Show that the ABCD parameters matrix for the two port network illustrated in Figure Q1.1 is given by: 1 + Z; ZA ABCD = Z8 ZA ZB Figure Q1.1: Two port network
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The network consists of an impedance ZA in series with port 1, and an impedance ZB connected as a shunt element between the two ports. Show more…
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(a) For the $T$ network in Fig. 18.97 , show that the $h$ parameters are: \[ \begin{array}{c} \mathbf{h}_{11}=R_{1}+\frac{R_{2} R_{3}}{R_{1}+R_{3}}, \quad \mathbf{h}_{12}=\frac{R_{2}}{R_{2}+R_{3}} \\ \mathbf{h}_{21}=-\frac{R_{2}}{R_{2}+R_{3}}, \quad \mathbf{h}_{22}=\frac{1}{R_{2}+R_{3}} \end{array} \] (b) For the same network, show that the transmission parameters are: \[ \begin{array}{c} \mathbf{A}=1+\frac{R_{1}}{R_{2}}, \quad \mathbf{B}=R_{3}+\frac{R_{1}}{R_{2}}\left(R_{2}+R_{3}\right) \\ \mathbf{C}=\frac{1}{R_{2}}, \quad \mathbf{D}=1+\frac{R_{3}}{R_{2}} \end{array} \]
Show that the transmission parameters of a two-port may be obtained from the $y$ parameters as: \[ \begin{array}{ll} \mathbf{A}=-\frac{\mathbf{y}_{22}}{\mathbf{y}_{21}}, & \mathbf{B}=-\frac{1}{\mathbf{y}_{21}} \\ \mathbf{C}=-\frac{\Delta_{y}}{\mathbf{y}_{21}}, & \mathbf{D}=-\frac{\mathbf{y}_{11}}{\mathbf{y}_{21}} \end{array} \]
A series-parallel connection of two two-ports is shown in Fig. $18.108 .$ Determine the $z$ parameter representation of the network.
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