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Unit 6 - Practice Quiz

ELE205 50 Questions
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1 What is the primary goal of Network Synthesis?

A. To calculate the response of a known network given an excitation.
B. To determine the power consumption of a circuit.
C. To design a network that produces a specified response or function.
D. To analyze the stability of a feedback system.

2 A polynomial is said to be a Hurwitz polynomial if:

A. All its roots lie in the left half of the s-plane.
B. All its roots lie on the imaginary axis only.
C. It has roots in both left and right half planes.
D. All its roots lie in the right half of the s-plane.

3 In a Hurwitz polynomial, if the polynomial is either purely even or purely odd, where do the roots lie?

A. At the origin only.
B. On the imaginary axis.
C. In the right half plane.
D. On the real axis.

4 For a polynomial to be Hurwitz, which of the following regarding its coefficients is necessary (though not sufficient)?

A. Coefficients must be complex numbers.
B. Coefficients can have alternating signs.
C. All coefficients must be non-zero and of the same sign.
D. Some coefficients can be zero without the polynomial being purely even or odd.

5 Which mathematical test is commonly used to determine if a polynomial is Hurwitz?

A. Fourier Transform.
B. Laplace Transform.
C. Routh-Hurwitz Array or Continued Fraction Expansion.
D. Thevenin's Theorem.

6 A function is a Positive Real Function (PRF) if and only if:

A. The poles of lie in the right half plane.
B. The residues of are negative.
C. is imaginary for real .
D. is real for real , and for .

7 If is a Positive Real Function, then is:

A. Hurwitz but not Positive Real.
B. Not necessarily Positive Real.
C. Always Positive Real.
D. Unstable.

8 For a Positive Real Function , the difference between the highest degree of the numerator and the denominator must be:

A. Exactly 2.
B. At most 1.
C. At least 2.
D. Any integer.

9 Which of the following functions is NOT Positive Real?

A.
B.
C.
D.

10 In the synthesis of LC networks, the driving point impedance has poles and zeros located:

A. On the negative real axis.
B. Alternating on the imaginary axis ( axis).
C. On the positive real axis.
D. Complex conjugate pairs in the left half plane.

11 The slope of the reactance function (where ) for an LC network is:

A. Alternating positive and negative.
B. Always strictly negative.
C. Zero.
D. Always strictly positive ().

12 Which synthesis form is obtained by performing a Partial Fraction Expansion of the impedance function ?

A. Foster Form I
B. Foster Form II
C. Cauer Form II
D. Cauer Form I

13 Foster Form II synthesis involves the partial fraction expansion of:

A.
B.
C. (Admittance)
D.

14 Cauer Form I synthesis is achieved by identifying the continued fraction expansion of the network function around:

A.
B.
C.
D. (descending powers of )

15 In Cauer Form II synthesis of an LC network, the polynomials are arranged in:

A. Random order.
B. Factored form.
C. Descending powers of .
D. Ascending powers of .

16 The structure of a Cauer Form I LC network is a:

A. Parallel of series LC tanks.
B. Ladder network with series inductors and shunt capacitors.
C. Series of parallel LC tanks.
D. Ladder network with series capacitors and shunt inductors.

17 If an LC impedance function has a pole at , the element representing this pole in Foster I form is:

A. A shunt Inductor.
B. A series Inductor.
C. A series Capacitor.
D. A shunt Capacitor.

18 If an LC impedance function has a pole at , the element representing this pole in Foster I form is:

A. A shunt Capacitor.
B. A series Inductor.
C. A series Capacitor.
D. A shunt Inductor.

19 For an RC network driving point impedance, the poles and zeros lie on:

A. The right half plane.
B. The imaginary axis.
C. The negative real axis.
D. Complex conjugate locations.

20 Which property describes the arrangement of critical frequencies for RC Impedance ?

A. Poles and zeros interlace, with the critical frequency nearest to the origin being a pole.
B. Poles and zeros lie on the imaginary axis.
C. Poles and zeros interlace, with the critical frequency nearest to the origin being a zero.
D. Poles occur in pairs.

21 The residue of the poles of an RC impedance function must be:

A. Imaginary.
B. Complex.
C. Real and Negative.
D. Real and Positive.

22 The value of the slope for an RC impedance is always:

A. Negative.
B. Undefined.
C. Zero.
D. Positive.

23 To synthesize an RC network using Foster Form I, we perform partial fraction expansion on:

A.
B.
C.
D.

24 To synthesize an RC network using Foster Form II, we perform partial fraction expansion on:

A.
B.
C.
D.

25 In Cauer Form I for an RC network (expansion at infinity), the first element extracted from impedance is a:

A. Series Capacitor.
B. Series Resistor.
C. Shunt Capacitor.
D. Shunt Resistor.

26 In Cauer Form II for an RC network (expansion at origin), the first element extracted from impedance is a:

A. Shunt Capacitor.
B. Series Capacitor.
C. Series Resistor.
D. Shunt Resistor.

27 Which of the following conditions describes the singularity closest to the origin for RL Impedance ?

A. It must be a zero.
B. RL networks have no singularities on the real axis.
C. It must be a pole.
D. It can be either a pole or a zero.

28 For RL networks, the properties of Impedance are analogous (dual) to the properties of:

A. LC Impedance.
B. None of the above.
C. RC Admittance.
D. RC Impedance.

29 To synthesize an RL network using Foster Form I, we perform partial fraction expansion on:

A.
B.
C.
D.

30 The slope of the impedance function plotted against is always:

A. Positive.
B. Zero.
C. Negative.
D. Depending on the values of R and L.

31 An impedance function represents which type of network?

A. Not a valid passive network
B. RL Network
C. RC Network
D. LC Network

32 Correction to previous logic: An impedance function represents:

A. RL Network
B. RC Network
C. LC Network
D. RLC Network

33 In Cauer Form I for an RL network (expansion at infinity), the structure consists of:

A. Series Resistors and Shunt Inductors.
B. Series Capacitors and Shunt Resistors.
C. Series Inductors and Shunt Resistors.
D. Series Resistors and Shunt Capacitors.

34 Which form of synthesis yields a ladder network?

A. Foster Form I
B. Partial Fraction Expansion
C. Foster Form II
D. Cauer Forms (I and II)

35 For a rational function to be an LC impedance, the residues at its poles must be:

A. Complex.
B. Real and Positive.
C. Real and Negative.
D. Purely Imaginary.

36 Identify the element values for .

A. Capacitor of 2 F.
B. Inductor of 2 H.
C. Capacitor of 0.5 F.
D. Resistor of 2 .

37 Identify the element values for .

A. Inductor of 3 H.
B. Capacitor of 3 F.
C. Resistor of 3 .
D. Inductor of 0.33 H.

38 In RC Foster II synthesis, the network consists of:

A. Parallel connection of series RC branches.
B. Series connection of series RC branches.
C. Ladder of R and C.
D. Series connection of parallel RC branches.

39 The condition holds true for:

A. Pure Inductance.
B. RL Impedance.
C. LC Impedance.
D. RC Impedance.

40 The continued fraction expansion represents which network type?

A. RC Foster I
B. RC Cauer I
C. RL Cauer I
D. LC Cauer I

41 For a function to be Positive Real, the sum of the residues of poles on the axis must be:

A. Zero.
B. Real and Positive.
C. Real and Negative.
D. Undefined.

42 If represents an RL impedance, then is:

A. Zero.
B. Greater than .
C. Less than or equal to .
D. Infinite.

43 Which theorem states that the roots of the even and odd parts of a Hurwitz polynomial interlace on the imaginary axis?

A. Maximum Modulus Theorem.
B. Hermite-Biehler Theorem.
C. Foster's Reactance Theorem.
D. Theorem of Interlacing Zeroes.

44 When synthesizing a network, if a degree of the numerator is less than the denominator, the first element in Cauer I synthesis (division) will be:

A. An inductor.
B. A capacitor.
C. Zero (requires inversion first).
D. A resistor.

45 A minimum phase function is a function where:

A. Poles are on the imaginary axis.
B. Only zeros are in the Left Half Plane.
C. All poles and zeros are in the Left Half Plane.
D. Only poles are in the Left Half Plane.

46 Which of the following is NOT a property of an LC driving point impedance?

A. It is a ratio of odd to even or even to odd polynomials.
B. The highest and lowest powers of numerator and denominator differ by exactly 1.
C. It has a constant real part for all frequencies.
D. Poles and zeros lie on the axis.

47 In the synthesis of using Foster I, the term corresponds to:

A. A Parallel Inductor.
B. A Series Inductor.
C. A Parallel Capacitor.
D. A Series Capacitor.

48 Sturm's Test is used to:

A. Check the number of real roots of a polynomial.
B. Synthesize a lattice network.
C. Determine the value of components.
D. Calculate bandwidth.

49 If is an RC impedance, then is:

A. Never Positive Real.
B. Not strictly defined in network synthesis.
C. An LC admittance.
D. Always Positive Real.

50 For a function to be realizable as a passive one-port network, it must be:

A. A Rational Function only.
B. Differentiable everywhere.
C. A Hurwitz Polynomial.
D. A Positive Real Function.
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