# Polar Plots Problem 3 Frequency Response Analysis | Summary and Q&A

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August 4, 2023
by
Ekeeda
Polar Plots Problem 3 Frequency Response Analysis

## TL;DR

Learn how to sketch the polar plot of a system with the given open loop transfer function.

## Key Insights

• 🐻‍❄️ The polar plot helps in visualizing the frequency response of a system.
• 🤣 The magnitude decreases as the frequency increases, indicating a high-frequency roll-off.
• 🛀 The phase angle shows the phase shift introduced by the system at different frequencies.
• 🐻‍❄️ The polar plot is useful in analyzing system stability and designing control systems.
• 💁 The polar plot provides valuable information about system behavior without complex calculations.
• 😥 The points on the plot can be used to determine system stability margins.
• 🐻‍❄️ The angle of the polar plot indicates the phase shift, while the distance from the origin represents the magnitude.

### Q: What is the first step to sketch the polar plot of a system?

The first step is to replace the variable "s" with "j omega" in the transfer function equation.

### Q: How do we calculate the magnitude and phase angle of gj omega?

The magnitude is given by 1 / (1 + omega^2), while the phase angle is -2 * tan inverse of omega.

### Q: How do we plot the magnitude and phase angle on polar coordinates?

The magnitude is represented by concentric circles, and the phase angle is represented by radial lines.

### Q: How do we obtain the polar plot from the plotted points?

The plotted points are connected to form a curve, which represents the polar plot of the system.

## Summary & Key Takeaways

• The video explains the steps to sketch the polar plot of a system with the given open loop transfer function.

• The first step is to replace the variable "s" with "j omega" in the transfer function equation.

• Then, the magnitude and phase angle of gj omega are calculated for various values of omega, and plotted on polar coordinates to obtain the polar plot.