Code: AE-08 Subject:
CIRCUIT THEORY & DESIGN 
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. The minimum amount of hardware required to make a lowpass filter is
(A) a resistance, a capacitance and an opamp.
(B) a resistance, an inductance and an opamp.
(C) a resistance and a capacitance.
(D) a resistance, a capacitance and an inductance.
b. A system is described by the transfer function 
. The value of its step
response at very large time will be close to
(A) -1 (B) 0
(C) 1 (D)
c. A network N is to be connected to load of 500 ohms. If the Thevenin’s equivalent voltage and Norton’s equivalent current of N are 5Volts and 10mA respectively, the current through the load will be
(B) 10mA (B) 5mA
(C) 2.5mA (D) 1mA
d. A unit impulse voltage is applied to one port network having two linear components. If the current through the network is 0 for t<0 and decays exponentially for t>0 then the network consists of
(A) R and L in series (B) R and L in parallel
(C) R and C in parallel (D) R and C in series
e. The two-port
matrix of an n:1 ideal transformer is 
. It describes the transformer in
terms of its
(A) z-parameters. (B) y-parameters.
(C) Chain-parameters. (D) h-parameters.
f. If F(s)
is a positive-real function, then 
(A) must have a single zero for
some value of 
.
(B)
must
have a double zero for some value of .
(C)
must
not have a zero for any value of .
(D)
may
have any number of zeros at any values of but 
for all.
g. The poles of a Butterworth polynomial lie on
(A) a parabola. (B) a left semicircle.
(C) a right semicircle. (D) an ellipse.
h. A
reciprocal network is described by 
and 
. Its transmission zeros are located
at
(A)
(B)
(C) and at (D) and at 
i. In order to apply superposition theorem, it is necessary that the network be only
(A) Linear and reciprocal.
(B) Time-invariant and reciprocal.
(C) Linear and time-invariant.
(C) Linear.
j. The Q-factor of a parallel resonance circuit consisting of an inductance of value 1mH, capacitance of value 10-5F and a resistance of 100 ohms is
(A) 1 (B) 10
(C) 
(D)
100
Answer any FIVE Questions out of EIGHT Questions.
Each question carries 16 marks.
Q.2 a. Write minimum number of integro-differential mesh equations required to solve for all node voltages and branch currents in the network of Fig.Q2.The term vg should not be present in your equations. (6)
 |
Fig.Q2
b. Derive the condition for maximum power transfer from a source whose internal impedance is resistive to a load which is a series combination of a resistance and a reactance. (10)
Q.3 a. In
Fig.Q3, 
and
the initial voltage on the capacitor is 50V. If the switch is closed at t=0,
determine the current through the capacitor and the voltage across the inductor
at t=0+. (6)
b. Assume that the switch in Fig.Q3 has been closed for a long time. Using phasor methods, find the current drawn from the source and the circuit impedance, resistance and reactance. (10)
 |
Q.4 a. Find the Thevenin’s voltage and the Thevenin’s equivalent resistance across terminals a-b in Fig.Q4. Assume V1=10V, R1=5 Ohms, R2= 2 Ohms, r= 1 Ohm, I=2A and V=12V. Determine the power drawn from the 12V source when the load is connected. (8)
 |
b. Consider a series resonance circuit consisting of a 10 Ohms resistance, a 2mH inductance and a 200nF capacitance. Determine the maximum energy stored , the energy dissipated per cycle and the bandwidth of the circuit. Write the normalized form of the admittance for this circuit. (8)
Q.5 For the given
network function 
, draw its pole-zero plot and
determine (i) 
, the frequency at which 
attains its
maximum value, (ii) 
, (iii) the half power points, and
(iv) the magnitude of the function at half power points. Using this
information, draw a neat sketch of the magnitude and the phase responses. (16)
Q.6 Determine the h-parameters of the network shown in Fig.Q6. (16)
 |
Q.7 a. Determine if the
function 
is positive real. (10)
b. Given that 
, determine a
realizable G(s). (6)
Q.8 a. Synthesise
the voltage transfer function 
by any method and obtain the realized
value of K. (9)
b. Determine the voltage transfer function of the network shown in Fig.Q8. All resistances are 1 ohm, inductors 1H and capacitors 1F. (7)
Q.9 a. Realize
the impedance 
in
three different ways. (12)
b. Show that the filter described by the transfer function
is a lowpass filter. (4)