Chapter 17 – Methods of Analysis & Sel Topics

Lecture 23

by Moeen Ghiyas

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Independent vs Dependent Sources

Source Conversions

Mesh Analysis

Bridge Networks

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Independent Sources

The term independent specifies that the magnitude of the

source is independent of the network to which it is applied and

that the source displays its terminal characteristics even if

completely isolated.

Dependent (Controlled) Sources

A dependent or controlled source is one whose magnitude is

determined (or controlled) by a current or voltage of the system in

which it appears

Old Symbols

New Symbols

Dependent (Controlled) Sources

Unlike with the independent source, isolation such that V or I = 0

will result in short-circuit or open-circuit equivalent as indicated

Source conversion can be accomplished in much the same

manner as for dc circuits, except now we shall be dealing

with phasors and impedances instead of just real numbers

and resistors

EXAMPLE - Convert the voltage source of fig to a current source

Solution:

EXAMPLE - Convert the current

source of fig to a voltage source

Solution:

For dependent sources, the direct conversion can be

applied if the controlling variable (V or I) is not determined

by a portion of the network to which the conversion is to be

applied

Conversions of the other kind, where V and I are controlled

by a portion of the network to be converted, are covered in

chapter 18 (Not part of syllabus for 2nd semester)

EXAMPLE - Convert the voltage source of fig to a current source

Solution:

Steps

1. Assign a distinct current direction

to each independent, closed loop

2. Indicate the polarities within

each loop for each resistor

(impedance) . Note that the

polarities be placed within each

loop. Thus 4 Ω resistor have two

sets of polarities across it.

Steps

3. Apply Kirchhoff’s voltage law around each closed loop

the total current through the element (impedance) is the assumed

current of the loop plus the assumed currents of the other loops

passing through in the same direction, minus the assumed currents

through in the opposite direction

The polarity of a voltage source is unaffected by the direction of the

assigned loop currents

4. Solve the resulting simultaneous linear equations for the

assumed loop currents

The general approach to mesh includes the same sequence of

steps as for dc except to substitute impedance for resistance and

admittance for conductance in the general procedure with minor

additional changes as mentioned below:

Independent Voltage Sources

Same as dc analysis with impedances and admittance values

Dependent Voltage Sources

Step 3 is modified: Treat each dependent source like an

independent source when KVL is applied. However, once the

equation is written, substitute the equation for the controlling

quantity (i.e an additional eqn is generated for controlling qty)

Independent Current Sources

Treat each current source as an open circuit (recall supermesh

concept), and write mesh equations for remaining paths.

Then relate the chosen mesh currents to the independent

sources to ensure that the unknowns of the final equations are

limited simply to the mesh currents

Dependent Current Sources

The procedure is same as for independent current sources (i.e.

supermesh concept), except now the dependent sources have

to be defined in terms of the chosen mesh currents so that the

final equations have only mesh currents as the unknown qtys.

EXAMPLE - Using the general approach to mesh analysis, find

the current I1 in Fig

Solution

The network is redrawn

Apply KVL,

Loop 1:

+E1 – I1Z1 – I1Z2 + I2Z2 = 0

I1Z1 + I1Z2 - I2Z2 = E1

I1(Z1 + Z2) – I2Z2 = E1 ----- A

Loop 2:

– E2 – I2Z2 + I1Z2 – I2Z3 = 0

– I1Z2 + I2Z2 + I2Z3 = – E2

– I1Z2 + I2(Z2 + Z3) = – E2 ------ B

Solve by determinants

Solve by determinants and then substitute values

I1(Z1 + Z2) – I2Z2 = E1

– I1Z2 + I2(Z2 + Z3) = – E2

EXAMPLE - Write the mesh currents for the network of fig having

a dependent voltage source.

Solution:

EXAMPLE - Write the mesh currents for the network of fig having

a independent current source.

Solution:

Apply supermesh concept

EXAMPLE - Write the mesh currents for the network of fig

having a dependent current source.

Solution:

Problem # 9 – Using mesh analysis, determine the current IL (in

terms of V) for the network of fig

Solution:

Problem # 9 – Using mesh analysis, determine the current IL (in

terms of V) for the network of fig

Solution:

Solving by determinants

Bridge networks with reactive components & ac voltage or current

Maxwell’s Bridge (V source & RC parallel)

From dc we remember, for IZ5 = 0,

the following condition must be met

or

Hay Bridge (I source & RC series)

From dc we remember, for VZ5 = 0,

the following condition must be met

or

or

Hay bridge – when Z5 is replaced by a sensitive galvanometer is

used for measuring the resistance and inductance of coils in

which the resistance is a small fraction of the reactance XL.

Maxwell bridge – when Z5 is replaced by a sensitive galvanometer

is used for inductance measurements when the resistance of the

coil is large enough not to require a Hay bridge.

Another popular bridge is the capacitance comparison bridge

of fig. An unknown capacitance and its associated resistance

can be determined using this bridge.

Independent vs Dependent Sources

Source Conversions

Mesh Analysis

Bridge Networks

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