In the Bode plot of an open loop transfer function with 8 poles and 5 zeros, slope of the Bode plot for very high frequencies

Explanation:

Bode Plot Analysis for an Open Loop Transfer Function

Definition: A Bode plot is a graphical representation of the frequency response of a system. It consists of two plots: one showing the magnitude (in decibels) versus frequency, and the other showing phase versus frequency. The slope of the magnitude plot at high frequencies depends on the number of poles and zeros in the transfer function.

Problem Statement: The given open loop transfer function has 8 poles and 5 zeros. The question asks for the slope of the Bode plot at very high frequencies.

Solution:

The slope of the Bode plot at very high frequencies is determined by the difference between the number of poles (P) and zeros (Z) in the transfer function. The general formula for the slope is:

Slope (in dB/decade) = -20 × (P - Z)

Step-by-Step Calculation:

1. Given data:
   • Number of poles (P) = 8
   • Number of zeros (Z) = 5
2. Calculate the difference between the number of poles and zeros:
   • P - Z = 8 - 5 = 3
3. Apply the formula for the slope:
   • Slope = -20 × (P - Z) = -20 × 3 = -60 dB/decade

Conclusion: The slope of the Bode plot at very high frequencies is -60 dB/decade. Hence, Option 1 is correct