EMLAB 1 회로 이론 (2014)

EMLAB 2 Review of circuit theory I 1.Linear system 2.Kirchhoff’s law 3.Nodal & loop analysis 4.Superposition 5.Thevenin’s and Norton’s theorem 6.Resistor, Inductor, Capacitor 7.Operational amplifier 8.First and second order transient circuit

EMLAB 3 Linear system L Linear system L Linear system L Linear system L Linear system L Linear system L A system satisfying the above statements is called as a linear system. Resistors, Capacitors, Inductors are all linear systems. An independent source is not a linear system. All the circuits in the circuit theory class are linear systems!

EMLAB 4 Resistor Examples of Linear system Capacitor input output R1 C1 input

EMLAB 5 Inductor

EMLAB 6 Kirchhoff’s Voltage law Sum of voltage drops along a closed loop should be equal to zero! R1 C1

EMLAB 7 Kirchhoff’s Current law R Current definition Sum of outgoing(incoming) currents from any node should be equal to zero! To define a current, a direction can be chosen arbitrarily. The value of a current can be obtained from a voltage drop along the direction of current divided by a resistance met. R2R2 R1R1 R3R3

EMLAB 8 Nodal analysis Unknowns : node voltages Kirchhoff’s current law is utilized to form matrix equations. For each node, the sum of out-going currents become zero.

EMLAB 9 Loop analysis Unknowns : loop currents Matrix equations are formed by Kirchhoff’s voltage law. For each loop, the sum of voltage drops are equal to zero.

EMLAB 10 Superposition Superposition is utilized to simplify the original linear circuits. If a voltage source is eliminated, it is replaced by a short circuit connected to the original terminals. If a current source is eliminated, it is replaced by an open circuit. Circuit + = Circuit with current source set to zero(OPEN) Circuit with voltage source set to zero (SHORT CIRCUITED)

EMLAB 11 Example

EMLAB 12 Thevenin and Norton equivalent Open circuited voltage measured by voltmeter Short circuited current measured by ammeter Resistance obtained with voltage source shorted and current source open A V

EMLAB 13 Example

EMLAB 14 Resistor – Input output relationship i(t) v(t)

EMLAB 15 i(t) v(t) i(t) v(t) Capacitor – Input output relationship

EMLAB 16 i(t) v(t) i(t) v(t) Inductor – Input output relationship

EMLAB 17 First order transient circuit The voltage drop across a capacitor cannot change instantaneously. The current through an inductor cannot change instantaneously.

EMLAB 18 Second order transient circuit Normalized form

EMLAB 19 Solution Critically damped : ζ = 1 Under-damped : ζ <1 Over-damped : ζ > 1

EMLAB 20 Critically damped: ζ=1 인 경우

EMLAB 21 Transient response Critically damped Under-damped Over-damped

EMLAB 22 Ringing in digital logics

EMLAB 23 Contents : Circuit theory 2 1.AC steady-state analysis : 60Hz sinusoidal input signal Power factor 2.Magnetically coupled networks : transformer 3.Poly-phase circuits : power distribution Single phase two wire Three phase 4 wire power distribution 4.Arbitrary input signal Fourier series and Fourier transform Laplace transform 5.Two-port network : black box

EMLAB 24 Chapter 8 AC steady-state analysis

EMLAB 25 Sinusoidal input signal 입력 전압의 형태

EMLAB 26 Sinusoids Dimensionless plot As function of time “Lag by t 0 ” “Lead by t 0 ”

EMLAB 27 AC (Alternating Current) Easy to generate ( 교류 전압은 만들기 쉽다.) Easy to change voltage levels. ( 전압을 변화하기도 쉽다.) Less damage on human compared with DC ( 직류에 비해 덜 위험하다.)

EMLAB 28 Solution of Differential Eq. To solve a differential equation, initial conditions must be specified.

EMLAB 29 Solution method #1 For a particular solution, choose a trial function that might produce V S (t) on entering the differential Eq.

EMLAB 30 Simpler method for sinusoidal source case

EMLAB 31 Phasor With sinusoidal source function, it is simpler to use a trial solution ~ Re{I e jwt }. The complex coefficient of the exponential function is called as a phasor.

EMLAB 32 Phasor - resistor Relationship between sinusoids

EMLAB 33 Relationship between sinusoids Phasor - inductor

EMLAB 34 Relationship between sinusoids Phasor - capacitor

EMLAB 35 Examples

EMLAB 36 Impedance and Admittance AC circuit Impedance : Admittance : ElementImpedanceAdmittance R L C

EMLAB 37 Series / parallel combination

EMLAB 38 Example Find the current i(t) in the network in Fig. E8.8.

EMLAB 39 Example 8.15 Super node