GUC_47_65_53490_2025-02-18T615_13_22.pdf

Circuits lecture

1. Electric Circuits II: (ELCT 401)
Instructor: Dr. Walid Omran
Dr. Wassim Alexan
Lecture 3: AC Analysis

2. Sinusoidal Steady-State Analysis
2

3. Objectives
To perform circuit analysis using the following techniques:
1.Basic Approach (KCL and KVL –Circuit reduction)
2.Nodal Analysis
3.Mesh Analysis
4.Superposition Theorem
5.Source Transformation
6.Thevenin and Norton Equivalent Circuits
7.Bridge Networks
3

4. Steps to Analyze AC Circuits:
1.Transform the circuit to the phasor (frequency) domain
2.Solve using an appropriate circuit technique such as nodal
analysis, mesh current analysis, superposition, etc…
3.Transform the resulting phasors back into the time domain
4

5. 5

6. 6

7. Example
Solution
7

8. Nodal Analysis
Example:
Using nodal analysis, find V
1and V
2.
Solution:
Solve 1& 2:
−3+
??????
1−??????
2
4
+
??????
1
−??????3
+
??????
2−??????
1
4
+
??????
2
??????6
+
??????
2
12
=0 (1)
??????
1−??????
2=10∠45° (2)

9. Mesh Analysis
Example
Find V
oin the following figure using mesh analysis.

10. Solution
•Mesh 1:
•Mesh 2:
•Super mesh:
•Constraint:
Solving the 4 equations:
−10+8(??????
1−??????
3)−??????2(??????
1−??????
2)=0
??????
2=−3
−??????4??????
3+6??????
4+??????5??????
4−??????
2+8(??????
3−??????
1)=0
??????
4−??????
3=4
??????
1=
41
145
−??????
523
145
??????,??????
2=−3??????,??????
3=−
271
145
−??????
642
145
??????,??????
4=
309
145
−??????
642
145
??????
??????
0=−2????????????
1−??????
2=−7.2134−??????6.568=9.756∠222.32°??????

11. Superposition Theorem
If a circuit has sources operating at different frequencies, then:
•The separate phasor circuit for each frequency must be
solved independently, and
•The total response is the sum of the time-domain responses
of all the individual phasor circuits

12. Superposition Theorem
Example 5
Calculate v
o(t) in the circuit shown below using the superposition theorem

13. Voltage divider
Currentdivider
??????=2��??????/�
??????=5��??????/�

14. Source Transformation
14

15. Thevenin and Norton Equivalent Circuits
Thevenin transform
Norton transform
15

16. Theveninand Norton Equivalent Circuits
16
IfaloadimpedanceZ
Lis
connected between the
terminalsaandb,themaximum
poweristransferredtotheload
when:
�
??????=�
??????ℎ
∗
In this case, the maximum
power transferred to the load is
given by:
??????
??????????????????=
??????
??????ℎ−??????????????????
2
8??????
??????ℎ

17. Example
Find the Thevenin equivalent circuit between terminals a & b
a
b
This means that we need to find ??????
??????ℎand �
??????ℎ

18. Solution:
Finding V
TH
a
b
Source
Transformation

19. Finding Z
TH
10Ω

20. •A bridge is a 4-arm circuit, connected as shown below
•It is used to measure unknown impedances
•We place the unknown impedance as �
4, a known impedance as �
1, then we
keep varying �
2and �
3until ??????and ??????are equal to zero
•At balance, the unknown quantities can be calculated
(1)
(2)
(1)/(2)
Bridge Networks

21. Example
Hay’s Bridge
L
4 & R
4are the
unknowns
At Balance:
Therefore
Since,