## 2 Proposed Circuits  
### Voltage-Mode Multifunction Biquadratic Filter  
The CFOA is a four-terminal analog building block shown symbolically in Figure 1[11], with a describing matrix equation of the following form:  
\[\left[ \begin{array}{c}\mathrm{I}_{\mathrm{Y}}\\ \mathrm{V}_{\mathrm{X}}\\ \mathrm{I}_{\mathrm{Z}}\\ \mathrm{V}_{\mathrm{O}}\end{array} \right]=\left[ \begin{array}{cccc}0&0&0&0\\ 1&0&0&0\\ 0&1&0&0\\ 0&0&1&0\end{array} \right]\left[ \begin{array}{c}\mathrm{V}_{\mathrm{Y}}\\ \mathrm{I}_{\mathrm{X}}\\ \mathrm{V}_{\mathrm{Z}}\\ \mathrm{I}_{\mathrm{O}}\end{array} \right] \tag{1}\]  
The CFOA is realized by the cascaded connection of a CCII+ followed by a VB, as shown in Figure 2[11; 12]. It gathers the advantages of the CCII+ and VB such as--high input impedance (Y terminal), low input impedance (X terminal), low output impedance (O terminal), high output impedance (Z terminal), high accuracy, and large bandwidth. The voltage at terminal X follows the voltage at terminal Y in magnitude. The output current at terminal Z follows the current at terminal X in magnitude. The voltage drop at terminal Z will be send to terminal O with the unity voltage gain. The proposed high-input impedance voltage-mode CFOA-based biquadratic filter with two inputs and three outputs is shown in Figure 3, which consists of three CFOAs, two grounded capacitors, and three resistors. The use of the grounded capacitors is particularly attractive for integrated circuit (IC) implementation. In Figure 3, the input voltage signal is connected directly to the Y-terminal of the CFOA and the input current to the Y-terminal of the CFOA is zero, the circuit has the feature of high-input impedance. Routine analysis of the filter in Figure 3 gives the following three output voltages:  
\[\mathrm{V}_{\mathrm{o1}}=\frac{\mathrm{V}_{\mathrm{i1}}-\mathrm{sC}_{\mathrm{ 2}}\mathrm{R}_{\mathrm{2}}\mathrm{V}_{\mathrm{i2}}}{\mathrm{s}^{\mathrm{2}} \mathrm{C}_{\mathrm{1}}\mathrm{C}_{\mathrm{2}}\mathrm{R}_{\mathrm{2}}\mathrm{ R}_{\mathrm{3}}+\mathrm{sC}_{\mathrm{1}}\mathrm{R}_{\mathrm{1}}+1} \tag{2}\]  
\[\mathrm{V}_{\mathrm{o2}}=\frac{\mathrm{sC}_{\mathrm{1}}\mathrm{R}_{\mathrm{3}} \mathrm{V}_{\mathrm{i1}}+(\mathrm{sC}_{\mathrm{1}}\mathrm{R}_{\mathrm{1}}+1) \mathrm{V}_{\mathrm{i2}}}{\mathrm{s}^{\mathrm{2}}\mathrm{C}_{\mathrm{1}} \mathrm{C}_{\mathrm{2}}\mathrm{R}_{\mathrm{2}}\mathrm{R}_{\mathrm{3}}+\mathrm{ sC}_{\mathrm{1}}\mathrm{R}_{\mathrm{1}}+1} \tag{3}\]  
\[\mathrm{V}_{\mathrm{o3}}=\frac{(\mathrm{s}^{\mathrm{2}}\mathrm{C}_{\mathrm{1}} \mathrm{C}_{\mathrm{2}}\mathrm{R}_{\mathrm{2}}\mathrm{R}_{\mathrm{3}}+1) \mathrm{V}_{\mathrm{i1}}+\mathrm{s}^{\mathrm{2}}\mathrm{C}_{\mathrm{1}} \mathrm{C}_{\mathrm{2}}\mathrm{R}_{\mathrm{1}}\mathrm{R}_{\mathrm{2}}\mathrm{ V}_{\mathrm{i2}}}{\mathrm{s}^{\mathrm{2}}\mathrm{C}_{\mathrm{1}}\mathrm{C}_{\mathrm{2}} \mathrm{R}_{\mathrm{2}}\mathrm{R}_{\mathrm{3}}+\mathrm{sC}_{\mathrm{1}}\mathrm{ R}_{\mathrm{1}}+1} \tag{4}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Parameter** & **(i)** & **(ii)** & **(iii)** & **(iv)** & **(v)** & **(vi)** & **(vii)** \\ \hline Reference [26] & yes & no & no & yes & yes & yes & no \\ Reference [27] & no & no & yes & yes & yes & yes & no \\ Reference [28] & no & yes & yes & yes & yes & yes & no \\ Reference [29] & no & no & yes & no & no & yes & no \\ Proposed & yes & yes & yes & yes & yes & yes & yes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the proposed circuit with previously CFOA-based multifunction biquadratic filters in the literature [26; 27; 28; 29]. Figure 1: Schematic symbol of CFOA.