# ELEC 441_6081_MT2_UG_W11

```Course
Number
Modern/Integrated Circuit Filter Design
Examination
Mid-Term Test#2
ELEC 441
WW
Time
# of pages
Date
April 2, 2012
Section
70 minutes
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.
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: The intermediate frequency filter in a GSM cellular phone system has the transfer function
Provide the design of one of the second order sections above using OTA and C elements. The capacitors must
be below 10pF in value. Calculate the gm and C values in your design.
Q.2: (a) Perform pre-warping on the zero and the pole frequencies in the transfer function
s 2  2.4212  10 5
H ( s)  2
, and derive the associated Switched Capacitor Filter (SCF) transfer
s  1004.2s  8.9833  10 5
function H(z), using bilinear s &gt; z transformation. Use a sampling frequency of 16 kHz.
(b) What will be the response of the SCF at (a) DC, and (b) 492 rad/sec?
The attached Table may be used for your calculations
Table (related to Q.2)
Q.3:
1
1
C
2
1
1
2
1
1
F
G
2
Vi
B
1
2
2
+
1
2
_
H
1
2
2
D
2
A
_
OA1
OA2
OA2
V1
1
2
+
V2
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-domain transfer
function H ( z ) 
Vi
( 2)

V2
(1)
Vi
(1)
. You can assume that the sample-and-hold property holds for the signals Vi , and V1 i.e.,
1
 z 2 Vi
(1)
etc.,.
Q.4: The schematic in Figure 4 represents a normalized low-pass Bessel-Thomson filter of order 3 with equal
terminating resistances.
1
0.8333H

Vi

0.1667 H


0 .48 F
V2

1
Vo

Figure 4
Use frequency dependent negative resistance (FDNR) technique, and show a design of the filter with
50 terminations, and a pass-band edge frequency of 3000 radians.
Show your schematic and the designed element values clearly.
```