Please solve as some answers may be wrong ### Nyquist Plot AnalysisConsider the following Nyquist plot, which provides details summarized in the table below. **Note:** The magnitude values are in absolute terms, not in decibels (dB).#### Diagram Description:The Nyquist plot is a complex plane diagram with the Real part \( \text{Re}(L) \) on the x-axis and the Imaginary part \( \text{Im}(L) \) on the y-axis. The plot includes the following key features:- A curve passing through the point where the real part is \(-1\).- A marked point at frequency \(\omega = 1\) with a phase angle of \(-135^\circ\).- A marked point at frequency \(\omega = 1.5\) with a phase angle of \(-180^\circ\).#### Table of Values:| Frequency (\(\omega\)) | Magnitude (\(|L|\)) | Phase Angle (\(\angle L\)) ||------------------------|---------------------|----------------------------|| 1 | 1 | \(-135^\circ\) || 1.5 | 0.5 | \(-180^\circ\) |### Calculations:Using the information provided:1. **Gain Crossover Frequency:** - The gain crossover frequency is \( 1 \) rad/sec. - The phase margin is calculated as: \[ 180^\circ - 135^\circ = 45^\circ \]2. **Phase Crossover Frequency:** - The phase crossover frequency is \( 1.5 \) rad/sec. - The gain margin is given by: \[ \text{Gain margin} = 20 \log_{10}(0.5) \, \text{dB} \]This analysis helps evaluate system stability margins, providing insights into the control system's robustness.

The Nyquist plot of a system is given byWe need to determineThe gain cross over frequency and the…

Consider the following Nyquist plot from which one may note down the details in the table below (NOTE: the magnitude values are in absolute, NOT in dB): ↑ Im (4) 0.5 # -135⁰ ون =1 Frequency Magnitude, Phase |L| Angle, ZL (w) 1 1 -135° -180° 1.5 Re (L) 0.5 With the above information, fill out the following sentences! 1) The gain crossover frequency is 1 ← 45 0 margin is 180-135 = 45 2) The phase crossover frequency 1.5 is ← margin is 20 log10 0.5 dB rad/sec, and the phase rad/sec, and the gain

Consider the following Nyquist plot from which one may note down the details in the table below (NOTE: the magnitude values are in absolute, NOT in dB): ↑ Im (4) 0.5 # -135⁰ ون =1 Frequency Magnitude, Phase |L| Angle, ZL (w) 1 1 -135° -180° 1.5 Re (L) 0.5 With the above information, fill out the following sentences! 1) The gain crossover frequency is 1 ← 45 0 margin is 180-135 = 45 2) The phase crossover frequency 1.5 is ← margin is 20 log10 0.5 dB rad/sec, and the phase rad/sec, and the gain

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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Please solve as some answers may be wrong

### Nyquist Plot Analysis

Consider the following Nyquist plot, which provides details summarized in the table below. **Note:** The magnitude values are in absolute terms, not in decibels (dB).

#### Diagram Description:
The Nyquist plot is a complex plane diagram with the Real part \( \text{Re}(L) \) on the x-axis and the Imaginary part \( \text{Im}(L) \) on the y-axis. The plot includes the following key features:
- A curve passing through the point where the real part is \(-1\).
- A marked point at frequency \(\omega = 1\) with a phase angle of \(-135^\circ\).
- A marked point at frequency \(\omega = 1.5\) with a phase angle of \(-180^\circ\).

#### Table of Values:

| Frequency (\(\omega\)) | Magnitude (\(|L|\)) | Phase Angle (\(\angle L\)) |
|------------------------|---------------------|----------------------------|
| 1 | 1 | \(-135^\circ\) |
| 1.5 | 0.5 | \(-180^\circ\) |

### Calculations:

Using the information provided:

1. **Gain Crossover Frequency:**
- The gain crossover frequency is \( 1 \) rad/sec.
- The phase margin is calculated as:
\[
180^\circ - 135^\circ = 45^\circ
\]

2. **Phase Crossover Frequency:**
- The phase crossover frequency is \( 1.5 \) rad/sec.
- The gain margin is given by:
\[
\text{Gain margin} = 20 \log_{10}(0.5) \, \text{dB}
\]

This analysis helps evaluate system stability margins, providing insights into the control system's robustness.

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