Design a circuit which produces the transfer function
Design a circuit which produces a transfer function of
Explanation of Solution
Given data:
The given transfer function is,
Calculation:
The transfer function of the circuit is,
Equation (1) is written as,
For numerator:
From equation (2), for the numerator
The Figure 14.39 (b) in the textbook, that shows a cascade two stages of the circuit with a zero at
From the Figure 1, a single zero can be written as,
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, consider that the transfer function for
Substitute 50 for
Completing the design by letting
Thus, the final design of the circuit is,
For denominator:
From the transfer function shown in equation (2), it has two repeated poles at
The Figure 14.39 (a) in the textbook, that shows a cascade two stages of the circuit with pole at
Consider that the cascaded circuit for the two poles representation as shown in Figure 2.
From Figure 2, and the denominator of given transfer function a first pole at
Where, the circuit parameters are considered as
Substitute
Let arbitrarily consider
Substitute 13.3 for
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 75 for
Completing the design by letting
Since, two repeated poles are at same
Therefore, the complete transfer function for the denominator part is,
Substitute
Thus, the final design of the two stages cascaded circuit for the denominator part is,
Thus, the overall transfer function of the complete circuit using the transfer function of numerator
Substitute
The input will be inverted, and adding an inverting amplifier with gain of 1 to provide the transfer function as follows.
Conclusion:
Thus, a circuit is designed which produces a transfer function of
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