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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. 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: 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 > 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.