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INC 112 Basic Circuit Analysis
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1. INC 112 Basic Circuit Analysis Week 7 Introduction to AC Current

2. 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.

3. 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

4. Signals • Signal is an amount of something at different time, e.g. electric signal. • Signals are mentioned is form of • Graph • Equation

5. 1st Form Graph Voltage (or current) versus time V (volts) t (sec) 2nd Form v(t) = sin 2t

6. DC voltage V (volts) t (sec) v(t) = 5

7. 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?

8. 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

9. 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

10. Square wave Sine wave

11. 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, …

12. Implication of Fourier Theorem Sine wave is a basis shape of all waveform. We will focus our study on sine wave.

13. Properties of Sine Wave • Frequency • Amplitude • Phase shift These are 3 properties of sine waves.

14. period Frequency volts sec Period ≈ 6.28, Frequency = 0.1592 Hz

15. Amplitude volts sec Blue 1 volts Red 0.8 volts

16. Period=6.28 Red leads blue 57.3 degree (1 radian) Phase Shift Phase Shift = 1

17. 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

18. Basic Components • AC Voltage Source, AC Current Source • Resistor (R) • Inductor (L) • Capacitor (C)

19. AC Voltage SourceAC Current Source Voltage Source Current Source เช่น Amplitude = 10V Frequency =1Hz Phase shift = 45 degree

20. What is the voltage at t =1 sec ?

21. Resistors Same asDC circuits Ohm’s Law is still usable V = IR R is constant, therefore V and I have the same shape.

22. Find i(t) Note: Only amplitude changes, frequency and phase still remain the same.

23. 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.

24. Assumev(t) in form Change variable of integration toθ Then, findinstantaneous power We get integrate from0 to2π

25. 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

26. 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

27. Inductors Inductance has a unit ofHenry (H) Inductors have V-I relationship as follows This equation compares to Ohm’s law for inductors.

28. Find i(t) from

29. ωL is calledimpedance (equivalent resistance) Phase shift -90

30. 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

31. DC Characteristics When stable,L acts as an electric wire. When i(t) is constant,v(t) = 0

32. Capacitors Capacitance has a unit of farad (f) Capacitors have V-I relationship as follows This equation compares to Ohm’s law for capacitors.

33. Impedance (equivalent resistance) Find i(t) Phase shift +90

34. 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

35. DC Characteristics When stable,C acts as open circuit. When v(t) is constant, i(t) = 0

36. Combination of Inductors

37. Combination of Capacitors

38. 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

39. Transient Responseand Forced response

40. 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

41. Characteristic of R, L, C • Resistor resist current flow • Inductor resists change of current • Capacitor resists change of voltage L and C have “dynamic”

42. I = 2A I = 1A Voltage source change from 1V to 2V immediately Does the current change immediately too?

43. AC voltage Voltage 2V 1V time Current 2A 1A time

44. I = 2A I = 1A Voltage source change from 1V to 2V immediately Does the current change immediately too?

45. AC voltage Forced Response Transient Response + Forced Response Voltage 2V 1V time Current 2A 1A time

46. 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

47. PSPICE Example • All R circuit, change R value • RL circuit, change L • RC circuit, change C

48. 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