## Circuit Theory - Dec 2013

### 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)** Find the current through 15? resistor
(4 marks)
**1 (b)** Obtain the voltage response of series R-L circuit(4 marks)
**1 (c) ** Determine V_{1}/l_{1} and V_{2}/l_{1} for the given network
(4 marks)
**1 (d)** What are standing waves? Define reflection coefficient and VSWR of a transmission line(4 marks)
**1 (e) ** A ?-section filter network consist of a series arm conductor of 20 mH and two shunt arm capacitor of 160 nF each.

Calculate : (i) cut off frequency (ii) attenuation (iii) Phase shift at 15kHz.

Also obtain the impedance in pass-band(4 marks)
**2 (a)** Find I_{1} through 10? by Thevinin's theorem
(6 marks)
**2 (b)** Find Ic and Vc for t>o
(8 marks)
**2 (c) ** Use Nodal analysis to find the voltage drop across 4? and 10? ref Qu. 2(a)(6 marks)
**3 (a)** Design a single stub match for a load of 150? + j232.5? for 75? line at 500MHz using Smith Chart(8 marks)
**3 (b)** Compare foster realization with caurer realizations(8 marks)
**3 (c) ** State the properties of Hurwitz polynomial(4 marks)
**4 (a)** Define T-parameters and relate them to other parameter as indicated.

(i) A and C interms of z-parameters

(ii) B interms of y-parameters

(iii) D interms of h-parameter(8 marks)
**4 (b)** Test whether the following functions are positive real functions with proper reasons.

$$F_1\left(s\right)=\frac{2s^3+2s^2+3s+2}{s^2+1}$$

$$F_2\left(s\right)=\frac{s^2+1}{s\left(s^2+4\right)}$$

(12 marks)
**5 (a)** What are scattering parameters? State their properties(6 marks)
**5 (b)** Derive an expression of m-derived ? section network starting from a constant k section (6 marks)
**5 (c) ** For given circuit,
switch 's' is opened at t=0. switch 's' was on for long time.
Determine
$$V_L\left(0^+\right),\frac{dV_L}{dt}\left(0^+\right)\ and\frac{d^2V_L}{dt^2}\left(0^+\right)$$
(8 marks)
**6 (a)** Explain the graphical representation of series resonance circuit(6 marks)
**6 (b)** Test whether following polynomials are Hurwitz

(i) P(s)=s^{4}+s^{3}+5s^{2}+3s+4

(ii) P(s)=s^{6}+6s^{4}+4s^{2}+2

(8 marks)
**6 (c) ** Find the characteristics impedance, cut off frequency and pass band for the network shown :
(6 marks)