Intrductn t Electrnc crcuts. Passve and Actve crcut elements. Capactrs, esstrs and Inductrs n AC crcuts. Vltage and current dvders. Vltage and current surces. Amplfers, and ther transfer characterstc. The fur types f amplfers (vltage, current, transcnductance and transresstance amplfers) Frequency respnse f amplfers. A lw pass and a hgh pass flter.
Passve crcut elements esstrs, Capactrs and Inductrs. Als called passve elements because nne f them can supply energy t the crcut. Fr a resstr we have: GV V Ohm s law. t q( t) V ( t) ( t ) dt C C Fr a capactr we have: r ( t) C ( t) dv dt Fr an nductr we have: d V ( t) L ( t) dt r ( t) V ( t ) dt L t
Actve crcut elements An Ideal vltage surce prvdes a termnal vltage V ndependent n the current thrugh t. An deal current surce prvdes a current I ndependent n the vltage acrss ts termnals. Cntrlled current and vltage surces prvde a vltage r current whch depends n the vltage acrss r the current thrugh anther element f the crcut.
Lnear Netwrks A lnear netwrk s frmed by ntercnnectng the termnals f lnear passve elements, lnear cntrlled r ndependent (vltage r current) surces t frm ne r mre clsed paths. In a lnear netwrk cntanng multple surces and passve elements the vltage acrss r the current thrugh any passve element s a lnear cmbnatn f the ndependent vltages r currents due t each f the ndependent surces actng alne. (superpstn therem).
Capactrs n AC crcuts Capactrs when cnnected t AC crcuts allw ac current t pass thrugh them and therefre alter the behavr f the crcut. They d nt cnsume electrc energy and therefre they d nt have resstance but reactance. The reactance f a capactr C s gven by the frmula: X C jc
Inductrs n AC crcuts Inductrs when cnnected t AC crcuts have an ac vltage drp acrss them and therefre alter the behavr f the crcut. They d nt cnsume electrc energy and therefre they d nt have resstance but reactance. The reactance f an nductr L s gven by the frmula: X L jl
Krchff s crcut laws Krchff s vltage law (KVL): The algebrac sum f all vltage drps arund any clsed lp f a crcut, s zer. Krchff s current law (KCL): The algebrac sum f all currents enterng a nde (junctn f elements), s zer.
Studyng ac crcuts. When we have t analyze an ac crcut wth passve elements (resstrs, capactrs and nductrs) we fnd the equvalent mpedance f the crcut by addng the (real) resstances wth the (magnary) reactances f the crcut n accrdance t the rules f addng resstances n seres and n parallel. Fnally we fnd the ttal cmplex resstance the mpedance f the crcut Z() whch s a functn f frequency. The relatnshp V 0 I 0 Z() defnes nt nly the ampltude f the current prvded by the ac surce but als the phase dfference between the vltage and the current. The current ampltude s gven by: I 0 ()V 0 / Z()
Thevenn s therem An arbtrary lnear, tw prt netwrk (such as netwrk A at the fgure belw) can be replaced at termnals, wth an equvalent vltage surce V Th cnnected n seres wth an mpedance Z Th Th jx Th Z Th Netwrk A Netwrk B - V Th Netwrk B V Th s the pen crcut vltage f netwrk A at pnts and and Z Th s the rat f that pen crcut vltage t the shrt crcut current f netwrk A determned at termnals and wth netwrk B dscnnected. Alternatvely Z Th s the equvalent mpedance lkng nt netwrk A thrugh termnals, wth all ndependent surces deactvated (vltage surces replaced wth shrt crcuts and current surces replaced wth pen crcuts).
Netwrk A V Th The resstance f the crcut between pnts and (wth all vltage surces shrted and all current surces pen) s the Thevenn resstance Th. Netwrk A I shrt Equvalently Th I V Th shrt
Cmplcated crcut Equvalent Thevenn crcut Netwrk A V Th V Th - Th
Nrtn s therem An arbtrary lnear, ne prt netwrk (such as netwrk A at the fgure belw) can be replaced at termnals, wth an equvalent current surce I N cnnected n parallel wth a resstance N. Netwrk A Netwrk B I N N Netwrk B I N s the shrt crcut current that flws frm termnal t termnal due t netwrk A and N s the rat f the pen crcut vltage at termnals and wth netwrk B dscnnected (whch s V Th ) ver the I N. (Obvusly N Th ).
The current passng frm the shrt crcuted pnts and s the Nrtn current f the crcut I N. Netwrk A I shrt I N The Nrtn esstance s equal t the Thevenn esstance V Th N I N Th
Cmplcated crcut Equvalent Nrtn crcut Netwrk A I N N Th
Vltage dvders Tw resstances n seres frm a vltage dvder. V - r r -
Vltage and Current dvders Tw resstances n parallel frm a current dvder. I r Ir r r
Vltage and Current surces A devce prducng a small electrcal sgnal can be mdeled as an deal vltage supply n seres wth a resstance and dependng n the lad t drves t can be mdeled as a vltage surce r a current surce. Current surce f >> L because: V - L Independent f lad L L Vltage surce f << L because: devce L L L L Independent f lad
Vltage and Current surces A vltage amplfer must have nfnte nput resstance. A current amplfer must have zer nput resstance.
Amplfers Amplfer s a devce we use t amplfy small sgnals (ac r dc). V V vltage current The pwer gan f the amplfer s: pwer gan n gan gan The vltage and the current gan f the amplfer are defned as: A p A n n decbels decbels A A A decbels 0lg A 0lg A A ( db) p 0lg A ( db) 0lg A ( db)
Amplfer pwer supples and utput sgnal lmtatn In rder fr an amplfer t perate t requres tw external dc pwer supples, a pstve V and a negatve ne V. V V The utput sgnal cannt becme larger than V r smaller than V. Fr suffcently large pstve r negatve nput sgnals the utput sgnal s clpped t be between V and V.
Amplfer effcency V V The amplfer takes external pwer frm these pwer supples n rder t amplfy the nput sgnal whch s delvered t the lad. If the pwer nput sgnal s neglgbly small the pwer delvered n the lad by the amplfer P lad and the pwer taken frm the dc pwer supples P dc the effcency f the amplfer s defned: η 00 P lad P dc
Amplfer transfer characterstc Saturatn regn V egn f lnear amplfcatn. Slpe: A. Saturatn regn V
Amplfer transfer characterstc Ths s the transfer characterstc f an amplfer wth ts negatve dc pwer supply termnal grunded. V In rder fr such an amplfer t perate we add a dc vltage t ur small sgnal, s that the amplfer wrks arund the quescent pnt Q. Q small V 0 V
The fur types f amplfers Dependng n the type f sgnal surce an amplfer can be mdeled as vltage amplfer, current amplfer, transcnductance amplfer transresstance amplfer.
The vltage amplfer. - A Open crcut vltage gan A 0 0 The deal vltage amplfer shuld have: 0 0
The current amplfer. shrt crcut current gan A A 0 0 The deal current amplfer shuld have: 0
The trans-cnductance amplfer. shrt crcut trans-cnductance G m G m 0 0 The deal trans-cnductance amplfer shuld have:
The trans-resstance amplfer. - m Open crcut trans-resstance m 0 0 0 The deal trans-resstance amplfer shuld have: 0 0
Frequency respnse f amplfers 0 lg A( ) A( ) 3dB Amplfer bandwdth Wthn amplfer bandwdth the amplfcatn s cnstant wthn 3 db.
A lw pass flter C j C j C j X X C C ) ( C 0 C 0
A lw pass flter ( ) C 0 lg A( ) 0 lg( C ) C 0 0 0 C -3dB
A hgh pass flter. C C j C j C j X C ) ( C C 0 0
A hgh pass flter. C ) ( C C 0 0 C 0-3dB 0lg ) ( 0lg C C A