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Chapter 14 - Transformers

electronics fundamentalscircuits, devices, and applications

THOMAS L. FLOYDDAVID M. BUCHLA

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• When two coils are placed close to each other:1. a changing flux in one coil will cause an

induced voltage in the second coil. • Electrical isolation – condition in which two

circuits have no common conductive path.• Mutual inductance (LM) determines the amount of

voltage induced in the second coil based on the amount of current in the first coil.

Mutual Inductance

LM

k

1 2L1 L2

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Mutual Inductance

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LM

1 2L1 L2

k

1 2ML k L L k = the coefficient of coupling (dimensionless)L1, L2 = inductance of each coil (Henry)

• The coefficient of coupling depends on:1. orientation of the coils to each other, 2. their proximity, and 3. if they are on a common core.

Mutual Inductance

• The coefficient of coupling is a measure of how well the coils are linked; it is a number between 0 and 1.

1

21

k - Flux (Wb)

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Example 1: Two coils are wound on a single core, and the Coefficient of coupling is 0.3. The inductance of coil 1 is 10µH, and the inductance of coil 2 is 15µH. What is Lm?

Example 2: Determine the coefficient of coupling whenLM = 2µH, L1 = 16µH, L2 = 4µH.

1 2ML k L L

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Transformer1. Electrical device constructed of two or more

coils of wire (windings)2. Electromagnetically coupled to each other3. With a mutual inductance to transfer power from

one coil to the other coil

Basic Transformer

Air core Ferrite core Iron core Small power transformer

Schematic symbols indicate the type of core.

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Basic Transformer

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Basic Iron Core Transformer

Core Type - Easy to insulate

Shell Type – higher core flux thus less turns are required

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Transformers with cylindrical-shaped cores.

Usually used for high frequency applications

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Some common types of transformers

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Ratio of turns in the secondary winding (Nsec) to the number of turns in the primary winding (Npri)

Turns ratio

sec

pri

Nn

N

Nsec = number of secondary windings

Npri = number of primary windings* Based on the IEEE dictionary definition for electronics power transformers.

Most transformers are not marked with turns ratio.

A transformer has 800 turns on the primary and a turns ratio of 0.25. How many turns are on the secondary? 200

n = turns ratio

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Determines the polarity of the voltage across the secondary winding with respect to the voltage across the primary. Phase dots are sometimes used to indicate polarities.

Direction of windings

In phase Out of phase

Phase Dots

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For any transformer:The ratio of secondary voltage (Vsec) to primary voltage (Vpri) is equal to the ratio of the number of turns in the secondary winding (Nsec) to the number of turns in the primary winding (Npri),

Step-up and Step-down transformers

pripri N

N

V

V secsec

prinVV sec

n = turns ratio

pripri

VN

NV

secsec

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120 Vrms

Vpri

In a step-up transformer, the secondary voltage is greater than the primary voltage and n > 1.

Step-up and step-down transformers

In a step-down transformer, the secondary voltage is less than the primary voltage and n < 1.

What is the secondary voltage?

4:1

?30 Vrms

What is the turns ratio? 0.25

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• A special transformer with a turns ratio of 1 is called an isolation transformer.

• Because the turns ratio is 1, the secondary voltage is the same as the primary voltage

• ac is passed from one circuit to another.

Isolation transformers

• The isolation transformer breaks the dc path between two circuits while maintaining the ac path.

• The dc is blocked by the transformer, because magnetic flux does not change with dc.

Isolation transformer

1:1

120 Vac 120 Vac

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• Transformers cannot increase the applied power. • If the secondary voltage is higher than the primary

voltage, then the secondary current must be lower than the primary current.

• If the secondary voltage is less than the primary voltage, then the secondary current must be higher than the primary current.

Current

Ppri=VpriIpri Psec=VsecIsecIdeally

Ppri must always equal Psec

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Current

pri

sec

In

I

The ideal transformer turns ratio equation for current is

Notice that the primary current is in the numerator.

• The ideal transformer does not dissipate power. • Power delivered from the source is passed on to the load

by the transformer.

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Non-ideal transformers

Winding resistance (causing power to be dissipated in the windings.)

Hysteresis loss (due to the continuous reversal of the magnetic field.)

Core losses due to circulating current in the core (eddy currents).

Winding capacitance that has a bypassing effect for the windings.

Flux leakage where boundary flux from the primary that does not link to the secondary

Operational losses occur due to:

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• The power-handling capacity of a transformer is dependent upon its ability to dissipate heat.

• If the heat can safely be removed, the power-handling capacity of the transformer can be increased.

• This is sometimes accomplished by immersing the transformer in oil, or by the use of cooling fins or both.

• The power-handling capacity of a transformer is measured in either the volt-ampere unit or the watt unit.

Power Ratings

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Transformer efficiency

The efficiency of a transformer is the ratio of power delivered to the load (Pout) to the power delivered to the primary (Pin).

100%out

in

P

P

120 Vrms

Vpri

What is the efficiency of the transformer?

RL

100 W

15 Vrms

20 mA

eta

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100%out

in

P

P

120 Vrms

Vpri

What is the efficiency of the transformer?

RL

100 W

15 Vrms

20 mA

2215 V100 100% 100% 94%

120 V 0.020 A

L

L

pri pri

VR

V I

W

94%

Transformer efficiency

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Example 2

• Example 2: You have a transformer that’s primary power is 150W. If 10.5 W are dissipated in the winding resistances, what is the output power to the load, neglecting any other losses?

• What is the efficiency of the above transformer?

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Tapped and multiple-winding transformers

• It is possible to use multiple taps (connection points) on a transformer to achieve different voltage ratings.

• Can be either on the primary side or the secondary side or both.

Secondary with center-tap

Primary with multiple-windings

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Tapped and multiple-winding transformers

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Tapped and multiple-winding transformers

Different taps, on the primary side, determine the voltage delivered to the customer.

Transformer

Distributionor breaker box

Building

Serviceentrance

Earthground

7200 V

120 V

120 V

120 V240 V

120 V

CT

The center-tapped secondary allows household wiring to select either 120 V or 240 V.

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Tapped and multiple-winding transformersTapped and multiple-winding transformers

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Three-phase transformers

• Three-phase power is used for power transmission and industrial applications.

• Voltages in a three-phase system can be transformed with1. three identical single phase transformers or 2. one three-phase transformer.

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Three-phase transformers

Three-phase transformers are wired in either a wye or a delta configuration or a combination of both.

This transformer is a wye-to-delta configuration, which is generally used in step down cases.

The delta-wye (not shown) is generally used in step up cases.

Three-phasewye to deltatransformer

Vpri Vsec

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Three-phase transformer combinations

Delta to Wye

Delta to Delta

Wye to Delta

Wye to Wye

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Converting three-phase utility voltages to single-phase residential

voltages.

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Mutual inductance

Transformer

Primary winding

Secondary winding

The inductance between two separate coils, such as in a transformer.

An electrical device constructed of two or more coils that are magnetically coupled to each other so that there is mutual inductance from one coil to the other.

The input winding of a transformer; also called primary.

The output winding of a transformer; also called secondary.

Selected Key Terms

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Magnetic coupling

Turns ratio

Reflected resistance

Impedance matching

The ratio of the turns in the secondary winding to the turns in the primary winding.

The resistance of the secondary circuit reflected into the primary circuit.

The magnetic connection between two coils as a result of the changing magnetic flux lines of one coil cutting through the second coil.

Selected Key Terms

A technique used to match a load resistance to a source resistance in order to achieve maximum transfer of power.

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Quiz

2. A step-up transformer refers to one in which

a. the voltage across the secondary is higher than the primary.

b. the current in secondary is higher than the primary.

c. the power to the load is higher than deleivered to the primary.

d. all of the above.

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Quiz

3. An isolation transformer

a. blocks both ac and dc.

b. blocks ac but not dc.

c. blocks dc but not ac.

d. passes both ac and dc.

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Quiz

4. If the current in the secondary is higher than in the primary, the transformer is a

a. a step-up transformer.

b. an isolation transformer.

c. a step-down transformer.

d. not enough information to tell.

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Quiz

5. An ideal transformer has

a. no winding resistance.

b. no eddy current loss.

c. power out = power in.

d. all of the above.

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Quiz

7. A transformer that can deliver more power to the load than it receives from the source is a(n)

a. step-up type.

b. step-down type.

c. isolation type.

d. none of the above.

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Quiz

10. A transformer that could be used for 110 V or 220 V operation is a

a. multiple-winding type.

b. center-tapped type.

c. isolation type.

d. all of the above.