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Find K (the constant) for the magnitude characteristic shown in Fig. P12.31, given t1 = 2, t2 = 5, t3 = 9, and t4 = 11, using the transfer function form of H (jw) = K(jw+z1)(jw+z2) (jw+p1)(jw+p2) IHI +20 dB/dec 40 20 dB/dec O dB t1 t2 t3 t4 w (rad/s) Notes on entering solution: • enter answer to two decimal places • Find K (not in dB) • Do not include units in your answer

Find K (the constant) for the magnitude characteristic shown in Fig. P12.31, given t1 = 2, t2 = 5, t3 = 9, and t4 = 11, using the transfer function form of H (jw) = K(jw+z1)(jw+z2) (jw+p1)(jw+p2) IHI +20 dB/dec 40 20 dB/dec O dB t1 t2 t3 t4 w (rad/s) Notes on entering solution: • enter answer to two decimal places • Find K (not in dB) • Do not include units in your answer

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
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Find K (the constant) for the magnitude characteristic shown in Fig. P12.31, given t1 = 2, t2 = 5, t3 = 9, and t4 = 11, using the transfer function form 

**Problem Statement:** **Objective:** Find \( K \) (the constant) for the magnitude characteristic shown in Fig. P12.31. **Given Data:** - \( t1 = 2 \) - \( t2 = 5 \) - \( t3 = 9 \) - \( t4 = 11 \) **Using the Transfer Function:** \[ H(j\omega) = \frac{K(j\omega+z_1)(j\omega+z_2)}{(j\omega+p_1)(j\omega+p_2)} \] **Diagram Explanation:** - The graph is a Bode plot representing the magnitude (in dB) vs. frequency (rad/s). - The y-axis represents magnitude in decibels (dB). - The x-axis represents angular frequency in radians per second (rad/s). - There are two slopes: - A rising slope of +20 dB/decade from \(t1\) to \(t2\). - A flat line from \(t2\) to \(t3\). - A declining slope of -20 dB/decade from \(t3\) to \(t4\). **Magnitude Levels:** - Starts at 0 dB, rises to 40 dB, remains constant, and then drops again to 40 dB beyond \(t4\). **Notes on Entering Solution:** - Enter the answer to two decimal places. - Find \( K \) (NOTE: Not in decibels). - Do not include units in your answer. **Instructions:** Use the provided transfer function and graph to calculate the constant \( K \) based on the given time intervals and slopes.
Transcribed Image Text:**Problem Statement:** **Objective:** Find \( K \) (the constant) for the magnitude characteristic shown in Fig. P12.31. **Given Data:** - \( t1 = 2 \) - \( t2 = 5 \) - \( t3 = 9 \) - \( t4 = 11 \) **Using the Transfer Function:** \[ H(j\omega) = \frac{K(j\omega+z_1)(j\omega+z_2)}{(j\omega+p_1)(j\omega+p_2)} \] **Diagram Explanation:** - The graph is a Bode plot representing the magnitude (in dB) vs. frequency (rad/s). - The y-axis represents magnitude in decibels (dB). - The x-axis represents angular frequency in radians per second (rad/s). - There are two slopes: - A rising slope of +20 dB/decade from \(t1\) to \(t2\). - A flat line from \(t2\) to \(t3\). - A declining slope of -20 dB/decade from \(t3\) to \(t4\). **Magnitude Levels:** - Starts at 0 dB, rises to 40 dB, remains constant, and then drops again to 40 dB beyond \(t4\). **Notes on Entering Solution:** - Enter the answer to two decimal places. - Find \( K \) (NOTE: Not in decibels). - Do not include units in your answer. **Instructions:** Use the provided transfer function and graph to calculate the constant \( K \) based on the given time intervals and slopes.
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