Introduction to Electric Circuit Analysis

Transcription

1 EE Practice of Electrical and Computer Engineering Lecture 2 and Lecture 4.1 Introduction to Electric Circuit Analysis Prof. Klaus Yung-Jane Hsu 2003/2/20

2 What Is An Electric Circuit? Electrical Systems Information, Power, Control, etc. Behavioral Model An electric circuit is a mathematical model which approximates the behavior of an actual electrical system.

3 What Is Electric Circuit Theory? A Special Case of Electromagnetic Field Theory The Study of Static and Moving Electric Charges

4 5 Basic Model Elements in Electric Circuit Theory Active Components Voltage Source Current Source Passive Components Resistor Capacitor Inductor

5 Atomic Theory N ucleus K L M N Simplified representation of the atom Nucleus normally consists of neutrons and protons (positively charged) Electrons orbit the nucleus in discrete orbits called shells (K, L, M, N, etc.) Atom is electrically neutral since No. of protons = No. of electrons The outer most shell is called the valence shell and electrons in this shell are called valence electrons

6 Different Types of Material Conductors are materials (e.g. copper, aluminum, gold) that have large numbers of free electrons. Insulators do not conduct (e.g. plastic, rubber, porcelain) because they have full or nearly full valence shells. Semiconductors have half-filled valence shells (e.g. silicon, germanium).

7 What Is Electric Charge? A body is said to be charged when it has an excess or deficiency of electrons. The unit of electrical charge is the coulomb (C) = 6.24 x electrons. Coulomb s Law: F = kq 1 Q 2 / r 2 where k = 9 x 10 9, Q 1 and Q 2 are charges in coulombs, and r in m.

8 Current 1 A of current is 1 C of charge passing a given point in 1 s, i.e. I = Q / t or Q = I x t.

9 Direction of Current Lamp E + - I Direction of conventional current Electrons flow from negative terminal to positive terminal but conventional current flows in the opposite direction.

10 Voltage When charges are transferred from one body to another, a potential difference or voltage results between them. The voltage between two points is 1 V if it requires 1 J of energy to move 1 C of charge from one point to the other; i.e. V = W / Q. Symbol for DC Voltage Sources:

11 Practical DC Voltage Source - Battery Primary batteries are not rechargeable; Secondary batteries are rechargeable. Batteries come in different shapes (e.g button), sizes (e.g. AAA, AA, C, D), types ( e.g. alkaline, carbon-zinc, lithium, NiCad, lead acid) and ratings. Battery capacity (Ah) = current drain x expected life.

12 Other DC Voltage Sources Electronic power supplies rectify ac to dc for use in equipment or labs. Solar/photovoltaic cells convert sunlight to electrical energy for remote areas or space applications. DC generators convert mechanical energy to electrical energy by rotating a coil of wire through a magnetic field.

13 Practical DC Current Sources Usually, a combination of DC voltage sources and other electrical devices (e.g. transistors, resistors, etc.) is required. Symbol of a DC Current Source:

14 Resistor A resistor is defined as a component whose terminal voltage is proportional to the current flowing through. That is, a resistor is a device that obeys the Ohm s Law. Ohm s Law: V=IR The constant R is called the resistance (Ω) of the resistor. Symbol:

15 Resistor Color Code Band 1, 2 Significant Figures 3 Multiplier 4 Tolerance 5 Reliability Colour: Bk, Br, R, O, Y, Gn, Bl, V, Gr, W, Gl, Band 1: Band 2: S, No Colour Band 3: Band 4: 5% 10% 20%

16 Capacitance Metal Plates Lead E C E ψ Lead Dielectric C n n n Parallel-plate capacitor Circuit symbol Electric field of capacitor A capacitor consists of two metal plates separated by an insulator (dielectric) which may be air, oil, mica, plastic, ceramic, etc. When a dc source is applied across the capacitor, one of the plates becomes positive and the other negative. The amount of charge stored by a capacitor is: Q = CV (C)

17 Capacitance (cont d) n Capacitance of a parallel-plate capacitor is: C = ε A / d (F), where ε is the permittivity of the dielectric, A is the area of each plate and d is the separation of the plates. Further, ε = ε r ε o where ε r is the relative permittivity or dielectric constant of the dielectric and ε o = 8.85 x F/m is the permittivity of air. n Energy stored between the plates is given by W = 1 / 2 CV 2 (J)

18 Induced Voltage & Induction 8FaradayÕs Law: voltage is induced in a circuit whenever the flux linking the circuit is changing and the magnitude of the voltage is proportional to the rate of change of flux linkages: dφ e = N (volts) dt 8LenzÕs Law: the polarity of the induced voltage (known as the counter emf or back emf) is such as to oppose the cause producing it.

19 v L =L Self-Inductance 4Induced voltage across the coil is: di dt (V) 4Approximate inductance of coil (when l/d > 10) is: L = 2 2 µ N A µ rµ on A or l l : = permeability (H) d I L + v L = L d i d t - Voltage across inductor l Inductor Coil A

20 Power The Rate of Doing Work: W P = (watts, W) t where W is the work (or energy) in joules and t is in seconds. P=V I

21 n n n Series Circuits & KVL E V 1 - R 1 R 2 V + 3 KirchhoffÕs Voltage Law states that for a closed loop: ΣV = 0, or Σ V rises = Σ V drops The total resistance of n resistors in series is: R T = R 1 + R R n The total power is: P T = P 1 + P P n - R 3 - I E V - 2

22 Voltage Divider Rule E V 1 - R 1 - R 3 V + 3 The voltage applied to a series circuit will be dropped across all the resistors in proportion to the magnitude of the individual resistors. I V x = (R x / R T ) E R 2 + V - 2

23 Parallel Circuit I T E + R T R 1 R 2 R 3 I 1 I 2 I 3 I x = E / R x ; KCL: I T = I 1 + I 2 + I 3 = E / R T n n Elements/branches are said to be parallel when they have only 2 nodes in common. The voltage across all parallel elements in a circuit will be the same. Voltage sources of different potentials should never be connected in parallel.

24 Parallel Circuits & KCL n n KirchhoffÕs Current Law: ΣI = 0, or Σ I in = Σ I out Overall conductance: G T =G 1 + G G n =1/R T i.e. Total resistance, R T = 1/(1/R 1 + 1/R /R n ) n For 2 resistors in parallel: R T = R 1 R 2 / (R 1 + R 2 ) n For n equal resistors in parallel: R T = R/n where R is the resistance of each resistor. n Current divider rule: I x = (R T /R x )I T n Total power dissipated: P T = P 1 + P P n where P 1 = E 2 /R 1 or EI 1 ;.... ; P n = E 2 /R n or EI n

25 Capacitor Charging v c v R = Ee -t/τ E a R E b i C + v - c 0 i Transient Interval Steady State t v c = E(1-e -t/τ ) i = (E/R)e -t/τ τ = RC E R 0 t

26 Current Buildup Transient in Inductor v L v R = E(1-e -t/τ ) R E E i L + - v L 0 i Transient Interval Steady State t v L = Ee -t/τ i = (E/R)(1-e -t/τ ) τ = L/R E R 0 t

27 What Will You Get in Learning Electric Circuit Theory? Being equipped with basic common sense, language, and analysis skill for studying the hardware of any electrical systems Extensive examples will be encountered in the courses of Microelectronics, Power Electronics, and Power Systems

28 Bon Voyage! 2003/2/20