Transformers and Coupled Circuits

1
Lecture 10

• Transformers and Coupled Circuits

2
Transformer Construction

• A transformer is a magnetically coupled circuit.
• It consists of two coils wound on a common core.
• Power flows from one circuit to the other circuit
  through the medium of the magnetic field.
• There is no electrical connection between the two
  coils.
• The coil to which we apply power is called the
  primary the side from which we receive power is
  called the secondary.

3
Transformer Construction

• Iron-core transformers are generally used for
  low-frequency applications (such as audio and
  power).
• The iron core provides an easy path for the
  magnetic flux.
• The two basic construction types are core type
  and shell type.
• Each type uses laminated sheets of metal to
  reduce eddy currents.

4
Transformer Construction

• Air-core and ferrite-core types are used for
  high-frequency applications (such as radio
  frequencies).
• These do not have the high hysteresis and
  eddy-current losses of iron-core transformers.
• Ferrite increases the coupling between the coils
  while maintaining low losses.

5
Transformer Construction

• A transformer may be used to change the polarity
  of an ac voltage depending on the directions of
  its windings.
• If most of the flux produced by one of the coils
  links the other, the coils are tightly coupled
  otherwise they are said to be loosely coupled.
• All transformer operations are described by
  Faradays law.

6
The Voltage Ratio for Ideal Transformers

• If we apply Faradays law, where N is the number
  of turns and ? is the flux, then
• The ratio of the primary voltage to the secondary
  voltage is equal to the ratio of the turns.

7
The Turns Ratio

• The turns ratio (or the transformation ratio) is
  a Np/Ns.
• Also, ep/es a.
• A step-up transformer is one in which the
  secondary voltage is higher than the primary
  voltage (a
• A step-down transformer is one in which the
  secondary voltage is lower (a 1).

8
The Current Ratio

• In an ideal transformer, power in equals power
  out.
• The ratios of the current are
• If the voltage is stepped up, the current is
  stepped down, and vice versa.

9
Reflected Impedance

• A load impedance ZL connected directly to a
  source is seen as ZL.
• This impedance will be seen by the source
  differently if a transformer is connected between
  the source and the load.
• The reflected impedance, Zp, is given by Zp
  a2ZL.

10
Reflected Impedance

• The load characteristics do not change -
  capacitive loads still look capacitive, etc.
• A transformer can make a load look larger or
  smaller, depending on the turns ratio.
• By using a transformer, we can match loads to
  sources.

11
Transformer Ratings

• Transformers are rated in terms of voltage and
  the apparent power.
• Rated current can be determined from these
  ratings.
• By dividing the apparent power rating by the
  voltage rating, the rated current is determined,
  regardless of the power factor.

12
Power Supply Transformers

• Power supply transformers are used to convert the
  incoming voltage levels to the voltage levels
  required by the circuit (load).
• Some have a multi-tapped secondary winding to
  provide different voltages for different
  applications.
• Electronic devices use low level DC voltage. To
  provide for them typically, an incoming voltage
  is stepped down, then rectified, smoothed by a
  filter, and passed through a voltage regulator.

13
Transformers in Power Systems

• Transformers are used at generating stations to
  raise the voltage for transmission (this lowers
  losses in the transmission lines).
• At the user end, the voltage is stepped down.
• For residential use, single phase is used.

14
Isolation Applications

• Transformers are sometimes used to isolate
  equipment.
• Isolation transformers are often used to make
  measurements involving high voltages.
• We can make readings on an oscilloscope that has
  a grounded lead without grounding out the circuit
  by using a 11 transformer.

15
Impedance Matching

• A transformer can be used to raise or lower the
  apparent impedance of a load.
• Impedance matching is sometimes used to match
  loads to amplifiers to achieve maximum power
  transfer.
• If load and source are not matched, a
  transformer, with the proper turns ratio, can be
  inserted between them.

16
Autotransformers

• In autotransformers, the primary circuit is not
  electrically isolated from its secondary.
• They cannot be used as isolation transformers.
• They are smaller and cheaper than conventional
  transformers with the same load kVA.

17
Practical Iron-Core Transformers

• Non-ideal transformers have several effects that
  cause loss of power.
• Leakage flux - will appear as small inductances
  in series with the windings.
• Winding resistance
• Core losses due to eddy currents and hysteresis.
• Magnetizing current.

18
Transformer Efficiency

• Efficiency is the ratio of output power to input
  power, given as a percentage.
• Losses are due to power losses in the windings
  and in the core.
• Large transformers have efficiencies of the order
  of 98 to 99 percent.
• Smaller transformers have efficiencies of about
  95 percent.

19
Transformer Tests

• Losses may be determined by making tests on
  transformers.
• Short-circuit tests will determine the losses due
  to resistance of the windings.
• Open-circuit tests will determine core losses.

20
Voltage and Frequency Effects

• As the applied voltage increases, core flux
  increases, causing greater magnetization current.
• Therefore, transformers should operated only at
  or near their rated voltage.
• At very low frequencies, the core flux and the
  magnetizing current increases, causing large
  internal voltage drops.
• At very high frequencies, stray capacitances and
  inductances cause voltage drops.

21
Loosely Coupled Circuits

• Circuits which have no iron core, where only a
  portion of the flux produced by one coil links
  another, are said to be loosely coupled.
• These circuits cannot be characterized by turns
  ratios instead, they are characterized by self-
  and mutual inductances.
• Air-core and ferrite-core transformers, and
  general inductive circuit coupling fall into this
  category.

22
Loosely Coupled Circuits

• The self-induced voltage in a coil is
• v L di/dt.
• The mutually induced voltage of a coil is
• v M di/dt
• where M is the mutual inductance between the
  coils.
• In each coil, the induced voltage is the sum of
  its self-voltage plus the voltage mutually
  induced due to the current in the other coil.

23
Coupled Coils Equations
24
Loosely Coupled Circuits

• The coefficient of coupling, k, describes the
  degree of coupling between coils.
• Mutual inductance depends on k
• Using coupled impedance the input impedance can
  be determined from