Question:
The transfer function of a real system, \( H(s) \), is given as:
\[
H(s) = \frac{As + B}{s^2 + Cs + D}
\]
where \( A \), \( B \), \( C \), and \( D \) are positive constants. This system cannot operate as:
The transfer function of a real system, \( H(s) \), is given as:
\[ H(s) = \frac{As + B}{s^2 + Cs + D} \] where \( A \), \( B \), \( C \), and \( D \) are positive constants. This system cannot operate as:
\[ H(s) = \frac{As + B}{s^2 + Cs + D} \] where \( A \), \( B \), \( C \), and \( D \) are positive constants. This system cannot operate as:
Show Hint
A system with a quadratic denominator and linear numerator is not typically suitable to function as a high pass filter or integrator.
Updated On: Nov 27, 2025
- low pass filter.
- high pass filter.
- band pass filter.
- an integrator.
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The Correct Option is B
Solution and Explanation
Step 1: Analyze the transfer function.
The given transfer function is in the form \( \frac{As + B}{s^2 + Cs + D} \), where the numerator and denominator are polynomials of \( s \). The system's behavior depends on the values of the constants \( A \), \( B \), \( C \), and \( D \). Step 2: Identify the system type.
- (A) Low pass filter: A low pass filter allows low frequencies to pass and attenuates higher frequencies. This system can behave as a low pass filter.
- (B) High pass filter: A high pass filter allows high frequencies to pass and attenuates lower frequencies. The given transfer function cannot operate as a high pass filter because it does not have the necessary form for a high-pass characteristic.
- (C) Band pass filter: A band-pass filter allows a certain range of frequencies to pass while attenuating frequencies outside this range. This system can operate as a band pass filter.
- (D) Integrator: An integrator typically has a transfer function with a denominator that is linear in \( s \) (i.e., \( s \) term only), but the given system has a quadratic denominator, so it cannot function as an integrator.
Step 3: Conclusion.
The correct answers are (B) and (D), as this system cannot operate as a high pass filter or an integrator.
The given transfer function is in the form \( \frac{As + B}{s^2 + Cs + D} \), where the numerator and denominator are polynomials of \( s \). The system's behavior depends on the values of the constants \( A \), \( B \), \( C \), and \( D \). Step 2: Identify the system type.
- (A) Low pass filter: A low pass filter allows low frequencies to pass and attenuates higher frequencies. This system can behave as a low pass filter.
- (B) High pass filter: A high pass filter allows high frequencies to pass and attenuates lower frequencies. The given transfer function cannot operate as a high pass filter because it does not have the necessary form for a high-pass characteristic.
- (C) Band pass filter: A band-pass filter allows a certain range of frequencies to pass while attenuating frequencies outside this range. This system can operate as a band pass filter.
- (D) Integrator: An integrator typically has a transfer function with a denominator that is linear in \( s \) (i.e., \( s \) term only), but the given system has a quadratic denominator, so it cannot function as an integrator.
Step 3: Conclusion.
The correct answers are (B) and (D), as this system cannot operate as a high pass filter or an integrator.
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