# High-Input Impedance Voltage-Mode Multifunction Filter
## 2 Proposed Circuit  
The circuit symbol of CFA is shown in Figure 1. Using standard notation, \(\rm I_{Y}=0\), \(\rm V_{X}=V_{Y}\), \(\rm I_{Z}=I_{X}\), and \(\rm V_{W}=V_{Z}\) can be used to characterize the port relationship of CFA [18]. Port Y has high-input impedance, and port X has low-input impedance. The input voltage of the X port follows the high-input impedance voltage of the Y port. Port Z has high-output impedance and the output current sinks the input port X current. Port W has low-output impedance and the output voltage follows the port Z voltage. The circuit symbol of AD844 is shown in Figure 1. The port relationship of AD844 can be characterized by I+ = 0, \(\rm V-=V+\), \(\rm I_{Tz}=I-\), and \(\rm V_{W}=V_{Tz}\)[24]. The positive port has high-input impedance and the negative port has low-input impedance. The negative-port input voltage (V\(-\)) follows the high-input impedance voltage (V+) of the positive port. Port Tz has high-output impedance and the output current (\(\rm I_{Tz}\)) sinks the negative-port input current (I\(-\)). Port W has low-output impedance and the output voltage (\(\rm V_{W}\)) follows the port Tz voltage (\(\rm V_{Tz}\)). Hence, the characteristics of CFA are exactly equivalent to commercial AD844 IC. The proposed high-input impedance single-input triple-output VM multifunction biquad filter is shown in Figure 2. Figure 3 shows a practical implementation of CFA using AD844 IC. As shown in Figures 2 and 3, the input voltage signal is applied to the high-input impedance Y or plus ports. Hence, the proposed circuit has a high-input impedance and  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Reference**} & **Number** & **Number** & **Ranking Filter** & \multirow{2}{*}{**All-Greard**} & \multirow{2}{*}{**No-Capplier**} & \multirow{2}{*}{**Orthogonal**} & \multirow{2}{*}{**No-Neel**} & \multirow{2}{*}{**High-Input**} & \multirow{2}{*}{**Central**} & \multirow{2}{*}{**Low**} & \multirow{2}{*}{**Low**} & \multirow{2}{*}{**S-Other**} \\  & **Class** & **of SEC** & & & & & & & & & & \\  & **Used** & **Used** & **Used** & & & & & & & & \\  & & & & & & & & & & & & \\ \hline
[8] & 2 & 4/2 & \multirow{2}{*}{no} & \multirow{2}{*}{no} & \multirow{2}{*}{yes} & \multirow{2}{*}{yes} & \multirow{2}{*}{no} & \multirow{2}{*}{yes} & \multirow{2}{*}{no} & 884 \(\pm\) & \multirow{2}{*}{none} & \multirow{2}{*}{none} \\
[9] & 2 & 2/2 & \multirow{2}{*}{no} & \multirow{2}{*}{no} & \multirow{2}{*}{yes} & \multirow  
can be easily cascaded to VM circuits. A routine analysis of Figure 2 gives the following three voltage transfer functions.  
\[\frac{\mathrm{V_{o1}}}{\mathrm{V_{in}}}=\frac{1}{\mathrm{s^{2}C_{1}C_{2}R_{3}+sC _{1}R_{1}+1}} \tag{1}\]  
\[\frac{\mathrm{V_{o2}}}{\mathrm{V_{in}}}=\frac{-sC_{1}R_{2}}{\mathrm{s^{2}C_{1}C _{2}R_{2}R_{3}+sC_{1}R_{1}+1}} \tag{2}\]  
\[\frac{\mathrm{V_{o3}}}{\mathrm{V_{in}}}=\frac{\mathrm{s^{2}C_{1}C_{2}R_{1}R_{2 }+1}}{\mathrm{s^{2}C_{1}C_{2}R_{2}R_{3}+sC_{1}R_{1}+1}} \tag{3}\]  
It can be seen from Equations (1) to (3) that \(\mathrm{V_{o1}}\) can obtain an NLP voltage response, \(\mathrm{V_{o2}}\) can obtain an IBP voltage response, and \(\mathrm{V_{o3}}\) can obtain an NBS voltage response. Hence, the proposed circuit can realize NLP, IBP, and NBS voltage responses simultaneously. The \(\omega_{\mathrm{o}}\) and Q of the filter can be obtained by the following equations:  
\[\omega_{\mathrm{o}}=\sqrt{\frac{1}{C_{1}C_{2}R_{2}R_{3}}} \tag{4}\]  
\[\mathrm{Q}=\frac{1}{R_{1}}\sqrt{\frac{C_{2}R_{2}R_{3}}{C_{1}}} \tag{5}\]  
Hence, the filter parameters of \(\omega_{\mathrm{o}}\) and Q offers orthogonal controllability.  
Figure 1: The circuit symbol. (**a**) Current-feedback amplifier (CFA) and (**b**) AD844.  
Figure 2: Proposed CFA-based voltage-mode (VM) multifunction biquad filter.