Introduction (cont )

Transcription

1 Active Filter 1

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 can be passive or active filter Passive Filters: The circuits built using components such as resistors, capacitors and inductors only. Active filters: The circuits that employ transistors or op-amps in addition to resistors and capacitors. 2

3 Introduction (cont ) Active Filters Consist of only amplifiers, resistors, and capacitors. Use resistors and capacitors in their feedback loops, to synthesize the desired filter characteristics. Have high input impedance, low output impedance, and virtually any arbitrary gain. They are also usually easier to design than passive filters. They lack inductors.. Performance at high frequencies is limited by the gain-bandwidth product of the amplifying. The op amp-based active filter can achieve very good accuracy, provided that low-tolerance resistors and capacitors are used. Active filters will generate noise due to the amplifying circuitry, but this can be minimized by the use of low-noise amplifiers and careful circuit design. 3

4 Advantages of Active Filters over Passive Filters 1. Active filters can be designed to provide required gain, and hence no attenuation as in the case of passive filters 2. No loading problem, because of high input resistance and low output resistance of op-amp. 3. Active Filters are cost effective as a wide variety of economical op-amps are available. 4

5 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

6 Active Filters There are 4 basic categories of active filters: 1. Low pass filters 2. High pass filters 3. Band pass filters 4. Band reject / stop 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

7 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 drop -3dB (70.7% of the input) from 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 occur. 7

8 Basic Filter Responses 1. Low-pass filter Allows the frequency from 0Hz to critical frequency,fc Ideal response actual response The critical frequency can be formula by 1 f c = 2πRC The BW is equal to fc 8

9 Basic Filter Responses 2. High-Pass filter Only allowing the frequencies above the critical frequency. Ideal response The critical frequency can be formula by actual response 1 f c = 2πRC 9

10 Basic Filter Responses 3. Band-pass filter Allows frequencies between a lower critical frequency (f c1 ) and an upper critical frequency (f c2 ). Ideal response actual response 10

11 3. Band-pass filter Basic Filter Responses Bandwidth, BW = f c2 -f c1 center frequency, f o f = f c f 0 1 c2 Quality factor (Q) is the ratio of center frequency f o to the BW Q = fo BW The narrower the bandwidth, the higher the quality factor. 11

12 Basic Filter Responses 4. Band-stop / notch filter / band-reject / band-elimination filter Opposite of a band-pass. Frequencies above and below f c1 and f c2 are passed. Ideal response actual response 12

13 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 This three types response characteristics can be realized with most active filter circuit configurations by proper selection of certain component values. High-pass and band-pass filters can also be designed to have any one of the characteristics. 13

14 Filter Response Characteristics 1. Butterworth Response Amplitude response is very flat. The roll-off rate -20 db per decade. Phase response is not linear. Phase shift is varies nonlinearly with frequency. This is the most widely used. Referred to as a maximally flat response. 14

15 Filter Response Characteristics 2. Chebyshev Response Ripples The roll-off rate greater than 20 db/decade/pole a nonlinear phase response. 15

16 Filter Response Characteristics 3. Bessel Response Linear phase response. No overshoot on the output. Ideal for filtering pulse waveforms. 16

17 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 R 1 and R 2. Damping factor (DF) DF = R 2 1 R 2 Diagram of an active filter 17

18 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. First order (one pole) low pass filter 18

19 Filter Response Characteristics The number of filter poles can be increase by cascading 19

20 Filter Response Characteristics Values for the Butterworth response Order Rool-off DB/Dacade 1 st Stage Poles DF R1/R Option 2 st Stage Poles DF R1/R