(a)
Design a circuit which produces a transfer function of
(a)
Explanation of Solution
Problem design:
Synthesize a circuit that will yield the transfer function
Calculation:
The transfer function of the circuit is,
The above equation is written as,
For the above transfer function, it has two repeated zeros at
The Figure 14.39 (b) in the textbook, that shows a cascade two stages of the circuit with a zero at
For a single zero,
Substitute
Let arbitrarily consider
Substitute
Transfer function:
The input impedance of the cascaded circuit is,
Then, write the Formula for the transfer function for the cascaded two stage amplifier.
Substitute
Thus, consider that the transfer function for
Substitute 1 for
Completing the design by letting
Since, two repeated zeros at
Therefore,
Substitute
Thus, the final design of the circuit is,
Conclusion:
Thus, a circuit is designed which produces a transfer function of
(b)
Design a circuit which produces a transfer function of
(b)
Explanation of Solution
Problem design:
Synthesize a circuit that will yield the transfer function
Calculation:
The transfer function of the circuit is,
Consider the transfer function for the cascaded circuit as below.
The above transfer function, it has two poles at
The Figure 14.39 (a) in the textbook, that shows a cascade two stages of the circuit with pole at
The above Figure 2, is the representation for the first stage and second stage of a cascaded circuit to be drawn.
Consider the denominator of given transfer function and the first pole as
Where,
Substitute
Let arbitrarily consider
Substitute
Transfer function:
Find the feedback impedance of the cascaded circuit in Figure 2.
Write the formula for the transfer function of the cascaded circuit in Figure 2 as follows
Substitute
Therefore, consider the transfer function for the first pole
Substitute 500 for
Completing the design by letting
Consider the denominator of given transfer function and the first pole as
Where,
Substitute
Arbitrarily consider
Substitute
Therefore, consider the transfer function for the second pole
Substitute 100 for
Completing the design by letting
Then, from the transfer function of the two stages write the complete transfer function as follows.
Substitute
Thus, the final design of the circuit is,
Conclusion:
Thus, a circuit is designed which produces a transfer function of
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Chapter 14 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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