chapter 9 network theorems. 2 superposition theorem total current through or voltage across a...
TRANSCRIPT
![Page 1: Chapter 9 Network Theorems. 2 Superposition Theorem Total current through or voltage across a resistor or branch –Determine by adding effects due to each](https://reader035.vdocuments.us/reader035/viewer/2022062322/56649e985503460f94b9b38f/html5/thumbnails/1.jpg)
Chapter 9
Network Theorems
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Superposition Theorem
• Total current through or voltage across a resistor or branch– Determine by adding effects due to each
source acting independently
• Replace a voltage source with a short
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Superposition Theorem
• Replace a current source with an open
• Find results of branches using each source independently– Algebraically combine results
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Superposition Theorem• Power
– Not a linear quantity– Found by squaring voltage or current
• Theorem does not apply to power– To find power using superposition– Determine voltage or current– Calculate power
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Thévenin’s Theorem
• Lumped linear bilateral network– May be reduced to a simplified two-terminal
circuit – Consists of a single voltage source and
series resistance
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Thévenin’s Theorem
• Voltage source– Thévenin equivalent voltage, ETh.
• Series resistance is Thévenin equivalent resistance, RTh
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Thévenin’s Theorem
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Thévenin’s Theorem• To convert to a Thévenin circuit
– First identify and remove load from circuit
• Label resulting open terminals
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Thévenin’s Theorem
• Set all sources to zero
• Replace voltage sources with shorts, current sources with opens
• Determine Thévenin equivalent resistance as seen by open circuit
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Thévenin’s Theorem
• Replace sources and calculate voltage across open
• If there is more than one source– Superposition theorem could be used
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Thévenin’s Theorem
• Resulting open-circuit voltage is Thévenin equivalent voltage
• Draw Thévenin equivalent circuit, including load
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Norton’s Theorem• Similar to Thévenin circuit
• Any lumped linear bilateral network– May be reduced to a two-terminal circuit – Single current source and single shunt
resistor
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Norton’s Theorem
• RN = RTh
• IN is Norton equivalent current
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Norton’s Theorem
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Norton’s Theorem• To convert to a Norton circuit
– Identify and remove load from circuit
• Label resulting two open terminals
• Set all sources to zero
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Norton’s Theorem• Determine open circuit resistance
– This is Norton equivalent resistance
• Note– This is accomplished in the same manner as
Thévenin equivalent resistance
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Norton’s Theorem• Replace sources and determine current
that would flow through a short place between two terminals
• This current is the Norton equivalent current
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Norton’s Theorem• For multiple sources
– Superposition theorem could be used
• Draw the Norton equivalent circuit– Including the load
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Norton’s Theorem
• Norton equivalent circuit– May be determined directly from a Thévenin
circuit (or vice-versa) by using source transformation theorem
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Norton’s Theorem
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Maximum Power Transfer
• Load should receive maximum amount of power from source
• Maximum power transfer theorem states – Load will receive maximum power from a
circuit when resistance of the load is exactly the same as Thévenin (or Norton) equivalent resistance of the circuit
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Maximum Power Transfer• To calculate maximum power delivered by
source to load– Use P = V2/R
• Voltage across load is one half of Thévenin equivalent voltage
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Maximum Power Transfer• Current through load is one half of Norton
equivalent current
44
22NN
Th
Thmax
RI
R
EP
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Maximum Power Transfer
• Power across a load changes as load changes by using a variable resistance as the load
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Maximum Power Transfer
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Maximum Power Transfer
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Efficiency• To calculate efficiency:
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Substitution Theorem• Any branch within a circuit may be
replaced by an equivalent branch– Provided the replacement branch has same
current voltage
• Theorem can replace any branch with an equivalent branch
• Simplify analysis of remaining circuit
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Substitution Theorem• Part of the circuit shown is to be replaced
with a current source and a 240 shunt resistor– Determine value of the current source
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Substitution Theorem
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Millman’s Theorem• Used to simplify circuits that have
– Several parallel-connected branches containing a voltage source and series resistance
– Current source and parallel resistance– Combination of both
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Millman’s Theorem• Other theorems may work, but Millman’s
theorem provides a much simpler and more direct equivalent
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Millman’s Theorem• Voltage sources
– May be converted into an equivalent current source and parallel resistance using source transformation theorem
• Parallel resistances may now be converted into a single equivalent resistance
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Millman’s Theorem• First, convert voltage sources into current
sources
• Equivalent current, Ieq, is just the algebraic sum of all the parallel currents
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Millman’s Theorem• Next, determine equivalent resistance, Req,
the parallel resistance of all the resistors
• Voltage across entire circuit may now be calculated by:
Eeq = IeqReq
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Millman’s Theorem• We can simplify a circuit as shown:
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Reciprocity Theorem• A voltage source causing a current I in any
branch – May be removed from original location and
placed into that branch
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Reciprocity Theorem• Voltage source in new location will
produce a current in original source location– Equal to the original I
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Reciprocity Theorem• Voltage source is replaced by a short
circuit in original location• Direction of current must not change
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Reciprocity Theorem• A current source causing a voltage V at
any node– May be removed from original location and
connected to that node
• Current source in the new location – Will produce a voltage in original location
equal to V
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Reciprocity Theorem• Current source is replaced by an open
circuit in original location
• Voltage polarity cannot change