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Network Synthesis MCQs

Practice Network Synthesis MCQs with four options, answers and explanations for focused Electronics & Telecommunication Engineering revision.

Question 1
Network TheoryNetwork Synthesis

For a physically realizable passive driving-point impedance, a necessary network-synthesis property is that the function be?

  • APositive real
  • BPurely negative real at all frequencies
  • CAn arbitrary non-rational function
  • DUnstable by definition
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Correct Answer: A. Positive real
Explanation: Driving-point immittance functions of passive RLC networks must satisfy positive-real conditions, including nonnegative real part in the right-half-plane where defined.
Reference: Standard network theory: positive-real functions
Question 2
Network TheoryNetwork Synthesis

A real-rational function F(s) is called positive real if, among other requirements, Re[F(s)] is?

  • ANonnegative for Re(s)>0
  • BAlways negative for Re(s)>0
  • CZero for every complex s
  • DInfinite on the entire j-omega axis
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Correct Answer: A. Nonnegative for Re(s)>0
Explanation: One defining condition of a positive-real function is Re[F(s)]>=0 in the open right-half s-plane, together with appropriate real-rational symmetry conditions.
Reference: Standard network theory: positive-real condition
Question 3
Network TheoryNetwork Synthesis

In a lossless LC driving-point reactance function, poles and zeros on the j-omega axis characteristically?

  • AInterlace
  • BAlways coincide
  • COccur only at positive real s
  • DHave no ordering relationship
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Correct Answer: A. Interlace
Explanation: For realizable LC reactance functions, simple poles and zeros lie on the imaginary axis and alternate, or interlace, with frequency.
Reference: Standard network theory: reactance functions
Question 4
Network TheoryNetwork Synthesis

Foster’s first form for an LC driving-point impedance is obtained from a partial-fraction expansion of?

  • AThe impedance function Z(s)
  • BOnly the time-domain current
  • CThe incidence matrix
  • DThe nodal determinant only
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Correct Answer: A. The impedance function Z(s)
Explanation: Foster-I impedance realization follows directly from expanding Z(s) into partial fractions, with terms represented by simple reactive sections.
Reference: Standard network theory: Foster realization
Question 5
Network TheoryNetwork Synthesis

Cauer network synthesis is based primarily on?

  • AContinued-fraction expansion
  • BFourier-series expansion
  • CTaylor expansion around infinity only
  • DMatrix inversion without a network function
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Correct Answer: A. Continued-fraction expansion
Explanation: Cauer forms are ladder realizations derived by successive continued-fraction expansion of a driving-point impedance or admittance.
Reference: Standard network theory: Cauer realization
Question 8
Network TheoryNetwork Synthesis

For a polynomial to be Hurwitz, all of its roots must lie in which region, allowing simple j-omega-axis roots only under the standard special conditions?

  • AClosed left-half plane
  • BOpen right-half plane
  • COnly positive real axis
  • DOnly at the origin
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Correct Answer: A. Closed left-half plane
Explanation: A Hurwitz polynomial has no roots in the open right-half plane; permitted imaginary-axis roots are simple under the standard network-synthesis definition.
Reference: Standard network theory: Hurwitz polynomial
Question 9
Network TheoryNetwork Synthesis

Which polynomial is Hurwitz?

  • As^2-3s+2
  • Bs^2+3s+2
  • Cs^2-1
  • Ds^2-2s+5
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Correct Answer: B. s^2+3s+2
Explanation: s^2+3s+2=(s+1)(s+2), whose roots -1 and -2 lie in the left-half plane.
Reference: Standard network theory: Hurwitz polynomial numerical
Question 10
Network TheoryNetwork Synthesis

For a positive-real rational function, any poles on the j-omega axis must be?

  • AMultiple with complex residues
  • BSimple with real nonnegative residues
  • CAlways double poles
  • DLocated only in the right-half plane
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Correct Answer: B. Simple with real nonnegative residues
Explanation: A positive-real function may have simple imaginary-axis poles, and their residues must be real and nonnegative.
Reference: Standard network theory: positive-real pole condition
Question 11
Network TheoryNetwork Synthesis

For a positive-real function F(s), complex poles and zeros must occur in?

  • AUnrelated locations
  • BComplex-conjugate pairs
  • COnly the right-half plane
  • DOnly at s=0
Report an error
Correct Answer: B. Complex-conjugate pairs
Explanation: Because a positive-real network function is real for real s, nonreal poles and zeros occur in complex-conjugate pairs.
Reference: Standard network theory: conjugate roots
Question 12
Network TheoryNetwork Synthesis

An RC driving-point impedance has poles and zeros on the negative real axis that characteristically?

  • AInterlace
  • BAlways coincide
  • CAppear only as complex pairs
  • DLie only on the positive real axis
Report an error
Correct Answer: A. Interlace
Explanation: For an RC driving-point impedance, realizability imposes alternating or interlacing negative-real poles and zeros with the appropriate ordering.
Reference: Standard network theory: RC impedance synthesis
Question 13
Network TheoryNetwork Synthesis

For an RL driving-point impedance, poles and zeros of a realizable simple ladder form are characteristically located on the?

  • APositive real axis
  • BNegative real axis
  • Cj-omega axis only
  • DUnit circle
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Correct Answer: B. Negative real axis
Explanation: RL driving-point functions have real nonpositive critical frequencies; their finite poles and zeros interlace on the negative real axis.
Reference: Standard network theory: RL impedance synthesis
Question 14
Network TheoryNetwork Synthesis

A Foster realization is especially associated with expansion of a driving-point function into?

  • APartial fractions
  • BA Fourier series only
  • CA determinant of the incidence matrix
  • DA power series in time
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Correct Answer: A. Partial fractions
Explanation: Foster synthesis decomposes an immittance into partial-fraction terms that map to simple circuit sections.
Reference: Standard network theory: Foster synthesis principle
Question 17
Network TheoryNetwork Synthesis

For a pure reactance one-port made only of ideal L and C elements, the real part of its impedance on the j-omega axis away from poles is?

  • APositive and frequency dependent
  • BNegative and frequency dependent
  • CZero
  • DAlways equal to 1 ohm
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Correct Answer: C. Zero
Explanation: An ideal lossless LC network absorbs zero average power, so its impedance is purely imaginary away from singularities.
Reference: Standard network theory: reactance function
Question 18
Network TheoryNetwork Synthesis

A rational function whose numerator degree exceeds its denominator degree by more than one cannot directly represent the driving-point impedance of a finite passive RLC network because it violates the usual?

  • APositive-real realizability requirements
  • BKCL sign convention only
  • CNode numbering rule
  • DTransformer turns-ratio rule
Report an error
Correct Answer: A. Positive-real realizability requirements
Explanation: Finite passive RLC driving-point immittances are positive-real rational functions with constrained high-frequency behavior; an excessive degree difference is incompatible with those realizability conditions.
Reference: Standard network theory: realizability condition