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Week 11 Force Response of a Sinusoidal Input and Phasor Concept

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1 Week 11 Force Response of a Sinusoidal Input and Phasor Concept
Network Analysis Week 11 Force Response of a Sinusoidal Input and Phasor Concept

2 Two Types of Analysis non-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 Period that have transient displacement

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 v1(t) Sine wave Sine wave vL(t) Sine wave

7 Phase shift Input Amplitude Output

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

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

10 L circuit Find i(t) from

11 ωL เรียก ความต้านทานเสมือน (impedance)
Phase shift -90

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

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

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

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

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

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 form 3+j4 Polar form 5∟53o Operation add, subtract, multiply, division?

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

19 บวก ลบ คูณ หาร vector ?? Rectangular form: 4 + j3
s = 4 + j3 3 σ 4 Rectangular form: 4 + j3 Polar form magnitude=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 Note: Impedance depends on frequency and R,L,C values
Example: Find impedance in form of polar value for ω = 1/3 rad/sec

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), vR(t), vL(t) Phasor form

27 V I

28 Example Find i(t), vL(t)

29

30 Phasor Diagram VL V I VR


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