1. INC 111 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 or current change with time. Example: We measure voltage difference between 2 points Time1pm2pm3pm4pm5pm6pm DC: 5V5V5V5V5V5V AC:5V3V2V-3V-1V2V

4. Signals Signal is an amount of something at different time, e.g. electric signal. Signals are mentioned is form of 1.Graph 2.Equation

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

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

7. Course requirement of the 2 nd half Students must know voltage, current, power at any point in the given circuits at any time. e.g. How much is the current at point A? How much is the voltage between point B and C at 2pm? How much is the current at point D at t=2ms?

8. Two Types of Analysis non-periodic electric source periodic electric source (Transient response analysis of a step input) (Steady state response analysis of a sinusoidal input)

9. Periodic Signals Periodic signals are signal that repeat itself. Definition Signal f(t) is a periodic 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

10. 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 where ω is the angular velocity with unit radian/sec

11. Sine wave Square wave

12. 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, …

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

14. Properties of Sine Wave 1. Frequency 2. Amplitude 3. Phase shift These are 3 properties of sine waves.

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

16. Amplitude sec volts Blue 1 volts Red 0.8 volts

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

18. Sine wave in function of time Form: v(t) = Asin( ω t+ φ) Amplitude Frequency (rad/sec) Phase (radian) e.g. v(t) = 3sin( 8 πt+π/4 ) volts Amplitude 3 volts Frequency 8π rad/sec or 4 Hz Phase π/4 radian or 45 degree

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

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

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

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

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

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

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

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

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

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

29. Combination of Inductors

30. Combination of Capacitors

31. 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

32. Non-periodic Signal There are infinite number of non-periodic signal. This course will cover only the most basic one, a step. A step is a result from on/off switches, which is common in our daily life. 0V 9V On switch

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

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

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

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

37. Unit Step Input and Switches u(t) time 0V 1V 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

38. This kind of input is normal because it come from on-off switches.

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

40. How all R circuit react to a step?

41. Voltage source Current

42. When there is L

43. Voltage source Current

44. decrease L

45. Voltage source Current L = 0.1HLook like a step, but sharper

46. increase L

47. Voltage source Current L = 2H Also a step, but rise slower.

48. 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 1.Oscillation 2.Forced position change Pendulum Example

49. Transient Response or Natural Response (e.g. oscillation, position change temporarily) Fade over time Resist changes Forced Response (e.g. position change permanently) Follows input Independent of time passed

50. Forced response Natural response at different time Mechanical systems are similar to electrical system

51. Transient Response RL Circuit RC Circuit RLC Circuit First-order differential equation Second-order differential equation