## 2 The Proposed Isomorphic Circuits  
Each of the isomorphic circuits' symbols of an LT1228 commercial IC from Linear Technology [25] is shown in Figure 1a, and its packed IC is shown Figure 1b. The LT1228 IC contains an OTA with a specially devised CFA. Figure 1c shows the equivalent circuit of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Figures 1 and** & **Figures 1 and** & **Figure 5** & **First Proposed** & **Second Proposed** \\  & **2 in [21]** & **4 in [22]** & **in [23]** & **in This Work** & **in This Work** \\ \hline Number of active devices & 5 (OTA) & 5 (OTA) & 3 (LT1228) & 3 (LT1228) & 3 (LT1228) \\ Number of passive elements & 2 (2C) & 2 (2C) & 7 (2C, 5R) & 5 (2C, 3R) & 5 (2C, 3R) \\ Orthogonal tunability of \(\omega_{\text{o}}\) and Q & yes & yes & NA & yes & yes \\ High-input and low-output & no & no & NA & yes & yes \\ impedance of the filter & & & & & \\ Independent tunability of the filter & no & no & NA & yes & yes \\ amplitude & no & yes & yes & yes & yes \\ Electronic and linear tune of & no & yes & yes & yes & yes \\ oscillation frequency & no & yes & yes & yes & yes \\ Oscillator CO and FO with fully & no & yes & yes & yes & yes \\ uncoupled electronic tuning law & no & no & yes & yes & yes \\ Oscillator’s amplitude tunability & no & no & yes & yes & yes \\ \hline \hline \end{tabular} Note: Q: quality factor; \(\omega_{\text{o}}\): resonance angular frequency; CO: condition of oscillation; FO: frequency of oscillation; and NA: not available.  
\end{table} 
Table 1: Comparison between recent electronic tunable filter/oscillator circuits. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Figure 1 in [21]** & **Figure 1 in [22]** & **First Proposed in** & **Second Proposed in** \\  & & & & **This Work** & **This Work** \\ \hline Supply voltage & \(\pm\)2 V & \(\pm\)15 V & \(\pm\)5 V & \(\pm\)5 V \\ Measured power dissipation & 0.14 W & 1.2 W & 0.22 W & 0.22 W \\ Designed center frequency & 159.16 kHz & 217 kHz & 165.8 kHz & 165.8 kHz \\ Measured maximum operating & 0 dB & 0 dB & 27.86 dB & 27.58 dB \\   voltage gain & \(-\)14.6 & NT & \(-\)11.4 & \(-\)9.77 \\ Measured output P1 dB (dBm) & \(-\)42.86 & \(-\)31.16 & \(-\)40.1 & \(-\)39.66 \\ Measured third-order intercept & & & & \\ point (dBm) & \(-\)5.47 & NT & \(-\)7.95 & \(-\)5.753 \\ Measured phase noise (dBc/Hz) & NT & NT & \(-\)83.86 & \(-\)73.87 \\ Figure of merit & NT & NT & \(3.07\times 10^{6}\) & \(3.08\times 10^{6}\) \\ \hline \hline \end{tabular} Note: P1 dB: 1-dB compression point; IMD3: third-order intermodulation distortion; and NT: not tested.  
\end{table} 
Table 2: The additional performance comparisons with previous VM filters. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Figure 2 in [21]** & **Figure 4 in [22]** & **Figure 5** & **First Proposed** & **Second Proposed** \\  & **in [23]** & **in This Work** & **in This Work** \\ \hline Supply voltage & \(\pm\)15 V & \(\pm\)15 V & \(\pm\)5 V & \(\pm\)5 V & \(\pm\)5 V \\ Measured power dissipation & NT & 1.2 W & 1.98 W & 0.22 W & 0.22 W \\ Measured total harmonic & NT & NT & \(<\)1.26 & 0.81 & 0.33 \\   distortion (\%) & NT & 150.1–2653 & 8.21–1117.51 & 82.15–1629 & 80.83–1626 \\ Measured frequency tunable & NA & NA & 1.97–15.92 & 1.51–24.05 & 1.51–24.03 \\   tunability range & & & & \(-\)40.18 (@ 30 Hz) & \(-\)34.7 (@ 30 Hz) \\ Measured phase noise (dBc/Hz) & NT & \(-\)73.23 (@ 1000 Hz) & NT & \(-\)40.18 (@ 30 Hz) & \(-\)34.7 (@ 30 Hz) \\ \hline \hline \end{tabular} Note: NA: not available; and NT: not tested.  
\end{table} 
Table 3: The additional performance comparisons with previous VM oscillators. the LT1228 IC, and the ideal port relations of LT1228 can be characterized by the following hybrid matrix [23]:  
\[\left[ \begin{array}{c}\mathrm{I}_{\mathrm{v+}}\\ \mathrm{I}_{\mathrm{v-}}\\ \mathrm{I}_{\mathrm{y}}\\ \mathrm{V}_{\mathrm{x}}\\ \mathrm{V}_{\mathrm{w}}\end{array} \right]=\left[