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Direct Form II System Realization 18. Draw Direct Form II system diagrams of the systems with these transfer functions. s? +8 (a) H(s) = 10 s3 +3s? + 7s+ 22

Direct Form II System Realization 18. Draw Direct Form II system diagrams of the systems with these transfer functions. s? +8 (a) H(s) = 10 s3 +3s? + 7s+ 22

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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**Direct Form II System Realization** **18.** Draw Direct Form II system diagrams of the systems with these transfer functions. **(a)** \( H(s) = 10 \frac{s^2 + 8}{s^3 + 3s^2 + 7s + 22} \) --- To construct a Direct Form II system diagram, one would typically separate the transfer function into its numerator and denominator parts, representing these as filters or block diagrams. The system can then be realized by using feedback and feedforward components to achieve the desired transfer function structure. **Explanation:** The given transfer function is a rational function, which consists of: - **Numerator**: \(s^2 + 8\) - **Denominator**: \(s^3 + 3s^2 + 7s + 22\) To realize this in a Direct Form II structure, consider breaking down the expressions into terms that can be represented as delay elements, gains (multipliers), and summations. Direct Form II typically involves: 1. **Combining Coefficients**: Connect coefficients to delay elements corresponding to the order of the polynomial. 2. **Structure**: Use a series of delays to handle the respective orders of the polynomials. Feedback paths are used for the denominator, whereas feedforward paths are used for the numerator. This system realization will require designing a block that calculates the output \(H(s)\) using both feedback and feedforward elements based on the given polynomial orders and coefficients.
Transcribed Image Text:**Direct Form II System Realization** **18.** Draw Direct Form II system diagrams of the systems with these transfer functions. **(a)** \( H(s) = 10 \frac{s^2 + 8}{s^3 + 3s^2 + 7s + 22} \) --- To construct a Direct Form II system diagram, one would typically separate the transfer function into its numerator and denominator parts, representing these as filters or block diagrams. The system can then be realized by using feedback and feedforward components to achieve the desired transfer function structure. **Explanation:** The given transfer function is a rational function, which consists of: - **Numerator**: \(s^2 + 8\) - **Denominator**: \(s^3 + 3s^2 + 7s + 22\) To realize this in a Direct Form II structure, consider breaking down the expressions into terms that can be represented as delay elements, gains (multipliers), and summations. Direct Form II typically involves: 1. **Combining Coefficients**: Connect coefficients to delay elements corresponding to the order of the polynomial. 2. **Structure**: Use a series of delays to handle the respective orders of the polynomials. Feedback paths are used for the denominator, whereas feedforward paths are used for the numerator. This system realization will require designing a block that calculates the output \(H(s)\) using both feedback and feedforward elements based on the given polynomial orders and coefficients.
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