Concept explainers
Determine the z parameters for the network in Fig. 19.118.
Figure 19.118
Find the impedance parameters for the given two-port network in Figure 19.118 in the textbook.
Answer to Problem 71P
The impedance parameters for the given two-port network are
Explanation of Solution
Given Data:
Refer to Figure 19.118 in the textbook for the given two-port network.
Formula used:
Write the expressions for transmission (ABCD) parameters of a two-port network as follows:
Refer to Figure 19.106 in the textbook and write the expression for transmission parameters for a T-network as follows:
Refer to TABLE 19.1 in the textbook, write the expression for g parameters in terms of transmission parameters as follows:
Write the expression for
From TABLE 19.1 in the textbook, write the expression for impedance parameters in terms of g parameters as follows:
Write the expression for
Calculation:
The given interconnected network is a series-parallel combination of two two-port networks. Find g parameters for each network and add them for overall g parameters of entire network. And then convert the overall g parameters into z parameters.
Consider upper network (T-network) as network
Compare upper network with the Figure 19.106 in the textbook and write the resistance values as follows:
Substitute
Convert the obtained transmission parameters into g parameters as follows:
Substitute 1.8 for
Substitute 1.8 for
As the lower network is a series combination of resistive network and transformer, find the transmission parameters for each network and product them to get the transmission parameters for lower network.
Consider resistive network as
Find the transmission parameters for network
The transmission parameters
Redraw the network
From Figure 1, write the expression for
Rearrange the expression as follows:
Substitute 1.8 for
From Figure 1, write the expression for
Substitute
Rearrange the expression as follows:
Substitute
The transmission parameters
Rearrange the expression as follows:
Redraw the network
From Figure 2, write the expression for
Rearrange the expression as follows:
Substitute
From Figure 2, write the expression for
From Equation (13), substitute
From the calculations, write the transmission parameters for the network
Find the transmission parameters for network
From the given transformer network
Rearrange the expression as follows:
From the given transformer network
Rearrange the expression as follows:
Compare Equation (14) with Equation (1) and obtain the parameters
Compare Equation (15) with Equation (2) and obtain the parameters
From the calculations, write the transmission parameters for the network
As the networks
Substitute
Convert the obtained transmission parameters into g parameters for lower network as follows:
Substitute 0.9 for
Substitute 0.9 for
Write the expression for overall g parameters for the given network as follows:
Substitute
Convert the obtained g parameters into impedance parameters to attain the required objective.
Substitute
Substitute
Conclusion:
Thus, the impedance parameters for the given two-port network are
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Chapter 19 Solutions
Fundamentals of Electric Circuits
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