Rangkaian Ekivalen Thevenin Dan Norton

8/9/2019 Rangkaian Ekivalen Thevenin Dan Norton

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Theveninand Norton

Equivalent Circuitshttp://hyperphysics.phy-

astr.gsu.edu/hbase/electric/thevenin.html

http://www.calvin.edu/~svleest/circuitExamples/Theven

inNorton/http://www.allaboutcircuits.com/vol_1/chpt_10/8.html
http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.allaboutcircuits.com/vol_1/chpt_10/8.htmlhttp://www.allaboutcircuits.com/vol_1/chpt_10/8.htmlhttp://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/http://www.calvin.edu/~svleest/circuitExamples/TheveninNorton/


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Thevenin's Theorem

Any combination of batteries and resistances with two terminals can be replaced

by a single voltage sourceeand a single series resistor r. The value of eis the

open circuit voltage at the terminals, and the value of ris edivided by the current

with the terminals short circuited

Thevenin Equivalent Circuit
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.html


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Thevenin Voltage

The Thevenin voltage VTh.used in Thevenin's Theoremis anideal voltage sourceequal to the open circuit voltage at the terminals. In

the example below, the resistance R2 does not affect this voltage and

the resistances R1 and R3 form a voltage divider
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/voldiv.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/voldiv.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.html


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Thevenin/Norton Resistance

The Thevenin resistance RTh.used in Thevenin's Theoremis the

resistance measured at terminals AB with all voltagesourcesreplaced by short circuits and all current sourcesreplaced

by open circuits. It can also be calculated by dividing the open circuit

voltage by the short circuit current at AB, but the previous method is

usually preferable and gives
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.html


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Examples

Vt= Vo- RoIL
http://upload.wikimedia.org/wikipedia/commons/b/ba/Thevenin_and_norton_step_1.pnghttp://upload.wikimedia.org/wikipedia/commons/b/ba/Thevenin_and_norton_step_1.pnghttp://upload.wikimedia.org/wikipedia/commons/b/ba/Thevenin_and_norton_step_1.pnghttp://upload.wikimedia.org/wikipedia/commons/b/ba/Thevenin_and_norton_step_1.pnghttp://upload.wikimedia.org/wikipedia/commons/b/ba/Thevenin_and_norton_step_1.pnghttp://en.wikipedia.org/wiki/File:Thevenin_step_2.pnghttp://en.wikipedia.org/wiki/File:Thevenin_step_2.pnghttp://en.wikipedia.org/wiki/File:Thevenin_step_2.pnghttp://en.wikipedia.org/wiki/File:Thevenin_step_2.pnghttp://en.wikipedia.org/wiki/File:Thevenin_step_2.pnghttp://en.wikipedia.org/wiki/File:Thevenin_step_4.pnghttp://en.wikipedia.org/wiki/File:Thevenin_and_norton_step_3.pnghttp://en.wikipedia.org/wiki/File:Thevenin_step_2.pnghttp://upload.wikimedia.org/wikipedia/commons/b/ba/Thevenin_and_norton_step_1.png


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Problem 1

Find the Thevenin equivalent with respect to the 7k ohm

resistor.


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Solution 1


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Problem 2

Let's suppose that we decide to

designate R2 as the load resistor

in this circuit

Problem: Determine the

Thevenin equivalent circuit !


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Solution 2We can determine the voltage across

the open load terminals by applying

the rules of series circuits, Ohm's

Law, and Kirchhoff's Voltage Law:


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AC Thevenin's Theorem

Any combination of sinusoidal AC sources and impedances with two

terminals can be replaced by a single voltage sourcee and a single series

impedance z.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.html


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Norton's Theorem

Any collection of batteries and resistances with two terminals is electrically

equivalent to an ideal current sourceiin parallel with a single resistor r. The

value of ris the same as that in the Thevenin equivalentand the current ican

be found by dividing the open circuit voltage by r.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/visource.html


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Norton Current

The value ifor the current used in Norton's Theoremisfound by determining the open circuit voltage at theterminals AB and dividing it by the Norton resistancer.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/norton.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/thevenin.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/norton.html


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Problem 3

2. Find the Norton Equivalent

with respect to the 20uF

capacitor.


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In order to find the Norton Short-circuitcurrent, short the terminalswhere the

capacitor used to be. Since we are finding the

Norton Superposition analysis to find the

current through the short means we solve

several simpler circuits (one for each source.

Since there are three sources, we have threesimpler circuits to solve.

Isc = Isc15 + Isc12 + Isc20

Solution 3

I-Norton


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2). Isc12 = -12V/6k = -2mA

3). Isc20 = 20mA

Isc = Isc15 + Isc12 + Isc20= 2.5mA - 2mA + 20mA= 20.5 mA

1). Isc15 = 15V/6k = 2.5mA


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R Norton = R TheveninIn order to find the Norton Short-circuit current, short the terminals

where the capacitor used to be, since we are finding the Norton


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Mesh-current

analysis to find the

current through the

short.

I3 is the current we are particularly interested in.

Here are the mesh current equations:

KVL for i1:

12k*i1 -1k*i4 -12 = 0KVL for i2:

-15 + 4k*i2 - 4k*i3 = 0

KVL for i3:

-4k*i2 + 10k*i3 -6k*i4 + 12 = 0

KVL for i4: We have trouble writing the voltage

over the current source, so we either must addanother variable, or simply write:

i4 = 20mA

Now solve the system of equations.

Solving the second equation for i2, we get:

i2 = (15 + 4k*i3) / 4k

Now rewrite equation 3, plugging in our formulasfor i2 and i4:

-4k*(15 + 4k*i3)/4k + 10k*i3 - 6k*20mA + 12 = 0

Solve for i3:

-15 - 4k*i3 + 10k*i3 -120 + 12 = 0

i3 = 123/6k = 20.5mA

Rangkaian Ekivalen Thevenin Dan Norton

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