Editing Two-port network (section)

===Cascade connection===
[[File:two-port cascade.svg|thumb|left|'''Fig. 16.''' Two two-port networks with the first's output port connected to the second's input port]]
When two-ports are connected with the output port of the first connected to the input port of the second (a cascade connection) as shown in figure 16, the best choice of two-port parameter is the {{mvar|ABCD}}-parameters.  The {{mvar|a}}-parameters of the combined network are found by matrix multiplication of the two individual {{mvar|a}}-parameter matrices.<ref>Farago, pp. 128–134.</ref>

:<math>[\mathbf a] = [\mathbf a]_1 \cdot [\mathbf a]_2</math>

A chain of {{mvar|n}} two-ports may be combined by matrix multiplication of the {{mvar|n}} matrices.  To combine a cascade of {{mvar|b}}-parameter matrices, they are again multiplied, but the multiplication must be carried out in reverse order, so that;

:<math>[\mathbf b] = [\mathbf b]_2 \cdot [\mathbf b]_1</math>

====Example====

Suppose we have a two-port network consisting of a series resistor {{mvar|R}} followed by a shunt capacitor {{mvar|C}}.  We can model the entire network as a cascade of two simpler networks:

:<math>\begin{align}[]
  [\mathbf{b}]_1 &= \begin{bmatrix} 1 & -R \\   0 & 1 \end{bmatrix}\\
  \lbrack\mathbf{b}\rbrack_2 &= \begin{bmatrix} 1 &  0 \\ -sC & 1 \end{bmatrix}
\end{align}</math>

The transmission matrix for the entire network {{math|['''b''']}} is simply the matrix multiplication of the transmission matrices for the two network elements:

:<math>\begin{align}[]
  \lbrack\mathbf{b}\rbrack &= \lbrack\mathbf{b}\rbrack_2 \cdot \lbrack\mathbf{b}\rbrack_1 \\
                           &= \begin{bmatrix} 1 &  0 \\ -sC & 1       \end{bmatrix} \begin{bmatrix} 1 & -R \\ 0 & 1 \end{bmatrix} \\
                           &= \begin{bmatrix} 1 & -R \\ -sC & 1 + sCR \end{bmatrix}
\end{align}</math>

Thus:

:<math> \begin{bmatrix} V_2 \\ -I_2 \end{bmatrix} = \begin{bmatrix} 1 & -R \\ -sC & 1 + sCR \end{bmatrix} \begin{bmatrix} V_1 \\ I_1 \end{bmatrix}</math>