c. The general transfer function of a 2nd order Butterworth active filter is: Ao H(s) = This filter can be implemented using a Sallen and Key second order filter section as illustrated in Figure Q3(c). R, R, ww Ov ww Figure Q3(c) The transfer function of such a structure is given by

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c. The general transfer function of a 2nd order Butterworth active filter is:
Ao
H(s) =
+ 23 ) + 1
This filter can be implemented using a Sallen and Key second order filter section as illustrated
in Figure Q3(c).
R,
R2
ww
ww
Ov
R
R
ww
ov
Figure Q3(c)
The transfer function of such a structure is given by
Transcribed Image Text:c. The general transfer function of a 2nd order Butterworth active filter is: Ao H(s) = + 23 ) + 1 This filter can be implemented using a Sallen and Key second order filter section as illustrated in Figure Q3(c). R, R2 ww ww Ov R R ww ov Figure Q3(c) The transfer function of such a structure is given by
R, + R2
Vout (s)
H(s) =
Vin (s)
(RCs)² + (3 – Ao)RCs + 1
An active low pass filter is required. The filter should have a cut off frequency of 2 kHz and
a 40 dB per decade roll off. A second order Sallen Key filter prototype, as illustrated in figure
Q3(c), is used for this purpose.
i. Explain briefly why a second order filter is an adequate choice here?
ii. Express the gain Ao, the natural frequency on and the damping ratio in terms of
the circuit elements R1, R2, R and C.
iii. If R1 = 10k and C =108 F, what are the values of R and R2?
Transcribed Image Text:R, + R2 Vout (s) H(s) = Vin (s) (RCs)² + (3 – Ao)RCs + 1 An active low pass filter is required. The filter should have a cut off frequency of 2 kHz and a 40 dB per decade roll off. A second order Sallen Key filter prototype, as illustrated in figure Q3(c), is used for this purpose. i. Explain briefly why a second order filter is an adequate choice here? ii. Express the gain Ao, the natural frequency on and the damping ratio in terms of the circuit elements R1, R2, R and C. iii. If R1 = 10k and C =108 F, what are the values of R and R2?
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