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Hafiz Zaheer Hussain

2. 3/16/2015 Hafiz Zaheer Hussain
Circuit Analysis-II Spring-2015 EE Instructor: Hafiz Zaheer Hussain Department of Electrical Engineering The University of Lahore Week 3
3/16/2015
Hafiz Zaheer Hussain

3. Fundamentals of Electric Circuits by Alexander-Sadiku
Chapter 9
Sinusoidal Steady-State Analysis
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Hafiz Zaheer Hussain

4. Content 9.1 Introduction 9.2 Sinusoids’ features 9.3 Phasors
9.4 Phasor relationships for circuit elements
9.5 Impedance and admittance
9.6 Kirchhoff’s laws in the frequency domain
9.7 Impedance combinations
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Hafiz Zaheer Hussain

5. 9.5 Impedance and Admittance (1)
The impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I, measured in ohms Ω.
V = I Z ,
Positive X is for L and negative X is for C.
The admittance Y is the reciprocal of impedance, measured in siemens (S).
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Hafiz Zaheer Hussain

6. 9.5 Impedance and Admittance (2)
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7. 9.5 Impedance and Admittance (3)
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8. Impedances and admittances of passive elements
9.5 Impedance and Admittance (4)
Impedances and admittances of passive elements
Element
Impedance
Admittance R L C
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Hafiz Zaheer Hussain

9. 9.5 Impedance and Admittance (5)
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10. Is impedance a phasor ??? 9.5 Impedance and Admittance (6)
No, it is not a phasor, because it does not represent a sinusoidal quantity.
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Hafiz Zaheer Hussain

11. 9.5 Impedance and Admittance (7)
After we know how to convert RLC components from time to phasor domain, we can transform a time domain circuit into a phasor/frequency domain circuit.
Hence, we can apply the KCL laws and other theorems to directly set up phasor equations involving our target variable(s) for solving.
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Hafiz Zaheer Hussain

12. 9.5 Impedance and Admittance (8)Example 9.9
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13. 9.5 Impedance and Admittance (9) Example 9.9
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14. 9.5 Impedance and Admittance (10) PP (9.9)
Refer to Figure below, determine v(t) and i(t).
Answers: i(t) = 1.118cos(10t – 26.56o) A; v(t) = 2.236cos(10t o) V
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Hafiz Zaheer Hussain

15. Content 9.1 Introduction 9.2 Sinusoids’ features 9.3 Phasors
9.4 Phasor relationships for circuit elements
9.5 Impedance and admittance
9.6 Kirchhoff’s laws in the frequency domain
9.7 Impedance combinations
3/16/2015
Hafiz Zaheer Hussain

16. 9.6 Kirchhoff’s laws in the frequency domain
Both KVL and KCL are hold in the phasor domain or more commonly called frequency domain.
Moreover, the variables to be handled are phasors, which are complex numbers.
All the mathematical operations involved are now in complex domain.
3/16/2015
Hafiz Zaheer Hussain

17. Content 9.1 Introduction 9.2 Sinusoids’ features 9.3 Phasors
9.4 Phasor relationships for circuit elements
9.5 Impedance and admittance
9.6 Kirchhoff’s laws in the frequency domain
9.7 Impedance combinations
3/16/2015
Hafiz Zaheer Hussain

18. 9.7 Impedance combinations (1)
The following principles used for DC circuit analysis all apply to AC circuit.
For example:
voltage division
current division
circuit reduction
impedance equivalence
Y-Δ transformation
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Hafiz Zaheer Hussain

19. (N impedances in series)
9.7 Impedance combinations (2)
(N impedances in series)
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Hafiz Zaheer Hussain

20. 9.7 Impedance combinations (2)
2 impedances in series
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21. N Impedances in Parallel
9.7 Impedance combinations (2)
N Impedances in Parallel
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22. 2 Impedances in parallel
9.7 Impedance combinations (2)
2 Impedances in parallel
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23. Example 9.10 9.7 Impedance combinations (2)
Find the input impedance of the circuit in Fig Assume that the circuit operations at  = 50 red/s.
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Hafiz Zaheer Hussain

24. 9.7 Impedance combinations (2)
Solution
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Hafiz Zaheer Hussain

25. 9.7 Impedance combinations (2)
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26. Example 9.11 9.7 Impedance combinations (2)
Determine v0(t) in the circuit
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27. 9.7 Impedance combinations (2)
Solution 9.11
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28. 9.7 Impedance combinations (2)
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29. 9.7 Impedance combinations (2)
Let
Z1 = Impedance of the 60-Ω resistor
Z2 = Impedance of the parallel combination of the 10-mF capacitor and the 5-H inductor
Then
Z1 = 60 Ω and
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Hafiz Zaheer Hussain

30. 9.7 Impedance combinations (2)
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31. Delta-Wye Wye-Delta Transformation
9.7 Impedance combinations (2)
Delta-Wye
Wye-Delta
Transformation
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32. 9.7 Impedance combinations (2)
The delta-wye and wye-delta transformation, that was applied to resistive circuits, are also valid for impedances.
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Hafiz Zaheer Hussain

33. 9.7 Impedance combinations (2)
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34. 9.7 Impedance combinations (2)
Wye(Y)-Delta(Δ) a b c Za Zc Zb Z1 Z2 Z3
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35. 9.7 Impedance combinations (2)
Summary
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Hafiz Zaheer Hussain

36. 9.7 Impedance combinations (2) Example-9.12
Find current I in the circuit.
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Hafiz Zaheer Hussain

37. 9.7 Impedance combinations (2)
Solution
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Hafiz Zaheer Hussain

38. 9.7 Impedance combinations (2)
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39. 9.7 Impedance combinations (2)
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40. 9.7 Impedance combinations (2)
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41. CHAPTER 10 Chapter 10 will show that other circuit techniques—such as
superposition,
nodal analysis,
mesh analysis,
source transformation,
the Thevenin theorem, and the Norton theorem
are all applied to ac circuits in a manner similar to their application in dc circuits.
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Hafiz Zaheer Hussain

42. Summary
1. A sinusoid is a signal in the form of the sine or cosine function. It has the general form
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Hafiz Zaheer Hussain

43. Summary
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44. 3/16/2015
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