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A system has 12 poles and 2 zeros. Its high frequency asymptote in its magnitude plot has a slope of
- a)-200 dB/decade
- b)-240 dB/decade
- c)-280 dB/decade
- d)-320 dB/decade
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A system has 12 poles and 2 zeros. Its high frequency asymptote in its...
-(12 - 2) 20 or - 200 dB/decade.
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A system has 12 poles and 2 zeros. Its high frequency asymptote in its...
Solution:
Given, the system has 12 poles and 2 zeros.
We know that the high-frequency asymptote for a transfer function H(s) with n poles and m zeros is given as:
|H(jω)| → K ω^(m-n) as ω → ∞
where K is a constant.
Here, n = 12 and m = 2.
So, the high-frequency asymptote for the given system is:
|H(jω)| → K ω^(-10) as ω → ∞
Now, we know that the slope of a straight line in dB/decade is given as:
Slope = 20 log|H(jω)| / log ω
So, the slope of the high-frequency asymptote can be found as:
Slope = 20 log(K) - 10 log(ω)
As ω → ∞, log(ω) → ∞ and the second term dominates. Hence, the slope of the high-frequency asymptote is -200 dB/decade.
Therefore, the correct option is (a) -200 dB/decade.
Given, the system has 12 poles and 2 zeros.
We know that the high-frequency asymptote for a transfer function H(s) with n poles and m zeros is given as:
|H(jω)| → K ω^(m-n) as ω → ∞
where K is a constant.
Here, n = 12 and m = 2.
So, the high-frequency asymptote for the given system is:
|H(jω)| → K ω^(-10) as ω → ∞
Now, we know that the slope of a straight line in dB/decade is given as:
Slope = 20 log|H(jω)| / log ω
So, the slope of the high-frequency asymptote can be found as:
Slope = 20 log(K) - 10 log(ω)
As ω → ∞, log(ω) → ∞ and the second term dominates. Hence, the slope of the high-frequency asymptote is -200 dB/decade.
Therefore, the correct option is (a) -200 dB/decade.
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