1. VADODARA INSTITUTE OF ENGINEERING
SUBJECT : Analog Electronics
TOPIC NAME : Active Filter
GROUP MEMBERS :
Parth Kachhiya. ( 14ELEE314 )
Vishruta Thite ( 14ELEE315 )
Aman Mishra ( 14ELEE316 )
Niteen Virda ( 14ELEE317 )

2. Filters
A filter is basically a “frequency selective” circuit. It is designed to pass a specific band of frequencies and block or attenuate input signals of frequencies outside this band.

3. Types of Filters There are two broad categories of filters:
An analog filter processes continuous-time signals
A digital filter processes discrete-time signals.
The analog or digital filters can be subdivided into four categories:
Low-pass Filters
High-pass Filters
Bandstop Filters
Band-pass Filters

4. Frequency Response characteristics 1) Law-pass filter
H(f)
Characteristic shows that a low-pass filter has a constant gain from 0 Hz to a high cut-off frequency fc.
At f = fc , the filter gain makes a sudden transition to zero. Therefore all the frequencies beyond fc are completely attenuated. f fc
Ideal “low-pass” filter

5. Characteristic shows that a frequency response of a practical low-pass filter gain does not change suddenly at
f = fc, instead as f increases, the gain reduce gradually.
f = fc the gain by 3 dB and after fc it reduces at a higher rate as shown in fig.
H(f) f fc
Practical low-pass filter

6. 2) High-pass filter
Characteristic shows that an ideal high-pass filter. Its “stopband” extends from f = 0 to f = fc. Where fc is the cut-off frequency.
The passband will be for all frequencies above fc.
The gain of an ideal high-pass filter is 0 over its stopband and constant over its passband.
The gain makes a sudden transition from 0 to 1 at f = fc shown in fig. 1
Stopband
Passband w c w
Highpass Filter

7. Fig shows the frequency response characteristics of a practical high-pass filter.
The filter gain changes gradually. Therefore the practical filter has a finite transition band.
Practical high pass filter

8. 3) Band-pass filter
Characteristic shows that an ideal band-pass filter. Its “passband” extends between the two cut-off frequencies C1 and C2 with C2 >C1. The frequencies outside this passband lie in the “stopband” or attenuation band.
The gain of an ideal band-pass filter is 0 over the stopband and constant over its passband.
The gain will make sudden transitions from 0 to 1 at C = C1 from 1 to 0 C = C2 as shown in fig.
Stopband
Passband
Stopband w c 1 w c 2 w
Band-pass Filter

9. Fig show the frequency response of a practical band pass filter.
The gain dose note change suddenly at C = C1 and C = C2 instead it change gradually.
At the cut-off frequencies C1 and C2 the gain is shown by 3 dB with respect to the pass-band gain.
Practical band pass

10. REAL FILTERS The approximations to the ideal filter are the:
Butterworth filter
Chebyshev filter
Cauer (Elliptic) filter
Bessel filter

11. STANDARD TRANSFER FUNCTIONS
Butterworth
Flat Pass-band.
20n dB per decade roll-off.
Chebyshev
Pass-band ripple.
Sharper cut-off than Butterworth.
Elliptic
Pass-band and stop-band ripple.
Even sharper cut-off.
Bessel
Linear phase response – i.e. no signal distortion in pass-band.

13. BUTTERWORTH FILTER The Butterworth filter magnitude is defined by:
where n is the order of the filter.

14. From the previous slide:
for all values of n
For large w:

15. And
implying the M(w) falls off at 20n db/decade for large values
of w.

16. 20 db/decade
40 db/decade
60 db/decade

17. To obtain the transfer function H(s) from the magnitude
response, note that

18. Because s = jw for the frequency response, we have s2 = - w2.
The poles of this function are given by the roots of

19. The 2n pole are:
e j[(2k-1)/2n]p n even, k = 1,2,...,2n
sk =
e j(k/n)p n odd, k = 0,1,2,...,2n-1
Note that for any n, the poles of the normalized Butterworth
filter lie on the unit circle in the s-plane. The left half-plane
poles are identified with H(s). The poles associated with
H(-s) are mirror images.

20. THANK YOU