## 3 Simulation and Experimental Measurements
### First Proposed Isomorphic Circuit Simulation and Experimental Results
To evaluate the performance of the proposed isomorphic circuit, the total harmonic distortion (THD) and the intermodulation distortion (IMD) of the isomorphic circuit were measured. The THD is defined as the ratio of the sum of the powers of all harmonic components (except the fundamental frequency) to the power of fundamental frequency. The IMD is defined as the two-tone test signals of different frequencies mixed together to form an additional signal at the excitation frequency. The THD and IMD can be expressed as follows [26; 27]:  
\[\text{THD}=\sqrt{\frac{\sum\limits_{n=2}^{\text{N}}\text{V}_{n}^{2}}{\text{V} _{1}^{2}}\times 100\%} \tag{40}\]  
where \(\text{V}_{1}\) is the fundamental frequency voltage content and \(\text{V}_{n}\) (n = 2, 3,..., N) is the nth harmonic voltage content:  
\[\text{IMD}(\text{f}_{1},\text{ f}_{2})\ =\frac{\sum\limits_{\text{k}=1}^{2}\text{p}( \text{f}_{2}-\text{k}\text{f}_{1})+\text{p}(\text{f}_{2}+\text{k}\text{f}_{1})} {\text{p}(\text{f}_{2})}\times 100\%} \tag{41}\]  
where \(\text{p}(\text{f}_{2}\pm(n-1))\text{f}_{1}\) is the root mean square value of the nth-order intermodulation component at the sum and difference of the two tones and \(\text{p}(\text{f}_{2})\) is the root mean square value of the fundamental component at the excitation frequency \(\text{f}_{2}\). Figure 15 shows the frequency spectrum of the NBPF response at the \(V_{\text{BP2}}\) output terminal. The NBPF response center frequency measured at the output of \(V_{\text{BP2}}\) was about 165.8 kHz. The THD, including the fundamental harmonic through the sixth harmonic components of Figure 15, was about 1.08%. Figure 16 shows the THD result of the NBPF response at the \(V_{\text{BP2}}\) output terminal with different input voltages by keeping a constant center frequency of 165.8 kHz. Figure 17 shows the spectrum of the NBPF at the output of V\({}_{\rm BP2}\), which was obtained by applying two-tone signals f\({}_{1}\) and f\({}_{2}\) around the theoretical value of f\({}_{0}\) = 165.8 kHz for IMD characterization. In Figure 17, the low-frequency tones of f\({}_{1}\) = 164.8 kHz and the high-frequency tones of f\({}_{2}\) = 166.8 kHz were used with an input amplitude of 63 mVpp. The measured value of the third-order IMD (IMD3) was about \(-\)40.1 dBc, and the third-order intercept (TOI) was about \(-\)7.95 dBm. Figure 18 shows the 1-dB compression point (P1 dB) of the NBPF measured at the output of V\({}_{\rm BP2}\) between the output power and the input power when the center frequency was 165.8 kHz. The measured output power P1 dB was about \(-\)11.4 dBm. Figure 19 shows the phase noise performance of the NBPF measured at the output of V\({}_{\rm BP2  
Figure 8: The measured magnitude responses of the \(\mathrm{V_{BP2}}\) when \(g_{\mathrm{m2}}\) was varied. Figure 10: The theoretical, simulated and measured results of the electronic amplitude adjustable NBPF voltage gains at the voltage output of \(\mathrm{V_{BP2}}\). Figure 9: The measured magnitude responses of the \(\mathrm{V_{BP3}}\) when \(\mathrm{R_{2}}\) was varied. Figure 11: The theoretical, simulated and measured results of the independent amplitude adjustable NBPF voltage gains at the voltage output of V\({}_{\text{BP3}}\). Figure 2.0 The Q parameters of the NBPF at the output of V\({}_{\text{BP2}}\) by varying R\({}_{1}\) while maintaining f\({}_{0}\). Figure 2.1 The measured magnitude responses of the V\({}_{\text{BP2}}\) with different Q values by varying R\({}_{1}\) while maintaining f\({}_{0}\). Figure 2.2 THD analysis results of the NBPF at the output of V\({}_{\rm BP2}\) with different input voltages. Figure 2.3 The measured time domain input and output voltage waveforms of the NBPF at the output of V\({}_{\rm BP2}\). Figure 2.4 The frequency spectrum results of the NBPF at the output of V\({}_{\rm BP2}\).