INC 112 Basic Circuit Analysis

128 Views

Download Presentation
## INC 112 Basic Circuit Analysis

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**INC 112 Basic Circuit Analysis**Week 7 Introduction to AC Current**Meaning of AC Current**AC = Alternating current means electric current that change up and down When we refer to AC current, another variable, time (t) must be in our consideration.**Alternating Current (AC)**Electricity which has its voltage orcurrent change with time. Example: We measure voltage difference between 2 points Time1pm 2pm 3pm 4pm 5pm 6pm DC: 5V 5V 5V 5V 5V 5V AC: 5V 3V 2V -3V -1V 2V**Signals**• Signal is an amount of something at different time, e.g. electric signal. • Signals are mentioned is form of • Graph • Equation**1st Form**Graph Voltage (or current) versus time V (volts) t (sec) 2nd Form v(t) = sin 2t**DC voltage**V (volts) t (sec) v(t) = 5**Course requirement of the2nd half**Students must know voltage, current, power at any point in the given circuits at any time. e.g. What is the current at point A? What is the voltage between point B and C at 2pm? What is the current at point D at t=2ms?**Periodic Signals**Periodic signals are signal that repeat itself. Definition Signalf(t) is aperiodic signal is there is T such that f(t+T) = f(t) , for all t T is called the period, where when f is the frequency of the signal**Example:**v(t) = sin 2t Period = πFrequency = 1/π v(t+π) = sin 2(t+π) = sin (2t+2π) = sin 2t (unit:radian) Note: sine wave signal has a form of sin ωt whereωisthe angular velocity with unitradian/sec**Square wave**Sine wave**Fact:**Theorem: (continue in Fourier series, INC 212 Signals and Systems) “Any periodic signal can be written in form of a summation of sine waves at different frequency (multiples of the frequency of the original signal)” e.g.square wave 1 KHz can be decomposed into a sum of sine waves of reqeuency 1 KHz, 2 KHz, 3 KHz, 4 KHz, 5 KHz, …**Implication of Fourier Theorem**Sine wave is a basis shape of all waveform. We will focus our study on sine wave.**Properties of Sine Wave**• Frequency • Amplitude • Phase shift These are 3 properties of sine waves.**period**Frequency volts sec Period ≈ 6.28, Frequency = 0.1592 Hz**Amplitude**volts sec Blue 1 volts Red 0.8 volts**Period=6.28**Red leads blue 57.3 degree (1 radian) Phase Shift Phase Shift = 1**Sine wave in function of time**Form: v(t) = Asin(ωt+φ) Phase (radian) Amplitude Frequency (rad/sec) e.g. v(t) = 3sin(8πt+π/4) volts Phase π/4 radian or 45 degree Amplitude 3 volts Frequency 8πrad/sec or 4 Hz**Basic Components**• AC Voltage Source, AC Current Source • Resistor (R) • Inductor (L) • Capacitor (C)**AC Voltage SourceAC Current Source**Voltage Source Current Source เช่น Amplitude = 10V Frequency =1Hz Phase shift = 45 degree**Resistors**Same asDC circuits Ohm’s Law is still usable V = IR R is constant, therefore V and I have the same shape.**Find i(t)**Note: Only amplitude changes, frequency and phase still remain the same.**Power in AC circuits**InAC circuits, voltage andcurrent fluctuate.This makes power at that time(instantaneous power)also fluctuate. Therefore,the use of average power (P) is prefer. Average power can be calculated by integrating instantaneous power within 1 period and divide it with the period.**Assumev(t) in form**Change variable of integration toθ Then, findinstantaneous power We get integrate from0 to2π**For sine wave Asin(ωt+φ)**Root Mean Square Value (RMS) In DC circuits InAC, we defineVrms andIrms for convenient in calculating power Note: Vrms andIrms are constant, independent of time**3 ways to tell voltage**V (volts) 311V t (sec) 0 V peak (Vp) = 311 V V peak-to-peak (Vp-p) = 622V V rms = 220V**Inductors**Inductance has a unit ofHenry (H) Inductors have V-I relationship as follows This equation compares to Ohm’s law for inductors.**Find i(t)**from**ωL is calledimpedance (equivalent resistance)**Phase shift -90**Phasor Diagram of an inductor**Phasor Diagram of a resistor v v i i Power = (vi cosθ)/2 = 0 Power = (vi cosθ)/2 = vi/2 Note: No power consumed in inductors i lags v**DC Characteristics**When stable,L acts as an electric wire. When i(t) is constant,v(t) = 0**Capacitors**Capacitance has a unit of farad (f) Capacitors have V-I relationship as follows This equation compares to Ohm’s law for capacitors.**Impedance (equivalent resistance)**Find i(t) Phase shift +90**Phasor Diagram of a capacitor**Phasor Diagram of a resistor i v v i Power = (vi cosθ)/2 = 0 Power = (vi cosθ)/2 = vi/2 Note: No power consumed in capacitors i leads v**DC Characteristics**When stable,C acts as open circuit. When v(t) is constant, i(t) = 0**Linearity**Inductors and capacitors are linear components If i(t) goes up 2 times, v(t) will also goes up 2 times according to the above equations**Purpose of the second half**• Know voltage or current at any given time • Know how L/C resist changes in current/voltage. • Know the concept of transient and forced response**Characteristic of R, L, C**• Resistor resist current flow • Inductor resists change of current • Capacitor resists change of voltage L and C have “dynamic”**I = 2A**I = 1A Voltage source change from 1V to 2V immediately Does the current change immediately too?**AC voltage**Voltage 2V 1V time Current 2A 1A time**I = 2A**I = 1A Voltage source change from 1V to 2V immediately Does the current change immediately too?**AC voltage**Forced Response Transient Response + Forced Response Voltage 2V 1V time Current 2A 1A time**Unit Step Input and Switches**Voltage 1V 0V time This kind of source is frequently used in circuit analysis. Step input = change suddenly from x volts to y volts Unit-step input = change suddenly from 0 volts to 1 volt at t=0**This kind of input is normal because it come from on-off**switches.**PSPICE Example**• All R circuit, change R value • RL circuit, change L • RC circuit, change C**Pendulum Example**I am holding a ball with a rope attached, what is the movement of the ball if I move my hand to another point? • Movements • Oscillation • Forced position change