University of Mumbai 2003 B.E Electronics & Tele-Communication Engineering FILTER THEORY - Question Paper

FILTER THEORY (DEC. 2003)
N.B.:
(1) Question No. one is compulsory.
(2) Attempt any 5 ques. from the remaining 9 ques..
part I
1. (a) What is the necessity of magnitude and phase approximation? (4)
(b) Compare Butterworth, Chebyshev and Elliptic magnitude approximation. (6)
(c) What are me advantages and limitations of active filters. (4)
(d) List the advantages and applications of switched capacitor filters. (4)

(a) Find a low-pass maximally flat magnitude network function whose magnitude characteristic is 3.0103 dB down from its dc value at one kHz and a maximum of 20 dB down at all frequencies greater than 2.5 kHz. (10)
(b) Find the filter realization for the above specifications using a single resistance terminated lossless ladder network. (6)
3. (a) Derive the expression to determine die order of a normalized lowpass
equal ripple Chebyshev filter. (6)
(b) The specifications for a Chebyshev filter are:
Passband ripple - 0.5 dB
Passband - 0- one MHz
Stop band loss - 40 dB at two MHz
i) Determine the order of the filter. (2)
ii) obtain Cn (w) for this filter. (3)
iii) Draw its pole location in s-plane. (5)
4. (a) obtain the transfer function of a 4th order normalized high pass
butterworth filter. If this filter is replaced to get a cutoff frequency of 5
kHz, obtain the new transfer function. (8)
(b) Use narrow band approximation to determine the pole locations and
transfer function of a 4 pole , maximally flat magnitude bandpass
function with a three dB bandwidth of 0.05 r/s ans a center frequency
of2r/s. (8)
(a) Find 2 Foster form and Cauer form realizations for die subsequent
driving point admittance function: (12)
Y(s)= ( s2 + 1) ( s2 + 3)
s ( s 2+ 2) (s2 + 4)

(b) Find a single- resistance (1 ohm) lossless ladder realization for the following: (4)
i) 1/{ s4 + s3 + s2 + s + 1} ii) s2 / { s4 + s3 + three s2 + s + 1}
6. (a) Use method of constrains to derive the expression for voltage
transfer function of a finite gain low pass Sallen-key filter. (8)
(b) Design an infinite gain, equal resistor and equal capacitor low pass,
Sallen-key filter for Q = 10 and Wn = 10 K rad/sec. (8)
7. (a) Design an equal resistance and equal capacitance Sallen-key high
pass filter for Q = 0.707 and Wn = 6283 r/ s. (8)
(b) Design an infinite gain, bandpass sallen-key filter with positive and
negative . Feedback for Wn = one rad/sec, Q = 10, C = one F, m=0.1andRB=1 ohm. (8)
8. (a) discuss with an example, how higher order (higher than two) active filters are realized (8)
(b) discuss the concept of state variable filter. (8)
9. (a) Draw a neat circuit diagram of a Akerberg-Mossberg filter and derive the expression for
its voltage transfer function having low pass characteristic. (10)
(b) discuss how a resistor is realized by a MOS switched capacitor. (6)
10. Explain with the help of neat circuit diagrams the working of Tow-Thomas and leapfrog filters.

Earning:   Approval pending.