robt203 lecture4 node voltage analysis

8/11/2019 Robt203 Lecture4 Node Voltage Analysis

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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


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Topics

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Todays Topics

Node Voltage Analysis of Circuits with Current Sources

Using Matlab to Solve Node Equations

NVA of Circuits with Current and Voltage Sources


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Course Logistics

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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)


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Nave Approach to Circuit Analysis

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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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Reference Node

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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


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Reference Node in a Real World Circuit

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7/17SST, Department of Robotics and Mechatronics, ROBT 203, Fall 2014

Node Voltages

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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



Node Voltage Method

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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.



Analyze the Circuit using Node Equations

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= 1, = = 0.5, and = 4.



Determine the Value of Resistance R

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Obtain the Node Equations for the Circuit

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= 1 , = 2 , = 3 , = 5, = 2, = 10, = 4, = 5, and

6= 2.



Using Matlab to Solve Node Equations

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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

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and =

These matrix equation can be solved in Matlab.



NVM for Circuits with Current and Voltage Sources

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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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Case 1

Case 2




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17/17SST Department of Robotics and Mechatronics ROBT 203 Fall 2014

Any Questions?

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robt203 lecture4 node voltage analysis

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