Physics 160 Lecture 3. R. Johnson April 6, 2015
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1 Physics 6 Lcur 3 R. Johnson April 6, 5
2 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx impdanc ou X C X C C R C ga H ou RC ( whr an April 6, 5 Physics 6
3 Low Pass Filr Rspons ( ou /. h( Magniud. Slop is 6 db/ocav (or db/dcad Plod for 4 ( Phas Th 3dB po is whr h oupu falls by (powr falls by ½ log( 3. log 3dB po : and ad 45 April 6, 5 Physics 6 3
4 Low Pass Filr (sgl pol Rcap ou Also known as an graor (im doma! Lousy xampl; w will mak narly prfc graors from op amps lar h quarr. ou ( d d C RC 3dB po is a f=/(rc 6dB/ocav falloff a high f Frquncy rspons: Phas shif ( ou is h volag across h capacior: ou lags dgrs a low frquncy 45 dgrs a h 3dB po 9 dgrs a high frquncy, far abov h 3dB po This is valid for only a shor im, whil ou ~. April 6, 5 Physics 6 4
5 RC Circui (High-Pass Filr Aga us an RC circui, bu w swappd h rsisor and capacior, so ha now h oupu volag is givn by h currn hrough h rsisor. RC whr R C ou R R R R C ou ( whr an April 6, 5 Physics 6 5
6 High Pass Filr Rspons ( ou / h(. Magniud... Plod for 8 6 ( 4 Phas.. Th 3dB po is whr h oupu falls by (powr falls by ½ log( 3. log 3dB po : and ad 45 April 6, 5 Physics 6 6
7 High Pass Filr (sgl pol Rcap ou Also known as a diffrniaor (im doma! Lousy xampl; w will mak narly prfc diffrniaors from op amps lar h quarr. dq d R RC d d 3dB po is a f=/(rc 6dB/ocav (fancy way of sayg uniy slop for low f Phas shif ( ou is proporional o h currn R Frquncy rspons ou ou lads dgrs a high frquncy 45 dgrs a h 3dB po 9 dgrs far blow h 3dB po This is valid for only a shor im, whil ou ~. April 6, 5 Physics 6 7
8 + nducor (AC Sady Sa s cos( d L Kirchhoff loop rul d d L L cos d L cos Currn lags volag by ¼ priod d(9 (9 ( (.5.5 Phasors : Th ral par racs ou h cos curvs as h vcor roas. April 6, 5 Physics 6 8
9 Phasors ar Complx Numbrs Physical volag and currn ar undrsood o b h ral par of h complx quaniy. Th ral and imagary pars don g mixd up by h circui quaions as long as h circui is lar. cos( L cos L ( Considrg and o b complx numbrs: L mpdanc April 6, 5 Physics 6 9
10 Summary All 3 lar circui lmns provid an impdanc ( o h flow of currn, bu on has o spcify a phas diffrnc bwn currn and volag as wll as a chang ampliud. Assum ha h volag is givn by ( max ( R ( and R and phas max ( C ( and C X C Racanc: lads by 9 C L ( C and L X L lags by 9 April 6, 5 Physics 6 L ( L
11 s Sris LCR Circui (Physics 5C ( cos ( AC ( ( max C L R max R L C an L C R is mimum whn whn LC hp://vnasci.lu.du/s_schnidr/physls/ma/rlc.shml L C ( R LC cos Maximum currn April 6, 5 Physics 6
12 Ohms Amprs X L f X C f R f 5 Rsonanc a Sris LCR Circui Rsisanc and Racanc f Pak Currn A rsonanc:. Th duciv and capaciiv racancs ar qual magniud.. Th currn is maximum. 3. Th phas angl bwn volag and currn is zro. dgrs 36 f 3 4 lags bhd f Phas Angl lads 3 4 Hz f rsonanc LC A low f, h circui looks RC. A high f, h circui looks RL. April 6, 5 Physics 6
13 Powr P( ( ( Bu usually w masur h avrag powr. P T * ( ( d T cos Complx ampliuds rms rms Powr facor Whr phi is h phas diffrnc bwn h volag and currn. = for rsisor (max. powr =/ for capacior (zro powr = / for ducor (zro powr April 6, 5 Physics 6 3
14 Rsonanc a Sris LCR Circui Powr Dissipaion Was P av f.4 Powr vs. frquncy R = ohms. 3 4 f Powr Dissipaion Hz Was P av f.4. Rsisiv R = ohms Larg dampg givs a broad low rsonanc. Capaciiv nduciv 3 4 Powr Hz f Dissipaion Was P av f.. R = ohms Small dampg givs a sharp, high rsonanc (good for a radio rcivr. 3 4 f April 6, 5 Hz Physics 6 4
15 Mor Elabora LRC Nworks Sraigh-forward applicaion of complx impdanc, rsulg simulanous complx quaions. Easy o solv wih a compur (bu mssy by hand. S xampl handou. Bu for mos of his cours w rally only nd h wo simpl RC filrs! 4 F 4.4 mh 3 = = 4 rad/s i 4 4 i i 3.5 i mpdanc sn by h sourc: q i April 6, 5 Physics 6 5
16 AC (lar Analysis wih PSpic 3 ac.dc S h PSpic uorial and HW #. R 6.m R 4.m 4 C uf 9 L mh Capur Schmaic PSpic Nlis _ N3 DC.dc AC ac R_R N3 N9 6 R_R N9 N 4 L_L N mh C_C C N9 uf LC 796 Hz PSpic Oupu (AC Analysis April 6, 5 Physics 6 6
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Considr a pair of wirs idal wirs ngh >, say, infinily long olag along a cabl can vary! D olag v( E(D W can acually g o his wav bhavior by using circui hory, w/o going ino dails of h EM filds! Thr
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