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
(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
Stable

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 true. 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 (Equivalent Resistance)
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)

30. Phasor Diagram VL V I VR