Chapter 19, Problem 1RQ

For the single-element two-port network in Fig. 19.64(a), z₁₁ is:

1. (a) 0
2. (b) 5
3. (c) 10
4. (d) 20
5. (e) undefined

Figure 19.64

To determine

Choose the option that represents a value of $z_{\text{11}}$ in the given single-element two-port network.

Answer to Problem 1RQ

The option that represents the value of $z_{\text{11}}$ in the given two-port network is “(c) 10”.

Explanation of Solution

Given Data:

Refer to Figure 19.64 (a) in the textbook for the given single-element two-port network.

Calculation:

Refer to Figure 19.5 (a) in the textbook for T-equivalent circuit.

As the given two-port network is a T-network, compare given two-port network in Figure 19.64 (a) with T-equivalent circuit in Figure 19.5 and write the expressions to find the z parameters as follows:

$z_{\text{11}}-z_{\text{12}}=0\Omega$ (1)

$z_{\text{12}}=10\Omega$ (2)

$z_{\text{22}}-z_{\text{12}}=0\Omega$ (3)

As $z_{\text{21}}$ is equivalent to $z_{\text{12}}$, the value of $z_{\text{21}}$ is $10\Omega$.

$\begin{array}{c}{z}_{\text{21}}=z_{\text{12}}\\ =10\Omega \end{array}$

Rearrange the expression in Equation (1) for $z_{\text{11}}$ as follows:

$z_{\text{11}}=0\Omega +z_{\text{12}}$

From Equation (2), substitute $10\Omega$ for $z_{\text{12}}$ to obtain the value of $z_{\text{11}}$.

$\begin{array}{c}{z}_{\text{11}}=0\Omega +10\Omega \\ =10\Omega \end{array}$

Rearrange the expression in Equation (3) for $z_{\text{22}}$ as follows:

$z_{\text{22}}=z_{12}$

From Equation (2), substitute $10\Omega$ for $z_{\text{12}}$ to obtain the value of $z_{\text{22}}$.

$z_{\text{22}}=10\Omega$

From the calculations, the obtained z parameters can be written as follows:

$z=\left[\begin{array}{cc}10& 10\\ 10& 10\end{array}\right]$

Conclusion:

Thus, the option that represents the value of $z_{\text{11}}$ in the given two-port network is “(c) 10”.