Question

Z parameters of a two port network are z11 = 10, z22 = 20 and z12 = z21 = 5. What are the corresponding abcd parameters?

Answer 1

Answer:

Concept:

A two-port network (also known as a quadripole or four-terminal network) is an electrical network (circuit) or device that has two pairs of terminals for connecting to external circuits. Two terminals form a port if the currents applied to them meet the port condition, which states that the electric current entering one terminal must be equal to the current emerging from the other terminal on the same port. The ports are the sites where signals are applied or outputs are taken, and where the network communicates to other networks. In a two-port network, port 1 is frequently used as the input port and port 2 as the output port.

Given:

Given Z parameters of a two port network are $Z_{11} =10, Z_{22} =20$  $and$

$Z_{12} =Z_{21} =5$

Find:

Find What are the corresponding ABCD parameters?

Answer:

In electrical engineering, Z parameters (also known as impedance parameters or open-circuit parameters) are properties that explain the electrical behaviour of linear electrical networks. These Z-parameters are used to determine the incoming and outgoing voltages and currents of a network using Z-matrixes (impedance matrices).

$Z= \left[\begin{array}{ccc}Z_{11} &Z_{12} \\Z_{21} &Z_{22} \\\end{array}\right]$

$Z=\left[\begin{array}{ccc}10&5\\5&20\\\end{array}\right]$

$Z=200-25$

$Z=175$

Now, find ABCD parameters are

$ABCD=\left[\begin{array}{ccc}10&5\\5&20\\\end{array}\right]$

$A=\frac{Z_{11} }{Z_{21} }$

   $=\frac{10}{5}$

   $=2$

$B=\frac{Z}{Z_{22} }$

   $=\frac{175}{5}$

   $=35$

$C=\frac{1}{Z_{11} }$

   $=\frac{1}{5}$

   $=0.2$

$D=\frac{Z_{22} }{Z_{21} }$

   $=\frac{20}{5}$

   $=4$

∴ The parameters of ABCD are $2,35,0.2,4$

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