Question

In a bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?

• A. -80 dB/decade
• B. -40 dB/decade
• C. 40 dB/decade
• D. 80 dB/decade

Hint:

Bode Plot Slopes. Each pole contributes -20 dB/decade (-6 dB/octave) to the magnitude slope at high frequencies. Each zero contributes +20 dB/decade (+6 dB/octave). The net high-frequency slope depends on the difference between the number of poles and finite zeros (relative degree). For an n-th order all-pole system, the high-frequency slope is -20n dB/decade.

Answer 1

The Correct Option is A

A Bode magnitude plot shows the logarithm of the magnitude of a system's frequency response (\(|H(j\omega)|\)) versus the logarithm of frequency (\(\omega\))
The slope of the plot indicates how the magnitude changes with frequency
An all-pole system has a transfer function with poles but no finite zeros
The high-frequency behavior is dominated by the poles
Each pole contributes a slope of -20 dB/decade to the magnitude plot beyond its corner frequency
A 4th order all-pole system has 4 poles
At high frequencies (well beyond all pole corner frequencies), the contributions from all 4 poles add up
Total high-frequency slope = (Number of poles) \(\times\) (-20 dB/decade/pole) Total slope = 4 \(\times\) (-20 dB/decade) = -80 dB/decade