ISU EE C.Y. Lee

Chapter 14Transformers

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Objectives

Explain mutual inductanceDescribe how a transformer is constructed and how it worksExplain how a step-up and -down transformer worksDiscuss the effect of a resistive load across the secondary windingDiscuss impedance matching with transformersExplain how the transformer acts as an isolation deviceDescribe a tapped transformer

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Mutual InductanceWhen two coils are placed close to each other, a changing electromagnetic field produced by the current in one coil will cause an induced voltage in the second coil because of the mutual inductance, LM

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Coefficient of CouplingThe coefficient of coupling (k) between two coils is the ratio of the lines of force (flux) produced by one coil linking the second coil (φ1-2) to the total flux produced by the first coil (φ1):

The coefficient of coupling depends on the physical closeness of the coils and the type of core material on which they are woundThe formula for mutual inductance:

LM = k√ L1L2

1

21

φφ −=k

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The Basic Transformer

Source voltage is applied to the primary windingThe load is connected to the secondary winding

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The Basic TransformerThe core (air, ferrite or iron) provides a physical structure for placement of windings and a magnetic path so that the magnetic flux lines are concentrated close to the coils

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Turns Ratio

Turns ratio (n) is defined as the ratio of the number of turns in the secondary winding (Nsec) to the number of turns in the primary winding (Npri)

pri

sec

NNn =

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Direction of Windings

The direction of the windings determines the polarity of the voltage across the secondary winding with respect to the voltage across the primary

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Direction of Windings

Phase dots are used to indicate polarities

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Step-Up Transformers

A transformer in which the secondary voltage is greater than the primary voltage is called a step-up transformerThe 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)

nNN

VV

pri

sec

pri

sec ==

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Step-Up Transformers

Example: The transformer has a turns ratio of 3. What is the voltage across the secondary?

Vsec = (3/1)(120V) = 360 V

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Step-Down Transformer

A transformer in which the secondary voltage is less than the primary voltage is called a step-down transformerThe amount by which the voltage is stepped down depends on the turns ratioThe turns ratio of a step-down transformer is always less than 1

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Step-Down Transformers

Example: The transformer is part of a laboratory power supply and has a turns ratio of 0.2. What is the secondary voltage?

Vsec = (0.2)(120V) = 24 V

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Primary Power Equals Load Power

For an ideal transformer, the power delivered in the secondary equals the power in the primaryIn a real transformer, some power is dissipated in the transformer, so primary power is always greater than secondary powerIn an ideal transformer, power transfer is not related to the turns ratioPpri = VpriIpri = VsecIsec = Psec

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Loading the Secondary Winding

When a load resistor is connected to the secondary winding, there is a current through the resulting secondary circuit because of the voltage induced in the secondary coilThis secondary current results in a primary current

sec

pri

pri

sec

NN

II

=

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Loading the Secondary WindingExample: The two transformers have loaded secondaries. If

the primary current is 100 mA in each case, what is the current through the load?

(a) IL = (1/10)(100mA) = 10 mA(b) IL = (2/1)(100mA) = 200 mA

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Reflected LoadThis reflected load is what the primary source effectively see, and it determines the amount of primary currentThe effective resistance that the primary sees is

LLsec

pripri R

nR

NN

R22

1⎟⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

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Reflected LoadExample: What is the reflected resistance seen by the source

Rpri = (1/4)2(100Ω) = 6.25 Ω

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Impedance MatchingWhen a source is connected to a load, maximum power is delivered to the load when the load impedance is equal to the fixed internal source impedance

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Matching TransformerOne application of transformers is in the matching of a load resistance to a source resistance in order to achieve maximum transfer of power

Lpri Rn

R21⎟⎠⎞

⎜⎝⎛= ( )300175

2

⎟⎠⎞

⎜⎝⎛=

n24

75300

===n

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DC IsolationA transformer does not pass dc, therefore a transformer can be used to keep the dc voltage on the output of an amplifier stage from affecting the bias of the next amplifierThe ac signal is coupled through the transformer between amplifier stages

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Tapped Transformers

The center tap (CT) transformer is equivalent to two secondary windings with half the voltage across each

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Tapped TransformersPower company step down the high voltage from the power line to 100V/220V service for residential and commercial customers

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Summary

There is mutual inductance between two magnetically coupled coilsWhen current in one coil changes, voltage is induced in the other coilThe primary is the winding connected to the source, and the secondary is the winding connected to the loadThe number of turns in the primary and the number of turns in the secondary determine the turns ratio

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Summary

The relative polarities of the primary and secondary voltages are determined by the direction of the windings around the coreA step-up transformer has a turns ratio greater than 1A step-down transformer has a turns ratio less than 1In an ideal transformer, the power from the source (input power) is equal to the power delivered to the load (output power)If the voltage is stepped up, the current is stepped down, and vice versa

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Summary

A load across the secondary winding of a transformer appears to the source as a reflected load having a value dependent on the reciprocal of the turns ratio squaredAn impedance-matching transformer can match a load resistance to an internal source resistance to achieve maximum power transfer to the load by selecting the proper turns ratioA typical transformer does not respond to dc