-T Sytem: Ung Bode Plot EEE 30 Sgnal & Sytem Pro. Mark Fowler Note Set #37 /3
Bode Plot Idea an Help Vualze What rcut Do Lowpa Flter Break Pont = / H ( ) j /3
Hghpa Flter c = / L Bandpa Flter n nn ( a) n n ( a)( b) (db) 0 0-0 -0-30 -40-50 7 588-60 00+j995 0 0 0 3 0 4 00-j995 0 5 T Frequency (rad/ec) All lope are 0 db/decade! 0. 3 000 000 3/3
A Better Bandpa Flter? Suppoe you want a BPF. wth ater rollo! Need an term n the numerator! At we need to change lope by 40 db/dec So need double pole @! At we need to change lope by 40 db/dec So need double pole @! K ( ) ( ) There are (at leat) three way to get th! K K ( )( ) ( )( ) K K ( ) ( ) K K ( ) ( ) BPF L w/ dtnct pole BPF L w/ repeated pole HPF L w/ ep. pole LPF L w/ ep. pole Same exact crcut jut derent choce o L!!! 4/3
Look lke we could jut cacade two o our L crcut Here we cacade BPF. Our cacade theory only hold when attachng the nd ytem doe not change how the rt one behave! Although TF Theory ay th wll work the problem that the econd crcut Load the rt one!!! So one approach would be to re-analyze th cacade and ee t wll tll work but wth ome tweek on the component choce. Another approach to ue an op amp a a buer between the tage! Bandpa L Bandpa L VEY large nput retance o op amp prevent loadng o rt tage! VEY mall output retance o op amp mnmze mpact on nd tage! emember there are two way to chooe the component here:. Each tage ha repeated pole. Each tage ha dtnct pole It may be derable to add another buer here 5/3
Another way to make a better BPF: Here we mut chooe the component o that each tage ha repeated pole. nd Ord Hghpa L nd Ord Lowpa L Although thee dea lead to workable crcut they are not necearly the bet For one thng they need nductor (whch are bg and can t be made n an I!) There are other orm See th lnk or the orm ued below. http://pderv.maxm-c.com/en/an/an795.pd nd Ord Hghpa nd Ord Lowpa + + 6/3
Degn Example ung Bode Plot Inght Suppoe you want to buld a treble booter or an electrc gutar. You decde that omethng lke th mght work: 0dB H ( ) 00Hz 68 rad/ = 0dB (Hz) 000Hz 683 rad/ = 00 000 Notce that we are dong our rough degn thnkng n term o Bode Plot approxmaton!!! The A trng on a gutar ha a undamental requency o 0 Hz The A note on 7 th ret o the hgh-e trng ha a undamental requency o 880 Hz From our Bode Plot Inght we know we can get th rom a ngle real pole, ngle real zero ytem wth the zero rt, then the pole : H ( ) ( ( / ) / ) H ( ) ( ( j / ) j / ) wth: = 68 rad/ = 680 rad/ 7/3
8/3 A ere combnaton ha mpedance Z() = + / Note: we could get + L wth an nductor but nductor are generally avoded when poble So what do we get we could ome how orm a rato o uch mpedance? / / ) ( ) ( Z Z / / : Let Aha!!! What we want! Now, how do we get a crcut to do th? Let explore! / / ) ( ) ( j j Z Z
Okay how do we buld a crcut that ha a traner uncton that a rato o mpedance?! ecall the op-amp nvertng ampler! v n v o Gan ato o retance Extendng the analy to nclude mpedance we can how that: Z () Z () v n v o H ( ) Z Z ( ) ( ) Won t aect our magntude: 9/3
v n v o Now, you can chooe the & to gve the dered requency pont p. 98, The Art o Electronc, Horowtz & Hll, ambrdge Pre, 980 But wat!! You then remember that op amp mut alway have negatve eedback at D o puttng here not a good dea So we have to contnue We alo mght not lke th crcut becaue t mght not gve u a very large nput mpedance and that mght excevely load the crcut that you plug nto th (e.g., the gutar) Back to the drawng board!!! 0/3
Okay, then you remember there alo Non-Invertng Op-Amp crcut Innte nput mpedance v n v o Gan We avod the no D eedback ue but we re not yet ure we ll get what we want! Applyng th gan ormula we get: ( / ) ( ) / / / / H ( ) Oh ool!! We Get What We want! ( ) Set: 683 rad/ 68 rad/ hooe: 5k 0.F.5k Ung tandard value /3
H( ) (db) omputed Frequency epone ung Matlab Dcrepancy due to ue o tandard value (Hz) /3
Summary o Bode-Plot-Drven Degn Example. Through nght ganed rom knowng how to do Bode plot by hand we recognzed the knd o traner uncton we needed. Through nght ganed n crcut cla about mpedance we recognzed a key buldng block needed: Sere - 3. Through nght ganed n electronc cla about op-amp we ound a poble oluton the nvertng op-amp approach 4. We then crutnzed our degn or any overlooked ue a. We dcovered two problem that we needed to x 5. We ued urther nght nto op-amp to realze that we could x the nput mpedance ue ung a non-nvertng orm o the op-amp crcut 6. We ddn t gve up at rt gn that the nvertng orm mght not gve u the orm we want a. Through mathematcal analy we howed that we dd n act get what we wanted!!!!!! 3/3