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7/29/2019 05 Useful Circuit Analysis
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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