Elecroncs and Mcroelecroncs AEBEM. lecure basc elecronc crcu conceps ressors, capacors, nducors Elecroncs and Mcroelecroncs AEBEM Sudng maerals: server MOODLE hp://moodle.kme.fel.cvu.cz AEBEM Elecroncs and Mcroelecroncs Book: Sedra, Smh: Mcroelecronc Crcus Basc concep Elecrc curren Amoun of charge ha passes hrough a ceran cross secon per un me SI Un Ampere Ampere s a consan elecrcal curren whch passes hrough wo drec parallel nfnely long wres of neglgble crcular cross secon placed n a vacuum n he dsance of one meer ha produces a consan force of. 7 Newons per mere of wre lengh Volage Volage The dfference of elecrcal poenal beween wo pons n space Un Vol The vol s defned as he value of he volage across a conducor when a curren of one ampere dsspaes one wa of power n he conducor. I can be wren n erms of SI base uns as: m kg s A. I s also equal o one joule of energy per coulomb of charge, J/C André Mare Ampére French mahemacan and physcs who became famous especally for hs work n he feld of magnesm and elecrodynamcs. Alessandro Guseppe Anono Anasaso Vola Ialan physcs famous for hs dscoveres n elecrcy. Invened such as frconal elecrcy, elecrcal cell or a capacor. Volage DC volage s a volage, whch does no change polary over me, he value may vary. AC volage s he volage ha changes over me wh a ceran perod, whle he medan value may be zero. Waveform (shape) can be any shape, mos ofen we can mee wh snusodal rack. MS (roo mean square) AC volage s a DC equvalen volage a whch he same conducors creae he same amoun of hea. Elecrc power Elecrc power Elecrc power s he rae a whch elecrcal energy s ransferred by an elecrc crcu. In drec curren ressve crcus, elecrcal power s calculaed usng Joule's law: P V. I where P s he elecrc power, V he poenal dfference, and I he elecrc curren. In he case of ressve (Ohmc, or lnear) loads, Joule's law can be combned wh Ohm's law (I = V/) o produce alernave expressons for he dsspaed power: V P I.
Krchhoff s laws Deals wh he conservaon of charge and energy n elecrcal crcus Frs Krchhoff s law (Krchhoff's curren law (KCL)) The algebrac sum of currens n a nework of conducors meeng a a pon s zero. Krchhoff s laws Second Krchhoff s law (Krchhoff's volage law (KVL)) The dreced sum of he elecrcal poenal dfferences (volage) around any closed crcu s zero. I I I I b V V V V V 5 U v Krchhoff s laws The sum of volage drop n a closed loop = V V 7 a V Blue loop from a V 7 V V 9 V = ed loop from b V V 5 V V V 9 V V V = Yellow loop from b Ohm s law Ohm's law saes ha he curren hrough a conducor beween wo pons s drecly proporonal o he poenal dfference or volage across he wo pons, and nversely proporonal o he ressance beween hem. U =. I s he ressance of he conducor (uns of ohms) beween wo pons on conducor V V 9 V V 5 V V 7 V V V V = Georg Smon Ohm (. března 79, Erlangen, Bavorsko 7. července 5) Ohm's and Krchhoff's laws Example Ohm's and Krchhoff's laws Example Calculae he volage drop across he ressor, and f you know, he power supply U cc = 5 V U D =.7 V red LED dode U D =. V green LED dode U D =. V blue LED dode Calculae he sze of he ressors, and and oal curren when (accordng o he caalog values) currens flowng hrough dodes I = ma red LED dode I = ma green LED dode I = ma blue LED dode Soluon: U cc U U D = U = U cc U D = 5.7 =. V U cc U U D = U = U cc U D = 5. =. V U cc U U D = U = U cc U D = 5. =. V Soluon: = U / I = 57 = U / I = 5 = U / I = Toal curren: I cc I I I = I cc = I I I = ma
Volage and curren sources Ideal volage source s a crcu elemen where he volage across s ndependen of he curren hrough Ideal curren source s a crcu elemen where he curren hrough s ndependen of he volage across Nondeal volage or curren source s a combnaon of deal source U or Ik and s nernal ressance Volage and curren sources Loaded volage or curren source The volage of across load ressance z s smaller hen reference volage U (nernal ressance volage dvder) The curren of a load ressance s smaller hen reference curren I k (nernal ressance ) Unloaded volage source Unloaded curren source Volage across he deal curren source approaches nfny as he load ressance approaches nfny (an open crcu) Loaded volage source volage drop on nernal ressance resul a volage decrease a he oupu ermnals of he source Loaded curren source Desred curren should flow hrough load ressance. equremen z << The dualy of volage and curren source In pracce, we ofen uses he dualy. Connecon of volage source and s nernal ressance can be convered o he curren source and s nernal ressance. Ths can be appled vce versa. Thévenn's heorem Any combnaon of volage sources, curren sources, and ressors wh wo ermnals s for lnear elecrcal neworks elecrcally equvalen o a sngle volage source U and a sngle seres ressor. Z Z. Z. U.U U. I k U Z Z Z Calculang procedure:. Calculae he oupu volage U, n open crcu condon (no load ressor meanng nfne ressance).. Now replace volage sources wh shor crcus and curren sources wh open crcus. eplace he load crcu wh an magnary ohmmeer and measure he oal ressance, "lookng back" no he crcu. Thévenn's heorem Example Smplfy he crcu n Fgure. Volage U = 5 V, ressance = KW and =. KW Volage U s gven as he open crcu volage U. U. V s deermned by parallel combnaon of and, volage source s replaced by a shor crcu. 5. 5W Thévenn's heorem Example Calculae curren I hrough ressance, when s gven: U = 5 V = 5 kω = 5 kω = kω = 5 kω U I Oupu volage: U U. I. 7.5. I
Thévenn's heorem Example Thévenn's heorem Example Every lnear sysem can be replaced by he volage source a he oupu ermnals. Frs, we have o ndcae he oupu ermnals. We won o calculae curren hrough ressance (I). A hese ermnals we can replace he remander of he crcu by volage source. Crcu s dvded no wo pars: Lnear sysem wh s oupu ermnals ( ) and Load () Crcu wll be convered o a equvalen crcu wh one alernave volage source s nernal ressance v. v I I v U U For he equvalen crcu s necessary o deermne he characersc parameers of he alernave power source and v. Volage across alernave volage source s deermned as he open crcu volage a he oupu ermnals ( = U ). Toal curren I creaes a volage drop U, U and U on ressors. Volage U s gven by: U = U U = U U Indvdual volage drops are calculaed from Ohm's Law :U = I.; U = I.; U = I. Subsung no he equaon for volage U Frs we calculae he oal curren I: U 5 I 5 5 By subsung we ge :,75 ma U = 5,75 = 7,5,75 =,5 V = I U U v U U U I Now we calculae he ndvdual volage drops : U I.,75.5,75 V U I.,75. 7,5 V U I.,75.5,75 V Thévenn's heorem Example The second equvalen parameer of he alernave source s nernal ressance v. The nernal ressance of alernave source: s deermned as oal ressance a he oupu ermnal when he volage sources of he sysem s removed (v = ). The sysem has only one deal volage source (U), ha wll be shored. The crcu can be adjused: For searched ressance s gven:,, //( ) 5//( 5),75 kw U v Thévenn's heorem Example I Thévenn's heorem Example The calculaon of I for specfed values of K O N E C Noron's heorem Is an exenson of Thévenn's heorem v I Searched curren I s gven by: I v ma;v, kw =, ma Any collecon of volage sources, curren sources, and ressors wh wo ermnals s elecrcally equvalen o an deal curren source, I, n parallel wh a sngle ressor,. =.5 V v =,75 kw
uc() [V] essor Capacor Indukor Passve elecronc componens Passve componens essors In praccal erms, ressors conver he curren o volage and vce versa For he ressance of elecrcally conducve maeral can be descrbed by: l r S r specfc elecrcal ressance l Wre lengh S Wre cross seconal area essors parameers Characerze he funconal characerscs of componens and are lsed n he caalog Eg. nomnal ressance value, load, olerance... anges of nomnal values essors (capacors, nducors) are manufacured only for ceran values accordng o he olerance Typcal ranges: E, E, E (dvde ressor values decades o a number of secons) ange essors parameers Power rang (Power dsspaon) V P V. I. I Temperaure coeffcen of ressance Volage coeffcen of ressance (dependence on he suppled volage) Dependence on he amben humdy Nose properes Parasc nducance and capacance maxmum workng volage Numercal Markng Color codng essors markng Capacors Passve elecronc componen conssng of a par of conducors separaed by a delecrc (nsulaor) Componen able o accumulae an elecrc charge Q The relaonshp beween volage and charge s: Q C. U Capacor curren s drecly proporonal o he volage change a he ermnals : du I C d Capacor chargng Capacor chargng 5 5 5 5 5 5 55 [ms]
uc() [V] u() [V] uc() [V] U () [ma] P u Capacor chargng uc C Swch P s off. For he crcu values condons: uc() = capacor s dscharged; () = he crcu s dsconneced (P n posson ); u() = due o he fac ha () =, here wll be no volage drop a ressance. Inal condons: e he condons a he me =. U () P u Capacor chargng uc C Now we swch he swch P from a poson o poson. Snce he capacor C s dscharged and v s equal o zero, he nal crcu curren wll be lmed only by ressor. () = U/. Capacor begns o charge hrough ressor and volage uc wll vary accordng o he relaon uc U.( e ) uc() = () = u() =. For he curren s vald: U e U uc U U.( e ) U U U. e The volage across he ressor s gven by : U u.. e Ue Capacor chargng Capacor chargng CAPACITO CHAGING uc() 5 5 5 5 5 5 55 [ms] CAPACITO CHAGING u() 5 5 5 5 5 5 55 [ms] he volage on he capacor uc() uc U.( e ) V; V, s,s he volage across he ressor u() u U. e V; V, s,s chargng curren () U. e A;V, W,s,s CAPACITO CHAGING (),,,,,,, 5 5 5 5 5 5 55 [ms] The lnes n one graph... Capacor chargng u() uc() () 5 5 5 5 5 5 55 [ms] Curves for dfferen values of ressance Capacor chargng Capacor chargng Tme consan = 5 kω; C = μf; τ = 5 ms = kω; C = μf; τ = ms = 5 kω; C = μf; τ = 5 ms 5 5 5 5 5 5 55 [ms] Capacors properes Capacy of plae capacor : S C r d Capacor parameers: Accuracy, Capacance nsably Temperaure coeffcen leakage curren Breakdown volage
Capacor ypes Polyeser flm capacors Bg dmensons, accurae, good F properes Ceramc capacors Small sze, very naccurae, nonlnear Elecrolyc Capacors Very large capacance o volume rao, nexpensve, polarzed. Prmary applcaons are as smoohng and reservor capacors n power supples Monolhc negraed capacors Very lmed sze Inducors Passve elecrcal componen ha can sore energy n a magnec feld creaed by he elecrc curren passng hrough. If elecrc curren passes hrough he closed crcu creaes a magnec flux: Inducance of henry produces an EMF of vol when he curren hrough he nducor changes a he rae of ampere per second L = nducance (H) μ = permeably of free space = π 7 H/m μr = relave permeably of core maeral N = number of urns l = lengh of col (m) S = crossecon area L.I Wb S L r.n l Inducance Example Calculae he nducance of he ar nducor n Fgure of lengh l = 5 mm, dameer d = mm, he number of urns N = S. d L r. N r. N.7 l. l Inducors Inducor parameers Nomnal value and power load DC ressance qualy facor Q (rao of reacance and ressance of unwaned dc) delecrc srengh (break down volage) Operang emperaure range Applcaons Choke Transformer The elecrc moor, speaker, relay... Flers, uned crcus Types of nducors Ar core col ado frequency nducors Ferromagnec core col A magnec core can ncrease he nducance of a col by a facor of several housand Varable nducor