Bode Magnitude Plot for a 4th Order All-Pole System at High Frequencies

To understand why option 'A' (-80 dB/decade) is the correct answer, let's first examine the characteristics of a 4th order all-pole system and how it affects the bode magnitude plot at high frequencies.

Characteristics of a 4th Order All-Pole System

A 4th order all-pole system is a type of filter that consists of four poles located at different frequencies in the complex plane. Each pole contributes to the transfer function of the system and affects the frequency response.

At high frequencies, the poles of the system dominate the behavior of the bode magnitude plot. The poles can be either real or complex conjugate pairs. In this case, we will consider the poles to be real.

Bode Magnitude Plot

The bode magnitude plot is a graph that represents the magnitude (in decibels) of the system's transfer function as a function of frequency. It shows how the system responds to different frequencies.

At high frequencies, the bode magnitude plot of a 4th order all-pole system exhibits a slope determined by the number of poles in the system. Each pole contributes a slope of -20 dB/decade to the overall slope of the plot.

Explanation of the Correct Answer

In a 4th order all-pole system, there are four poles. Each pole contributes a slope of -20 dB/decade, resulting in a total slope of -80 dB/decade at high frequencies.

Therefore, the correct answer is option 'A' (-80 dB/decade). This means that as the frequency increases, the magnitude of the system's transfer function decreases by 80 dB for every decade increase in frequency.

Summary

- A 4th order all-pole system consists of four poles that affect the frequency response of the system.
- At high frequencies, the poles dominate the behavior of the bode magnitude plot.
- The bode magnitude plot of a 4th order all-pole system exhibits a slope determined by the number of poles in the system.
- Each pole contributes a slope of -20 dB/decade to the overall slope of the plot.
- Therefore, a 4th order all-pole system exhibits a slope of -80 dB/decade at high frequencies.