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 | \( \frac{N_1{P}_2-{N}_2{P}_1}{D_2{P}_1-{D}_1{P}_2} \) |