ME3100 SAMPLE slide07 Active Filter Design and Implementation v1.01.ppt

Analog Circuit Design using ME3100

1. 1
ME3100 Analog Circuit Design
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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

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:
RC
f
c
2
1

V
IN V
O
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

LC2
1
f
C


2nd order filter
•used L and C (with R due to source or line resistance)
V
IN
V
O
R
C
L

R
X

R
X
Q
CL

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
)RRif
CR22
1
f
ST
S
C


 (
+
V
IN
-
+
V
O
-
R
S
C
R
S
R
T
R
T
= input impedance or termination at the receiver

R2R
R
SF
ST
T



15. 15
Differential LC Filter

LC22
1
f
c


2
nd
order RLC differential filter
+
V
IN
–
+
V
O
–
R
S
C
R
S
R
T
L
L
 
ST
S
C
S
L
RR
R 2
X

R
X
Q 

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
RC 2π
1
f
C


17. 17
Active Filters

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.

23. 23
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).

24. 24
Frequency Responses of Filters
Butterworth Bessel

25. 25
Frequency Response of Filters (cont’d)
Chebyshev with different ripple

26. 26
Active Filter
Implementations

27. 27
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.

28. 28
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)

29. 29
Sallen-Key Filter Circuits
Low-pass filter
High-pass filter

30. 30
Sallen-Key Filter Design Table
Poles Butterworth Chebyshev (0.5 db)

K
1
K
2
K
1
K
2

2 1.414 0.707 1.949 0.653

4 1.082 0.924 2.582 1.298
2.613 0.383 6.233 0.180

6 1.035 0.966 3.592 1.921
1.414 0.707 4.907 0.374
3.863 0.259 13.40 0.079

8 1.019 0.981 4.665 2.547
1.202 0.832 5.502 0.530
1.800 0.556 8.237 0.171
5.125 0.195 23.45 0.044

Design Table for Unity Gain Sallen-Key Low-Pass and High-Pass Filters

31. 31
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)
Poles Butterworth Chebyshev (0.5 db)

K
1
K
2
K
1
K
2

2 1.414 0.707 1.949 0.653

4 1.082 0.924 2.582 1.298
2.613 0.383 6.233 0.180

6 1.035 0.966 3.592 1.921
1.414 0.707 4.907 0.374
3.863 0.259 13.40 0.079

32. 32
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

33. 33
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

34. 34
Example: Sallen-Key Filter Design (cont’d)
4
th
Order LPF
Discussion:
Are these components values good choices?

35. 35
VCVS Filter Design
Low-Pass VCVS Filter
K3 = RC

o K3 = 1/(RC

o)
High-Pass VCVS Filter

36. 36
VCVS Filter Design (cont’d)
Poles Butterworth Chebyshev (0.5 db)
K
3
G K
3
G
2 1.000 1.586 1.129 1.842
4 1.000 1.152 1.831 1.582
1.000 2.235 1.060 2.660
6 1.000 1.068 1.332 1.537
1.000 1.586 1.355 2.448
1.000 2.483 1.029 2.846
8 1.000 1.038 3.447 1.552
1.000 1.337 1.708 2.379
1.000 1.889 1.188 2.711
1.000 2.610 1.017 2.913
Table 2.4 Design table for VCVS Lowpass and Highpass Filters

37. 37
Example: VCVS Filter Design
Requirement
Filter type = Low-Pass Butterworth
Filter order required = 4
f
o = 10 Khz (
o = 62830 rad/Sec)
Poles Butterworth Chebyshev (0.5 db)
K
3
G K
3
G
2 1.000 1.586 1.129 1.842
4 1.000 1.152 1.831 1.582
1.000 2.235 1.060 2.660
6 1.000 1.068 1.332 1.537
1.000 1.586 1.355 2.448
1.000 2.483 1.029 2.846

38. 38
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

39. 39
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

40. 40
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