8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 1/22
Circuit Analysis Techniques and
Network Theorems
A. Mesh Analysis
Mesh
It is a loop which does not contain any other
loop within it.
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 2/22
In mesh analysis, Kirchhoff·s Voltage Law (KVL) is
used.
Steps:
1. Draw a current loop for each mesh. All
mesh
currents must be in the same or uniform indirection (clockwise or counterclockwise).
2. Formulate mesh equations following the
pattern. For an n-mesh network, we have n-
mesh equations.3. Solve for the unknown mesh current by
applying techniques involved in evaluating
linear equations.
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 3/22
Equation Pattern:
V1
= R11
I1
- R12
I2
- . . . . . . - R1N
IN
.
V2 = -R21I1 + R22I2 - . . . . . . . - R2NIN .
.
.
VN
= -RN1
I1
- RN2
I2
- . . . . . . + RNN
IN
.
where:
V1 , V2 . . . . Vn = algebraic sum of all voltage
sources in a mesh
R11 , R22 . . .RNN = sum of all resistance in a mesh
R12 , R22 . . .RN = common or mutual resistance
between two meshes
I1 , I2 . . . . . . .IN = mesh currents
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 4/22
V1
V2
V3
R1 R2
R3
1 2
I1 I2
Mesh 1: V1 - V2 = (R1 + R3) I1 - R3 I2
Mesh 2: V2 - V3 = - R3 I1 + (R2 + R3) I2
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 5/22
1 2
I1 I2
10V
2 3
4
6V
3V
;
; ;
4 A 5 ohms
10 V
40 ohms
1 ohm4 ohms
2 ohms
10 A
io
1. Determine mesh currents I1 and I2.
2. Determine io by mesh analysis.
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 6/22
3. Determine the mesh currents.
2
2
3 4
10V
15V
10A 1
;
;
;
;
;
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 7/22
B. Nodal Analysis
I3
I1 I2
R3
R1 R2
Node
A point at which two or more elements have a
common connection.
Nodal analysis is a method that uses Kirchhoff·s Current Law
(KCL) to obtain a solution of simultaneous equations that
when manipulated will provide a means of solving for the
voltages on each node and for every branch.
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 8/22
Steps:
1. Identify the nodes of the given circuit
(including the reference node). All nodeshave corresponding voltages (except the
reference node) and must have the same
voltage sign convention where the given
node is positive and the reference node isnegative.
2. Formulate node equations following the
pattern. For an n - node network, we have
n -1 node equations.3. Solve for the unknown mesh current by
applying techniques involved in evaluating
linear equations
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 9/22
Equation Pattern:
I1 = G11 V1 - G12 V2 - . . . . . . - GN1 VN
I2 = G21 V1 - G22 V2 - . . . . . . - G2N VN
.
.
IN
= -GN1
V1
- GN2
V2
- . . . . . .+ GNN
VN
where:
I1 , I2 , IN = algebraic sum of all current sources
connected to a node.
G11 , G22 , GNN = sum of all conductance connectedto a node.
G12 , G21 , GN = common conductance between two
nodes.
V1 , V2, VN = unknown node voltages
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 10/22
Node 1 :
I1
- I3
= (G1
+ G3) V
1- G
3V
2----1
Node 2 :
I3
+ I2
= - G3
V1
+ (G3
+ G2) V
2---2
2
3
1
31
31
111V
RV
R R I I ¹¹
º
¸©©ª
¨!
1
32
1
3
23
111V
R RV
R I I ¹¹
º
¸©©ª
¨!
I3
I1 I2
R3
R1 R2
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 11/22
Sample Problems:
Determine the node voltages.5A
10A 3A
4S
2S 3S
Determine Vx.
10A
5A0.5Vx1;
2;
3;
- Vx +
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 12/22
Find i using nodal analysis.
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 13/22
B. Superposition theorem
Find v using superposition theorem.
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 14/22
Solution: To get v1, we set the current source to zer o.
Applying KVL,
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 15/22
Find i. Answer: 2A
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 16/22
i3
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 17/22
Thevenin Equivalent Circuit
(TEC)
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 18/22
Obtain the TEC. Determine the current thru R L if R L = 6 ohms, 16 ohms, 36 ohms
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 19/22
Applying mesh analysis;
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 20/22
The TEC is shown below.
The current thru R L is now calculated :
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 21/22
TH N R R !
TH
TH
N
R
V I !
Norton Equivalent Circuit (NEC)
To get INNOTE:
8/3/2019 Ee Lecture
http://slidepdf.com/reader/full/ee-lecture 22/22