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Find the gain

Find the gain

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Problem Statement:** Find the gain \(|H(j\omega)|\) and the phase shift \(\angle H(j\omega)\) of a system with the following transfer function (no need to plot the answers). \[ H(j\omega) = \frac{(5 + j\omega)(1 + 6j\omega)}{j\omega(4 + 2j\omega)} \] **Explanation:** The transfer function \(H(j\omega)\) is given as a complex ratio involving polynomials in terms of imaginary unit \(j\) and angular frequency \(\omega\). - **Numerator:** \((5 + j\omega)(1 + 6j\omega)\) - This product involves two binomials, where each term contains a real part and a complex part. - **Denominator:** \(j\omega(4 + 2j\omega)\) - This is a product of a single imaginary component \(j\omega\) and a binomial with both a real and a complex part. **Objective:** - Calculate the magnitude \(|H(j\omega)|\), which represents the gain. - Determine the phase \(\angle H(j\omega)\), which represents the phase shift.
Transcribed Image Text:**Problem Statement:** Find the gain \(|H(j\omega)|\) and the phase shift \(\angle H(j\omega)\) of a system with the following transfer function (no need to plot the answers). \[ H(j\omega) = \frac{(5 + j\omega)(1 + 6j\omega)}{j\omega(4 + 2j\omega)} \] **Explanation:** The transfer function \(H(j\omega)\) is given as a complex ratio involving polynomials in terms of imaginary unit \(j\) and angular frequency \(\omega\). - **Numerator:** \((5 + j\omega)(1 + 6j\omega)\) - This product involves two binomials, where each term contains a real part and a complex part. - **Denominator:** \(j\omega(4 + 2j\omega)\) - This is a product of a single imaginary component \(j\omega\) and a binomial with both a real and a complex part. **Objective:** - Calculate the magnitude \(|H(j\omega)|\), which represents the gain. - Determine the phase \(\angle H(j\omega)\), which represents the phase shift.
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