Chapter 17 – Methods of Analysis & Sel Topics Lecture 24 by Moeen Ghiyas 13/08/2015 1.

Chapter 17 – Methods of Analysis & Sel Topics

Lecture 24

by Moeen Ghiyas

19/04/23 1

Chapter 17 – Methods of Analysis & Sel Topics

Nodal Analysis

∆ to Y and Y to ∆ Conversions

Assignment # 5

19/04/23 3

Steps

Determine the number of nodes within the network

Pick a reference node, and label each remaining node with a

subscripted value of voltage: V1, V2, and so on

Apply Kirchhoff’s current law at each node except the reference

Assume that all unknown currents leave the node for each

application of KCL. Each node is to be treated as a separate

entity, independent of the application of KCL to the other

nodes

Solve the resulting equations for the nodal voltages

The general approach to nodal analysis includes the same

sequence of steps as for dc with minor changes to substitute

impedance for resistance and admittance for conductance in the

general procedure:

Independent Current Sources

Same as above

Dependent Current Sources

Step 3 is modified: Treat each dependent source like an

independent source when KCL is applied. However, take into

account an additional equation for the controlling quantity to

ensure that the unknowns are limited to chosen nodal voltages

Independent Voltage Sources

Treat each voltage source as a short circuit (recall the

supernode classification ), and write the nodal equations for

remaining nodes.

Relate another equation for supernode to ensure that the

unknowns of final equations are limited to the nodal voltages

Dependent Voltage Sources

The procedure is same as for independent voltage sources,

except now the dependent sources have to be defined in terms

of the chosen nodal voltages to ensure that the final equations

have only nodal voltages as the unknown quantities

EXAMPLE - Determine the voltage across the inductor for the

network of Fig

Solution:

KCL at node V1

KCL at node V2

Grouping both equations

Thus the two equations become

Solving the two equations

EXAMPLE - Write the nodal equations for the network of fig

having a dependent current source.

Solution:

Step 3 at Node 1:

EXAMPLE - Write the nodal equations for the network of fig

having a dependent current source.

At Node 1:

Step 3 at Node 2:

EXAMPLE - Write the nodal equations for the network of fig

having an independent source between two assigned nodes.

Solution:

Replacing E1 with short circuit

to get supernode circuit,

Apply KCL at node 1 or 2,

Relate supernode in nodal voltages

Solve both equations

EXAMPLE - Write the nodal

equations for the network of fig

having a dependent voltage source

between two assigned nodes.

Solution:

Replace µVx with short circuit

And apply KCL at node V1:

And apply KCL at node 2:

No eqn for node 2 because V2 is

is part of reference node

Revert to original circuit and make

eqn

Note that because the impedance Z3 is in parallel with a voltage

source, it does not appear in the analysis. It will, however, affect the

current through the dependent voltage source.

Corresponds exactly with that for dc circuits ∆ to Y,

Note that each impedance of the Y is equal to the product of the

impedances in the two closest branches of the ∆ , divided by the

sum of the impedances in the ∆.

Corresponds exactly with that for dc circuits Y to ∆,

Each impedance of the ∆ is equal to sum of the possible product

combinations of impedances of the Y, divided by the impedances

of the Y farthest from the impedance to be determined

Drawn in different forms, they are also referred to as the T

and π configurations

EXAMPLE - Find the total impedance ZT of the network of fig

Solution: Converting the upper

Δ of bridge configuration

to Y.

EXAMPLE - Find the total impedance ZT of the network of fig

EXAMPLE - Find the total impedance ZT of the network of fig

Note: Since ZA = ZB.

Therefore, Z1 =

Z2

EXAMPLE - Find the total impedance ZT of the network of fig

EXAMPLE - Find the total impedance ZT of the network of fig

. Replace the Δ by the Y

EXAMPLE - Find the total impedance ZT of the network of fig

. Solving first for series circuit

EXAMPLE - Find the total impedance ZT of the network of fig

. Resolving Parallels

. Final series solution

Ch 17 - Q 4, Q 8 (a), Q 10, Q 24

Deposit by 09:00 am Monday, 30 Apr 2012.

19/04/23 27

Nodal Analysis

∆ to Y and Y to ∆ Conversions

Assignment # 5

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