## Circuit Theory - May 2016

### Electronics Engineering (Semester 3)

TOTAL MARKS: 80

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

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

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1(a)** test for following polynomial using continued fraction expansion only P(s) = s^{5} + 12s^{4} + 45s^{3} + 60s^{2} + 44s + 48(5 marks)
**1(b)** Obtain transmission parameters (ABCD) in terms of z-parameters.(5 marks)
**1(c)** List the types of damping in a series R-L-C circuit and mention the condition for each damping.(5 marks)
**1(d)** Obtain S-domain (Laplace Transform) equivalent circuit diagram of an inductor and capacitor with initial condition.(5 marks)
**2(a)** Calculate voltage across the resistor 6Ω using source shifting technique.

**2(b)**Compare and obtain Foster-I and Foster-II form using example of RC circuit $ Z(s)=\dfrac{(s+1)(s+6)}{s(s+4)(s+8)} $(10 marks)

**3(a)**Design a short circuit shunt stub match for Z

_{L}=450 ' 600j(&Omega(10 marks)

**3(b)**In the circuit shown determine current I

_{1}and I

_{2}when switch is closed at t=0 (10 marks)

**4(a)**Determine Y-parameter using interconnection of two port networks (10 marks)

**4(b)**Check for positive real function test $$F(s)=\dfrac{2s^2+2s+1}{s^3+2s^2+s+2}$$(5 marks)

**4(c)**Compare Cauer-I and Cauer-II form of LC network $$Z(s)=\dfrac{2(s^2+1)(s^2+4)}{s(s^2+2)}$$(5 marks)

**5(a)**Obtain i(t) for t>0

where r(t) is a ramp signal (10 marks)

**5(b)**Derive an expression for charateristics euqation of a transmission line. Also obtain 'α', 'β' and γ' of the line.(10 marks)

**6(a)**Find Thevenin's equivalent of following n/w (8 marks)

**6(b)**Explain various types of filters.(4 marks)

**6(c)**Obtain Z

_{11}(s), Z

_{21}(s), G

_{21}(s) for the ladders n/w. (8 marks)