Chapter 9 Ideal Transformer

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Chapter 9Ideal Transformer
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Ideal Transformer

• Introduction
• Transformers are one of the most useful
  electrical devices ever invented.
• It can raise or lower the voltage or current in
  an ac circuit.
• It can isolate circuits from each other.
• It can change the apparent value of impedance.
• The transformer enables us to transmit electrical
  energy over great distances.

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Eelements of transformer
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Transformer application
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Voltage Induction

• For a coil consisting of N turns placed in a
  variable flux ?, the flux alternates sinusoidally
  at a frequency f, periodically reaching positive
  and negative ?max. The flux induces a sinusoidal
  ac voltage.

• Where
• E effective voltage induced V
• f the frequency of flux Hz
• N number of turns.
• max is the peak value of flux Wb
• (The reason for using peak flux is that it is
  proportional to peak flux density Bmax which in
  iron cores, determine the value of saturation.)

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Applied Voltage Induced Voltage

• Consider a coil connected across an AC voltage
  source Eg.
• The coil and source resistances are negligible.
• The induced voltage E must equal the source
  voltage Eg.
• A sinusoidal AC flux ? must exist to generate the
  induced voltage on the N turns of the coil.
• ?max varies in proportion to Eg.
• Placing an iron core in the coil will not change
  the flux ?.

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Applied Voltage Induced Voltage

• Magnetization current Im drives the AC flux
• The current is 90 out-of-phase and lagging with
  respect to the voltage.
• To produce the same flux a smaller magnetomotive
  force is needed with an iron core than an air
  core. Less magnetizing current is required. So
  with an iron core, less current is needed to
  drive the AC flux.

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Applied Voltage Induced Voltage
Example A coil, having 4000 turns, links an AC
flux with a peak value of 2mWb at a frequency of
60 Hz Calculate the rms value of the induced
voltage What is the frequency of the induced
voltage?   E 4.44 f N ?max E 4.44 x
60 x 4000 x 0.002 E 2131 V The induced voltage
has rms value of 2131 V and a frequency of 60
Hz. The peak voltage is 2131 x v2 3014 V
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Applied Voltage Induced Voltage
Example A coil, having 90 turns, is connected to
a 120 V, 60 Hz source the rms magnetization
current is 4 A. Find a) Peak value of the flux.
b) Peak value the mmf. c)
Inductive reactance of the coil. d)
Inductance of the coil.
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Elementary Transformer

• Consider an air-core coil, excited by an AC
  source Eg, draws a magnetization current Im,
  produces a total flux ?
• A second coil is brought close to the first
• a portion ? m1 of the flux couples the second
  coil, the mutual flux
• an AC voltage E2 is induced
• the flux linking only the first coil is called
  the leakage flux, ? f1

• Improved flux coupling
• concentric windings, iron core
• weak coupling causes small E2

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Elementary Transformer

• The magnetization current Im produces both fluxes
  ?m1 and ?f1
• The fluxes are in-phase
• The voltages Eg and E2 are in-phase
• Terminal orientation such that the
• coil voltages are in-phase and are said to
  possess the same polarity