## 2 Proposed Electronically Tunable VM OTA-C Biquad
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Features** & [25] & [26] & [27] & [28] & [29] & [30] & **Proposed** \\ \hline Power supply & \(\pm 15\) V & \(\pm 5\) V & \(\pm 15\) V & \(\pm 15\) V & \(\pm 15\) V & \(\pm 15\) V & \(\pm 15\) V \\ Verification of & yes/yes & yes/yes & yes/yes & yes/yes & yes/yes & yes/yes & yes/yes \\ simulation/measurement & & & & & & & & \\ Simulated the power & & & & & & & \\ dissipation (W) & none & none & none & none & 0.86 & 0.92 & 0.92 \\ Measured the power & & & & & & & & \\ dissipation (W) & & none & none & 0.86 & 1.2 & 1.23 & 0.96 \\ Central frequency of the filter (kHz) & 10 & 32.9 & 238.7 & 159.15 & 217 & 144.7 & 144.7 \\ Maximum output noise (\(\mathrm{nV}/\sqrt{\mathrm{Hz}}\)) & none & none & none & none & none & none & 7.937 \\ Measured the output P1 dB & & & & & & & \\ point (dBm) & none & none & \(-9.2\) & none & \(-5.9\) & \(-7\) \\ Measured the TQI point (dBm) & none & none & \(-5.66\) & none & \(-2.597\) & \(5.136\) \\ Measured the IMD3 (dBc) & none & & & \(-30.03\) (@ & \(-42.35\) (@ & \(-31.16\) (@ & \(-48.67\) @ & \(-50.83\) (@ \\  & & & & & & & \\  & & & & & & & \\ FoM (\(\times 10^{3}\)) & none & none & none & none & none & 268.75 \\ \hline \hline \end{tabular} Note: P1 dB: 1 dB power gain compression; TOI: third-order intercept; IMD3: third-order intermodulation distortion; FoM: figure-of-merit.  
\end{table} 
Table 2: Characteristic comparisons of the proposed biquad with the biquads previously reported in the literature [25; 26; 27; 28; 29; 30]. with four inputs and three outputs. It is configured by only one DO-OTA, three OTAs, and two grounded capacitors. Routine analysis of the proposed electronically controllable OTA-C biquad in Figure 2 yielded the following three-output voltage signals. \[\mathrm{V_{o1}}=\frac{1}{\mathrm{D(s)}}\big{[}\mathrm{g_{m1}}\mathrm{g_{m2}} \mathrm{g_{m3}}\mathrm{V_{i1}}+\mathrm{g_{m1}}\mathrm{g_{m3}}\mathrm{g_{m4}} \mathrm{(V_{i2}-V_{i4})}+\mathrm{sC_{2}}\mathrm{g_{m1}}\mathrm{g_{m3}}\mathrm{ V_{i3}}\big{]} \tag{1}\]  
\[\mathrm{V_{o2}}=\frac{1}{\mathrm{D(s)}}\big{[}-\mathrm{sC_{1}}\mathrm{g_{m1}} \mathrm{g_{m2}}\mathrm{V_{i1}}-\mathrm{sC_{1}}\mathrm{g_{m1}}\mathrm{g_{m4}} \mathrm{(V_{i2}-V_{i4})} \tag{2}\]  
\[\mathrm{V_{o3}}=\frac{1}{\mathrm{D(s)}}\big{[}(\mathrm{s}^{\,2}\mathrm{C_{1}} \mathrm{C_{2}}\mathrm{g_{m1}}+\mathrm{g_{m1}}\mathrm{g_{m2}}\mathrm{g_{m3}}) \mathrm{V_{i1}}-\mathrm{sC_{1}}\mathrm{g_{m3}}\mathrm{g_{m4}}\mathrm{(V_{i2}- V_{i4})} \tag{3}\]  
where the denominator D(s) is:  
\[\mathrm{D(s)}=\mathrm{s}^{2}\mathrm{C_{1}}\mathrm{C_{2}}\mathrm{g_{m1}}+ \mathrm{sC_{1}}\mathrm{g_{m2}}\mathrm{g_{m3}}+\mathrm{g_{m1}}\mathrm{g_{m2}} \mathrm{g_{m3}} \tag{4}\]  
From Equations (1)-(4), the VM transfer functions can be obtained according to input and output conditions as follows:  
Part I: If only \(\mathrm{V_{i1}}\) is applied to the input voltage signal, \(\mathrm{V_{in}}\), the output voltage functions \(\mathrm{V_{o1}}\), \(\mathrm{V_{o2}}\), and \(\mathrm{V_{o3}}\) can be simultaneously obtained, as shown in Equations (5)-(7):  
\[\frac{\mathrm{V_{o1}}}{\mathrm{V_{in}}}=\frac{\mathrm{g_{m1}}\mathrm{g_{m2}} \mathrm{g_{m3}}}{\mathrm{D(s)}} \tag{5}\]  
\[\frac{\mathrm{V_{o2}}}{\mathrm{V_{in}}}=\frac{-\mathrm{sC_{1}}\mathrm{g_{m1}} \mathrm{g_{m2}}}{\mathrm{D(s)}} \tag{6}\]  
\[\frac{\mathrm{V_{o3}}}{\mathrm{V_{in}}}=\frac{\mathrm{s}^{2}\mathrm{C_{1}} \mathrm{C_{2}}\mathrm{g_{m1}}+\mathrm{g_{m1}}\mathrm{g_{m2}}\mathrm{g_{m3}}}{ \mathrm{D(s)}} \tag{7}\]  
Figure 1: Symbol of the OTA. (**a**) Single-ended output OTA and (**b**) DO-OTA. Figure 2: Proposed VM OTA-C biquad. Equations (5)-(7) show that the LPF, IBPF, and BRF signals can be simultaneously implemented. Part II: According to Equation (3), the proposed biquad can realize six different generic filtering signals.