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2. 2 7. Active Filter Design and Implementation

3. 3 Applications of Filter In a data acquisition system, the analog signal to be acquired may contain unwanted components that need to be removed before the signal can be processed. noise and interference carrier component Typically can be done by using an analog filter but increasingly being performed digitally (i.e., digital filters) In addition, filters are also used to prevent aliasing from occurring during the sampling process.

4. 4 Filter Characteristics Four classifications of filters i.Low-Pass Filters (LPF) ii.High-Pass Filters (HPF) iii.Band-Pass Filters (BPF) iv.Band-Rejection Filters (BRF) Three regions common to all filters Passband Stopband Transition band

5. 5 Ideal Filter Characteristics PassbandStopband fHfH f |A| Passband Stopband fLfL f |A| Passband Stopband f L f H f |A| Stopband PassbandStopband f L f H f |A| Passband Low-pass High-pass Band-pass Band-stop

6. 6 Combination of Filters Band Pass Filter can be constructed by cascading LPF and HPF in series with the appropriate passband and stopband frequencies Similarly, Band Reject Filter can be constructed by combining LPF and HPF in parallel with the appropriate cutoff frequencies

7. 7 Filter Specifications Ideal filter characteristics are never realisable practical filters are only an approximation of the ideal filter Main parameters used to describe filters: Cutoff frequency (or corner frequency, f C ) –typically the –3 dB point –or frequency at which it exits the ripple band (e.g., for ripple type of filters) Order of filter –related to the transition steepness from Passband to Stopband

8. 8 Low-Pass Filter Characteristics

9. 9 Filter Specifications Passband Gain ( G pass ): usually flat but there are exceptions. Passband Corner Frequency (f C ): typically the –3 dB point Stopband Attenuation (G stop ): minimum attenuation required in the SB (stopband) Stopband (SB) Frequency (f S ): frequency at which SB begins Transition Region: frequency range between f C and f S

10. 10 Desirable Filter Properties Low Insertion Loss for signals that are supposed to pass through a filter the amount of attenuation of a passband signal when passing through the filter should be as low as possible Steep Roll-Off for signals that are supposed to be attenuated a measure of how much they are attenuated

11. 11 Passive RC Filter Utilizes passive R and C components For example, an RC Low pass filter: V IN VOVO R C

12. 12 Higher Order RC Filter Higher order filter can be constructed by cascading multiple stages of 1 st order filters (e.g. filters used for RF applications) but difficult to design due to interaction between the stages (i.e. loading effect) Second-order low-pass filter

13. 13 LC Filter 2nd order filter used L and C (with R due to source or line resistance) V IN VOVO R C L What happens if R → 0 ?

14. 14 Differential RC Filter Differential signalling is commonly used in a high-speed circuit, need a differential RC filter not to degrade the common mode performance + V IN - +VO-+VO- RSRS C RSRS RTRT R T = input impedance or termination at the receiver

15. 15 Differential LC Filter 2 nd order RLC differential filter + V IN – +VO–+VO– RSRS C RSRS RTRT L L

16. 16 Active filters utilize op-amps in the circuit provide gain provide buffering between stages (no loading effect) can be used to implement higher order filters without the need of L (excessively big at low frequency) For 1 st order active filter corner frequency always occurs at where R is the equivalent resistance seen by the capacitor. Active Filter

17. 17 Active Filters Low-pass High-pass

18. 18 High Order Active Filter High order Active filter can be designed by combining RC filters around the op-amp. Discussion: Find the corner frequencies of the following filter:

19. 19 High Order Active Filter (cont’d) However, there are a few families of active filters that can be designed to exhibit particular good qualities of performance in certain aspects of the filter response characteristics. Example: very flat response in the passband sharp transition band good time-domain response But these features are usually mutually exclusive from each order. For example, it is not possible to have a flat passband with a steep transition band.

20. 20 Common Active Filters Families Three of the commonly used filters families are as follows: Butterworth Flat response in Passband Chebyshev Sharp transition between Passband and Stopband Bessel Linear phase variation that preserve shape of signals

21. 21 Butterworth Filter Response Main features: maximally flat response in the passband flatness increases with the order maximum deviation occurs at the PB edge

22. 22 Chebyshev Filter Response Main features: –sharp cutoff (steep transition band) –ripple in the passband (PB) (gain oscillates in PB) Suitable for signals that can tolerate amplitude (and phase) distortion. An example is Audio. Ripple = 2dB

23. 23 Frequency Response of Filters (cont’d) Chebyshev with different ripple (ripple = 0.5 dB)

24. 24 Bessel Filter Response Main features: phase shift varies linearly with frequency in the passband, i.e., the delay is same for all the frequency components. no oscillatory step response Important for applications such as vision, video display systems, and pattern matching. An example is electrocardiography (ECG).

25. 25 Active Filter Implementations

26. 26 Filter Circuits Implementation All three families of the active filter can be design based on the same circuit topologies different component values are chosen to obtain the desired response Two common topologies: 1.Unity Gain Sallen-Key (SK): low parts count, unity gain but part sensitive 2.Voltage Controlled Voltage Source (VCVS) (Equal Component Sallen-Key): low parts count, variable gain but part sensitive.

27. 27 SK and VCVS Filter Circuits Both circuit topologies are applicable for both low pass and high pass design, by simply interchange the positions of R and C components in the circuit can be cascaded for higher order filter implementation Design can be done based on Filter Design Table components values are calculated based on the parameters given and the desired corner frequency (Though most likely filter design will be done using software package nowadays)

28. 28 Sallen-Key Filter Circuits Low-pass filter High-pass filter K 1 =RC 1  o K 2 =RC 2  o K 1 =1/(R 1 C  o ) K 2 =1/(R 2 C  o )

29. 29 Sallen-Key Filter Design Table

30. 30 Example: Sallen-Key Filter Design Requirement Filter type = Low-Pass Chebyshev with 0.5 db ripple Order of filter required = 4 f o = 10 KHz (  o = 62830 rad/sec)

31. 31 Example: Sallen-Key Filter Design (cont’d) First Stage:K 1 = 2.582 RC 1 = K 1 /  o = 2.582/62830 = 41.1x10 –6 Choosing R = 10K, C 1 = 4.1 nF K 2 = 1.298 RC 2 = K 2 /  o = 1.298/62830 = 20.7x10 –6 For R = 10K, C 2 = 2.1 nF K 1 =RC 1  o K 2 =RC 2  o

32. 32 Example: Sallen-Key Filter Design (cont’d) Second Stage:K 1 = 6.233 RC 1 = K 1 /  o = 6.233/62830 = 99.2x10 –6 Choosing R = 10K, C 1 = 9.9 nF K 2 = 0.180 RC 2 = K 2 /  o = 0.180/62830 = 2.86x10 –6 For R = 10K, C 2 = 286 pF K 1 =RC 1  o K 2 =RC 2  o

33. 33 Example: Sallen-Key Filter Design (cont’d) 4 th Order LPF Discussion: Are these components values good choices?

34. 34 VCVS Filter Design Low-Pass VCVS Filter High-Pass VCVS Filter

35. 35 VCVS Filter Design (cont’d)

36. 36 Example: VCVS Filter Design Requirement Filter type = Low-Pass Butterworth Filter order required = 4 f o = 10 Khz (  o = 62830 rad/Sec)

37. 37 Example: VCVS Filter Design (cont’d) First Stage:K 3 = 1 RC = K 3 /  o = 1/62830 = 15.9x10 –6 Choosing R = 10K, C = 1.59 nF G = 1.152 Choosing R 1 = 10K, (G–1)R 1 = 1.52K

38. 38 Example: VCVS Filter Design (cont’d) Second Stage:K 3 = 1 Use the same values of R and C as that of the first stage R = 10K, C = 1.59 nF G = 2.235 Choosing R 1 = 10K, (G–1)R 1 = 12.35K

39. 39 Example: VCVS Filter Design (cont’d) 4 th Order VCVS LPF Note: Gain in the passband = (1.152x2.235) = 2.575 = 8.21 dB