Inductance - Oakton Community College · 19 -5: Mutual Inductance LM Calculating LM Mutual inductance increases with higher values for primary and secondary inductances. LM where
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Topics Covered in Chapter 19Topics Covered in Chapter 19
19-7: Transformer Ratings
19-8: Impedance Transformation
19-9: Core Losses
19-10: Types of Cores
19-11: Variable Inductance
19-12: Inductances in Series or Parallel
19-13: Energy in Magnetic Field of Inductance
19-14: Stray Capacitive and Inductive Effects
19-15: Measuring and Testing Inductors
McGraw-Hill
1919--1: Induction by 1: Induction by
Alternating CurrentAlternating Current
Induced voltage is the result of flux cutting across a conductor.
This action can be produced by physical motion of either the magnetic field or the conductor.
Variations in current level (or amplitude) induces voltage in a conductor because the variations of current and its magnetic field are equivalent to the motion of the flux.
Thus, the varying current can produce induced voltage without the need for motion of the conductor.
A change in current induces an EMF that opposes the change in current .This ability is called self-inductance, or simply
1919--1: Induction by 1: Induction by
Alternating CurrentAlternating Current
Induction by a varying current results from the change in current, not the current value itself. The current must change to provide motion of the flux.
The faster the current changes, the higher the induced voltage.
Fig. 19-1: Magnetic field of an alternating current is effectively in motion as it expands and
contracts with the current variations.
At point A, the current is zero and there is no flux.
At point B, the positive direction of current provides some field
lines taken here in the counterclockwise direction.
1919--1: Induction by 1: Induction by
Alternating CurrentAlternating Current
Point C has maximum current and maximum counterclockwise flux.
At point D there is less flux than at C. Now the field is collapsing
because of reduced current.
1919--1: Induction by 1: Induction by
Alternating CurrentAlternating Current
Point E with zero current, there is no magnetic flux. The field can be
considered collapsed into the wire.
The next half-cycle of current allows the field to expand and collapse
again, but the directions are reversed.
When the flux expands at points F and G, the field lines are clockwise.
From G to H and I, this clockwise field collapses into the wire.
1919--1: Induction by 1: Induction by
Alternating CurrentAlternating Current
Characteristics of inductance are important in:
AC circuits: In these circuits, the current is continuously changing and producing induced voltage.
DC circuits in which the current changes in value: DC circuits that are turned off and on (changing between zero and its steady value) can produce induced voltage.
1919--2: Self2: Self--InductanceInductance LL
The symbol for inductance is L, for linkages of magnetic flux.
VL is in volts, di/dt is the current change in amperes per second.
The henry (H) is the basic unit of inductance.
One henry causes 1 V to be induced when the current is changing at the rate of 1 A per second.
L = VL
di / dt
1919--2: Self2: Self--InductanceInductance LL
Inductance of Coils
The inductance of a coil depends on how it is wound.
A greater number of turns (N) increases L because more voltage can be induced (L increases in proportion to N).
More area enclosed by each turn increases L.
The L increases with the permeability of the core.
The L decreases with more length for the same number of turns, as the magnetic field is less concentrated.
1919--2: Self2: Self--InductanceInductance LL
Where: L is the inductance in henrys.
µris the relative permeability of the core
N is the number of turns A is the area in square meters l is the length in meters
The coefficient of coupling is increased by placing the coils close together, possibly with one wound on top of the other, by placing them parallel, or by winding the coils on a common core.
A high value of k, called tight coupling, allows the current in one coil to induce more voltage in the other.
Loose coupling, with a low value of k, has the opposite effect.
Two coils may be placed perpendicular to each other and far apart for essentially zero coupling to minimize interaction between the coils.
Manufacturers always specify the voltage rating of the primary and secondary windings.
Under no circumstances should the primary voltage rating be exceeded.
In many cases, the rated primary and secondary voltages are printed on the transformer.
Regardless of how the secondary voltage is specified, the rated value is always specified under full load conditions with the rated primary voltage applied.
Typical ratings for a power transformer are 50, 60, and 400 Hz.
A power transformer with a frequency rating of 400 Hz cannot be used at 50 or 60 Hz because it will overheat.
Many power transformers are designed to operate at either 50 or 60 Hz.
Power transformers with a 400-Hz rating are often used in aircraft because these transformers are much smaller and lighter that 50- or 60-Hz transformers.
Transformers are used when it is necessary to achieve maximum transfer of power from a generator to a load when the generator and load impedances are not the same.
This application of a transformer is called impedance matching.
Fig. 19-21: Cross-sectional view of iron core showing eddy currents.
1919--9: Core Losses9: Core Losses
Hysteresis losses
The hysteresis losses result from the additional power needed to reverse the magnetic field in magnetic materials in the presence of alternating current.
The greater the frequency, the more hysteresis loss.
Air-core coils
Air has practically no losses from eddy currents or hysteresis.
The inductance for small coils with an air core is, however, limited to low values (e.g. mH or µH).
1919--10: Types of Cores10: Types of Cores
Losses can be reduced by using a laminated core or a powered-iron core.
The type of steel used can reduce hysteresis losses.
The most common types of insulation are:
Laminated core
Powdered iron core
Ferrite core
1919--10: Types of Cores10: Types of Cores
Laminated core
A shell-type core formed with a group of individual laminations.
Each laminated section is insulated by a very thin coating of iron oxide.
Powdered iron
Consists of individual insulated granules pressed into one solid form called a slug.
Ferrite core
Synthetic ceramic materials that are ferromagnetic.
Fig. 19-28: Inductances L1 and L2 in series but with mutual coupling LM. (a) Aiding magnetic
fields. (b) Opposing magnetic fields.
The coupling depends on the coil connections and direction of
winding. Reversing either one reverses the field.
1919--12: Inductances in 12: Inductances in
Series or ParallelSeries or Parallel
To calculate the total inductance of two coils that are series-connected and have mutual inductance,
LT = L1 + L2 ±2LM
The mutual inductance LM is plus, increasing the total inductance, when the coils are series-aiding, or minus when they are series-opposing to reduce the total inductance.
1919--13: Energy in Magnetic 13: Energy in Magnetic
Field of InductanceField of Inductance
The magnetic flux of current in an inductance has electric energy supplied by the voltage source producing the current.
The energy is stored in the field, since it can do the work of producing induced voltage when the flux moves.
The amount of electric energy stored is
Energy = ε = ½ LI2
The factor of ½ gives the average result of I in producing energy.
1919--14: Stray Capacitive and 14: Stray Capacitive and
Inductive EffectsInductive Effects
Stray capacitive and inductive effects can occur in all circuits with all types of components.
A capacitor has a small amount of inductance in the conductors.
A coil has some capacitance between windings.
A resistor has a small amount of inductance and capacitance.
1919--14: Stray Capacitive and 14: Stray Capacitive and
Inductive EffectsInductive Effects
A practical case of problems caused by stray L and C is a long cable used for rf signals.
If the cable is rolled in a coil to save space, a seriouschange in the electrical characteristic of the line will take place.
For twin-lead or coaxial cable feeding the antenna input to a television receiver, the line should not be coiled because the added L or C can affect the signal.
1919--14: Stray Capacitive and 14: Stray Capacitive and