University of Mumbai 2004 B.E Electronics & Tele-Communication Engineering FILTER THEORY (.) - Question Paper

FILTER THEORY (DEC.2004)
N.B.
(1) Question No. one is compulsory.
(2) Answer any 4 from the remaining 6 ques..

1. (a) What is Biquadratic function? (10)
A Biquadratic function has poles at- 10 ± j 1000, zeros at ± j 1200 and the magnitude at infinite frequency is 0 dB. Determine:
i) An expression for the function. (ii) The pole Q.
iii) The magnitude at 1000 and 1200 rad/sec.
(b) Explain the importance of sensitivity measure for network design issues. What is gain sensitivity ? (10)
The transfer function of an active RC ( one /R2 R3 C1 C2)
S2 + ( one / R1C1) S + ( one / { R1 R3 C1 C2 } )
circuit is as provided above, Identify the biquadratic parameters and determine their sensitivities to the elements.
2. (a) i) obtain the order of Chebyshev magnitude function needed to meet the subsequent
specifications: (2)
Wp = one rad/sec, Kp = 0.5 dB
Ws = 2.33 rad/sec, Ks = 20 dB
ii) Determine transfer function from table and synthesis it for a termination in 50 Q. (6)
iii) obtain Cn (W) for this filter. (2)

(b) The equivalent low pass magnitude response with a normalized pass band corresponding third order high .pass filter is provided by a Butterworth magnitude function of third order.
NLP = H / ( S3 + 2S2 + 2S + 1)

i) Determine transfer function of the high pass filter having Butterworth response with cut-off frequency of three KHz. (3)
ii) Synthesize the high pass filter having the transfer function in (i) for a termination* of 50 ? and show real values of the components. (6)
iii) Determine the per decade in transfer region of the frequency response. * (1)
3. (a) Derive an expression for state variable (KHN) filter configuration for a transfer function of a band pass 2nd order filter provided by - (10)
V2(s)/ V1(s) = - (H) s
s2 + a1s + a0

Hence derive expression for Wn, Q and H0
(b) Draw the circuit configuration for Generalized Impedance Converter (GIC). Analyses it and determine transmission parameters. (10)


4
(a) Realize and draw a schematic circuit for 2nd order finite gain single amplifier active RC band pass filter. find expressions for Wn, Q, HO in terms of circuit parameter.
Hence design Sallen key band pass filter for Wn = one rad/sec, Q = 2, R1 = C3 = C5= and K=2. (10)
(b) Realize the provided 2nd order elliptic voltage transfer function with Biquadratic Positive and negative feedback. (10)
V2(s) = 0.1397 s2+1.0428
V1(s) s2 +0.9989 s+1.1701
I
S. (a) i) obtain the order of Butterworth response that realize the subsequent specifications in normalized
form. (2)
Wp=l rad/sec., Kp = 3.01dB
Ws = 2rad/sec., Ks = 15dB
ii) Determine transfer function from table and synthesize it for a termination of one ?. (8)
(b) What is Chebyshev Rational Function? (10)
List the properties of an elliptic function.
obtain the order of an elliptic function to meet the subsequent
specifications:
fp = 1000Hz, Kp =3.01dB fs = 1300 Hz, K s = 22dB.

6. (a) Derive the transfer function for 2nd order infinite gain high pass single amplifier filter. Hence realize an infinite gain single amplifier filter for subsequent specifications: ' (10)
fn=l KHz, Q-1/v2, |Hol = five chooseC = 0.01 µF.
(b) Draw a neat circuit diagram of a Akerberg-Mossberg filter and derive the expression for its voltage transfer function having low pass characteristics. (10)
7. (a) elaborate the advantages of switch-capacitor filter? discuss working of switch capacitor LEAP-
FROG and TWO-THOMAS filters with the help of neat circuit diagram. (10)
(b) i) discuss the principle of realization of a resistor in a switch capacitor filter. How it could be implemented in a MOSIC ? (6)
ii) Draw MOS circuit configuration for a lossy integrator having voltage transfer function. (4)
V2 (s) = -1/(R1C1)
V1 (s) S + (1/ R3 C2)


To realize it as a switch capacitor filter.

Earning:   Approval pending.