1. INC 111 Basic Circuit Analysis Week 11 Force Response of a Sinusoidal Input and Phasor Concept

2. 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)

3. Forced Response of Sinusoidal Input In this part of the course, we will focus on finding the force response of a sinusoidal input.

4. Start oscillate from stop input displacement Period that have transient

5. Have oscillated for a long time input displacement We will only be interested in this case for force response (not count the transient)

6. Theory Force response of a sinusoidal input is also a sinusoidal signal with the same frequency but with different amplitude and phase shift. v2(t) Sine wave Sine wave v1(t) Sine wave v L (t) Sine wave

7. Input Output Phase shift Amplitude

8. What is the relationship between sin(t) and i(t) ? sin(t) i(t) Phase shift

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

10. Find i(t) from L circuit

11. ωL เรียก ความต้านทานเสมือน (impedance) Phase shift -90

12. Phasor Diagram of an inductor v i Phasor Diagram of a resistor v i Note: No power consumed in inductors i lags v 90 o

13. Find i(t) ความต้านทานเสมือน (impedance) Phase shift +90 C circuit

14. Phasor Diagram of a capacitor v i Phasor Diagram of a resistor v i Note: No power consumed in capacitors i leads v 90 o

15. Kirchhoff's Law with AC Circuit vR i vC i v(t) KCL,KVL still hold.

16. This is similar to adding vectors. Therefore, we will represent sine voltage with a vector. 4 3 5

17. Vector Quantity Complex numbers can be viewed as vectors where X-axis represents real parts Y-axis represents imaginary parts There are two ways to represent complex numbers. Cartesian form3+j4 Polar form5∟53 o Operation add, subtract, multiply, division?

18. Interchange Rectangular, Polar form a b r θ Complex Number Forms (Rectangular, Polar Form)

19. s = 4 + j3 jωjω σ 3 4 Rectangular form:4 + j3 Polar formmagnitude=5, angle = 37 บวก ลบ คูณ หาร vector ??

20. Rectangular form Add, Subtraction Polar form Multiplication Division

21. Impedance Compare to ohm’s law, impedance is a ratio of V/I in when V and I is in the vector format. Inductor

22. Capacitor

23. Example: Find impedance in form of polar value for ω = 1/3 rad/sec Note: Impedance depends on frequency and R,L,C values

24. Rules that can be used in Phasor Analysis Ohm’s law KVL/KCL Nodal, Mesh Analysis Superposition Thevenin / Norton

25. Summary of Procedures Change voltage/current sources in to phasor form Change R, L, C value into phasor form Use DC circuit analysis techniques normally, but the value of voltage, current, and resistance can be complex numbers Change back to the time-domain form if the problem asks.

26. Example Find i(t), v R (t), v L (t) Phasor form

27. V I

28. Example Find i(t), v L (t)

30. V I VR VL Phasor Diagram