows the theoretical, simulated and measured NBPF responses on the VBP5 output terminal with different values of R4 when C3 = C4 = 0.96 nF, R5 = R6 = 1 k\(\Omega\) and gm1 = gm2 = gm3 = 1 mS. Figure 34 shows the measurement results of the VBP5 gain response with different Q values. In this case, the four values of R4 were changed to 1, 1.5, 2 and 3 k\(\Omega\), and the measured values of Q were 1.14, 1.59, 2.06 and 2.98, respectively. As is shown in Figures 33 and 34, the Q parameter of the NBPF could be independently controlled by adjusting the different values of R4 without affecting the parameters of f0, as depicted in Equations (28) and (29). For the experimental test, Figure 35 shows the input and output voltage waveforms of the NBPF response at the VBP5 output terminal, which could be extended to an amplitude of 120 mVpp without signification distortion. As shown in Figure 35, the input voltage waveform was a 165.8-kHz sinusoidal waveform, and the output voltage waveform was measured as a 165.8-kHz sinusoidal waveform with a phase difference of 0.57\({}^{\circ}\). Figure 36 shows the frequency spectrum of the NBPF response at the VBP5 output terminal. The NBPF response center frequency measured at the output of VBP5 was 165.8 kHz. The THD, including the fundamental harmonic through the sixth harmonic components of Figure 36, was about 1.12%. Figure 37 shows the THD result of the NBPF response at the VBP5 output terminal with different input voltages while keeping a constant center frequency of 165.8 kHz. Figure 38 shows the spectrum of the NBPF at the output of VBP5, which was obtained by applying two-tone signals f1 and f2 around the theoretical value of f0 = 165.8 kHz for IMD characterization.