Determine the input impedance Zin of the one-port shown in Fig. 16.51 if ω is equal to (a) 50 rad/s; (b) 1000 rad/s.
(a)
The value of the input impedance for
Answer to Problem 23E
The value of the input impedance is
Explanation of Solution
Given data:
The value of
The given diagram is shown in Figure 1.
Calculation:
Let the inductances be
Let the capacitance
The expression for the inductive impedance
The expression for the capacitive impedance
Substitute
Substitute
Substitute
Substitute
The value of
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The conversion of
Substitute
Mark the impedances and redraw the circuit.
The required diagram is shown in Figure 2
The
The required diagram is shown in the Figure 3.
Here,
The impedance
The impedance
The impedance
The required diagram is shown in Figure 4.
Add the impedances in series in the above network and redraw the network.
The required diagram is shown in Figure 5.
In the above circuit
Thus, the parallel combination
Mark the equivalent impedance and redraw the circuit.
The required figure is shown in Figure 6.
The value of the input impedance
Solve it further as,
Conclusion:
Therefore, the value of the input impedance for
(b)
The input impedance of the circuit is determined for
Answer to Problem 23E
The value of the input impedance for
Explanation of Solution
Given data:
The value of
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Mark the impedances and redraw the circuit.
The required diagram is shown in Figure 7
The
The required diagram is shown in the Figure 8
Here,
The impedance
The impedance
The impedance
The modified diagram is shown in Figure 9.
Add the impedances in series in the above network and redraw the network.
The required diagram is shown in Figure 10.
In the above circuit
Thus, the parallel combination
Mark the equivalent impedance and redraw the circuit.
The required figure is shown in Figure 11.
The value of the input impedance
Solve it further as,
Conclusion:
Therefore the value of the input impedance for
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