## Electrical Network Analysis and Synthesis - Jun 19

### Electronics Engineering (Semester 3)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

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

(3) Draw neat diagrams wherever necessary.

**1.a.**By constructing Millman's equivalent voltage source at the left of terminals a and b in the given circuit, find the current I.

**1.b.**A network and its pole zero diagram are shown in the figure. Determine the values of R, L, C if Z(O)= 1.

**1.c.**Obtain Z- parameters in terms of ABCD parameters.

**1.d.**Explain various types of filters.

**2.a.**Find the current through the 1$\Omega$ resistor in the given network.

**2.b.**Find the value of load impedance ZL so that maximum power can be transferred to it in the network of figure. Find maximum power.

**2.c.**Design a constant-k low-pass T and $\pi$ section filters having cut-off fequency of 4kHz and nominal impedance of 500 $\Omega$

**3.a.**Check whether the following polynomials are Hurwitz polynomials:

(i) $\mathrm{F}(\mathrm{s})=\mathrm{s}^{4}+\mathrm{s}^{3}+4 \mathrm{s}^{2}+2 \mathrm{s}+3$

(ii) $\mathrm{F}(\mathrm{s})=(\mathrm{s}+2)^{3}$

**3.b.**Find the voltage across the 15 $\Omega$ resistor in the given network using mesh analysis.

**4.a.**Test whether the following functions are positive real functions:

(i) $F|s|=\frac{s^{3}+6 s^{2}+7 s+3}{s^{2}+2 s+1}$

(ii) $F|s|=\frac{s|s+3||s+5|}{|s+1||s+4|}$

**4.b.**The network shown in figure has attained steady state with the switch closed for t < 0. At t=0, the switch is opened. Obtain i(t) for t > 0.

**5.a.**Realize Cauer Form I and Cauer Form II of the following LC impedance function.

$Z(s)=\frac{|s+1||s+3|}{s(s+2)}$

**5.b.**Determine Y-parameters for the circuit given in figure.

**5.c.**The voltage $V(s)$ of a network is given by $V(s)=\frac{3 s}{|s+2|\left|s^{2}+2 s+2\right|}$. Plot its pole-zero diagram and hence obtain v(t).

**6.a.**In the circuit given, switch is changed from position 1 to position 2 at a time t=0. Find $i, \frac{d i}{d t}$ and $\frac{d^{2} i}{d t^{2}}$ at time $t=0^{+}$

**6.b.**Find the transmission parameters of the resulting circuit when both are in cascade connection.