Lecture 9. RC Filters. Outlines of Filter Design

Transcription

1 Lecture 9 Filters 9- Outlines of Filter Design input Filter output Filtering: ertain desirable features are retained Other undesirable features are suppressed 9-

2 Filters Filters have the property of removing unwanted frequencies from our signal. lasses: Types: Passive (made of capacitors, resistors, inductors) Active (involving an amplifier) Low-Pass (remove high frequencies) High-Pass (remove low frequencies or D) Band-Pass (remove a range of frequencies on two sides) Notch (removes frequencies in the middle) 9-3 lassification of Filters Signal Filter Analog Filter Digital Filter Element Type Frequency Band Active Passive Low-Pass Band-Pass All-Pass High-Pass Band-eject 9-4

3 Filters Type of filters Passive filters Terminology in Filter Design Signal-To-Noise atio (S/N) S W S 0 log db N W N Bandwidth the range of frequencies of G(jw) >0.707 utoff Frequency the end of pass-band frequency Break-point of a filter the point with a gain of -3dB 9-6

4 Filters In combination with a resistor, a capacitor s variation in reactance with frequency can be used to construct a simple low-pass or high-pass filter: in High-pass filter Low-pass filter out Z X in Z + X πf Z out X in X Z + X πf 9-7 Passive Low-Pass Filter H( jω) ω p ω s L ω The pass-band is from 0 to some frequency w p. Its stop-band extends form some frequency w s, to infinity. In practical circuit design, engineers often choose amplitude gain of 0.95 for passive filters: 9-8

5 Passive High-Pass Filter H( jω) Its stop-band is form 0 to some frequency w s The pass-band is from some frequency w p to infinity. ω s ω p ω In practical circuit design, engineers choose amplitude gain of 0.95 for passive filters: 9-9 Design of Passive Filters The amplitude response: L out in + ( ω ) Transfer Function H H ( jω ) () s jω + s + The amplitude gain: ZL G Z + Z F The 3dB break-point is at: L π πτ f3 db 9-0

6 Guideline of Pass Filter Design H Transfer Function () s τ τ s + Time onstant L Select resistor based on amplitude gain: ZL G Z + Z Z F F L ZL Select capacitor based on cut-off freq: τ πf 3dB L 9- Higher Order Filters in First Order Low Pass Second Order Low Pass The higher the order of the filter, the closer it approaches ideal characteristics. 9-

7 Active Filters Active filters employ Op-Amps to attenuate select frequencies and amplify signal during filtering process. Q factor of a filter is defined as the ratio of the center frequency f c to the bandwidth f H - f L : f Q f f ( ) H L 9-3 Active filters- cascading low pass filters First order Second order 3 rd order Op Amp for everyone, on Mancini, Ed, Texas instrument, th order 9-4

8 Low-Pass Active Filter Passive filters take up lots of space in a circuit and cause signal to be lost. ombining a passive filter with an op amp for amplification creates what is known as an active filter. By active we mean that the filter requires power to operate. Here is an example of an active low-pass filter. The signal + is provided to the noninverted input through an low-pass filter made up of and. Feedback to limit gain comes through and F. The parallel combination of and F presents an impedance which decreases with increasing frequency, meaning that more negative feedback is provided to the inverting input at higher frequencies, reducing gain at those frequencies. - F 9-5 Design of Low Pass Active Filters A B - + Transfer Function: T. F. K LP F ω0 s + ω 0 The -3 db cut-off frequency: f H ( π ) The D gain: K F LP F Example: Design a low pass filter with cut-off frequency of 5 khz, and D gain of 0: Two equations, three unknowns 9-6

9 High-Pass Active Filter - + F Here is an example of an active high-pass filter. and make up an high-pass filter at the input of the op amp. 3 provides a path for the input when the frequency is too low for to freely conduct. When the 3 input signal passes through 3 instead of into the amplifier, the output is tied directly to the input and the gain is reduced. So, this amplifier has low gain at low frequencies and higher gain at high frequencies. prevent any D at the input from being coupled to the output. 9-7 Design of High Pass Active Filters The -3 db cut-off frequency: A B - + F f H π The D gain: K HP ( ) F Two equations, three unknowns Transfer Function: s T. F. K HP s +ω 0 Select one component based on other conditions, and determine the values of the other two components. 9-8

10 Filter lass A filter of a given order can be made to approximate to ideal characteristics in a number of ways, depending on the values of the filter components (or say: depending on the filter class. Two useful classes are Butterworth (maximally flat) and hebyshev (equal-ripple) filters (n is the filter order) Butterworth Filter hebyshev Filter out in out in + f + E f f n n f 9-9 Higher Order Active Filters Filter lass K Buterworth db at ω H + - b a GainK hebyshev db ripple The above list gives the gain and component valves for one of the many choices for ω H. You may find more combinations from filter design handbook(s). 9-0

11 Active Filters High Pass Filters Low pass High pass 9- Op Amp for everyone, on Mancini, Ed, Texas instrument, 00. Active Filters Band Pass Filter 9- Op Amp for everyone, on Mancini, Ed, Texas instrument, 00.

12 Active Filters Band eject Filter Active band Passive band reject filter reject filter Op Amp for everyone, on Mancini, Ed, Texas instrument, eferences Op Amp for everyone, on Mancini, Ed, Texas instrument,