## Network Analysis - Jun 2014

### Electronics & Communication (Semester 3)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1 (a)** The node equations of a network are $$ \left [ \dfrac {1}{5}+ \dfrac {1}{2}j + \dfrac {1}{4} \right ]V_1 - \dfrac {1}{4}V_2 = \dfrac {50 \angle 06^\circ}{5} \ and \ -\dfrac {1}{4} V_1 + \left [ \dfrac {1}{4}- \dfrac {1}{2j}+ \dfrac {1}{2} \right ]v_2 = \dfrac {50 \angle 906^\circ}{2} $$(10 marks)
**1 (b)** Find the current 1 in 28Ω resistor by mesh analysis in Fig. Q1 (b)
(5 marks)
**1 (c)** Using source transformation find power delivered by 50 V source in given network of Fig Q1 (c).
(5 marks)
**2 (a)** Define the following terms with respect to network topology and give example:

i) Oriented and unoriented graphs.

ii) Isomorphic graphs

iii) Fundamental cut set.(6 marks)
**2 (b)** For the network shown in Fig Q2(b), write the tie set schedule selecting centre star as tree and find all the branch currents by solving equilibrium equations.
(10 marks)
**2 (c)** For the network shown in Fig Q2(c) draw the dual network.
(4 marks)
**3 (a)** State and prove superposition theorem.(6 marks)
**3 (b)** Find i_{8} and hence verify reciprocity theorem for the network in Fig Q3 (b).
(8 marks)
**3 (c)** Using Millman's theorem find I_{L} through R_{L} for the network of Fig. Q3 (c).
(6 marks)
**4 (a)** State and prove Thevenin's theorem.(6 marks)
**4 (b)** Find the value of load resistance when maximum power is transfered across it and also find the value of maximum power transferred for the network of Fig. Q4(b).
(8 marks)
**4 (c)** Find the current through 16Ω resistor using Norton's theorem in Fig. Q4(c).
(6 marks)
**5 (a)** Define the following terms i) Resonance

ii) Q-Factor

iii) Selectivity of series RIC circuit

iv) Bandwidth(4 marks)
**5 (b)** Prove that $$ f_0 = \sqrt{f_1, f_2} $$ where f_{1} and f_{2} are the two half power frequencies of a resonant circuits.(8 marks)
**5 (c)** A series RLC circuit has R=4Ω, L=1mH and C=10 μF. Calculate Q factor, band width resonant frequency and the half power frequencies f_{1} and f_{2}.(8 marks)
**6 (a)** For the circuit shown in Fig Q6 (a), determine complete solution for current when switch K is closed at t=0. Applied voltage is y(t) which is given as $$ 100\cos \left (10^3 t + \dfrac {\pi}{2} \right ) $$
(10 marks)
**6 (b)** For the given circuit of Fig. Q 6(b) switch K is changed from position 1 to position 2 at t=0, the steady having been reached before switching. Find the value of$$ i, \dfrac {di}{dt} \ and \ \dfrac {d^2i}{dt^2} $$ at t=0^- $$
(10 marks)
**7 (a)** State and prove initial value and final value theorem.(8 marks)
**7 (b)** Obtain the Laplace transform of the saw tooth waveform shown in Fig. Q7(b).
(8 marks)
**7 (c)** Find the Laplace transform of (i) t (ii) Δ (t)(4 marks)
**8 (a)** Obtain the relationship between h and y parameters of a two port network.(8 marks)
**8 (b)** Determine the transmission parameters for the network shown in fig Q8 (b).
(8 marks)
**8 (c)** Define z parameter and draw the equivalent network in terms of z parameters.(4 marks)