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8/11/2019 Robt203 Lecture4 Node Voltage Analysis
1/17
SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
ROBT 203Electrical and Electronics Circuits I
with Laboratory
Lecture 4Node Voltage Analysis
29 August 2012, Thursday
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
2/17
SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Topics
2
Todays Topics
Node Voltage Analysis of Circuits with Current Sources
Using Matlab to Solve Node Equations
NVA of Circuits with Current and Voltage Sources
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
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SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Course Logistics
3
Important Dates and TasksReading Assignment: Dorf Chapter 1 and 2 due 25thof September
(Monday)
Laboratory Session 1 next week
Homework #1 due 3rdof September (Wednesday)
Problems: Dorf P1.2-4, P1.3-6, P1.5-2, P1.5-5, P1.5-9, P2.2-4, P2.4-5,
P2.4-9, P2.5-5, P2.6-6, P2.9-1
Quiz #1 on 4thof September (Thursday)
Homework #2 due 10thof September (Wednesday)
Problems: Dorf P3.2-2, P3.2-5, P3.2-7, P3.2-13, P3.2-15, P.3.2-20, P3.2-
27, P3.2-29, P3.3-5, P3.3-10, P3.4-2, P3.4-9, P3.4-15, P3.5-3, P3.6-3,
P3.6-13, P3.6-23, DP3-3 (This will take a long time, start early)
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
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SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Nave Approach to Circuit Analysis
4
The unknown variables are element currents and voltages.
We write Kirchoffscurrent and voltage laws to get some equations.
Then, we generate additional equations using the constitutive equations
of the circuit elements (Ohms Law for resistors = ).
This method works well for small circuits, but moderately sized circuits
the number of equations grow quickly (6 elements12 equations).
We need a systematic approach to analyze circuits: Two possible approaches are:
Node voltage method
Mesh current method
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SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Reference Node
5
For analyzing a circuit with n
connected nodes will require
n-1 KCL equations.
The node at which KCL is not
applied is called reference
node.
Any node in a circuit can be the
reference node (usually at the
bottom of the circuit).
In circuits with groundedpower supply, the ground
node of the power supply is
usually selected as the
reference node. reference node
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
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SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Reference Node in a Real World Circuit
6
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
7/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Node Voltages
7
The voltage at any node of the circuit relative to the reference node is called a
node voltage.
In the circuit below, the node voltage can be represented as and .
However, we simply call them and .
The voltage at the reference node is zero. = = 0.
reference node
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
8/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Node Voltage Method
8
In the node voltage method, we write and solve the node equations.
To write the node equations, we do:
Express element current as functions of node voltages.
Apply KCL at each of the nodes of the circuit except the reference node.
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
9/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Analyze the Circuit using Node Equations
9
= 1, = = 0.5, and = 4.
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
10/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Determine the Value of Resistance R
10
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
11/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Obtain the Node Equations for the Circuit
11
= 1 , = 2 , = 3 , = 5, = 2, = 10, = 4, = 5, and
6= 2.
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
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Using Matlab to Solve Node Equations
12
Simplified node equations for the circuit in the previous
slide are given by:
0.9 0.20.7= 3
0.2+ 0.550.1= 1
0.7 0.1+1.3= 1
Node voltages can be written using matrices as
=
where
=
0.9 0.2 0.7
0.2 0.55 0.10.7 0.1 1.3
, =
3
11
and =
These matrix equation can be solved in Matlab.
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
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NVM for Circuits with Current and Voltage Sources
13
A supernode(or generalized node) consists of two
nodes connected by an independent or a dependent
voltage sources.
Case 1: The voltage source is between
node q and reference node:
Set equal to the source voltage
taking into account the polarities and
write KCL.
Case 2: The voltage source is between two nodes a and b.
Create a supernode that incorporates a and b and equate the sum of all
currents entering the supernode to zero.
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14/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Obtain the Node Equations for the Circuit
14
Case 1
Case 2
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
15/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Obtain the Node Equations for the Circuit
15
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
16/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014
Obtain the Node Equations for the Circuit
16
8/11/2019 Robt203 Lecture4 Node Voltage Analysis
17/17SST Department of Robotics and Mechatronics ROBT 203 Fall 2014
Any Questions?
17