1. EMT212 Analog Electronic II
Chapter 5 Active Filter By
En. Rosemizi Bin Abd Rahim

2. Introduction
Filters are circuits that are capable of passing signals within a band of frequencies while rejecting or blocking signals of frequencies outside this band. This property of filters is also called “frequency selectivity”.
Filter circuits built using components such as resistors, capacitors and inductors only are known as passive filters.
Active filters employ transistors or op-amps in addition to resistors and capacitors.

3. Advantages of Active Filters over Passive Filters
Active filters can be designed to provide required gain, and hence no attenuation as in the case of passive filters
No loading problem, because of high input resistance and low output resistance of op-amp.
Active Filters are cost effective as a wide variety of economical op-amps are available.

4. Applications
Active filters are mainly used in communication and signal processing circuits.
They are also employed in a wide range of applications such as entertainment, medical electronics, etc.

5. Active Filters There are 4 basic categories of active filters:
1. Low pass filters
High pass filters
Band pass filters
Band reject filters
Each of these filters can be built by using op-amp as the active element combined with RC, RL or RLC circuit as the passive elements.

6. Active Filters
The passband is the range of frequencies that are allowed to pass through the filter.
The critical frequency, fc is specified at the point where the response drops by 3dB from the passband response (i.e. to 70.7% of the passband response)
The stopband is the range of frequencies that have the most attenuation.
The transition region is the area where the fall-off occurs

7. Basic Filter Responses
1. Low-pass filter
Allows the frequency from 0 Hz to critical frequency fH (also known as cutoff frequency).
Ideally, the response drops abruptly at the critical frequency fH.
Fig 15-1a
Ideal response

8. Basic Filter Responses
1. Low-pass filter
In an RC low-pass filter, the critical frequency can be calculated from the expression:
Fig 15-1a

9. Basic Filter Responses
Actual response

10. Basic Filter Responses
2. High-Pass filter
Allows the frequencies above the critical frequency fL. (also known as the cutoff frequency.
Ideally, the response rises abruptly at the critical frequency
Ideal response

11. Basic Filter Responses
2. High-Pass filter
In an RC high-pass filter, the critical frequency can be calculated from the expression;

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15. Basic Filter Responses
Fig 15-2a High pass filter response
actual response

16. Basic Filter Responses
3. Band-Pass filter
Allows frequencies between a lower cutoff frequency (fL) and an upper cutoff frequency (fH).
Fig 15-3
Ideal response

17. Basic Filter Responses
Fig 15-3
actual response

18. Basic Filter Responses
3. Band-Pass filter
Fig 15-3
Bandwidth,

19. Basic Filter Responses
3. Band-Pass filter
Center frequency,
Fig 15-3

20. Basic Filter Responses
3. Band-Pass filter
Quality factor (Q) is the ratio of center
frequency fo to the BW;
Fig 15-3

21. Basic Filter Responses
4. Band-stop filter
Opposite of a band-pass.
Frequencies above fc1 (fL) and above fc2 (fH) are passed
Fig 15-4
Ideal response

22. Basic Filter Responses
Fig 15-4
Actual response

23. Animation
A "Group" of waves passing through a Typical Band-Pass Filter

24. Filter Response Characteristics
Identified by the shape of the response curve
Passband flatness
Attenuation of frequency outside the passband
Three types:
1. Butterworth
2. Bessel
3. Chebyshev
Fig 15-5 Three response types

25. Filter Response Characteristics
Fig 15-5 Three response types

26. Filter Response Characteristics
1. Butterworth Response
Amplitude response is very flat.
The roll-off rate -20 dB per decade (per filter order).
This is the most widely used.
Fig 15-5 Three response types

27. Filter Response Characteristics
2. Chebyshev
Ripples.
The roll-off rate greater than –20 dB.
a nonlinear phase response.
Fig 15-5 Three response types

28. Filter Response Characteristics
3. Bessel
Linear phase response.
ideal for filtering pulse waveforms.
Fig 15-5 Three response types

29. Filter Response Characteristics
Damping Factor
The damping factor of an active filter determines the type of response characteristic either Butterworth, Chebyshev, or Bessel.
The output signal is fed back into the filter circuit with negative feedback determined by the combination of R1 and R2.
Fig 15-6 general active filter

30. Filter Response Characteristics
Damping Factor
Fig 15-6 general active filter
Diagram of an active filter

31. Filter Response Characteristics
Critical Frequency and Roll-off rate
Greater roll-off rates can be achieved with more poles.
Each RC set of filter components represents a pole.
Cascading of filter circuits also increases the poles which results in a steeper roll-off.
Each pole represents a –20 dB/decade increase in roll-off
Fig 15-8 cascaded filters

32. Filter Response Characteristics
Fig 15-8 cascaded filters
First order (one pole) low pass filter

33. Filter Response Characteristics
The number of filter poles can be increased by cascading
Fig 15-8 cascaded filters

34. Filter Response Characteristics
Fig 15-8 cascaded filters

35. Active Low-Pass Filters
Basic Low-Pass filter circuit
At critical frequency,
Resistance = capacitive reactance
i.e.
Fig Sallen-Key low pass or

36. Active Low-Pass Filters
Basic Low-Pass filter circuit
So, critical frequency;
Fig Sallen-Key low pass

37. Active Low-Pass Filters
Low Pass Response
Roll-off depends on number the of poles.
Fig Sallen-Key low pass

38. Active Low-Pass Filters
A Single-Pole Filter
One pole
Fig Sallen-Key low pass

39. Active Low-Pass Filters
A Single-Pole Filter
Fig Sallen-Key low pass

40. Active Low-Pass Filters
The Sallen-Key
second-order (two-pole) filter
roll-off -40dB per decade
Fig Sallen-Key low pass
Two-pole
Low-pass
circuit

41. Active Low-Pass Filters
The Sallen-Key
For RA = RB = R and CA = CB = C;
Fig Sallen-Key low pass

42. Active Low-Pass Filters
Example
For the following circuit;
Determine critical frequency
Set the value of R1 for Butterworth response
Fig Sallen-Key low pass

43. Active Low-Pass Filters
Example (cont’d)
Fig Sallen-Key low pass

44. Active Low-Pass Filters
Solution
Critical frequency
Fig Sallen-Key low pass

45. Active Low-Pass Filters
Solution
Butterworth response from Table 15.1 Floyd, page 744, R1/R2 = 0.586;
Fig Sallen-Key low pass

46. Active Low-Pass Filters
Cascaded LPF – Three-pole
cascade two-pole and single-pole
roll-off -60dB per decade
Fig Sallen-Key low pass

47. Active Low-Pass Filters
Cascaded LPF – Four pole
cascade two-pole and two-pole
roll-off -80dB per decade
Fig Sallen-Key low pass

48. Active Low-Pass Filters
Example
For the fourth order filter circuit shown in the following figure, determine the capacitance values required to produce a critical frequency of 2680 Hz if all resistors in RC low pass circuit is 1.8 k.
Fig Sallen-Key low pass

49. Active Low-Pass Filters
Example (cont’d)
Fig Sallen-Key low pass

50. Active Low-Pass Filters
Example – SOLUTION
Fig Sallen-Key low pass

51. Active High-Pass Filters
Basic High-Pass circuit
At critical frequency,
Resistance
= capacitive reactance
i.e;
Fig Sallen-Key low pass
or;
or;

52. Active High-Pass Filters
Basic High-Pass circuit
So, critical frequency ;
Fig Sallen-Key low pass

53. Active High-Pass Filters
High Pass Response
Roll-off depends on number the of poles.
Fig Sallen-Key low pass

54. Active High-Pass Filters
A Single-Pole Filter
Fig Sallen-Key low pass
Circuit

55. Active High-Pass Filters
A Single-Pole Filter
Response curve
Fig Sallen-Key low pass

56. Active High-Pass Filters
The Sallen-Key
second-order (two-pole) filter
roll-off -40dB per decade
Fig Sallen-Key low pass

57. Active High-Pass Filters
The Sallen-Key
Fig Sallen-Key low pass

58. Active High-Pass Filters
The Sallen-Key
Lets RA = RB = R and CA = CB = C;
Fig Sallen-Key low pass

59. Active High-Pass Filters
Cascaded HPF – Six pole
cascade 3 Sallen-Key two-pole stages
roll-off -120 dB per decade
Fig Sallen-Key low pass

60. Active Band-Pass Filters
A cascade of a low-pass and high-pass filter.
Fig 15-17a

61. Active Band-Pass Filters
Fig 15-17b band-pass curve

62. Active Band-Pass Filters
Fig 15-17b band-pass curve

63. Active Band-Pass Filters
Fig Mult feedback band-pass

64. Active Band-Pass Filters
Multiple-Feedback BPF
The low-pass circuit consists of R1 and C1.
The high-pass circuit consists of R2 and C2.
The feedback paths are through C1 and R2.
Center frequency;
Fig Mult feedback band-pass

65. Active Band-Pass Filters
State-Variable BPF
State-Variable BPF is widely used for band-pass applications.
Fig 15-20

66. Active Band-Pass Filters
State-Variable BPF
It consists of a summing amplifier and two integrators.
It has outputs for low-pass, high-pass, and band-pass.
The center frequency is set by the integrator RC circuits.
R5 and R6 set the Q (bandwidth).
Fig 15-20

67. Active Band-Pass Filters
The band-pass output peaks sharply the center frequency giving it a high Q.
Fig state-variable curve

68. Active Band-Stop Filters
The BSF is opposite of BPF in that it blocks a specific band of frequencies.
The multiple-feedback design is similar to a BPF with exception of the placement of R3 and the addition of R4.
Fig Mult.-feedback band stop

69. Active Band-Stop Filters
Fig Mult.-feedback band stop

70. Filter Response Measurements
Measuring frequency response can be performed with typical bench-type equipment.
It is a process of setting and measuring frequencies both outside and inside the known cutoff points in predetermined steps.
Use the output measurements to plot a graph.
More accurate measurements can be performed with sweep generators along with an oscilloscope, a spectrum analyzer, or a scalar analyzer.

71. Summary
The bandwidth of a low-pass filter is the same as the upper critical frequency.
The bandwidth of a high-pass filter extends from the lower critical frequency up to the inherent limits of the circuit.
The band-pass passes frequencies between the lower critical frequency and the upper critical frequency.

72. Summary
A band-stop filter rejects frequencies within the upper critical frequency and upper critical frequency.
The Butterworth filter response is very flat and has a roll-off rate of –20 B
The Chebyshev filter response has ripples and overshoot in the passband but can have roll-off rates greater than –20 dB

73. Summary
The Bessel response exhibits a linear phase characteristic, and filters with the Bessel response are better for filtering pulse waveforms.
A filter pole consists of one RC circuit. Each pole doubles the roll-off rate. The Q of a filter indicates a band-pass filter’s selectivity. The higher the Q the narrower the bandwidth.
The damping factor determines the filter response characteristic.

74. Active Filters EXAMPLE With reference to the following circuit;
Name the type of circuit. Determine the critical frequency
Modify the circuit to increase roll-off to 120dB/decade.
Convert the circuit to become a high pass filter.
Fig Mult.-feedback band stop

75. Active Filters
EXAMPLE (cont’d)
Fig Mult.-feedback band stop

76. Active Filters SOLUTION (i) Type of circuit:
FOUR-POLE LOW-PASS ACTIVE FILTER
Critical frequency
Fig Mult.-feedback band stop

77. Active Filters
SOLUTION (cont’d)
Fig Mult.-feedback band stop

78. Active Filters SOLUTION (cont’d) (ii) Modification
Add the following 3rd stage to the output of the 2nd stage
Fig Mult.-feedback band stop

79. Active Filters
SOLUTION (cont’d)

80. Assignment on Active Filters
Due date : 30th Sept 2005
Refer to Floyd text book
page 766 – 770
Q5, Q10, Q15, Q16, Q19
Fig Mult.-feedback band stop