Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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![**Title: How to Sketch the Magnitude Characteristic of a Bode Plot**
**Objective:** Follow the steps to sketch the magnitude characteristic of the Bode plot for the given transfer function.
**Transfer Function:**
\[
H(j\omega) = \frac{1000(j\omega + 10)}{(j\omega + 50)(j\omega + 200)}
\]
**Task:** Convert the transfer function to standard form.
**Notes:**
- The given transfer function is represented in a complex frequency domain using \( j\omega \) where \( j \) is the imaginary unit and \( \omega \) is the angular frequency.
- Standard form conversion involves rewriting the function in a way that is easier to interpret or analyze in the context of control systems and signal processing.
**Guidance:**
- Carefully separate the terms in the numerator and denominator.
- Factor out constants where possible.
- Express each term in the format that shows the relationship between poles and zeros clearly.
Understanding how to perform this conversion is crucial for accurately depicting the behavior of the system in a Bode plot, which is a key tool for analyzing the frequency response of linear time-invariant systems.](https://content.bartleby.com/qna-images/question/b78840cf-991a-43cf-baf3-7d430789620d/5bc6ea27-061c-4409-bce1-b6556253f9f2/1qr4bmj_processed.jpeg)
Transcribed Image Text:**Title: How to Sketch the Magnitude Characteristic of a Bode Plot**
**Objective:** Follow the steps to sketch the magnitude characteristic of the Bode plot for the given transfer function.
**Transfer Function:**
\[
H(j\omega) = \frac{1000(j\omega + 10)}{(j\omega + 50)(j\omega + 200)}
\]
**Task:** Convert the transfer function to standard form.
**Notes:**
- The given transfer function is represented in a complex frequency domain using \( j\omega \) where \( j \) is the imaginary unit and \( \omega \) is the angular frequency.
- Standard form conversion involves rewriting the function in a way that is easier to interpret or analyze in the context of control systems and signal processing.
**Guidance:**
- Carefully separate the terms in the numerator and denominator.
- Factor out constants where possible.
- Express each term in the format that shows the relationship between poles and zeros clearly.
Understanding how to perform this conversion is crucial for accurately depicting the behavior of the system in a Bode plot, which is a key tool for analyzing the frequency response of linear time-invariant systems.
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- Draw the magnitude plot and phase plot for the following transfer function. jw + 10 H(w) = jw(jw + 5)²arrow_forward3. Consider a causal continuous-time LTI system described by the transfer function below: 5 H(s) = 5 s+2 +10 (a) Sketch the Bode diagram of this system. Label the frequencies, magnitude, phase angles, and slopes wherever necessary. Magnitude (dB) Phase (deg) 50 0 -50 -100 45 -90 -135 -180 10-¹ 10⁰ Bode Diagram 10¹ Frequency (rac/s) 10² 10³ (b) For a sinusoidal input x (t) = 2 sin(2t + 45°), determine the steady-state response of the system.arrow_forward2. Draw the complete bode plot for the following transfer function. jw + 10 H(w) jw(jw + 5)2arrow_forward
- Will upvotearrow_forwardA user has an incoming signal that is the sum of two synchronized cosine waves, a 8V signal at 10Hz, and a 4V signal at 100Hz. [Vin=2cos(At)+cos(Bt)]. What is the transfer function of the circuit?arrow_forwardExpress the transfer function (Vo(w)/Vin(w)) and draw the bode plot of both magnitude and phase of it.arrow_forward
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