(a)
Design a circuit which produces a transfer function of
(a)
Explanation of Solution
Given data:
The given transfer function is,
Calculation:
The transfer function of the circuit is,
The above transfer function has a zero 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
Consider the value of
Substitute
Transfer function:
The input impedance of the cascaded circuit in Figure 1 is,
Then, write the Formula for the transfer function for the cascaded two stage amplifier.
Substitute
Thus, the transfer function for
Substitute 1 for
Completing the design by letting
If the input will be inverted, add an inverting amplifier with gain of 1 to provide the transfer function as follows.
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
Given data:
The given transfer function is,
Calculation:
The transfer function of the circuit is,
The above transfer function has pole at
The Figure 14.39 (a) in the textbook, that shows a cascade two stages of the circuit with pole at
For pole
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
Substitute 1 for
Completing the design by letting
If the input will be inverted, add an inverting amplifier with gain of 1 to provide the transfer function as follows.
Thus, the final design of the circuit is,
Conclusion:
Thus, a circuit is designed which produces a transfer function of
(c)
Design a circuit which produces a transfer function of
(c)
Explanation of Solution
Given data:
The given transfer function is,
Calculation:
The transfer function of the circuit is,
For the above transfer function, it has a zero at
Refer to Figure 1 in Part (a), that shows a cascade two stages of the circuit with a zero at
For a single zero,
Substitute
Let arbitrarily consider
Substitute
Consider the same circuit shown in Figure 1 and the transfer function as in a cascaded circuit,
Substitute 1 for
Completing the design by letting
Thus, the final design of the circuit is,
The given transfer function has a pole at
Refer to Figure 2 in Part (b), that shows a cascade two stages of the circuit with pole at
For pole
Substitute
Let arbitrarily consider
Substitute
The above equation becomes,
Consider the same circuit shown in Figure 2 and the transfer function as in a cascaded circuit,
Substitute 2 for
Completing the design by letting
Thus, the final design of the circuit is,
Therefore, the overall transfer function of the cascaded circuit is,
Substitute
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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