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Table 1 Port admittance matrix descriptions of VCVS and CCCS [12]

From: Active filter synthesis based on nodal admittance matrix expansion

  Type I Type II Type III Type IV
VCVS A = A v
=N/D
\( \left[\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill {\infty}_1\hfill & \hfill -{\infty}_1\hfill \\ {}\hfill - N\hfill & \hfill 0\hfill & \hfill D\hfill \end{array}\right] \) \( \left[\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill {\infty}_1\hfill & \hfill 0\hfill & \hfill -{\infty}_1\hfill \\ {}\hfill 0\hfill & \hfill - D\hfill & \hfill N\hfill \end{array}\right] \) \( \left[\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill {\infty}_1\hfill \\ {}\hfill - N\hfill & \hfill - D\hfill & \hfill Q\hfill \end{array}\right] \) \( \left[\begin{array}{cccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill {\infty}_1\hfill & \hfill -{\infty}_1\hfill \\ {}\hfill -{N}_1\hfill & \hfill -{D}_1\hfill & \hfill {p}_1\hfill & \hfill 0\hfill \\ {}\hfill -{N}_2\hfill & \hfill -{D}_2\hfill & \hfill 0\hfill & \hfill {P}_2\hfill \end{array}\right] \)
CCCS A = A i
=N/D
\( \left[\begin{array}{ccc}\hfill {\infty}_1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill - N\hfill \\ {}\hfill -{\infty}_1\hfill & \hfill 0\hfill & \hfill D\hfill \end{array}\right] \) \( \left[\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill - D\hfill \\ {}\hfill {\infty}_1\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill -{\infty}_1\hfill & \hfill 0\hfill & \hfill N\hfill \end{array}\right] \) \( \left[\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill - D\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill - N\hfill \\ {}\hfill {\infty}_1\hfill & \hfill 0\hfill & \hfill Q\hfill \end{array}\right] \) \( \left[\begin{array}{cccc}\hfill 0\hfill & \hfill 0\hfill & \hfill -{D}_1\hfill & \hfill -{D}_2\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill -{N}_1\hfill & \hfill -{N}_2\hfill \\ {}\hfill {\infty}_1\hfill & \hfill 0\hfill & \hfill {P}_1\hfill & \hfill 0\hfill \\ {}\hfill -{\infty}_1\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill {P}_2\hfill \end{array}\right] \)
A N/D N/D -N/D \( \frac{N_1{P}_2-{N}_2{P}_1}{D_2{P}_1-{D}_1{P}_2} \)