AL- Quds University
Najjad Zeenna's Faculty of Engineering
Department of Electronic Engineering
Introd to Circuit the and Electronic
[lab 0701213]
Exp (#4): Nodal, Mesh & Superposition
Prepared by: Nabeel Isa
Stu#:21910243
Dr. Ahmed Al-Qutb
Supervisor: Eng -Anas Eid
12 October 2020
Table of contents:
The content
Introduction
Page number
Conclusion:
3
3
3
3
4
8
9
The figure
Page number
Figure 1Circit (part 1)
Figure 1Circit (part 2)
Figure 1Circit (part 3)
4
5
6
The Table
Page number
Table Calculations results ":
7
7
8
8
8
9
Equipment
Objectives
Theoretical Background
Procedure
Experimental & Theoretical results
Table
Simulations results":
Table Measurements results ":
Table result Part 1":
Table result Part 2":
Table result Part 3":
Equipment:
Power supplies (2), Digital millimeter (DMM), breadboards (1), resistors (3 kΩ [2],
1 kΩ [2], 2KΩ), jumper wires.
Objective:
Students successfully completing this preparatory exercise will accomplish the
Following objectives:
1. Gain increased understanding of the applications of mesh analysis.
2. Verify, by measurements, the results of mesh anaylsis.
3. Demonstrate, by measurements, the theorem of superposition as a means
achieve results similar to those of objective 2.
to
Theoretical Background
Mesh Analysis 1.2.1* .A mesh is one of the smallest circuit loops Applying KVL for
each mesh (∑v in each mesh .(= 0 Mesh equations are written for every mesh in
.terms of unknown current :Nodal Analysis 1.2.2* .Determine # of node- .Choose the
reference node3 .Label all node voltage- .(Apply KCL at each node (∑i leaving= 0Equations are written for every unknown .node :Superposition Techniques 1.2.3*
Using the superposition method, we remove all independent source, except one and
analyze the circuit for that one, Then we repeat the procedure for anther source, and
so on, Finally the net results is found by .summing all signal-source result
Procedure
Circuit Part 1":
Calculations results
Mesh 1:
0= -10 +1ki1 +3k(i1-i2)
10=1ki1+3ki1-3k2
10= 4ki1 -3ki2 [1]
Mesh 2:
0=3k(i2-i1)+2Ki2 +3k(i2-i3)
0=3ki2 -3Ki1+2ki2+3ki2 -3ki3
0= -3k +8ki2 -3Ki3 [2]
Mesh 3:
0= 3k(i2-i1) +2ki2 +3k (i2-i3)
0 = -3ki2+ 1ki3 [3]
i1 = 4.1mA and i2 = 2.14mA and i3 = 1.6mA
Procedure
Part 2":
Mesh 1:
0= 1ki1 +3k(i1-i2)
0=1ki1+3ki1-3k2
0= 4ki1 -3ki2 [1]
Mesh 2:
0=6+3k(i2-i1)+2Ki2 +3k(i2-i3)
-6=3ki2 -3Ki1+2ki2+3ki2 -3ki3
-6= -3k +8ki2 -3Ki3 [2]
Mesh 3:
0= -6+3k(i2-i1) +2ki2 +3k (i2-i3)
6 = -3ki2+ 4ki3 [3]
i1 = -0.32mA and i2 = -0.42mA and i3 = 1.17mA
Procedure
Part 3":
Mesh 1:
0= -10 +1ki1 +3k(i1-i2)
10=1ki1+3ki1-3k2
10= 4ki1 -3ki2 [1]
Mesh 2:
0=6+3k(i2-i1)+2Ki2 +3k(i2-i3)
-6=3ki2 -3Ki1+2ki2+3ki2 -3ki3
-6= -3k +8ki2 -3Ki3 [2]
Mesh 3:
0= -6+3k(i2-i1) +2ki2 +3k (i2-i3)
6 = -3ki2+ 4ki3 [3]
i1 = 3.78mA and i2 = 1.71mA and i3 = 2.78mA
Mesh current (mA)
Due to 10V only
Due to 6V only
Due to 10V and 6V
I1
I2
I3
4.1mA
2.14mA
1.6mA
-0.31mA
-0.42mA
1.17mA
3.78mA
1.69mA
2.78mA
Nodal voltage (V)
Due to 10V only
Due to 6V only
Due to 10V and 6V
V1
V2
V3
5.88V
0.32V
6.2V
1.6V
1.17V
2.78V
1.6V
1.17V
2.78V
)Vs( ‫ المعرفت الفولة نضرب التيار الذي اوجدناة بالمقاومة الموازية المصدر الطاقة‬: ‫مالحظة‬
[ ‫االنة نفس النقطة‬V2 =V3]
Calculations results
Mesh current (mA)
Due to 10V only
Due to 6V only
Due to 10V and 6V
I1
I2
I3
4.11mA
2.14mA
1.81mA
-0.32mA
-0.43mA
1.18mA
3.79mA
1.71mA
2.79mA
Nodal voltage (V)
Due to 10V only
Due to 6V only
Due to 10V and 6V
V1
V2
V3
5.89V
1.61V
1.61V
0.32V
1.18V
1.18V
6.21V
2.79V
2.79V
Simulations results:
Mesh current (mA)
Due to 10V only
Due to 6V only
Due to 10V and 6V
I1
I2
I3
4.11mA
2.14mA
1.81mA
-0.32mA
-0.43mA
1.18mA
3.79mA
1.71mA
2.79mA
Nodal voltage (V)
Due to 10V only
Due to 6V only
Due to 10V and 6V
V1
V2
V3
5.89V
1.6V
1.6V
32.143mV
1.17V
1.17V
6.214V
2.78V
2.78V
Measurements results
Table result Part 1":
The value of:
Theoretical value
Experimental value
V1
V2
V3
I1
I2
I3
5.89V
1.61V
1.61V
4.11mA
2.14mA
1.81mA
5.88V
1.6V
1.6V
4.1mA
2.13mA
1.6mA
Percentage error
0.2%
0.6%
0.6%
0.2%
0.5%
11%
The value of:
Theoretical value
Experimental value
Percentage error
V1
V2
V3
I1
I2
I3
0.32V
1.18V
1.18V
-0.32mA
-0.43mA
1.18mA
0.31V
1.17V
1.17V
-0.31mA
-0.42mA
1.17mA
3.1%
0.8%
0.8%
3.1%
2.3%
0.8%
Table result Part 2":
Table result Part 3":
The value of:
Theoretical value
Experimental value
Percentage error
V1
V2
V3
I1
I2
I3
6.21V
6.2V
0.2%
2.79V
2.78V
0.4%
2.79V
2.78V
0.4%
3.79mA
3.78mA
0.3%
1.71mA
1.69mA
1.2%
2.79mA
2.78mA
0.4%
___________________________________________________________
3. Compare the theoretical and the experimental sets of results, and
comment on the differences between them (if any). Where you able to
verify the superposition principle?
There is a slight difference between scientific experiment and theoretical
experiment.
Conclusion:
Mesh analysis: applying (KVL) at each -1.mesh
Nodal analysis: applying (KCL) at each -2.node
Superposition technical :( killing all -3
independent source except one then find I or
V "apply it at each source" then
……I=I1+I2+I3
………+V=V1+V2+V3