Network Functions MCQs

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

Question 1

Network TheoryNetwork Functions

A first-order network has transfer function H(s)=1/(s+1000). Its pole is located at?

As=0
Bs=+1000
Cs=-1000
Ds=-1/1000

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Correct Answer: C. s=-1000

Explanation: The pole is the root of s+1000=0, hence s=-1000 rad/s.

Reference: Standard network theory: network functions

Question 2

Network TheoryNetwork Functions

For H(s)=(s+2)/(s+5), the zero and pole are respectively?

A-2 and -5
B-5 and -2
C+2 and +5
D+5 and +2

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Correct Answer: A. -2 and -5

Explanation: The numerator becomes zero at s=-2 and the denominator becomes zero at s=-5.

Reference: Standard network theory: network functions

Question 3

Network TheoryNetwork Functions

For a network with zero initial conditions, its transfer function H(s) is generally defined as?

AInput divided by output
BOutput transform divided by input transform
COutput plus input
DOnly the denominator polynomial

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Correct Answer: B. Output transform divided by input transform

Explanation: With zero initial conditions, H(s)=Y(s)/X(s), the ratio of output transform to input transform.

Reference: Standard network theory: network functions

Question 4

Network TheoryNetwork Functions

The poles of a network transfer function are the values of s that make its?

ANumerator zero
BDenominator zero
CInput resistance zero only
DOutput voltage always one

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Correct Answer: B. Denominator zero

Explanation: Poles are roots of the denominator polynomial of the transfer function after common factors have been removed.

Reference: Standard network theory: network functions

Question 5

Network TheoryNetwork Functions

The zeros of a transfer function are the values of s that make its?

ANumerator zero
BDenominator zero
CTime constant infinite only
DSupply voltage zero

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Correct Answer: A. Numerator zero

Explanation: Zeros are roots of the numerator polynomial after common factors have been removed.

Reference: Standard network theory: network functions

Question 6

Network TheoryNetwork Functions

For a stable continuous-time LTI network with a rational transfer function, all poles must lie where in the s-plane for asymptotic stability?

AStrictly in the left half-plane
BStrictly in the right half-plane
COnly on the positive real axis
DAnywhere with positive real part

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Correct Answer: A. Strictly in the left half-plane

Explanation: For a causal rational continuous-time system to be asymptotically stable, its poles must have negative real parts, i.e. lie strictly in the left half-plane.

Reference: Standard network theory: network functions

Question 7

Network TheoryNetwork Functions

For a causal system with transfer function H(s)=10/(s+10), the DC gain H(0) is?

A0
B1
C10
D100

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Correct Answer: B. 1

Explanation: H(0)=10/(0+10)=1.

Reference: Standard network theory: network functions

Question 8

Network TheoryNetwork Functions

A transfer function has poles at s=-2 and s=-5. Which pole is dominant in the usual time-response sense?

As=-5
Bs=-2
CBoth are always equally dominant
DNeither pole affects response

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Correct Answer: B. s=-2

Explanation: The pole closer to the imaginary axis, s=-2, corresponds to the slower decaying exponential and generally dominates the long-term transient.

Reference: Standard network theory: network functions

Question 9

Network TheoryNetwork Functions

A first-order network has a pole at s=-200 rad/s. Its time constant is?

A0.5 ms
B5 ms
C20 ms
D200 ms

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Correct Answer: B. 5 ms

Explanation: For a first-order pole at -1/tau, tau=1/200 s=0.005 s=5 ms.

Reference: Standard network theory: network functions

Question 10

Network TheoryNetwork Functions

For a linear network, the driving-point impedance at a port is defined as?

AVoltage at the port divided by current entering the same port
BCurrent at one port divided by voltage at another port
COutput power divided by input voltage
DVoltage multiplied by current

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Correct Answer: A. Voltage at the port divided by current entering the same port

Explanation: A driving-point impedance relates voltage and current at the same pair of terminals: Z(s)=V(s)/I(s).

Reference: Standard network theory: driving-point impedance

Question 11

Network TheoryNetwork Functions

A transfer impedance network function is generally defined as?

AOutput voltage divided by input current
BInput voltage divided by input current at the same port only
COutput current divided by output voltage
DInput power divided by output power

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Correct Answer: A. Output voltage divided by input current

Explanation: Transfer impedance, or transimpedance, relates a response voltage at one location to an excitation current at another: Zt(s)=Vout(s)/Iin(s).

Reference: Standard network theory: transfer impedance

Question 12

Network TheoryNetwork Functions

A transfer admittance is generally expressed as?

AOutput current divided by input voltage
BOutput voltage divided by input current
CInput voltage divided by input current
DOutput voltage divided by output current

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Correct Answer: A. Output current divided by input voltage

Explanation: Transfer admittance relates response current to excitation voltage, typically Yt(s)=Iout(s)/Vin(s).

Reference: Standard network theory: transfer admittance

Question 13

Network TheoryNetwork Functions

A transfer function has a zero at s=-4. Which factor appears in its numerator?

As-4
Bs+4
C1/(s+4)
Ds^2+4

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Correct Answer: B. s+4

Explanation: A zero at s=-4 means the numerator becomes zero at -4, so it contains the factor (s+4).

Reference: Standard network theory: zeros

Question 14

Network TheoryNetwork Functions

A stable causal rational network function requires all natural-response poles to lie where in the s-plane?

AOpen right-half plane
BOpen left-half plane
COnly at the origin
DAnywhere on the real axis

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Correct Answer: B. Open left-half plane

Explanation: For asymptotic stability of a causal continuous-time rational network, natural modes must decay, requiring poles in the open left-half plane.

Reference: Standard network theory: stability and poles

Question 15

Network TheoryNetwork Functions

A pole located at s=-50 corresponds to an exponential natural mode with time constant?

A0.002 s
B0.02 s
C0.05 s
D50 s

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Correct Answer: B. 0.02 s

Explanation: A pole at -1/tau=-50 gives tau=1/50=0.02 s.

Reference: Standard network theory: pole and time constant

Question 16

Network TheoryNetwork Functions

For H(s)=(s+2)/[(s+5)(s+10)], the finite zero is located at?

As=-10
Bs=-5
Cs=-2
Ds=+2

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Correct Answer: C. s=-2

Explanation: The numerator becomes zero when s+2=0, so the finite zero is at s=-2.

Reference: Standard network theory: pole-zero identification

Question 17

Network TheoryNetwork Functions

The impulse response of a causal LTI network is obtained from its transfer function H(s) by?

ATaking the inverse Laplace transform of H(s)
BDifferentiating H(s) only with respect to resistance
CSetting s=0 only
DTaking the square of H(s)

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Correct Answer: A. Taking the inverse Laplace transform of H(s)

Explanation: For zero initial conditions, the causal impulse response h(t) is the inverse Laplace transform of H(s).

Reference: Standard network theory: impulse response

Question 18

Network TheoryNetwork Functions

If H(s)=1/(s+4), the causal impulse response is?

Ae^(-4t)u(t)
B4e^(-t)u(t)
C1-e^(-4t)
Ddelta(t-4)

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Correct Answer: A. e^(-4t)u(t)

Explanation: The inverse Laplace transform of 1/(s+a) is e^(-at)u(t), so h(t)=e^(-4t)u(t).

Reference: Standard network theory: impulse response numerical

Question 19

Network TheoryNetwork Functions

For zero initial conditions, the output transform of an LTI network with transfer function H(s) and input X(s) is?

AY(s)=H(s)+X(s)
BY(s)=H(s)X(s)
CY(s)=H(s)/X(s)
DY(s)=X(s)-H(s)

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Correct Answer: B. Y(s)=H(s)X(s)

Explanation: By definition of the transfer function under zero initial conditions, H(s)=Y(s)/X(s), hence Y(s)=H(s)X(s).

Reference: Standard network theory: transfer function input-output relation

Question 20

Network TheoryNetwork Functions

A network function H(s)=(s+3)/(s^2+5s+6) has poles at?

A-1 and -6
B-2 and -3
C+2 and +3
D-3 only

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Correct Answer: B. -2 and -3

Explanation: The denominator factors as (s+2)(s+3), so the poles are at s=-2 and s=-3.

Reference: Standard network theory: pole calculation

Question 21

Network TheoryNetwork Functions

For H(s)=(s+3)/[(s+2)(s+3)], exact pole-zero cancellation reduces the algebraic expression to?

A1/(s+2)
B1/(s+3)
Cs+2
Ds+3

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Correct Answer: A. 1/(s+2)

Explanation: The common factor (s+3) cancels algebraically, leaving H(s)=1/(s+2), subject to the usual caveat that internal system behavior may require separate consideration.

Reference: Standard network theory: pole-zero cancellation

Question 22

Network TheoryNetwork Functions

A rational network function is strictly proper when?

ADegree of numerator is less than degree of denominator
BDegree of numerator equals degree of denominator
CDegree of numerator is greater than degree of denominator
DIts denominator is a constant

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Correct Answer: A. Degree of numerator is less than degree of denominator

Explanation: A strictly proper rational function has numerator degree lower than denominator degree, so its magnitude tends to zero as |s| tends to infinity.

Reference: Standard network theory: proper network functions

Question 23

Network TheoryNetwork Functions

For H(s)=(2s+5)/(s+4), the high-frequency gain limit as |s| tends to infinity is?

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Correct Answer: C. 2

Explanation: For numerator and denominator of equal degree, the high-frequency limit is the ratio of leading coefficients, 2/1=2.

Reference: Standard network theory: high-frequency gain

Question 24

Network TheoryNetwork Functions

A unit-step input has Laplace transform 1/s. For H(s)=5/(s+5), the output transform is?

A5/(s+5)
B1/[s(s+5)]
C5/[s(s+5)]
Ds/(s+5)

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Correct Answer: C. 5/[s(s+5)]

Explanation: Y(s)=H(s)X(s)=[5/(s+5)](1/s)=5/[s(s+5)].

Reference: Standard network theory: step response in s-domain

Question 25

Network TheoryNetwork Functions

For H(s)=5/(s+5) excited by a unit step, the final output value is?

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Correct Answer: B. 1

Explanation: Using the final-value theorem, y(infinity)=lim(s->0) s·5/[s(s+5)]=5/5=1.

Reference: Standard network theory: step final value

Question 26

Network TheoryNetwork Functions

The convolution integral for the zero-state output of a continuous-time LTI network is?

Ay(t)=integral x(tau)h(t-tau)d tau
By(t)=x(t)+h(t)
Cy(t)=x(t)/h(t)
Dy(t)=dx(t)/dt only

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Correct Answer: A. y(t)=integral x(tau)h(t-tau)d tau

Explanation: The zero-state response of an LTI system is the convolution of the input x(t) with the impulse response h(t).

Reference: Standard network theory: convolution

Question 27

Network TheoryNetwork Functions

If x(t)=delta(t) is applied to an LTI network with impulse response h(t), the zero-state output is?

A0
B1
Ch(t)
DIntegral of h(t) only

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Correct Answer: C. h(t)

Explanation: The delta function is the identity element of convolution: delta(t)*h(t)=h(t).

Reference: Standard network theory: impulse input

Question 28

Network TheoryNetwork Functions

For two causal LTI networks with transfer functions H1(s)=1/(s+1) and H2(s)=2/(s+3) connected in cascade, the overall transfer function is?

A3/(2s+4)
B2/[(s+1)(s+3)]
C2/(s+4)
D1/[(s+1)+(s+3)]

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Correct Answer: B. 2/[(s+1)(s+3)]

Explanation: Transfer functions multiply in cascade, so H(s)=H1(s)H2(s)=2/[(s+1)(s+3)].

Reference: Standard network theory: cascade transfer functions

Question 29

Network TheoryNetwork Functions

For a passive one-port, the driving-point admittance Y(s) is the reciprocal of?

ADriving-point impedance Z(s)
BTransfer impedance only
CLoop-current matrix
DIncidence determinant only

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Correct Answer: A. Driving-point impedance Z(s)

Explanation: At the same port, Y(s)=I(s)/V(s)=1/Z(s), provided the reciprocal is defined.

Reference: Standard network theory: driving-point immittance

Question 30

Network TheoryNetwork Functions

A zero of a driving-point impedance Z(s) becomes what in the corresponding admittance Y(s)=1/Z(s), assuming no cancellation?

AA zero
BA pole
CA constant
DA branch current source

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Correct Answer: B. A pole

Explanation: Taking the reciprocal interchanges poles and zeros, so a zero of Z becomes a pole of Y.

Reference: Standard network theory: impedance-admittance poles and zeros

Question 31

Network TheoryNetwork Functions

If Z(s)=(s+2)/(s+5), the corresponding admittance Y(s) is?

A(s+2)/(s+5)
B(s+5)/(s+2)
C1/[(s+2)(s+5)]
Ds+7

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Correct Answer: B. (s+5)/(s+2)

Explanation: Admittance is the reciprocal of impedance, hence Y(s)=(s+5)/(s+2).

Reference: Standard network theory: immittance conversion numerical

Question 32

Network TheoryNetwork Functions

A pole of multiplicity two at s=-a produces a time-domain natural-response term containing?

AOnly e^(-at)
Bt e^(-at) in addition to e^(-at)
Csin(at) only
DA constant only

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Correct Answer: B. t e^(-at) in addition to e^(-at)

Explanation: A repeated pole of order two generates terms proportional to e^(-at) and t e^(-at).

Reference: Standard network theory: repeated poles

Question 33

Network TheoryNetwork Functions

A complex-conjugate pole pair at s=-2 plus or minus j5 produces a natural response with an envelope proportional to?

Ae^(+2t)
Be^(-2t)
Ce^(-5t)
DA constant

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Correct Answer: B. e^(-2t)

Explanation: The real part of the poles determines the exponential envelope, so the oscillation decays as e^(-2t).

Reference: Standard network theory: complex poles

Question 34

Network TheoryNetwork Functions

For H(s)=(s+4)/(s+8), the high-frequency gain approaches?

A0
B0.5
C1
D4

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Correct Answer: C. 1

Explanation: The numerator and denominator have equal degree and equal leading coefficients, so the limit as |s| tends to infinity is 1.

Reference: Standard network theory: high-frequency gain numerical

Question 35

Network TheoryNetwork Functions

A network function has a pole at the origin. Its corresponding natural mode includes which behavior?

AA nondecaying constant term
BOnly an exponentially decaying term
COnly a growing sinusoid
DNo time-domain contribution

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Correct Answer: A. A nondecaying constant term

Explanation: A simple pole at s=0 corresponds to a constant time-domain mode rather than an exponentially decaying mode.

Reference: Standard network theory: pole at origin

Question 36

Network TheoryNetwork Functions

For F(s)=1/[s(s+2)], the residue associated with the pole at s=0 is?

A0
B0.5
C1
D2

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Correct Answer: B. 0.5

Explanation: For a simple pole at zero, the residue is lim(s->0) sF(s)=1/(s+2)|s=0=1/2.

Reference: Standard network theory: residue numerical

Question 37

Network TheoryNetwork Functions

For F(s)=1/[(s+2)(s+3)], the residue at s=-2 is?

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Correct Answer: B. 1

Explanation: The residue at s=-2 is lim(s->-2)(s+2)F(s)=1/(s+3)|s=-2=1.

Reference: Standard network theory: residue at simple pole

Question 38

Network TheoryNetwork Functions

For F(s)=1/[(s+2)(s+3)], the residue at s=-3 is?

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Correct Answer: A. -1

Explanation: The residue at s=-3 is lim(s->-3)(s+3)F(s)=1/(s+2)|s=-3=-1.

Reference: Standard network theory: second residue numerical

Question 39

Network TheoryNetwork Functions

For a stable causal rational network function, moving a pole closer to the imaginary axis generally makes its associated transient?

ADecay faster
BDecay more slowly
CDisappear instantly
DBecome independent of pole location

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Correct Answer: B. Decay more slowly

Explanation: A pole with a smaller-magnitude negative real part produces a slower exponential decay and a longer transient.

Reference: Standard network theory: pole location and transient

Question 40

Network TheoryNetwork Functions

For a stable pair of complex poles -sigma plus or minus j omega_d, increasing sigma while keeping omega_d fixed causes the oscillatory transient to?

ADecay faster
BDecay slower
COscillate at zero frequency
DGrow without bound

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Correct Answer: A. Decay faster

Explanation: The envelope is e^(-sigma t); increasing positive sigma increases the decay rate while omega_d fixes the oscillation frequency.

Reference: Standard network theory: damping from pole location

Question 41

Network TheoryNetwork Functions

A transfer function has poles at -1 and -10. Which pole normally dominates the long-time response if its mode is present?

APole at -10
BPole at -1
CBoth always decay at identical rates
DNeither pole affects settling

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Correct Answer: B. Pole at -1

Explanation: The pole closest to the imaginary axis, -1, has the slowest exponential decay and therefore dominates the long-time response.

Reference: Standard network theory: dominant pole

Question 42

Network TheoryNetwork Functions

For H(s)=10/[(s+1)(s+10)], the DC gain is?

A0.1
B1
C10
D100

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Correct Answer: B. 1

Explanation: H(0)=10/(1×10)=1.

Reference: Standard network theory: DC gain numerical

Question 43

Network TheoryNetwork Functions

For H(s)=K/[(s+2)(s+5)], what value of K gives a DC gain of 1?

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Correct Answer: C. 10

Explanation: H(0)=K/(2×5)=K/10. Setting H(0)=1 gives K=10.

Reference: Standard network theory: normalized DC gain numerical

Question 44

Network TheoryNetwork Functions

A one-port network has driving-point impedance Z(s)=(s^2+4s+3)/(s^2+2s+2). At omega=1 rad/s, what is the real part of Z(j omega)?

A1 ohm
B2 ohm
C3 ohm
D4 ohm

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Correct Answer: B. 2 ohm

Explanation: At s=j, the numerator is (j)^2+4j+3=2+4j and the denominator is (j)^2+2j+2=1+2j. Thus Z(j)=(2+4j)/(1+2j)=2 ohm, so its real part is 2 ohm.

Reference: Standard network theory: driving-point impedance evaluation