Code: DE-07                                                Subject: NETWORK AND TRANSMISSION LINES

Time: 3 Hours                                                                                                     Max. Marks: 100

NOTE: There are 9 Questions in all.

· Question 1 is compulsory and carries 20 marks. Answer to Q. 1. MUST BE WRITTEN IN THE SPACE PROVIDED FOR IT in the answer book supplied and nowhere else.

· Out of the remaining EIGHT Questions answer any FIVE Questions. Each question carries 16 marks.

· Any required data not explicitly given, may be suitably assumed and stated.

Q.1       Choose the correct or best alternative in the following:                                         (2x10)

a. Given V_TH = 20V and R_TH = 5 Ω, the current in the load resistance of a network,   

(A)  is 4A                                            (B)  is more than 4A.

(C)  is 4A or less                                 (D) is less than 4A.

b. The Laplace transform of a function is 1/s x Ee^–as. The funtion is

(A) E sin ωt                                        (B) Ee^at

(C)  E u(t–a)                                        (D) E cos ωt                                                         

             c.   For a symmetrical network

(A) Z₁₁ = Z₂₂ (B) Z₁₂ = Z₂₁

(C) Z₁₁ = Z₂₂ and Z₁₂ = Z₂₁ (D) Z₁₁ x Z₂₂ – Z₁₂² = 0                                        

             d.   A constant k low pass T-section filter has Z₀ = 600Ω at zero frequency. At f = f_c the characteristic impedance is

(A) 600Ω (B)  0

(C) (D)  More than 600Ω

             e.   In m-derived terminating half sections, m =

(A) 0.1                                               (B) 0.3

(C) 0.6                                                (D) 0.95

             f.    In a symmetrical T attenuator with attenuation N and characteristic impedance R₀, the resistance of each series arm is equal to   

(A) R₀ (B)  (N–1)R₀

(C) (D) 

             g.   For a transmission line, open circuit and short circuit impedances are 20Ω and 5Ω. The characteristic impedance of the line is

(A) 100 Ω (B) 50 Ω

(C) 25 Ω (D) 10 Ω.

             h.   If K is the reflection coefficient and S is the Voltage standing wave ratio, then

(A) (B)

(C) (D)

             i.    A parallel RLC network has R=4Ω, L =4H, and C=0.25F, then at resonance Q=

(A) 1                                                   (B)  10

(C)20.                                                 (D)  40

             j.   A delta connection contains three impedances of 60 Ω each. The impedances of the equivalent star connection will be

(A) 15Ω each.                                     (B) 20Ω each.

(C) 30Ω each.                                     (D) 40Ω each.

Answer any FIVE Questions out of EIGHT Questions.

Each question carries 16 marks.

Q.2     a.   Differentiate between:

(i) Unilateral and Bilateral elements. Give examples.

(ii) Distributed and lumped elements.                                               (8)

             b.   A sinusoidal current, I = 100 cos2t is applied to a parallel RL cir cuit. Given R=5Ω and L=0.1H, find the steady state voltage and its phase angle.                                                              (8)

Q.3     a.   State and prove Convolution Theorem.                                                               (6)

             b.   Define the unit step, ramp and impulse function. Determine the Laplace transform for these functions.                                                                     (6)

c. Find the inverse Laplace transform of

(4)

Q.4     a.   Design a symmetrical T section having parameters of  and .                (6)

b.   A transmission line has the following primary constants per Km loop, R=26 Ω, L=16mH, C=0.2μF and G=4μ mho. Find the characteristic impedance and propagation constant at ω=7500 rad/sec.          (4)

             c.   Determine the elements of a π-section, which is equivalent to a given T-section.                  (6)

Q.5     a.   Find out the Z parameters and hence the ABCD parameters of the network shown in Fig 5.a. Check if the network is symmetrical or reciprocal.   (10)

Fig 5.a

     b.   Calculate the driving point impedance Z(s) of the network shown in Fig 5.b. Plot the poles and zeros of the driving point impedance function on the s-plane.                                                                 (6)

  Q.6     a. State Thevenin’s theorem. Using Thevenin’s theorem, calculate the current in the branch XY, for the circuit given in Fig. 6.a.                                  (2+6)

Fig 6.a

             b.   State and prove Superposition theorem with the help of a suitable example.         (8)

Q.7     a.   Determine the condition for resonance. Find the resonance frequency when a capacitance C is connected in parallel with a coil of inductance L and resistance R. What is impedance of the circuit at resonance? What is the Quality factor of the parallel circuit?                                                                              (8)

b. A coil having a resistance of 20Ω and inductive reactance of 31.4Ω at 50Hz is connected in series with capacitor of capacitance of 10 mF. Calculate

(i) The value of resonance frequency.

(ii) The Q factor of the circuit.                                                                             (8)

Q.8     a.   Derive the expression for the characteristic impedance and propagation constant of a transmission line.                                                                   (8)

             b.   A transmission line with characteristic impedance of 500Ω is terminated by a purely resistive load. It is found by measurement that the minimum value of voltage upon it is 5μV and maximum voltage is 7.55μV. What is the value of load resistance?                                                                               (8)

Q.9     a.   What is an attenuator? Define the terms Decibel and Neper. Derive the relation between the two.                                                              (2+3+3)

b.   Design a m-derived low pass filter (T and π section) having a design resistance of Ro=500Ω and the cut off frequency (f_c) of 1500 Hz and an infinite attenuation frequency  of 2000 Hz. (8)