Chapter 13. Filters Introduction Ideal Filter

Transcription

1 Chapter 3 Flters 3.0 Introducton Flter s the crcut that capable o passng sgnal rom nput to output that has requency wthn a speced band and attenuatng all others outsde the band. Ths s the property o selectvty. They are our basc types o lters. They are lowpass, hgh-pass, band-pass, and band-stop. The basc lter s acheved wth varous combnatons o resstors, capactors, and sometmes nductors. These are named as passve lters. Actve lters besdes usng passve element, t also uses actve element such as transstors or operatonal amplers to provde desred voltage gans or mpedance characterstcs. Each type o lter response can be talored by crcut component values that have Butterworth, Chebyshev, or Bessel characterstcs. Each o these characterstcs s dented by the shape o ts response curve and each has an advantage n certan applcaton. In ths chapter, we shall explore the basc concepts o desgnng passve and actve lters namely the low-pass, hgh-pass, band-pass, and band-stop lters. The characterstcs o each lter type n terms o t bandwdth, crtcal requency, and gan would be dscussed n detals. We shall not be dscussng the methods to desgn lter that has Butterworth, Chebyshev, or Bessel characterstcs. Ths part o the lecture shall be let to be dscussed n the analogue crcut desgn subject. 3. Ideal Flter Ideally, lter should have the characterstcs as shown n Fg. 3.. In practce, such characterstcs are not possble to be acheved. In practce, the attenuaton o the sgnal ater the crtcal requency s ether exponentally ncreased or decreased. It s not abruptly decreased or ncreased as shown n Fg

2 3 Flter Fgure 3.: Ideal lter characterstc low-pass, hgh-pass, band-pass, and band-stop 3. Passve Flters Four basc passve lters namely the low-pass, hgh-pass, band-pass, and bandstop are be dscussed n ths secton. 3.. Low-Pass Flter A basc passve low-pass crcut s shown n Fg. 3.. The transer uncton H(s) o the lter s Fgure 3.: Passve low pass lter - -

3 3 Flter H(s) 0 / jωc + / jωc (3.) The magntude o the uncton shall be the lter shall be + ( ωc). The crtcal requency C o C πc (3.) It can determned ether by settng uncton by settng ωc and the 3dB requency s determned by settng + ( ωc). The phase o the lter shall be φ - tan - (ωc). Based on equaton (3.), as requency ncreases, the uncton H(s) s approachng zero. As requency decreases, the uncton H(s) s approachng one. The characterstc o the lter s shown n Fg Hgh-Pass Flter Fgure 3.3: The characterstcs o a passve low pass lter A basc passve hgh-pass lter crcut s shown n Fg

4 3 Flter The transer uncton o the lter H(s) s Fgure 3.4: Passve hgh-pass lter H(s) 0 + / jωc (3.3) The magntude o the uncton shall be the lter shall be ωc + ( ωc). The crtcal requency C o C πc (3.4) It can determned ether by settng uncton ωc and the -3dB requency can be determned by settng ωc + ( ωc). The phase o the lter shall be φ tan - (ωc). Based on equaton (3.3), as requency ncreases, the uncton H(s) s approachng one. As requency decreases, the uncton H(s) approaches zero. The characterstc o the lter s shown n Fg

5 3 Flter Fgure 3.5: The characterstcs o a passve hgh pass lter 3..3 Passve Band-Pass Flter A basc passve band-pass lter crcut s shown n Fg The transer uncton o the lter H(s) s Fgure 3.6: Passve band-pass lter H(s) 0 + j( ωl / ωc) (3.5) The magntude o the uncton shall be requency o o the lter shall be + ( ωl / ωc). The resonant o π LC (3.6) - 5 -

6 3 Flter It can be determned by settng the magnary part o the mpedance to zero. The 3dB requences are determned by solvng expresson + ( ωl / ωc). Based on equaton (3.5), the characterstc o the lter s shown n Fg Fgure 3.7: The characterstcs o a passve band pass lter 3..4 Passve Band-Stop Flter A basc passve band-stop lter crcut s shown n Fg The transer uncton o the lter H(s) s Fgure 3.8: Passve band pass lter H(s) 0 j( ωl / ωc) + j( ωl / ωc) (3.7) - 6 -

7 The magntude o the uncton shall be requency o o the lter shall be ( ωl / ωc) + ( ωl / ωc) 3 Flter. The resonant o π LC (3.8) It can be determned by settng the magnary part o the mpedance to zero. The 3dB requences are determned by solvng ( ωl / ωc) + ( ωl / ωc) Based on equaton (3.7), the characterstc o the lter s shown n Fg Actve Flter Fgure 3.9: The characterstcs o a passve band-pass lter Four basc actve lters employng operatonal ampler namely the low pass, hgh pass, band pass, and band reject are be dscussed n ths secton Actve Frst-Order Low-Pass Flter A basc rst-order low-pass lter s shown n Fg

8 3 Flter Fgure 3.0: An actve rst-order low pass lter The transer uncton, whch the voltage gan uncton H(s) s H(s) + jωc (3.9) The magntude o the gan uncton s C ω, whle the phase s tan - (ωc ). C + ( ωc ). The crtcal requency s 3.3. Actve Frst-Order Hgh Pass Flter A basc rst order low pass lter s shown n Fg. 3.. The transer uncton, whch the voltage gan uncton H(s) s H(s) jωc (3.0) + jωc The magntude o the gan uncton s ωc + ( ωc ) ω, whle the phase φ s φ 90 0 tan - (ωc ). C C. The crtcal requency s - 8 -

9 3 Flter Actve Band-Pass Flter Fgure 3.: An actve rst-order hgh pass lter The basc crcut o an actve band-pass lter s shown n Fg. 3.. The crcut comprses o a low-pass lter stage, a hgh-pass lter stage, and an nvertng stage that provdes voltage gan. Fgure 3.: An actve band-pass lter - 9 -

10 3 Flter Actve Band-Stop Flter The basc crcut o an actve band-pass lter s shown n Fg The crcut comprses o a low-pass lter stage, a hgh-pass lter stage, and summng ampler stage that provdes voltage gan and band-reject. Fgure 3.3: An actve band-stop lter - 0 -

11 3 Flter Exercses 3.. Show that crcut below s a low-pass lter. Calculate the corner requency c L mh, C 0 µf, and 0 kω. 3.. Fnd the transer uncton o / s o the crcut n the gure. Show that the crcut s a low-pass lter Determne the type o lter or the crcut shown n the lter and nd ts corner requency Desgn an L low-pass lter that uses a 50 mh col and has a cuto requency o 5.0 khz Desgn a seres LC type band-pass lter wth cuto requences o 0 khz and khz. Assumng that C 80.0 pf, nd, L, and Q Fnd the transer uncton or each o the actve lters. - -

12 3 Flter 3.7. Obtan the transer uncton o the actve lter n the gure and determne the type A hgh-pass lter s shown n the gure, show that the transer uncton s H(ω) + jωc + jωc. Bblography. Charles K. Alexander and Matthew N.O Sadku, Electrc Crcuts, nd edton, McGraw-Hll