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The slope of log-magnitude asymptote changes by - 40 dB/ decade at a frequency ω1. This means that
  • a)
    a double pole is present
  • b)
    a pair of complex conjugate poles is present
  • c)
    either a double pole or a pair of complex conjugate poles is present
  • d)
    a pole or zero at origin is present
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The slope of log-magnitude asymptote changes by - 40 dB/ decade at a f...
A double pole or pair of complex poles result in - 40 dB/decade slope in log magnitude graph.
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Most Upvoted Answer
The slope of log-magnitude asymptote changes by - 40 dB/ decade at a f...
Explanation:
The slope of log-magnitude asymptote of a transfer function is given by the number of poles or zeros present in the transfer function.

- For a single pole or zero, the slope changes by -20 dB/decade.
- For a double pole or zero, the slope changes by -40 dB/decade.
- For a triple pole or zero, the slope changes by -60 dB/decade, and so on.

In this question, the slope of log-magnitude asymptote changes by -40 dB/decade at a frequency ω1. Therefore, either a double pole or a pair of complex conjugate poles is present in the transfer function.

This is because a double pole or a pair of complex conjugate poles both contribute to a slope change of -40 dB/decade. They are visually represented as two straight lines with a slope of -40 dB/decade, intersecting at the frequency ω1.

Hence, option C is the correct answer.
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The slope of log-magnitude asymptote changes by - 40 dB/ decade at a frequency ω1. This means thata)a double pole is presentb)a pair of complex conjugate poles is presentc)either a double pole or a pair of complex conjugate poles is presentd)a pole or zero at origin is presentCorrect answer is option 'C'. Can you explain this answer?
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