reportean

7/29/2019 ReporteAN

1/7

INSTITUTO POLITCNICO NACIONALESCUELA SUPERIOR DE COMPUTO

Node AnalysisFundamental Analysis of Circuits Laboratory

Arceta Torres Fernando

Pazarn Rodrguez Samy Zabdiel

Urquiza Lpez Carlos Ariad

Mexico D. F. 23 of October of 2012

7/29/2019 ReporteAN

2/7

INSTITUTO POLITCNICO NACIONAL

Escuela Superior de Cmputo

Fundamental Analysis of Circuits Laboratory

Practice 5: Node Analysis

Target:

The student applied the method to determine the voltage nodes present in an electrical circuit, sothat at the end of practice, this in a position to employ this technique in calculating the voltage

drop present in networks that contain multiple nodes.

Equip provided by Laboratory:

1 Digital Multimeter

1 Variable Voltage sources CD

4 Banana-alligator connectors

4 Banana-Banana connectors Cutting pliers

Nose pliers

Material owned by students: 1 Protoboard

2 Resistors of 680 .





2 Resistors of 1 k ..

Connection cables for Breadboard.

7/29/2019 ReporteAN

3/7

I Theoretical Introduction

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current

method is a method of determining the voltage (potential difference) between "nodes"

(points where elements or branches connect) in an electrical circuit in terms of the branch

currents.

In analyzing a circuit using Kirchhoff's circuit laws, one can either do nodal

analysis using Kirchhoff's current law (KCL) or mesh analysis using

Kirchhoff's voltage law (KVL). Nodal analysis writes an equation at each

electrical node, requiring that the branch currents incident at a node must

sum to zero. The branch currents are written in terms of the circuit node

voltages. As a consequence, each branch constitutive relation must give

current as a function of voltage; an admittance representation. For

instance, for a resistor, Ibranch = Vbranch * G, where G (=1/R) is the

admittance (conductance) of the resistor.

Nodal analysis is possible when all the circuit elements' branch constitutive

relations have an admittance representation. Nodal analysis produces a compact set of

equations for the network, which can be solved by hand if small, or can be quickly solved

using linear algebra by computer. Because of the compact system of equations, many

circuit simulation programs use nodal analysis as a basis. When elements do not have

admittance representations, a more general extension of nodal analysis, modified nodal

analysis, can be used.

Method:

1. Note all connected wire segments in the circuit. These are the nodes of nodal

analysis.

2. Select one node as the ground reference. The choice does not affect the result and is

just a matter of convention. Choosing the node with most connections can simplify the

analysis.

3. Assign a variable for each node whose voltage is unknown. If the voltage is already

known, it is not necessary to assign a variable.

4. For each unknown voltage, form an equation based on Kirchhoff's current law.

Basically, add together all currents leaving from the node and mark the sum equal to zero.

5. If there are voltage sources between two unknown voltages, join the two nodes as a

supernode. The currents of the two nodes are combined in a single equation, and a new

equation for the voltages is formed.

6. Solve the system of simultaneous equations for each unknown voltage.

Kirchhoff's current law

is the basis of nodal

analysis.

7/29/2019 ReporteAN

4/7

II Practice Development

II.1 Applying the method of circuit nodes to the figure, find a theoretical way (analytical

method), the corresponding current values called for in certain items and list them on the

table.

II.2 Without turning the voltage source, build the circuit, on the protoboard. Once armed,

proceed to set the voltage value indicated and applied to the circuit through the probes, the

power supply on.

II.3 Check the validity of previous theoretical results by measuring with the ammeter, the

current in the above points and report their practical values of the table.

MeasurementsTheoretical value

(ampers)Measured value (ampers)

Current I - 0 4.92 A 4.90 A

Current II - I 2.31 A 2.32 A

Current II - 0 2.75 A 2.75 A

7/29/2019 ReporteAN

5/7

II.4 The same circuit voltage obtained theoretical values obtained in the simulator and

experimental, report them in the following table.

MeasurementsTheoretical value

(volts) Measured value (volts)

Voltage V I 0 3.81 V rms 3.6 V rms

Voltage V II 0 600 mV rms 550 mV rms

Voltage V I II 3.22 V rms 3.04 V rms

II.5 Finally calculate the power dissipated by each resistor and record in the table.

Resistors (K)power dissipated

(watts)

R1 12.9 mW

R2 3.02 mW

R3 77 mW

7/29/2019 ReporteAN

6/7

III.- Questionary

1. Define what is a node in an electrical circuit.

In an electrical circuit connection points of three or more drivers which we callnodes or knots. Half point or a field that remains unchanged when more than one

disturbance simultaneously acting on it.

2. Define what is the voltage of a node.

In a series circuit the sum of the potential difference across each element ofconsumption hereinafter called voltage drop is equal to the voltage that providesthe power source or battery.

3. What we call the reference node?

The reference node is chosen arbitrarily, although it is common to choose the nodewhich is connected to a larger number of branches or a node with a voltagesource. In most cases, this procedure involves a smaller number of equations.

4. Briefly define the method that consists of nodes.

It is a general method of circuit analysis is based on determining the voltages of allcircuit nodes with respect to a reference node. Known these voltages candetermine all the currents in the various circuit elements.

7/29/2019 ReporteAN

7/7

IV.- Conclusions

Arceta Torres Fernando

In developing this practice we saw the issue of analysis of nodes seen in class, which this

method is much easier to me than the Kirchoff current law.

Pazarn Rodrguez Samy Zabdiel

This practice could apply and verify knowledge previously obtained theoretical classes on

the use of the method of Node Analysis for the calculation of voltages and currents in a

circuit of four meshes with current sources later gaining power in each of the nine

resistance existed.

Urquiza Lpez Carlos Ariad

In this practice we could see the reasoning of the Node Analysis by circuit simulation, and

by calculating the equations for the node.

The use of the law is very useful for resuloucion in cases that include current sources in

the mesh.

reportean

Documents