ACTIVE FILTERS EXPERIMENT 2 (EXPERIMENTAL)

Transcription

1 EXPERIMENT ATIVE FILTERS (EXPERIMENTAL) OBJETIVE T desig secd-rder lw pass ilters usig the Salle & Key (iite psitive- gai) ad iiite-gai apliier dels. Oe circuit will exhibit a Butterwrth respse ad the ther will be based a hebyshev respse. Scalig techiques will be used t esure practical cpet values. INTRODUTION Active ilters are cstructed usig a cbiati resistrs, capacitrs ad a active device. The active device is usually a p-ap. The ai advatages these ilters are: -Expesive ad bulky cils are eliiated. -Arbitrary circuit gai ca be realized. -High iput/lw utput ipedaces yield gd islatig prperties. Se disadvatages iclude: -Op-aps require pwer supplies. -At higher requecies p-ap gai is reduced csiderably. -The circuit is sesitive t cpet chage. Tw c ilter ciguratis are the Salle & Key psitive gai ad the Negative-eedback class ilters. I this lab yu will desig ad build, a secd rder lw-pass Butterwrth ilter usig the Salle & Key del, ad a secd-rder lw-pass hebyshev ilter usig the Negativeeedback del. BUTTERWORTH RESPONSE A Butterwrth respse exhibits speciic characteristics. A Butterwrth respse has a traser ucti T w w 0 Fr a ralized requecy, w the traser ucti is: T w Where w = hal -pwer-requecy, ad = uber ples

2 Let w, the T 0. 5, ad , r w 0lgT 0lg(0.707) 3dB The Butterwrth characteristics ca be suarized: T. T at w 0 is r all.. T at w is r all. 3. Fr a large w, T exhibits -ple rll-. 4. The respse is axially lat, sice the irst (-) derivatives the Taylr series expasi T ( j) is zer at w 0 (i.e., D). HEBYSHEV RESPONSE The hebyshev r equal-ripple apprxiati has a traser ucti: T ( w) Where ( w) cs( cs w) r 0 w ( w) csh( csh w) r w. w is the ralized requecy with respect t the pass-bad edge requecy w. th T (jw) is the rder hebyshev plyial. Therere: T ( w) The hebyshev characteristics ca be suarized as llws.. At w = 0; T ( 0) r eve T ( 0) 0 r dd. At w = ; T ( ) r all The agitude the hebyshev respse decreases tically i the stp bad. Because the ripples i the pass-bad the hebyshev ilter exhibits a sharper atteuati i the stpbad tha a Butterwrth ilter the sae rder. SALLEN & KEY FILTER The Salle & Key lw-pass ilter which uses a psitive gai apliier is shw i igure.

3 R R 5V Vut + - Vi -5V Fig. Salle & Key Lw-pass Mdel A special case the Salle & Key del is the uity gai S&K shw i igure. R R 5V Vut + - Vi -5V Fig. Salle & Key Lw-pass Mdel Uity Gai INFINITE GAIN AMPLIFIER BASED MULTIPLE FEED BAK SINGLE AMPLIFIER BIQUADTI (SAB) LOW-PASS FILTER The ultiple eedback (iiite gai apliier based) lw-pass ilter is shw i igure 3. et [u]: hage the igure capti t: Iiite gai ultiple lp SAB (lw-pass) ilter R R R V Vut Vi -5V Fig. 3 Salle & Key Lw-pass Mdel Uity Gai 3

4 SALING (MAGNITUDE & FREQUENY SALING) A circuit ca be desiged r practical cpet values eplyig agitude scalig. T agitude scale cpets the llwig equatis are used. R K R ew L K ew ew K Fr exaple i the desig value the capacitr is 0.µF ad yu ly have uf capacitrs, the 6 7 yu eed a scalig actr, K 0 /0 0. ew A circuit desiged r e requecy ca be trasred t perate at ather requecy by eplyig requecy scalig. The equatis r requecy scalig are siilar t the agitude scalig equatis. With the excepti that resistrs are t requecy scaled. L L Lew, K ew K Where K rati ial t iitial cut- requecies i radias = w /w i. This techique is particularly useul whe yu desig a ilter that is ralized r w i = w. I this case K = w. PROEDURE. Desig a secd- rder Butterwrth lw-pass ilter usig the Salle & Key del (Fig. ) r the cut- requecy 0KHz. Desig the circuit t perate usig F capacitrs ad equal resistrs. The ple requecy (cut- requecy) is give by: w. Apply a V peak-peak siusidal iput sigal, startig at KHz RR ad sweep thrugh the cut- requecy t 5 KHz, i steps 500Hz. Make sure t take re readigs, at saller itervals, arud the cut- requecy i.e. r 9 KHz t 5KHz reduce the iterval size t 50Hz.. Desig a secd-rder hebyshev lw-pass ilter with a pass-bad ripple db, usig the cigurati i Fig.3, r the ple- requecy 0KHz. Desig the circuit t perate usig 0F capacitrs. Apply a V peak-peak siusidal iput sigal, startig at KHz ad sweep thrugh the cut- requecy t 5KHz, i steps 500Hz. Make sure t take re readigs, at saller itervals, arud the cut- requecy, i.e.: r 9KHz reduce the iterval size t 50Hz. 3. Usig the requecy scalig techique, re-desig ad test the ilter i step- r a cut- requecy KHz RESULTS & DISUSSION. Derive the traser ucti V ut /V i r the ilter circuits i igures,, ad 3. 4

5 . Plt experietal ad theretical curves (V ut /V i ) the sae graph r the ilters i Figs. ad What is the value Q p prduced by yur desig i prcedure step #? 5