Circuit Theory I

Transcription

1 16.1 Crcut Theory I Tngshu Hu Offce: Ball Hall 45 Phone: 4374, Fax: 37 Emal: tngshu_hu@uml.edu Offce Hours: MW: 1am-1pm Rectaton Instructor: Dr. Rachel Wakm Introducton: About ths course: Foundaton to all branches of electrcal and computer engneerng Communcaton systems : all nformaton s encoded n electrcal sgnals (dgtal, lke 111, analog, lke a snusod) Computer systems: all operaton and data handlng are performed a electrcal arables Eerythng s composed of and 1. Control systems: physcal quanttes, such as speed, force, temperature, pressure, are transformed nto electrcal sgnals. Control algorthms process these sgnals and fgure out the optmal actuaton strategy, lke how much force to apply, whch drecton. Power systems: all forms of energy (mechancal, nuclear, wnd, chemcal, hydraulc) are conerted nto or from electrcal power, snce electrcal energy can be easly stored (n battery, supercapctor) and transported. Sgnal and mage processng: all forms of nformaton conerted nto electrcal sgnals, and processed a computer, dgtal/analog flter, for pattern recognton, comparson, dentfcaton. 1

2 Also mportant to other engneerng systems, n actuaton, sensng, nstrumentaton and arous purposes for automaton Mechancal and aerospace systems Chemcal process, actuaton, sensng, nstrumentaton. To adjust the temperature, pressure, densty, flow rate. Bomedcal systems, electrcal deces are wdely used n dagnosng and treatment Many physcal quanttes are transformed nto electrcal sgnals because electrcal sgnals are easy to transfer and manpulate, e.g., to be processed by computers Imagne how your lfe wll be changed wthout electrcty? It drectly mpacts your career: You wll not be qualfed as an electrcal engneer f you fal ths course: you cannot moe on to other core courses. Most mportantly: It s a lot of fun to buld a useful crcut! 3 A buck-boost Conerter wth Control crcut An AC-DC Conerter wth Control crcut 4

3 A boost conerter controlled by a mcrocontroller The controller s constructed usng Matlab/Smulnk, Then wrtten nto the mcroprocessor 5 My most recent project: A hgh effcent hgh performance LED drer wth dmmng control The paper by my PhD student and myself wll be publshed by IEEE Transactons on Power Electroncs. Funded by Natonal Scence Foundaton 6 3

4 The courses nsde the red box all need ths course as prerequste Currculum check sheet of BS n EE Crcut I Crcut II 7 Textbook: C. K Alexander and M. N. O. Sadku, Fundamentals of Electrc Crcuts, edton 6, 5,or 3,4, (McGraw Hll). GRADING POLICY: Homework+Attendance: 11% 3 Tests: 54% Fnal Exam: % Quzzes:15% HOMEWORK POLICY: Late homework s NOT accepted. Homework should be clear, concse, and complete. Attendance: Wll be taken eery class. Poste atttude s a key to success. Beng half hearted s a waste of tme. Course materals: (homework assgnment/soluton, sample tests/solutons) Lecture notes: Prerequste: Calculus II wth grade C or better 8 4

5 Crcut Theory I Tentate Class schedule (Sprng 18) Perod 1: Chapter 1,: Basc concepts, Basc laws 1/(M): Course oerew, (1.), Charge & Current(1.3), reference drecton of current 1/4(W): ref. dr of current; oltage(1.4), power & energy(1.5), crcut elements(1.6) 1/9(M): Ohm s law (.);Nodes, branches, loops(.3), KCL, KVL(.4) 1/31(W): Use basc laws to sole crcut problems (.4) /5(M): Ways of connecton; Seres resstors & oltage dson (.5) Parallel resstors & current dson(.6), /7(W ): Solng crcut problems usng basc laws and tools /1(M): More practce problems /(Tu): Test 1 (no cheat sheet) Perod : Chapter 3, Methods of analyss /14(W): Nodal analyss (.) /1(W): Nodal analyss wth oltage sources (.3) /6(M): Mesh analyss (.4); Mesh wth current sources (.5) /8(W): More mesh analyss problems n lecture, Perod reew n rectaton 3/5(M): Test (no cheat sheet) 9 Perod 3: Chapter 4, Crcut Theorems 3/7(W): Lnearty (4.), Superposton wthout dependent source(4.3) 3/19(M): Superposton wth dependent source (4.3), Source transformaton (4.4) 3/1(W): Theenn s theorem (4.5) 3/6(M): Norton s theorem (4.6), Maxmum power transfer (4.7) 4/(M): Test 3 (no cheat sheet) Perod 4: Chapters 6,7,8 3/8(W): Chapter 6, capactors and nductors 4/4(W): More on Ch.6, Source free RC (7.) 4/9(M): Source free RL (7.3), Sngularty functons (7.4) 4/11(W): Step resp. of RC (7.5), Step resp. of RL (7.6) 4/18(W): Solng nd -order dfferental equatons 4/3(M): Fndng ntal alues (8.), Step resp. of a seres RLC crcut(8.3, 8.5) 4/5(W): Step resp. of a seres RLC crcut (8.5), Other nd -order crcuts (8.6,8.7) 4/3(M): Reew 5/(W): Offce hours Fnal Exam wll coer Chapters 7,8 All tests and exam are closed-book, closed-notes. Makeup test/exam wll only be gen n extreme emergency or llness (Edence requred). Ask for help before the fnal exam, NOT after! NO extra work to rase your grade after fnal! Attenton: You need to pass Crcut I wth grade C- or better to take Crcut II. 1 5

6 A sample score and gradng table from a preous term ID Name: Secton x Test 1 Test Test 3 Qz hw/att FE opt1 opt Fnal score grade 1% C B A C F F C C W W B C D D F F A C A D D C F F B+ Note: Need C- or better to take Crcut II Questons? Internatonal Systems of unts (SI) Unts: Standard measurements of physcal quanttes. facltate nternatonal communcaton Prncpal unts (basc SI unts): Quantty Basc unt Symbol Length meter m Mass klogram kg Tme second s Electrc Current ampere A Temperature keln K Lumnous Intensty candela cd Other quanttes, lke, force, speed, toque, power, energy, are dered from these. 1 6

7 Prefxes based on the power of 1 Multpler Prefx Symbol 1 18 exa E 1 15 peta P 1 1 tera T 1 9 gga G 1 6 mega M 1 3 klo k 1 hecto h 1 deka da.1 dec d.1 cent c 1-3 mll m 1-6 mcro 1-9 nano n 1-1 pco p 1-15 femto f 1-18 atto a Under certan stuatons, the quanttes are wthn a partcular range, e.g.,.1s to.1s; It would be more conenent to say 1s to 1s. Sometmes, 1 meter may be too Large, e.g., to measure the length of an atom, we may use nm or pm. In other stuatons, 1 meter may be too small, e.g., to measure the dstance between planets, we may Lke to use Em or Pm 13 In the rest of Chapter 1, we reew 5 basc concepts Charge Current Voltage Power Energy We wll deal wth these concepts more rgorously. Pay attenton to: Reference drecton of current Polarty of oltage Passe sgn conenton Acte sgn conenton Dependent oltage source Dependent current source 14 7

8 1.3 Charge and Current Charge: Fundamental concept for explanng all electrcal phenomena, such as, lght, heat, sgnal, data, Charge s an electrcal property of atomc partcles of whch matter conssts, measured n Coulombs ( C ) Notaton of charge: q Charge on one electron, q = C. Charge on one proton, q= C. Charge on an atom = charge on electrons + charge on protons, q =. 1 C s a huge quantty. We need electrons (or protons) to make 1C of charge. Quanttes to the order of pc, or nc are usually used n the lab. -1pC = electrons, 1nC = electrons. Charge can nether be created nor destroyed. It can only be transferred. 15 Current: the moton of charges current current Drecton of current: the drecton of moton of poste charges. In metallc conductors, current s caused by the moton of electrons. Drecton of the current: opposte to the moton of electrons All electrcal phenomena are caused by the flow of charges: Heatng Lght Force - In a solenod. Make a col of wre around an ron core. - Fundamental concept behnd electro-mechancs Electrcal energy Mechancal Energy 16 8

9 Defnton of current: Current s the tme rate of change of charge, measured n ampere (A). Notaton: Also, current s the amount of charge flowng through a substance, or a cross sectonal area, n 1 second. 1 ampere = 1 Coulomb/second; 1A=1C/s, ampere s a dered unt Gen the current as a functon of tme, (t), for t [t, t], the total charge flowng through a substance oer, s q ( t) q( t ) ( ) d t t Example: q( t) sn t C, q( t) cos3 t ( mc ), qt () qt ( ) ( ) d t t ( t) dq / dt cost A ( t) dq / dt 3sn 3 t ( ma) A lst of q(t), (t) qt ( ) t ( ) dq/ dt sn t cos t cos t - sn t e t k at ae k t at k1 17 Product Rule: Let f ( t) f1( t) f( t) Then df ( t) df1( t) df( t) dt f( t) f1( t) dt dt Example: 3t q( t) t e C, ( t)? ;,, 3 dt ( t) dq / dt e t dt de dt 3t 3t te t ( 3) e 3t 3t 3t = (t 3 t ) e A Gen current (t), how to obtan charge q(t)? Example: ( t) sn t A, q( t)? 1 cos constant 18 9

10 Example: A,? 1 cos? You need the alue of q(t) at one tme nstant to unquely determne q(t). Suppose q()=.5c. Method 1: Plug n t=..5 1 cos cos 1 Method : sn.5 cos Notaton:.5 1 cos 1 cos 1 cos 1 19 Practce problem 1: Determne the current (t) flowng through an element f the charge s gen by: 3 sn4 R1 Practce problem : Determne the charge q(t) flowng through an element f q()=c and the current s gen by 4 4 cos 1

11 Practce problem 3: Determne the current (t) flowng through an element f the charge s gen by: 4sn R1 Practce problem 4: Determne the charge q(t) flowng through an element f q()=1.5c and the current s gen by 3 4sn 1 Practce 5: The charge q(t) s gen by a pecewse lnear functon below. Fnd the current (t). R (second) ?,,1?, 1,?,,3 Practce 6: The current (t) s gen by a pecewse lnear functon below. Fnd the total charge oer the nteral [,4] 3 1 (second)

12 L Last tme: Relatonshp between charge and current : Current s the amount of charge flowng through a substance, or a cross sectonal area, n 1 second. 1 ampere = 1 Coulomb/second; 1A=1C/s, ampere s a dered unt Gen the current as a functon of tme, (t), for t [t, t], the total charge flowng through a substance oer, s q ( t ) q ( t ) ( ) d t t qt () qt ( ) ( ) d t t 3 More concepts: Drect current (DC): a current that remans constant wth tme,.e., (t) = I for all t. Denoted as I. Alternatng current (AC): a current aryng snusodally wth tme: (t)=i m sn(t+) A. Wll be studed n Crcut II. L Next s a ery mportant concept n crcut analyss Reference drecton of current: A drecton that s assgned to any current arable. If >, then the actual current drecton s the same as the reference drecton; If <, then the actual drecton s opposte to the reference drecton. If > If < Actual current drecton Actual current drecton Reference drecton can be arbtrarly assgned, but must be assgned. For a complex crcut, t may be hard to tell whch way the current go. Ref. Dr. makes t more conenent to sole a crcut problem. 4 1

13 1.4 Voltage -- Why electrons moe? The drng force s the oltage. a Defnton: oltage between two ponts a,b, denoted as ab, s the ab energy needed to moe 1C of charge from a to b, measured n olts (V) b (J=joule) 1J = 1 V 1C = 1olt 1 Coulomb Recall n mechancs, 1J= 1 Meter 1 Newton Voltage can also be consdered as the potental dfference between two ponts. We spend energy f we moe poste charge from low potental to hgh potental L Voltage polarty: Assgned wth + and - a If ab >, then pont a has hgher oltage If ab <, then pont b has hgher oltage ab ab can be called as oltage rse from b to a, b or, oltage drop from a to b. Voltage polarty can be arbtrarly assgned, but must be assgned. 5 a b 9V Same thng a b 9V L Same thng 3 A 3 A DC olatge: (t)= constant AC oltage: (t)= V m sn(t+) V 6 13

14 1.5 Power and energy We need energy to run a crcut. L Energy: total amount of work done oer a perod of tme, measured n joules (J). Notaton w. Power: amount of work done n one unt of tme, typcally, n 1 second, measured n watts (W). Notaton: p. Defnton: power s the tme rate of absorbng or generatng energy., 1 1/ What s the relatonshp between power, current and oltage? dw dq Recall:, dq dt dw dq dw dq dt dt p 7 In summary: p, w pdt dt 1 t w( t ) w( t ) dt t1 L In a crcut, an element may absorb power or generatng power. p also has a sgn If p >, the element absorbs power; If p <, the element generates power. How to tell f an element s absorbng or generatng power? The reference drecton of current and the polarty of oltage are needed. The passe sgn conenton and acte sgn conenton wll be ntroduced 8 14

15 The passe sgn conenton and acte sgn conenton: L Case 1: the current enters an element through + termnal. Called the passe sgn conenton p = If p >, the element absorbs power If p <, the element generates power Case : the current enters an element through termnal. Called the acte sgn conenton p = If p >, the element absorbs power If p <, the element generates power 9 Wth reference drecton of current and oltage polarty arbtrarly assgned, both and can be poste or negate. Examples: Determne the power consumed by each element 3V 3A Generates power 3A Absorbs power 3V + 3A + 3V (a) (b) (c) Passe sgn: Acte sgn: Passe sgn: 3, 3 3,3 3, Absorbs power 3 L 15

16 Law of conseraton of energy: L In any crcut, the power absorbed = the power generated. Equalently, The total amount of power absorbed = N n 1 p n Example: 3 A p 1 p 3 V p1 p p W ; 33 9W 1 p 31 L 1.6 Crcut elements A crcut s an nterconnecton of elements to realze a certan functon, e.g., amplfer, flter, power conerson. Two types of elements: Passe element: consumes or stores energy, such as resstors, capactors, nductors. Neer generates power Acte element: generates energy, such as batteres, generators. May absorb energy, e.g., when a battery s charged. Acte elements nclude current source and oltage source. Independent source: a oltage/current source that prode specfc oltage or current that s ndependent of the other elements. Independent oltage source: +_ s a constant or a gen functon of tme, e.g., 5V, snt V Current can be anythng as needed Independent current source: s a constant or a gen functon of tme, e.g., 4A, cost A Voltage can be anythng as needed 3 16

17 Dependent source (controlled source): an acte element where the source quantty s controlled by another oltage or current. L Four types of dependent sources: 1. Voltage controlled oltage source (VCVS) k x + s x kx, eg.., k 3 If x V, then k 3 6V The coeffcent k has no unt. Current controlled oltage source (CCVS) k, eg.., k.5 Example: If 4 A, s then k4.54 V k + Example: 3 x.5 k s unt s V/A Be careful: k s a oltage. It s a huge mstake to make s = k. s k Current controlled current source (CCCS) kx, e. g., k 1.5 x Example: If x 6 A, then k A kx 1.5 x k has no unt L 4. Voltage controlled current source (VCCS) k Example: k, e. g., k If.5 V, then k.5.5 1A k s unt s A/V Be careful: k s a current. It s a huge mstake to make = k. k 34 17

18 All the arables we hae learned so far: q,,, p, w. Ther relatonshp: dq t dw, q( t) q( t ) dt; dt t dq p (f passe sgn), p - (f acte sgn) wt () wt ( )+ dt t t Important detals to remember: Current should always be assgned wth a reference drecton Wrong Correct Correct Volatge should always be assgned wth polarty Wrong Correct Correct L Passe sgn conenton Acte sgn conenton 35 Example 1: L 5V A 1 5 A 1 1 If A =.5V, then 1 =5 A =.5A If =.A, then 1 =1=V Example : Compute the power of each element I 5A V 5 1V 6A 8V.I. 1 p p p 5 1 p = -8W Total power = = 36 18

19 Practce 7: Gen cos3, sn3. Fnd the total energy oer tme perod [,.] second. Assume passe sgn conenton. R Practce 8: Fnd the power of each element.? Hnt: use the law of conseraton of energy. (Don t use KCL or KVL) 37 Practce 9: Fnd the power of each element.? R