Network Theory Test 6

Result

Network Theory Test 6

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Question 1
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A system transfer function is \(H\left( s \right) = \frac{{{a_1}{s^2} + {b_1}s + {c_1}}}{{{a_2}{s^2} + {b_2}s + {c_2}}}\). If a₁ = b₁ = 0, and all other coefficients are positive, the transfer function represents a

A
low pass filter

B
high pass filter

C
band pass filter

D
notch filter

Solution

\(H\left( s \right) = \frac{{{a_1}{s^2} + {b_1}s + {c_1}}}{{{a_2}{s^2} + {b_2}s + {c_2}}}\)
a₁ = b₁ = 0
\(\Rightarrow H\left( s \right) = \frac{{{c_1}}}{{{a_2}{s^2} + {b_2}s + {c_2}}}\)
at s = 0, H(0) = \(\frac{{{c_1}}}{{{c_2}}}\)
at s = ∞, H (∞) = 0
The given function passes the signal at low frequencies only.
Hence the given transfer function represents low pass filter.