## 2 Description of the Proposed Method
For the circuit in Figure 3a, moving the injected voltage source equivalent circuit to node V\({}_{\text{in4}}\) with nodes V\({}_{\text{in1}}\), V\({}_{\text{in2}}\), V\({}_{\text{in3}}\), V\({}_{\text{in}}\) and V\({}_{\text{in6}}\) as grounded nodes, we can obtain the filter represented by (18). grounded. Another notch function at \(\mathrm{V_{out1}}\) can be also obtained by injecting the input voltage source to the merged node of \(\mathrm{V_{in2}}\) and \(\mathrm{V_{in6}}\) in Figure 3a with nodes \(\mathrm{V_{in1}}\), \(\mathrm{V_{in3}}\), \(\mathrm{V_{in4}}\) and \(\mathrm{V_{in5}}\) being grounded. \[ \begin{bmatrix}1&0&0&0&0&0&0\\ \multicolumn{1}{c}{\multicolumn{1}{c}{\(\infty_{1}\)}}&\multicolumn{1}{c}{\(\infty_{1}\)} &0&0&0&0&0\\ 0&\multicolumn{1}{c}{\(-\infty_{2}\)} &\mathrm{G_{1}}+\infty_{2}&\multicolumn{1}{c}{\(-\infty_{3}\)} &\multicolumn{1}{c}{\(-\infty_{2}\)} &\multicolumn{1}{c}{\(\infty_{3}\)} &0\\ 0&\multicolumn{1}{c}{\(-\infty_{4}\)} &\multicolumn{1}{c}{\(\infty_{4}\)} &\multicolumn{1}{c}{\(\mathrm{SC_{2}}\)} &0&0&\multicolumn{1}{c}{\(-\infty_{4}\)} \\ 0&\multicolumn{1}{c}{\(\infty_{2}\)} &\multicolumn{1}{c}{\(-\infty_{2}\)} &0&\multicolumn{1}{c}{\(\mathrm{SC_{1}}+\infty_{2}\)} &0&0\\ 0&0&0&\multicolumn{1}{c}{\(-\infty_{3}\)} &0&\mathrm{G_{2}}+\infty_{3}&0\\ 0&\multicolumn{1}{c}{\(\infty_{4}\)} &\multicolumn{1}{c}{\(-\infty_{4}\)} &0&0&0&\mathrm{G_{3}}+\infty_{4}\end{bmatrix}  \tag{21}\]  
Applying the input voltage source to terminal-\(\mathrm{Y_{2}}\) of DDCC(1), terminal-\(\mathrm{Y_{2}}\) of DDCC(2) and terminal-\(\mathrm{Y_{2}}\) of DDCC(3), terms \(-\mathrm{SC_{1}}+\mathrm{G_{2}}\) and \(-\mathrm{G_{3}}\) will be created in positions (2, 1) and (3, 1) of (12), respectively, then an allpass function at \(\mathrm{V_{out1}}\) (with \(\mathrm{G_{2}}=\mathrm{G_{1}}\)) can be achieved. This operation corresponds to the insertion of the terms \(\pm\infty_{2}\), \(\infty_{3}\) and \(\pm\infty_{4}\) to the second column of (14) as shown in (22). In Figure 3a, moving the injected voltage source to the merged node of \(\mathrm{V_{in1}}\), \(\mathrm{V_{in3}}\) and \(\mathrm{V_{in5}}\) with nodes \(\mathrm{V_{in2}}\), \(\mathrm{V_{in4}}\) and \(\mathrm{V_{in6}}\) being grounded, we can obtain the filter represented by (22). Another allpass function at \(\mathrm{V_{out1}}\) can be also obtained by injecting the input voltage source to the merged node of \(\mathrm{V_{in2}}\), \(\mathrm{V_{in4}}\) and \(\mathrm{V_{in6}}\) in Figure 3a with nodes \(\mathrm{V_{in1}}\), \(\mathrm{V_{in3}}\), and \(\mathrm{V_{in5}}\) being grounded. \[ \begin{bmatrix}1&0&0&0&0&0\\ \multicolumn{1}{c}{\multicolumn{1}{c}{\(\infty_{1}\)}}&\multicolumn{1}{c}{\(\infty_{1}\)} &0&0&0&0&0\\ 0&\multicolumn{1}{c}{\multicolumn{1}{c}{\(-\infty_{2}+\infty_{3}\)}} &\mathrm{G_{1}}+\infty_{2}&\multicolumn{1}{c}{\(-\infty_{3}\)} &\multicolumn{1}{c}{\(-\infty_{2}\)} &\multicolumn{1}{c}{\(\infty_{3}\)} &0\\ 0&\multicolumn{1}{c}{\multicolumn{1}{c}{\(-\infty_{4}\)}} &\multicolumn{1}{c}{\(\infty_{4}\)} &\multicolumn{1}{c}{\(\mathrm{SC_{2}}\)} &0&0&\multicolumn{1}{c}{\(-\infty_{4}\)} \\ 0&\multicolumn{1}{c}{\(\infty_{2}\)} &\multicolumn{1}{c}{\(-\infty_{2}\)} &0&\multicolumn{1}{c}{\(\mathrm{SC_{1}}+\infty_{2}\)} &0&0\\ 0&\multicolumn{1}{c}{\(\infty_{3}\)} &0&\multicolumn{1}{c}{\(-\infty_{3}\)} &0&\mathrm{G_{2}}+\infty_{3}&0\\ 0&\multicolumn{1}{c}{\(\infty_{4}\)} &\multicolumn{1}{c}{\(-\infty_{4}\)} &0&0&0&\mathrm{G_{3}}+\infty_{4}\end{bmatrix}  \tag{22}\]  
In the same way, the synthesized procedure can be applied to the matrices for cases 2-8 in Table 1. Four equivalent circuits of the derived filters for cases 1-4 of derived type-A filters in Table 1 are shown in Figure 3. The output transfer functions of the synthesized circuits for case 1 are given by (23) and (24). Besides, four equivalent circuits of the synthesized filters for cases 5-8 of derived type-A filters in Table 1 are shown in Figure 4. The output transfer functions of the synthesized circuits for case 5 are given by (25) and (26).