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Chapter 5

Handy Circuit Analysis Techniques

Prof. SeongHwan ChoDept. of EE, KAIST

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Linear Elements and Circuits

A linear circuit element has a linear voltage-current relationship:

ifi(t) produces v(t), then Ki(t) produces_____

ifi1(t) produces v1(t) and i2(t) produces v2(t), then i1(t) + i2(t)

produces_____________,

resistors, sources are linear elements1

a linear circuit is one with only linear elements

1Dependent sources need linear control equations to be linear elements.

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The Superposition Concept

For the circuit shown, the solution can be expressed as:

Question: How much ofv1

is due to source A, and how much is

because of source B?

We use the superposition principle to answer.

1

2

0.7 0.2

0.2 1.2

a

b

iv

iv

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The Superposition Concept

If we define A asA

0.7 0.2

0.2 1.2

then

v1

v2

A

1ia

ib

A

10

ib

A

1ia

0

Superposition:the response is the sum of experiments A and B.

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The Superposition Theorem

In a linear network, the voltage across or the currentthrough any element may be calculated by adding

algebraically all the individual voltages or currents

caused by the separate independent sources acting

alone, i.e. with

all other independent voltage sources replaced by

_______ circuits and

all other independent current sources replaced by________ circuits.

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Applying Superposition

Leave one source ___ and turn all other sources____:

How to turn off sources:

voltage sources: set v=_____.

These become_______ circuits.

current sources: set i=_____.

These become_______ circuits.

Find the response from this source.

Add the resulting responses

to find the total response.

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Superposition Example

xi

xi

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Superposition with a Dependent Source

When applying superposition to circuits with dependent sources,these dependent sources are never turned off.

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Practical Sources

Ideal voltage sources: a first approximation model for a battery. Why do real batteries have a current limit and experience

voltage drop as current increases?

Practical Battery model:

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Practical Voltage Source

The source has an internal resistance or output resistance,

which is modeled as Rs

______circuit current (when RL=____)

______ circuit voltage (when RL=____)

vL

iL

0

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Practical Current Source

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Practical Current Source

The source has an internal parallel resistance which is modeled as

Rp

_____ circuit current (when RL=___)

_____ circuit voltage (when RL=___)

vL

iL

0

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Source Transformation & Equivalent Sources

The sources are equivalent if

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Source Transformation

The circuits (a) and (b) are equivalent at the terminals.

If given circuit (a), but circuit (b) is more convenient, switch

them!

This process is called source transformation.

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Example: Source Transformation

We can find the current I in the circuit below using sourcetransformation, as shown.

I = (45-3)/(5+4.7+3) = 3.307 mA

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Thvenin Equivalent Circuits

Thvenins theorem: a linear network can be replaced by itsThvenin equivalent circuit, as shown below:

How to find Thevinin Equivalent

1. Source transformation

2. Thevenin Theorem

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Thvenin Equivalent using Source Transformation

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Thvenin Theorem

Disconnect the load. Find the open circuit voltage voc

Find the equivalent resistance Req by applying a _____________

with all independent sources turned off.

Then: VTH=voc and RTH=Req

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Thvenin Equivalent using Thvenin Theorem

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Norton Equivalent Circuits

Nortons theorem: a linear network can be replaced by its Nortonequivalent circuit, as shown below:

How to find Norton Equivalent

1. Source transformation

2. Norton Theorem

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Norton Equivalent using Source Transformation

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Norton Theorem

Replace the load with a short circuit.

Find the short circuit current isc

Find the equivalent resistance Req by applying ____________

with all independent sources turned off.

Then: IN=isc and RN=Req

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Norton Equivalent using Norton Theorem

Use either Norton or Thevenin, (dont do both) as they are basically the samething.

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Example: Norton and Thvenin

Find the Thvenin and Norton equivalents for the network facedby the 1-k resistor.

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Example: Handling Dependent Sources

2 3

4

xv

Source transformation? Theorems?

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Thvenin Ex.: Handling Dependent Sources

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Maximum Power Transfer

What is the maximum power that can be delivered to the load? What load resistor will results in maximum power to the load?

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Maximum Power __________

What is the maximum power that can bedelivered from the practical source?

What is the maximum power efficiency, PL/PS? What load resistor results in maximim power efficiency?

Dont be confused about the term maximum power transfer

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-Y (delta-wye) Conversion

The following resistors form a :

The following resistors form a Y:

Y (d lt ) C i

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-Y (delta-wye) Conversion

this is equivalent to the Y if this Y is equivalent to the if