Pictrial Illuminatin 2 ui a H u = u i a u () () H() H() z() () H (): ui H u = ui u H() u()/ ui()with ()= Extra Element Therem 2 u i I V V z(): z = u z() V()/ I()with ui ()= I I V V ζ = u = I (): u i () V ()/ I ()with u ()= 2
Applicatin t MOSFET Amplifier 22 C gd vi Cg v g g v m g r v Extra Element Therem 22 Evaluate the vltage gain Cnider vi C gd Cg a the extra element v g C gd g v () uing EET v () v i m g r v () v () () () H H() v () z() i () with ( ) C gd 22
Applicatin t MOSFET Amplifier 23 MOSFET amplifier withcgd ( ) C gd vi G Cg v g S g D v m g r v v i v () () H g r v () i ( ) m Extra Element Therem 23 MOSFET amplifier withcgd ( ) C vi Cg v g C gd gmvg r v gd () v () () () H H() v () () i z ( ) ( ) g r m C ( ) gd C z ( ) gd 23
Applicatin t MOSFET Amplifier 24 Evaluatin f z( ) Evaluatin f ( ) v T v i T () () T v ( ) O z() r i T i Cg v g = gmv g= r vi Cg v g gmvg r v = Extra Element Therem 24 ( ) i) v ( ) i i g v T m g ii) v ( ) v v T g v () ( ) Tranfer gain ( ) Cgd H gm r v () C z( ) i g r m C g C gd m r gd v vg () T i g v g gd T m g m 24
Alternative Frm f EET 25 ui a H u = u i a u () () H() H() () z() H (): ui H u = u i u H () u ()/ u ()with ()= i Extra Element Therem 25 u i I V z(): z() V()/ I()with ui ()= V z = I u I V V (): u i ζ = I u = () V ()/ I ()with u ()= 25
Extenin t 2 EET 26 2 ui u Firt adptin f EET 2 Extra Element Therem 26 ui u () ui () ( ) ( ) 2 H () u ui 2() u() () u ( ) ( ) i 2 () H 2 () ( ) z2 ( ) 2 u 26
Extenin f EET 2 EET 27 2 ui u Secnd adptin f EET 2 2 Extra Element Therem 27 ui 2() u() () u () () i 2 () H 2 () ( ) z2 ( ) 2 u ui u() u ( ) i ( ) ( ) 2 u 2() () () () H 2 () z2() () 2( ) z( ) 27
LadCupled Cnverter 28 Uncupled cnverter iu U vs io vˆ AuU v = ˆ v ˆ L= vˆ î T mu F v Fv( ) Ladcupled cnverter Lad Cupled Cnverter 28 v S F v i O L il vˆ v AuL = ˆ v ˆ L¹ L Fv( ) T ml î vˆ L 28
Perfrmance f LadCupled Cnverter 29 il L vˆ v AuL = ˆ v ˆ L¹ î vˆ L T ml Fv( ) Lad Cupled Cnverter 29 AuL ( ) AuU ( ) L ( ) U ( ) T ( ) T ( ) ml mu U ( ) TmU ( ) L ( ) U ( ) U L ( ) ( ) il( ) iu ( ) L U L ( ) ( ) ( ) Fv( ) U L U î ( ) ( ) U :cledlp inputpen utput impedance 29
Perfrmance f LadCupled Bt Cnverter 3 24V 6μH 45. W 5. W 47μF 2A V O = 46 V L 2μH 5. W 3. W 25μF Buck cnverter (92 W) 5 khz R i = 45. S e = 384. 4V/ 96nF. Filter tage kw Lad ubytem Lad Cupled Cnverter 3 PWM 27. nf 28kW 2V 455 W L () Magnitude (db) 4 2 2 4.. Frequency (khz) 3
Perfrmance f LadCupled Bt Cnverter 3 Lad Cupled Cnverter 3 Magnitude (db) Magnitude (db) 2 4 6 A ul A uu 8.. Frequency (khz) 6 4 2 2 Audiuceptibilty :ladcupled cnverter :uncupled cnverter T mu T ml Lp gain :ladcupled cnverter :uncupled cnverter 4.. Frequency (khz) Magnitude (db) Magnitude (db) 2 L U :ladcupled cnverter :uncupled cnverter 4.. Frequency (khz) 5 4 3 2 Output impedance Input impedance iu il :ladcupled cnverter :uncupled cnverter.. Frequency (khz) 3
SurceCupled Cnverter 32 Uncupled cnverter iu U vs io vˆ AuU v = ˆ v ˆ L= vˆ î T mu F v Fv( ) SurceCupled Cnverter 32 Surcecupled cnverter v S F v io vˆ vˆ AuS = v ˆ ¹ S Fv( ) T ms vˆ î 32
Perfrmance f SurceCupled Cnverter 33 S vˆ vˆ AuS = v ˆ ¹ vˆ î T ms Fv( ) SurceCupled Cnverter 33 AuS ( ) AuU ( ) TmS ( ) TmU ( ) ( ) ( ) iu ( ) ( ) i ( ) ( ) i ( ) i ( ) S ( ) U ( ) ( ) ( ) iu 33
Input Impedance Definitin 34 iu i vˆ vˆ Fv( ) iu :cledlpinput impedance F v () i:penlp utputhrted input impedance i i Extra Element Therem 34 vˆ Fv( ) vˆ = i:utputnullifiedinputimpedance vˆ Fv( ) i:penlp input impedance 34
Perfrmance f SurceCupled Bt Cnverter 35 Audiuceptibilty 6 Lp gain SurceCupled Cnverter 35 Magnitude (db) Magnitude (db) 2 4 6 A us A uu :urcecupled cnverter :uncupled bt cnverter 8.. Frequency (khz) 2 4 6 Output impedance S U :urcecupled cnverter :uncupled bt cnverter 8.. Frequency (khz) Magnitude (db) Phae (deg) 4 2 2 4 9 8 T ms T mu T ms :urcecupled cnverter :uncupled bt cnverter T mu :urcecupled cnverter :uncupled bt cnverter 27.. Frequency (khz) 35
Surce/LadCupled Cnverter 36 vˆ ˆ v î L T mc Fv( ) Surce/LadCupled Cnverter 36 Ladcupled cnverter: TmL ( ) TmU ( ) T ( ) mu U L ( ) ( ) Surce/lad cupled cnverter: ( ) i ( ) TmC ( ) TmU ( ) ( ) ( ) ( ( )) U mu T L ( ) i ( ) 36
Middlebrk Feedback Therem 37 ui u u i2 a () u 2 A () Twutput feedback cntrlled ytem A():feedback gain a ():frwardgain Feedback Therem 37 u ( ) T ( ) H( ) = H () H ( ) u ( ) T ( ) T ( ) i m i m m H () H() :feedbackignal nullified tranfer gain u 2 H () H() :penlptranfergain A T () A() a():lpgain mu 37
Pictrial Illuminatin 38 ui u u i2 a () A () u 2 T ( ) ( ) () m H H H ( ) T ( ) T ( ) m m Tm () u i = u i2 a( ) u 2 u T () A() a() m A () Feedback Therem 38 H () ui u u () () a( ) u 2 H u ui () i2 A H () ui u i2 a( ) A () u u 2 = H u () u ( ) () () i u2 38
SingleOutput Feedback Sytem 39 u i u i2 a () u A () u ( ) T ( ) H( ) = H () H ( ) u ( ) T ( ) T ( ) m i m m Feedback Therem 39 i H u ( ) () u ( u ( ) ( ) H = H ( ) u ( ) T ( ) ) u i ( ) m 39
Input Impedance f Uncupled Cnverter 4 i T v T T mu ˆv î Fv( ) Extra Element Therem 4 it ( ) TmU ( ) ( ) v ( ) ( ) T ( ) ( ) T ( ) iu T i mu i mu ():utputnullifiedinputimpedance i ():penlpinputimpedance T i mu ():lpgain æ i() fr frequencie where TmU iu ()» ç çè i () Gv() fr frequencie where TmU 4
Chapter Summary 4 DC Pwer Ditributin Sytem Uncupled Cnverter Pwer Stage Dynamic and Cntrl Deign f Uncupled Cnverter Cupled Cnverter and Middlebrk Extra Element Therem Ladcupled cnverter Surcecupled cnverter Surce/ladcupled cnverter 4 Middlebrk Feedback Therem 4