EE40 Lec 13. Prof. Nathan Cheung 10/13/2009. Reading: Hambley Chapter Chapter 14.10,14.5
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1 EE4 Lec 13 Filter and eonance Pro. Nathan Cheung 1/13/9 eading: Hambley Chapter Chapter 14.1,14.5 Slide 1
2 Common Filter Traner Function v. Freq H ( ) H( ) Low Pa High Pa Frequency H ( ) H ( ) Frequency Band dpa Band deject Frequency Frequency Slide
3 Filter Paive: reonant circuit that contain only paive element, namely reitor (), capacitor (C), and inductor (L) Active: reonant circuit that contain op amp, tranitor, and/or other active device, in addition to the paive element Slide 3
4 Filter Order The order o a ilter i equal to the abolute value o the highet power o ω in it traner unction Slide 4
5 Firt-Order Filter Circuit High Pa Low Pa V S + C Low Pa V S + L High Pa H / ( + 1/jωC) H C (1/jωC) / ( + 1/jωC) H / ( + jωl) H L jωl / ( + jωl) Slide 5
6 Firt Order Low Pa Filter Slide 6
7 Second-Order LC Filter Circuit Band Pa Z + 1/jωC + jωl V S + Low Pa High Pa C L Band eject H BP / Z H LP (1/jωC) j / Z H HP jωl / Z H B H LP + H HP Slide 7
8 Second Order BandPa Filter Write the expreion or V : Now ind H BP (ω): H BP V ( ω) V V S jωc ( 1 ω ω LC ) + j ω C Slide 8
9 Paive Filter: Bandpa Linear-Linear plot H BP V ( ω ) V S jωc ( 1 ω LC ) + jωc Slide 9
10 eonance Frequency Deined a requency when the total impedance i purely reitive ( i.e. zero imaginary i component) j Z( ω) + jωl ωcc Thereore Slide 1
11 db The Quality Factor Q The Quality Factor (Q) characterize the degree o electivity o the circuit. It i determined by: For a bandpa ilter: Notice that Q depend on the reonant requency Linear ω cale Slide 11
12 eonance Bandwidth / o 1/ At reonance with large Q, * Thi i a Linear-Linear plot V L and V C >>V L C Slide 1
13 Another Way to write H() (See Hambley text ) H H c c Hc 1 ( ) 1 1 L + jωl 1 jω jωc + + jωc + 1 ( ) ω ω 1 ωol 1 + jq ( ) QS ω ω ωoc 1 ( ) 1 ω o 1 + Q ( ) LC Slide 13
14 To Generate the Bode Plot 1 1 Low : dominate Hc( ) ; Hc( ) jq Q y 1log Hc ( ) K + log Slope : db / dec H ( ) 9 c High : dominate Hc( ), H ( ) y 1log H ( ) K log Slope : db / dec HH ( c ) 9 1 c jq Q c at : ( ) 1, ( ) 1 H H y db c c H ( ) c Slide 14
15 Bode Plot +db/dec -db/dec Slide 15
16 Second Order LowPa Filter V C 1 HLP ( ω ) V M LP ( ω) S ( 1 ω LC ) 1 + jωc { [ ( ) ] ( ) } 1 ω / ω + ω / ω 1/ 1 LC Q 1 ω L ω o Q ω o C o Slide 16
17 Another Way to write H() (See Hambley) H c 1 1 jωc jωc ( ) 1 1 L + + jωl 1+ + jω jω C jω C 1 1 ω L 1 Let ω, Hence ω L ; deine Q LC C ω C ω L jω ω L jω 1 ω 1 jω jω Q, Q ω ω jωc jω ω C ω H H c ω jq ( ) ω ω ω 1 + jq ( ) ω ω c ( ) Q 1 + Q ( ) Slide 17
18 Second Order HighPa Filter H M HP HP ( ω) ( ω) V V L S ω LC + jωc ( 1 ω LC ) ( ω / ω ) [ 1 ( ω / ω ) ] + ( ω / Qω ) { } 1/ Q Slide 18
19 Second Order Bandreject Filter H B VL + VC ( ω ) 1 H BP ( ω ) V S Slide 19
20 Parallel LC Circuit (See Hambley 6.7) 1 Z p jωc j ω L IZ p 1 1 H( ) I jωc 1+ + jωc jωl j ω L jω jω ω jω Qp, jωc j ωc Q jωl ω ωl ω ω ω 1 Hc( ) Q C 1 + jqp ( ) p ω ωl H c ( ) Qp ( ) I in L C p Slide
21 Active Filter Contain le component (no inductor) Traner unction that i inenitive to component tolerance or load variation Eaily adjuted d Allow a wide range o ueul traner unction Slide 1
22 Single Pole Lowpa Filter H LP Vout ( ω ) V 1 jωc jω C H LP ( ω ) G LP jω / ω LP G LP ; ωlp 1 C Slide
23 Single Pole Highpa Filter H HP H ( ω ) HP G ( ω) HP V V out jω / ω 1 + jω / ω HP HP Z Z j/ ω C G HP ; ωhp 1 C Slide 3
24 Cacaded Active Filter Slide 4
25 Cacaded Active Filter Slide 5
26 Cacaded Active Filter Slide 6
27 Cacaded Active Filter Slide 7
28 Cacaded Active Filter Slide 8
29 Cacaded Active Filter Slide 9
30 Appendix (For reerence only) See Hambley 14.5 The open loop gain o an Op Amp decreae with requency The unity-gain bandwidth t ~ everal MHz or typical op amp Slide 3
31 Appendix (For reerence only) Circuit uppoed to have a cloed lop gain o 1 (db) Given: t 4MHz, circuit can operate with < 4kHz Slide 31
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