NOTE: You would have to clearly mark out the cut-off frequencies and the slopes of the magnitude lines (e.g., ±20 dB/decade), and the phase angle values in your asymptotic Bode plots. For your convenience, it is okay to approximate phase angle and magnitude values in your Bode plots. Let us draw the asymptotic Bode plot of the following transfer function: 10 (s+1) S (s + 10) but we will do so by constructing the Bode plots for each of the first order terms separately, H(s) = H3(s) · H4(s) H5(s) . 10 H3(s) = s+10' Problem 2 where, H(s) 1 HA(S) = S' and H5(s) = s +1 and then putting those plots together (i.e., by stacking them on top of each other). a) Draw the asymptotic Bode plot of H₁(s) = 1 b) Draw the asymptotic Bode plot of H5(s) = s +1 c) Finally, use the above results to draw the asymptotic Bode plot of: H(s) = H3(s) H4(s). H5(s). Note: You should reuse the asymptotic Bode plot of H3(s) = 10 from the previous problem. s+10

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**Problem 2**

Let us draw the asymptotic Bode plot of the following transfer function:

\[ H(s) = \frac{10(s+1)}{s(s+10)} \]

but we will do so by constructing the Bode plots for each of the first-order terms separately,

\[ H(s) = H_3(s) \cdot H_4(s) \cdot H_5(s) \]

where,

\[ H_3(s) = \frac{10}{s+10}, \]

\[ H_4(s) = \frac{1}{s}, \]

and

\[ H_5(s) = s+1 \]

and then putting those plots together (i.e., by stacking them on top of each other).

a) Draw the asymptotic Bode plot of \( H_4(s) = \frac{1}{s} \)

b) Draw the asymptotic Bode plot of \( H_5(s) = s+1 \)

c) Finally, use the above results to draw the asymptotic Bode plot of:

\[ H(s) = H_3(s) \cdot H_4(s) \cdot H_5(s) \]

**Note:** You should reuse the asymptotic Bode plot of \( H_3(s) = \frac{10}{s+10} \) from the previous problem.

**Explanation:**

- **Magnitude Plot**: For each transfer function, you need to plot the magnitude in dB against frequency on a logarithmic scale.
- **Phase Plot**: Similarly, the phase angle in degrees should be plotted against frequency.

- **\( H_4(s) = \frac{1}{s} \)** corresponds to a slope of -20 dB/decade starting at 0 dB.
- **\( H_5(s) = s+1 \)** corresponds to a slope of +20 dB/decade starting at 0 dB.
- **\( H_3(s) = \frac{10}{s+10} \)**, from a previous problem, needs its magnitude and phase plot reused here.

Combine these plots by stacking magnitudes and phases, taking care to maintain consistent units and scaling for accurate representation of the overall transfer function \( H(s) \).
Transcribed Image Text:**Problem 2** Let us draw the asymptotic Bode plot of the following transfer function: \[ H(s) = \frac{10(s+1)}{s(s+10)} \] but we will do so by constructing the Bode plots for each of the first-order terms separately, \[ H(s) = H_3(s) \cdot H_4(s) \cdot H_5(s) \] where, \[ H_3(s) = \frac{10}{s+10}, \] \[ H_4(s) = \frac{1}{s}, \] and \[ H_5(s) = s+1 \] and then putting those plots together (i.e., by stacking them on top of each other). a) Draw the asymptotic Bode plot of \( H_4(s) = \frac{1}{s} \) b) Draw the asymptotic Bode plot of \( H_5(s) = s+1 \) c) Finally, use the above results to draw the asymptotic Bode plot of: \[ H(s) = H_3(s) \cdot H_4(s) \cdot H_5(s) \] **Note:** You should reuse the asymptotic Bode plot of \( H_3(s) = \frac{10}{s+10} \) from the previous problem. **Explanation:** - **Magnitude Plot**: For each transfer function, you need to plot the magnitude in dB against frequency on a logarithmic scale. - **Phase Plot**: Similarly, the phase angle in degrees should be plotted against frequency. - **\( H_4(s) = \frac{1}{s} \)** corresponds to a slope of -20 dB/decade starting at 0 dB. - **\( H_5(s) = s+1 \)** corresponds to a slope of +20 dB/decade starting at 0 dB. - **\( H_3(s) = \frac{10}{s+10} \)**, from a previous problem, needs its magnitude and phase plot reused here. Combine these plots by stacking magnitudes and phases, taking care to maintain consistent units and scaling for accurate representation of the overall transfer function \( H(s) \).
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