EENG36000 Electronics 1
DEPARTMENT OF ELECTRICAL & ELECTRONIC ENGINEERING
ELECTRONICS (Analogue Filters)
Examples Sheet
1. (i) Determine the pole positions of a normalized 4th-order low-pass Butterworth
filter.
[-0.3827 ±j0.9239, -0.9239 ±j0.3827]
(ii) Design a passive 4th-order low-pass Butterworth filter, using the ladder
network realisation, having a cut-off frequency of 410 rad/s and terminating
resistances of 50Ω .
[ F53.11 µ=C , mH24.92 =L , F70.33 µ=C , mH83.34 =L ]
(iii) What is the attenuation relative to 0 rad/s at
(a) 4105.0 × rad/s
(b) 4102× rad/s
[-0.0169dB, -24.1dB]
2. Determine the pole positions for a normalised 2nd-order low-pass Chebyshev filter
with
(i) 0.5dB ripple in the pass-band
(ii) 1.0dB ripple in the pass-band
[-0.7128 ±jl.004, -0.5489 ±j0.8951]
3. Design a passive band-pass filter with cut-off frequencies of 410 rad/s and 4103×
rad/s, basing your design on a Butterworth 3rd-order low-pass filter.
[Source and terminating Ω=1R ; parallel LC combinations of H7.66 µ=L and
F50µ=C at i/p and o/p of filter, separated by H100µ=L and F3.33 µ=C in series]
4. Design a 4th-order Butterworth active high-pass filter with a cut-off frequency of
500Hz, using cascaded 2nd-order circuits of the ‘multiple feedback infinite gain
amplifier’ type, and an impedance scale factor 1000=IK .
[2nd-order filter 1: F318.0431 µ=== CCC , Ω= 1.2552R , Ω= 39205R ;
2nd-order filter 2: F318.0431 µ=== CCC , Ω= 9.6152R , Ω= 16245R ]
5. Design a 4th-order Butterworth active low-pass filter with a cut-off frequency of
1000Hz, using cascaded 2nd-order ‘state variable’ sections with 1000=IK .
[2nd-order filter 1: Ω== 1307/1 11 aR , all other Ω= k1R , both F159.0 µ=C ;
2nd-order filter 2: Ω== 2.541/1 11 aR , all other Ω= k1R , both F159.0 µ=C ].
6. Starting with a 3rd order normalised Butterworth LP prototype, a band-stop filter to
reject 50 Hz mains interference is to be designed. If the bandwidth between
frequencies where the response is -3dB with respect to the maximum response is
10Hz, determine the parameters 210 and , , ΩΩΩ for the normalised band-stop filter.
If the filter is to work between source and load resistances of Ω600 , determine the
values of the other circuit components.
[5 rad/s, 4.525 rad/s and 5.525 rad/s; see circuit diagram over page for components].
EENG36000 Electronics 2
600
600
1.061 x 10-6 F
9.549H
1.061 x 10-6 F
0.764H
13.26 x 10-6 F 9.549H