Active Filter. Low pass filter High pass filter Band pass filter Band stop filter

Transcription

1 Active Filter Low pass filter High pass filter Band pass filter Band stop filter

2 Active Low-Pass Filters Basic Low-Pass filter circuit At critical frequency, esistance capacitance X c ω c πf c So, critical frequency ; f c π

3 Active Low-Pass Filters Low Pass esponse oll-off depends on number the of poles. 3

4 A Single-Pole Filter Active Low-Pass Filters A cl + f c π 4

5 Active Low-Pass Filters The Sallen-Key LPF second-order (two-pole) filter roll-off -40dB per decade f c π A B A B For A B and A B ; f c π 5

6 Active Low-Pass Filters Example Determine critical frequency set the value of for Butterworth response. ritical frequency f 7. khz c 3 π Butterworth response from table 5. floyd, page 744 / Ω 6

7 Active Low-Pass Filters ascaded LPF Three pole cascade two-pole and single-pole roll-off -60dB per decade 7

8 ascaded LPF Four pole Active Low-Pass Filters cascade two-pole and two-pole roll-off -80dB per decade 8

9 Example : Active Low-Pass Filters Determine the capacitance values required to produce a critical frequency of 680 Hz if all resistors in low pass circuit is.8kω f c π πf c 0.033μF A B A B 0.033µf 9

10 Example : Active Low-Pass Filters Design a single pole low pass filter at a cutoff frequency of khz with a passband gain of and sketch the response curve. Assume 0.0uF and kω. 0

11 Active High-Pass Filters Basic High-Pass circuit At critical frequency, esistance capacitance X c ω c πf c So, critical frequency ; f c π

12 Active High-Pass Filters High Pass esponse oll-off depends on number the of poles.

13 A Single-Pole Filter Active High-Pass Filters A cl + f c π 3

14 Active High-Pass Filters The Sallen-Key HPF second-order (two-pole) filter roll-off -40dB per decade f c π A B A B Lets A B and A B f c π 4

15 Active High-Pass Filters ascaded LPF Six pole cascade 3 Sallen-Key two-pole stages roll-off -0 db per decade 5

16 Active High-Pass Filters Exercise : Design cascades 3 pole high pass filters. Given: A A, A, A, B, B,,, 3,, 4 And also sketch the response curve for this filter. Assume, the gain is normalized to. Label the critical frequency and the roll-off rates. 6

17 Active Band-Pass Filters A cascaded of a low-pass and high-pass filter ascaded of arrangement of a HPF & LPF oll-off rates are -40 db/decade 7

18 8 Active Band-Pass Filters 0 c f c f f B A B A c f π B A B A c f π

19 Active Band-Pass Filters Multiple-Feedback BPF The low-pass circuit consists of and. The high-pass circuit consists of and. The feedback paths are through and. center frequency f 0 π ( // 3 ) 9

20 0 Active Band-Pass Filters With Vin replaced by a short Multiple-Feedback BPF (cont ) ( ) 3 // f o π ( ) ( ) ) / ) // ( // // f o + + π π π π π ritical frequency/ utoff frequency

21 Active Band-Pass Filters Multiple-Feedback BPF (cont ) The resistor values can be found 3 Q πf A 0 πf 0 Q πf 0 0 Q (Q A 0 ) Solving for Q Q Q πf πf 0 0 A 0 Therefore, A 0 BW f Q Maximum gain 0 Bandwidth

22 Active Band-Pass Filters Exercise: Based on the figure, determine: a) The center frequency, fo b) Maximum gain, Ao c) The bandwidth Given: Ω Ω 0.0uF, 56k, Ω 3.3k and 35k 3

23 State-Variable BPF Active Band-Pass Filters Widely used for band-pass applications. 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 circuits. 5 and 6 set the Q (bandwidth). 3

24 Active Band-Pass Filters State-Variable BPF (cont ) The band-pass output peaks sharply the center frequency giving it a high Q. 4

25 Multiple-feedback 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 3 and the addition of 4. 5

26 State Variable Active Band-Stop Filters Summing the LP and HP responses Application: to minimize the 60 Hz hum in audio systems by setting the center frequency to 60 Hz. 6

27 Filter esponse 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. 7

28 Filter esponse Measurements Test setup for discrete point measurement of the filter response. 8

29 Filter esponse Measurements Swept Frequency Measurement 9

30 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. 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 0 B. 30

31 Summary The hebyshev filter response has ripples and overshoot in the passband but can have roll-off rates greater than 0 db. 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 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. 3