Course
Number
Modern/Integrated Circuit Filter Design
Examination
Mid-Term Test#2 (Special)
Section
ELEC 6081
Date
Time
April 13, 2012
70 minutes
WW
# of pages
3
Instructor(s)
Dr. R. Raut
Only ENCS approved calculator allowed
Crib-sheet with hand-written formula on two sides of a A-sized paper allowed.
Special Instructions: (Read very carefully)
Attempt ALL questions
Show all steps clearly in neat and legible handwriting.
Students are required to return question paper together with exam booklet(s).
Q.1: For figure 1, find the voltage transfer function Vo/V
Figure 1:
0.8919s 2  1.1409  10 8
, derive the sampled data
s 2  356s  1.1409  10 8
transfer function H(z) for a sampling frequency of 16kHz. What will be the magnitude of H(z) at
Q.2: Given the low-pass notch function H ( s) 
(a) DC , and at
(a) a frequency of 1700 Hz?
Table (related to Q.2)
(1)
Q.3: For the SCF circuit shown in figure 3, find an expression for the transfer function Vo 2 ( z )
Vi (1) ( z )
.
Figure 3
Figure 3 shows a second order switched capacitor filter using parasitic insensitive switched capacitor
integrators. 1, 2 are non- overlapping clock signals of period T. Find an expression for the Z(1)
V2
domain transfer function H(z)= (1) . You can assume that the sample-and-hold property holds for the
Vi
signals Vi , and V1 i.e., Vi
( 2)

1
 z 2 Vi
(1)
etc.,.
Q.4: The schematic in Figure 4(a) represents a normalized low-pass Bessel-Thomson filter of order 3
with equal terminating resistances.
0.8333H
1

0.1667 H


Vi
0 .48 F

1
V2
Vo


Figure 4(a)
Using Operational Simulation technique produce an active RC design for the above ladder filter with
50 terminations, and a pass-band edge frequency of 3000 radians. You may use the leap-frog
interconnection as shown below (Fig.4(b)). T1, T2, T3 are voltage transfer functions realized with
Operational amplifiers, R, and C elements.
V3 '
Vi '
T1
-T2
V2
V1
Figure 4(b)
Show your schematic and the designed element values clearly.
T3