ELG4139: Passive Filters
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1 EG439: Paive Filter A ilter i a ytem that procee a ignal in ome deired ahion. There are two broad categorie o ilter: An analog ilter procee continuou-time ignal A digital ilter procee dicrete-time ignal. The analog or digital ilter can be ubdivided into our categorie: owpa Filter Highpa Filter Bandtop Filter Bandpa Filter
2 Serie eonance reonance For ( : ( rom Subtitute eitance reonance at inductance o eactance ( (
3 Serie eonance and Subtitute ( ( ( / ( I I
4 Parallel eonance p At reonance P i purely reitive: rom Subtitute reonance at inductance o eactance eitance P P ( ( (59. ( 59., 59.,, H Hz x Hz x pf H k P I 9 9 ( I I I I
5 Second Order ow-pa Filter H S S in in in in / ( ( 9 H Tan H S S in
6 Second Order High-Pa Filter At low requency the capacitor i an open circuit At high requency the capacitor i a hort and the inductor i open
7 Second Order Band-Pa Filter At low requency the capacitor i an open circuit At high requency the inductor i an open circuit
8 Second Order Band-eect Filter At low requency the capacitor i an open circuit At high requency the inductor i an open circuit
9 Example: Deign a ilter with S = that pae requency component lower than 5 khz and reect component higher than 5 khz. hoe =5 mh. 5kHz 3 3 ( ( (5x (5x.6F 3 (5kHz (5x H 57.
10 Example: Deign a ilter that pae requency component between =45 khz and H =55 khz. hooe = mh. 5kHz. 3nF 3 3 ( ( (5x (x B H khz 5kHz 5 B khz (5kHz (x 5 3 H 6.83
11 Filter Speciication Tranmiion peciication or a bandpa ilter. The magnitude repone o a ilter that ut meet peciication i alo hown. Note that thi particular ilter ha a monotonically decreaing tranmiion in the paband on both ide o the peak requency.
12 Ideal Filter owpa Filter Highpa Filter M(w Paband Stopband Stopband Paband w c w w c w Bandtop Filter Bandpa Filter M(w Paband Stopband Paband Stopband Paband Stopband w c w w w c c w c w
13 Paive and Active Filter Paive ilter employ reitor, capacitor, and inductor ( network. To minimize ditortion in the ilter characteritic, it i deirable to ue inductor with high quality actor, however thee are diicult to implement at requencie below khz, becaue. They are non-ideal (loy! They are bulky and expenive! Active ilter overcome thee drawback and are realized uing reitor, capacitor, and active device (uually op-amp which can all be integrated: Active ilter replace inductor uing op-amp baed equivalent circuit. The Problem o the Inductor! High accuracy (% or %, mall phyical ize, or large inductance value are required! Standard value o inductor are not very cloely paced. Diicult to ind an o-the-hel inductor within percent o any arbitrary value. Adutable inductor are ued. Tuning uch inductor to the required value i time-conuming and expenive or larger quantitie o ilter. Inductor are oten prohibitively expenive.
14 Op Amp-baed Active Filter Advantage: educed ize and weight, and thereore paraitic. Increaed reliability and improved perormance. Simpler deign than or paive ilter and can realize a wider range o unction a well a providing voltage gain. In large quantitie, the cot o an I i le than it paive counterpart. Diadvantage: imited bandwidth o active device limit the highet attainable pole requency and thereore application above khz (paive ilter can be ued up to 5 MHz. The achievable quality actor i alo limited. equire power upplie (unlike paive ilter. Increaed enitivity to variation in circuit parameter caued by environmental change compared to paive ilter. For application, particularly in voice and data communication, the economic and perormance advantage o active ilter ar weigh their diadvantage.
15 Bode Plot and db Bode plot are important when conidering the requency repone characteritic o ampliier. They plot the magnitude or phae o a traner unction in db veru requency. Two level o power are compared uing a unit o meaure called the bel. The decibel i deined a: B log P P bel = decibel (db db log A common db term i the hal power point which i the db value when the P i one- hal P. P P log 3.dB 3dB
16 ogarithm A logarithm i a linear tranormation ued to impliy mathematical and graphical operation. It i a one-to-one correpondence. Any number (N can be repreented a a bae number (b raied to a power (x. N ( b The value power (x can be determined by taking the logarithm o the number (N to bae (b. x log b Although there i no limitation on the numerical value o the bae, calculator are deigned to handle either bae (the common logarithm or bae e (the natural logarithm. Any bae can be ound in term o the common logarithm by: log w x N log q log q w
17 Pole and ero o the Traner Function Pole value o where the denominator goe to zero. ero value o where the numerator goe to zero. Single-Pole Paive Filter (Firt-Order ow-pa Filter v in v ut-o requency = / rad/ v v in / / / / Diadvantage: Any load (or ource impedance will change the requency repone.
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