Sketch and label accurately the straight line Bode plots of the following frequency response H(jw). You may NOT use MATLAB or a graphing calculator (including online calculators) to plot the Bode diagrams: (jw + 1000) H(jw) = (jw)2 + 10jw + 100

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**Task:** Sketch and accurately label the straight-line Bode plots for the following frequency response \( H(j\omega) \). You may NOT use MATLAB or a graphing calculator (including online calculators) to plot the Bode diagrams:

\[
H(j\omega) = \frac{(j\omega + 1000)}{(j\omega)^2 + 10j\omega + 100}
\]

**Guidelines for Bode Plot Construction:**

1. **Magnitude Plot:**
   - Break down the transfer function into standard form to identify poles and zeros.
   - Determine the asymptotic behavior of each pole and zero contributing to the magnitude.
   - Use straight-line approximations for each section of the frequency response.

2. **Phase Plot:**
   - Determine the phase contribution of each factor in the transfer function.
   - Calculate the phase shift introduced by poles and zeros over the frequency range.
   - Sketch the phase plot using standard phase characteristics of poles and zeros.

3. **Frequency Response:**
   - Identify the corner frequencies, where the slope changes in the magnitude plot.
   - Calculate the values of \(\omega\) that make the real and imaginary parts zero (if applicable).

4. **Labeling:**
   - Clearly label axes and important points such as corner frequencies, gain margin, and phase margin.
   - Include the initial gain and the slope changes at each identified frequency.

This is a manual exercise to gain a deeper understanding of Bode plot characteristics and their use in analyzing system dynamics.
Transcribed Image Text:**Task:** Sketch and accurately label the straight-line Bode plots for the following frequency response \( H(j\omega) \). You may NOT use MATLAB or a graphing calculator (including online calculators) to plot the Bode diagrams: \[ H(j\omega) = \frac{(j\omega + 1000)}{(j\omega)^2 + 10j\omega + 100} \] **Guidelines for Bode Plot Construction:** 1. **Magnitude Plot:** - Break down the transfer function into standard form to identify poles and zeros. - Determine the asymptotic behavior of each pole and zero contributing to the magnitude. - Use straight-line approximations for each section of the frequency response. 2. **Phase Plot:** - Determine the phase contribution of each factor in the transfer function. - Calculate the phase shift introduced by poles and zeros over the frequency range. - Sketch the phase plot using standard phase characteristics of poles and zeros. 3. **Frequency Response:** - Identify the corner frequencies, where the slope changes in the magnitude plot. - Calculate the values of \(\omega\) that make the real and imaginary parts zero (if applicable). 4. **Labeling:** - Clearly label axes and important points such as corner frequencies, gain margin, and phase margin. - Include the initial gain and the slope changes at each identified frequency. This is a manual exercise to gain a deeper understanding of Bode plot characteristics and their use in analyzing system dynamics.
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