Analysis of coupled ckts'

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Analysis of coupled circuits
Review of EE341- Energy Conversion Ali
Keyhani Coupled magnetic circuits
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Analysis of coupled circuits.

• Voltage sources in both coils.

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• 1. Assume the direction of currents.
• 2. Apply right hand rule to each coil.(ie
  fingers are in the current direction and thumb
  points in the direction of the flux.)
• 3. If the fluxes ?1 and ?2 due to the assumed
  positive current directions aid one another, then
  the signs on voltages of mutual-inductance are
  positive.

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Natural Current

• 1. Assume i1 direction according to V1 polarity.
• 2.Apply right hand rule to determine the
  direction of the Flux ?12.

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• 3. LENZS LAW The polarity of the induced Voltage
  is such that if the circuit is closed, a current
  will pass through the coil in a direction which
  creates a flux opposing the main flux set up by
  current i1.
• The ??21 according to Lenzs Law is opposite to
  ?12
• Now apply the right hand rule with the thumb
  pointing in the direction of ?21, the fingers
  will wrap around coil 2 in the direction of the
  natural current.

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• ?12 opposes ?21,signs of mutual Voltages are
  negative

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• The instantaneous polarity of the voltage of
  mutual inductance at coil two is positive at the
  terminal where the natural current leaves the
  winding

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Dot Rule for Coupled Coils

• 1.Assume a current direction in one coil(ie 1)
  and place a dot at the terminal where this
  current enters the winding.
• 2. Apply right hand rule and find the direction
  of the flux.

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• 3.Second Coil Flux must oppose this flux,
  according to LENZs LAW.
• 4. Use the right hand rule to find the direction
  of the mutual current. Since the Voltage of
  mutual inductance is positive at the terminal
  where this natural current leaves the winding,
  place a dot at this terminal.

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• To Determine the sign of the Voltage of mutual
  inductance
• 1. When both currents enter or leave a pair of
  coupled coils at the dotted terminals, the signs
  of the M terms will be the same as the signs of
  the L terms.
• 2. IF one current enters at a dotted terminal and
  one leaves by a dotted terminal the signs of the
  M terms are opposite to the signs of the L terms.

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Transformers and Coupled Coils

• Dot Notations determination by experiments
• method 1

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• 1) Assume in coil 1 which is connected to
  positive terminal of these battery.
• 2) Close the switch S. Now i1 is directed into
  the dot and di1/dt is positive. Connect a
  voltmeter to terminal of coil 2. If voltmeter
  reads upscale , for increasing i1, then the
  terminal which is connected to side of the
  voltmeter should be dotted.

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If voltmeter measures (v1-v2) then H2 is positive
i.e. dotted terminal, and x2 is positive I.e.
dotted terminal
If voltmeter measures (v1v2) then H2 is positive
i.e. dotted terminal, and x1 is positive i.e.
dotted terminal
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Example
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Step1
For example
Set VS480
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If voltmeter reads
Then, H2 and X2 are dotted terminals H1
and X1 are undotted terminals
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(No Transcript)
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• If voltmeter reads, VM V1V2480120
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  600V
• Then H2 and X1 are the dotted terminals
• H1 and X2 are the undotted terminals