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Question Bank

Course:Electronics and Communication Engineering Session: 2006-2007

Subject:EE-4105 Network Theory Semester: IV

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Module -1 Network Theorem

1)What are nullators and norators? What are their importances in circuit theory?

2)Differentiate between linear and nonlinear networks with the aid of suitable examples.

3)State and explain with suitable examples (i) Reciprocity (ii) Substitution and (iii) Tellegen’s theorem.

4)Determine current i(t) through the 2 resistor, for the network shown in Fig.(1.1). Also sketch i(t).

5)Determine current i(t) through the inductor, L, in the network shown in Fig.(1.2).

6)Find (i) ammeter current when battery is at A and ammeter at B, and (ii) when battery is at B and ammeter at A. Also calculate the transfer resistance for Fig. (1.3)

7)
B, and (ii) when battery is aiVerity reciprocity theorem for V and I in the circuit shown in Fig. (1.4) and Fig.(1.5).

8)
B, and (ii) when battery is aiVerity reciprocity theorem for V and I in the circuit shown in Fig. (1.6) and Fig.(1.7).

9)Verify Tellegen’s theorem for the circuit given in Fig. (1.8). Given that

V1 = 4; V2 = -2;V3 = 2; V4 = 8; V5 = -6 (All voltages are in volts)

I1 = 2; I2 = 2; I3 = -6; I4 = 4; I5 = 4(All currents are in amperes)

10)Verity reciprocity theorem for the circuit shown in Fig. (1.9)

11)Verify Tellegen’s theorem for the circuit given in Fig. (1.10). Given that

V1 = 4; V2 = 2;V3 = 2; V4 = 3; V5 = -1; V6 = -5 (All voltages are in volts)

I1 = 2; I2 = 2; I3 = 4; I4 = -2; I5 = -6; I6 = 4 (All currents are in amps)

12)In the network shown in Fig.(1.11), V1 = 10V, V2 = 4V, V4 = 6V, I1 = I2 = 2A while I3 = 4A. Check the validity of Tellegen’s theorem.

13)In Fig.(1.12a) and Fig.(1.12b) obtain V0 and establish the reciprocity theorem.

14)Verify Tellegen’s theorem for a network having four branches where voltage and current as function of time are given as:

V1(t) = 10 cos ωt + 4 sin ωt: i1(t) = 2 cos ωt + 0.8 sin ωt

V2(t) = 8 cosωt - 4 sin ωt: i2(t) = 4 cos ωt + sin ωt

V3(t) = 8 cosωt- 5 sin ωt: i3(t) = -3 cos ωt -1.5 sin ωt

V4(t) = -10 cosωt -3.5 sinωt: i4(t) = 2 cos ωt + 1.2 sin ωt

15)Verify Tellegen’s Theorem for the network shown in Fig.(1.13).

Module-2: Network Topology

16)Define the terms with suitable examples: tree, co-tree, forest, co-forest, cut-sets, loops, fundamental-cut-sets, fundamental-loops, twigs and links.

17)Show that the graph of Fig.(2.1) has 16 trees. Make all these trees.

18)Draw the oriented graph of the networks shown in Fig.(2.2).

19)Draw the oriented graph of the networks shown in Fig.(2.3).

20)Fig.(2.4) represents a network. Draw the directed graph, trees and show the loops.

21)Fig.(2.5) represents the oriented graph of a network.

a)Show the tree, twigs and links and henceobtain the f-loop matrix.

b)Show the f-cut sets and henceobtain the f-cut set matrix.

c)Obtained reduced incidence matrix

22)An oriented graph is shown in Fig.(2.6)

a)Obtain the incidence matrix.

b)Obtain the f-loop matrix

c)Obtain the f-cut set matrix

23)For the graph of Fig.(2.7) write down the incidence matrix, tie-set matrix, and f-cut set matrix.

24)For the network of Fig.(2.8), find the number of twigs and links. Obtain the tie-set matrix,incidence matrix, and f-cut set matrix.

25)A graph is shown in Fig. (2.9). Find the tie-set and cut-set matrices and obtain the KCL and KVL equation.(lines indicate twigs while the doted lines the links).

26)Fig (10) represents resistive network. Draw its graph.

a)Select a suitable tree and obtain the tie-set matrix. Write down the KVL equations from the tie-set matrix.

b)Select a suitable tree and obtain the f-cut set matrix. Write down the KCL equations from the f-cut set matrix.

c)Obtain the reduced incidence matrix, A and write down the KCL equations.

27)Develop the f-cut set matrix of the network shown in Fig.(2.11).

28)Draw the incidence matrix of the graph given in Fig.(2.12).

29)Develop the reduced incidence matrix of the graph shown in Fig.(2.13).

30)Incidence matrix of a graph is given below. Draw the directed graph.

Branches

12 34567

-1 0-1 1 0 0 1

0-1 0-1 0-1 0

1 1 0 0-1 1 0

0 0 1 0 1 0-1

31)Draw the graph of the network given in Fig. (2.14) and write down the:

a)tie-set matrix. Obtain the network equilibrium equation in matrix form using KVL.

b)f-cut set matrix. Obtain the network equilibrium equation in matrix form using KCL.

c)incidence matrix. Obtain the network equilibrium equation in matrix form using KCL.

32)For the LTI network shown in Fig. (2.15), which is assumed to be the sinusoidal steady-state, draw the network graph, obtain the dual network; write the mesh equation for the given network and the node equation for the dual network.

33)Let the linear time-invariant network shown in Fig. (2.16.a) be in the sinusoidal steady-state. An oriented graph of this network is shown in Fig. (2.16.b). Use node analysis to find all branch voltage and current given es(t) = cos 10 t.

34)(a) Formulate the rules for writing the mesh equation for planar network by inspection.

(b) Formulate the rule for writing the cut-set equation for a network by inspection.

35)Write the mesh equations for the network shown in Fig. (2.17).

.

36)Write the cut-set and loop equation for the network shown Fig. (2.18).

37)Solve and find out currents and voltages across all branches of the network shown in Fig.(2.19) using current variables method (loop current).

38)Solve the problem shown in Fig.(2.20) using voltage variables method.

39)Draw the oriented graph of the network shown in Fig.(2.21). Select at least four trees. Write down the incidence matrix, tie-set matrix and f-cut set matrix.

40)In the circuit of Fig. (2.22), switch K is closed at time, t = 0. Find the values of at t = 0. Given that V0 = 10 V, R = 100 Ω and C = 1 F.

41)In the circuit of Fig. (2.23), switch K is closed at time, t = 0 with zero current in the inductor. Find the values of at t = 0. Given that V0 = 100 V, R = 10 Ω and L = 1 H.

42)In the circuit of Fig. (2.24), switch K is opened at time, t = 0. Find the values of at t = 0+ if I = 10 A, R = 1000 Ω and C = 1 μF.

43)In the circuit of Fig. (2.25), switch K is opened at time, t = 0. Find the values of at t = 0+ if I = 1 A, R = 100 Ω and L = 1 H.

44)In the circuit of Fig. (2.26), switch K is changed from position (1) to (2) at time, t = 0, steady-state condition having reached before switching. Find at t = 0. ( Ans, 1A, -10/3a/sec; 10/9 A/sec.)

45)In the circuit of Fig. (2.27), switch K is changed from position (A) to (B) at time, t = 0, steady-state condition having reached before switching. Find at t = 0.

46)In the network of Fig. (2.28), switch K is closed at time, t = 0 with zero capacitor voltage and zero inductor current. Solve for (a) v1(t) and v2(t) at t = 0+ (b) v1(t) and v2(t) at t = ∞ (c) at t = 0+ and (d) at t = 0+.

47)The network shown in Fig. (2.29) is in the steady state with the switch K closed. At time, t = 0 the switch is opened. Determine the voltage across the switch vk(t) and at t = 0+.

48) Find the initial conditions in the network shown in Fig. (2.30).

Determine the new circuit element after scaling for the circuit shown in Fig.(3) which is to be scaled to an impedance level of 5 kΩ and a resonant frequency of 5M rad/sec.

49)Determine the new circuit element after scaling for the circuit shown in Fig.(3) which is to be scaled to an impedance level of 600 Ω | E2 / I1| equal to 1/√2 at 3.5 kHz.

50)

51)The circuit shown in fig. (23) is to be sdcaled an impedance level of 600 Ohm with IE2/I1; equal to 1/2 at 3.5 KHz.

  1. In the circuit shown in fig. (33), find the voltage across the capacitor.
  1. For the circuit in fig. (34), Find the voltage across the 5 Ohm resistance.

(Ans: -24.8V)

  1. Explain the term Tndefinits Admittance Matrix (IAM). Mention its properties.
  1. What are the advantange of using nounalized element values?
  1. Determine the IAM of Point N1, N2 and N: as shown in the fig. (35)

Module – 3:Multi-Terminal Networks :

  1. Find the natural frequency of the network shown in fig. (36) .
  1. The natural frequency of a linear time-invaliant network given by:

(i) S1 =-2, S2 = 3, (ii) S1 =2J, S2 = -2J.

Give expressions for the zero input response in term of retime functions.

  1. Derive the relationship between the admittance and transmission parameters.
  1. Find the impedance admittance, hybrid and transmissionmatrices for the network shown ifn fig. (37).
  1. Find the Z-parameters for network shown in fig. (38).
  1. In a T – network, as shown in fig(39), Z1 = 20, Z2 = 5-90, Z3 = 390, Find the Z-parameters.
  1. The following readings were obtained experimentally for unknown two-port network.

V1 V2 I1 I2

Output open 100V 60V 10A 0

Input open 30V 40V 0 3A

Compute the Z-parameters.

  1. Draw the Z-parameter equivalent of prob.(52).
  1. Two identical T-sections, as one shown in fig.(41) are connection in series. Determine the Z-parameters of the combination.

55. In a network, the series arm impedance is 0.0510 -90 mho and shunt arm impedance are 0.110, 0 and 0.210 -90 mho. Find the -parameters.

56A T – type attenuator has been shown in fig.(42). Find the -parameters and draw the equivalent Y-parameter circuit.

  1. A CE transistor equivalent circuit has been shown in fig. (43). Find the h-parameters.

58Find the hybried parameters for tye circuit shown in fig.(44).

59For fig.(45), obtain Z-parameters and show that the network is not reciprocal.

  1. Obtain transmission parameters for the network shown in fig.(46).
  1. In a two-port network, Z11 =100 ohm, Z12 = 120 ohm; Z21 = 120 ohm, Z22 = 50 ohm. Compute Y-parameters.
  2. The Voltage at the two ports of a network are represented as

V1 = 5 I1 + 5 I2

V2 = I1 = 2I2

If the load impedance of 3 Ohm is connected at the output port, determine the input impedance.

  1. Find (V2/V1) and (V2/I1) for the circuit, Shown in fig.(47).
  1. Find the expression of voltage transfer ratio for the network shown in fig.(48).
  1. Describe (i) the necessary for transfer functions (ii) the restrictions on location of poles and zeros in driving point functions.
  2. Check, if the DP impedance Z(cs) given by

can represent a passive one port network.

  1. (a) Determine the Z- parameters for the network of fig.(2) [4]

(b)Obtain the Y- parameters of the same network and also verify the inverse relationship between Z and Y . [6]

3.Determine the current I(t) through L in the network shown in fig.(2)(a) and (b) [10]

4 Synthesize the Foster network for the function

F(s) = (S+1) (S+3)

(S+2)(S+5) ,

Also verify whether the given function is a valid driving point p r impedance/admittance function.

[10]

5. (a) How can you realise Butterworth polynomial using approximation method ? Also plot

magnitude response characteristic for Butterworth filter. [4]

(b)Design a Butterworth LP type of filter, having a cut-off frequency of 1 rad/sec. and the

terminating resistances R1 = R2 = 1  [6]

6. (a) Write the fundamental loop and fundamental cut –set matrices for the oriented graph

shown in fig.(3) [5]

(b)Draw the oriented graph of the network shown in fig. (4). Obtain a tree and prepare the

loop incidence matrix. [5]

(b) Show how will you transform a LP filter to a band elimination type of filter.

(c) Draw the oriented graph of the network shown in fig. (5) Select at least four trees.

  1. Design a low pass Butterworth filter which is having the following specifications:

αp = 1 dB at 1 kHz

αs = 6 dB at 6 kHz

  1. a) Derive the formula for calculating the cut-off frequency of a Butterworth filter

b) Explain duality of a graph with suitable example

Prepared by Mohammad Mohatram 1