## 2 Circuit Description
### Proposed Current-Mode Analog Filter  
The proposed current-mode analog filter, implemented using CDTAs, is shown in Figure 4. The circuit comprises two CDTAs and two grounded capacitors. The inclusion of grounded capacitors simplifies the compensation of parasitic passive components in the circuit.  
When \(I_{1}\) to \(I_{4}\) serve as the input terminals and \(I_{01}\) to \(I_{06}\) as the output terminals, the current outputs of Figure 4 can be derived using the CDTA characteristics given in Equation (1) and nodal analysis as follows:  
\[I_{01}=\frac{s^{2}C_{1}C_{2}I_{1}-(sC_{2}g_{ml}+g_{m1}g_{m2})I_{2}-sC_{1}g_{m2 }I_{3}-sC_{1}g_{m2}I_{4}}{s^{2}C_{1}C_{2}+sC_{2}g_{m1}+g_{m1}g_{m2}} \tag{11}\]  
Figure 4: Proposed current-mode analog filter using CDTAs.  
\[I_{o2}=\frac{sC_{2}g_{m1}I_{1}+sC_{2}g_{m1}I_{2}-g_{m1}g_{m2}I_{3}-g_{m1}g_{m2}I_{4}} {s^{2}C_{1}C_{2}+sC_{2}g_{m1}+s_{m1}g_{m2}} \tag{12}\]  
\[I_{o3}=\frac{sC_{2}g_{m1}I_{1}+sC_{2}g_{m1}I_{2}+\left(s^{2}C_{1}C_{2}I_{1}+sC_{ 2}g_{m2}\right)I_{3}-g_{m1}g_{m2}I_{4}}{s^{2}C_{1}C_{2}+sC_{2}g_{m1}+g_{m1}g_{m2}} \tag{13}\]  
\[I_{o4}=\frac{\left\{-g_{m1}g_{m2}I_{1}-g_{m1}g_{m2}I_{2}-\left(sC_{1}g_{m2}+g_{ m1}g_{m2}\right)I_{3}\right\}}{-(sC_{1}g_{m2}+g_{m1}g_{m2})I_{4}}\right\} \tag{14}\]  
\[I_{o5}=\frac{-sC_{2}g_{m1}I_{1}-sC_{2}g_{m1}I_{2}+g_{m1}g_{m2}I_{3}+g_{m1}g_{m2 }I_{4}}{s^{2}C_{1}C_{2}+sC_{2}g_{m1}+g_{m1}g_{m2}} \tag{15}\]  
\[I_{o6}=\frac{\left\{g_{m1}g_{m2}I_{1}+g_{m1}g_{m2}I_{2}+(sC_{1}g_{m2}+g_{m1}g_{ m2})I_{3}\right\}}{+(sC_{1}g_{m2}+g_{m1}g_{m2})I_{4}} \tag{16}\]  
Here, \(g_{m1}\) and \(g_{m2}\) refer to the transconductance of the first and second CDTA blocks employed in the proposed filter architecture.  
Table 1 demonstrates that five standard filtering functions, LPF, HPF, BPF, BSF, and APF, can be realized using a single topology, providing a total of 19 transfer functions. These filtering functions are achieved with a single input signal, eliminating the need for multiple input signals that would require additional components, such as a multiple-input current mirror. Furthermore, the output signals can be directly connected without the need for buffer circuits. As a result, the proposed current-mode analog filter can efficiently realize all five standard filtering functions without requiring any extra circuitry. To implement these filtering functions, inverting-type input signals are not required, thereby eliminating the need for additional inverting current amplifiers. The output terminals \(I_{o1}\), \(I_{o2}\), \(I_{o3}\), \(I_{o4}\), \(I_{o5}\), and \(I_{o6}\) exhibit high impedance, allowing them to be directly connected to the next stage without the need for buffer circuits.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Filtering Function**} & \multicolumn{1}{c}{**Output**} & \multicolumn{1}{c}{**Input**} & \multicolumn{1}{c}{**Transfer Functions**} \\ \hline \multirow{8}{*}{LPF} & \multirow{2}{*}{Non-inverting} & \(I_{o5}\) & \(I_{4}\) & \(g_{m1}g_{m2}/D(s)\) \\ \cline{3-5}  & & \(I_{66}\) & \(I_{1}\) or \(I_{2}\) & \(g_{m1}g_{m2}/D(s)\) \\ \cline{3-5}  & & \(I_{o1}+I_{o6}\) & \(I_{3}\) & \(g_{m1}g_{  
The parameters \(\omega_{o}\) and \(Q\) can be expressed, respectively, as follows:  
\[\omega_{o}=\sqrt{\frac{g_{m1}g_{m2}}{C_{1}C_{2}}} \tag{17}\]  
\[Q=\sqrt{\frac{g_{m2}C_{1}}{g_{m1}C_{2}}} \tag{18}\]  
It is evident from Equations (17) and (18) that the parameter \(\omega_{o}\) can be controlled by adjusting the transconductance \(g_{m}\) (where \(g_{m}=g_{m1}=g_{m2}\)), while the parameter \(Q\) can be adjusted by the ratio \(C_{1}/C_{2}\).