Chapter 23

Transformers and
Coupled Circuits

Transformer Construction

Transformer is a magnetically coupled circuit

It consists of two coils wound on a common core

Transformer Construction

Power flows from one circuit to the other circuit

Through the medium of the magnetic field

Transformer Construction

There is no electrical connection between the two coils

Coil (winding) on side of the transformer to which we apply power is called primary

Transformer Construction

Coil on side to which we connect the load is called the secondary

Transformer Construction

Iron-core transformers

Generally used for low-frequency applications (such as audio and power)

Iron core provides an easy path for magnetic flux

Transformer Construction

Two basic construction types

Core and shell

Each type uses laminated sheets of metal to reduce eddy currents

Transformer Construction

Air-core and ferrite-core types

Used for high-frequency applications (such as radio frequencies)

Transformer Construction

These do not have high hysteresis and eddy-current losses of iron-core transformers

Ferrite

Increases coupling between coils while maintaining low losses

Transformer Construction

Transformer may be used to change polarity of an ac voltage

Depending on the directions of its windings

Transformer Construction

If most of the flux produced by one of the coils links the other

Coils are tightly coupled

Otherwise loosely coupled

All transformer operations are described by Faraday’s law

Voltage Ratio for Ideal Transformers

If we apply Faraday’s law, where N is the number of turns and f is the flux, then

Voltage Ratio for Ideal Transformers

Ratio of primary voltage to secondary voltage

Equal to ratio of the number of turns

The Turns Ratio

Turns ratio (or the transformation ratio)

a = N_p/N_s

Also, e_p/e_s = a

The Turns Ratio

A step-up transformer

Secondary voltage is higher than the primary voltage (a < 1)

A step-down transformer

Secondary voltage is lower (a > 1)

The Current Ratio

In an ideal transformer

Power in equals power out (η = 100%)

Ratios of the current are

The Current Ratio

If voltage is stepped up

Current is stepped down, and vice versa

Reflected Impedance

A load impedance Z_L connected directly to a source is seen as Z_L

Impedance will be seen by the source differently

If a transformer is connected between the source and the load

Reflected Impedance

Reflected impedance, Z_p, is given by

Z_p = a²Z_L

Reflected Impedance

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

Reflected Impedance

Using a transformer

We can match loads to sources (such as amplifiers)

Relates to the maximum power theorem discussed in a previous section

Transformer Ratings

Transformers are rated in terms of voltage and apparent power

Rated current can be determined from these ratings

Transformer Ratings

By dividing the apparent power rating by the voltage rating

Rated current is determined, regardless of the power factor

Power Supply Transformers

Used to convert the incoming 120 V source to voltage levels required by circuit

Some have a multi-tapped secondary winding to provide different voltages for different applications

Power Supply Transformers

Typically, an incoming voltage is

Stepped down

Rectified

Smoothed by a filter

Passed through a voltage regulator

Transformers in Power Systems

Transformers are used at generating stations to raise voltage for transmission

This lowers losses in the transmission lines

At the user end

Voltage is stepped down

Transformers in Power Systems

Transformers have a split secondary

This permits both 120-V and 240-V loads to be supplied from the same transformer

For residential use

Single phase is used

Isolation Applications

Transformers are sometimes used to isolate equipment

Isolation transformers are often used to make measurements involving high voltages

Isolation Applications

They can also ensure that a grounded metal chassis is not connected to a hot wire

Isolation Applications

Readings can be made on an oscilloscope

Must have a grounded lead without shorting circuit components across ground connections by using a 1:1 transformer

Impedance Matching

A transformer can be used to raise or lower apparent impedance of a load

Impedance matching

Sometimes used to match loads to amplifiers to achieve maximum power transfer

Impedance Matching

If load and source are not matched

A transformer, with the proper turns ratio, can be inserted between them

Autotransformers

In autotransformers

Primary circuit is not electrically isolated from its secondary

They cannot be used as isolation transformers

Autotransformers

Smaller and cheaper than conventional transformers with the same load kVA

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

Practical Iron-Core Transformers

Winding resistance

Core losses due to eddy currents and hysteresis

Magnetizing current

Transformer Efficiency

Efficiency is ratio of output power to input power

Given as a percentage.

Losses

Due to power losses in the windings and in core

Transformer Efficiency

Large transformers can have efficiencies of 98 to 99 percent

Smaller transformers have efficiencies of about 95 percent

Transformer Tests

Losses may be determined by making tests on transformers

Short-circuit tests

Determine losses due to resistance of windings

Open-circuit tests will determine core losses

Voltage and Frequency Effects

As applied voltage increases, core flux increases, causing greater magnetization current

Therefore, transformers should be operated only at or near their rated voltage

Voltage and Frequency Effects

At very low frequencies

Core flux and the magnetizing current increases

Causing large internal voltage drops

At very high frequencies

Stray capacitances and inductances cause voltage drops

Loosely Coupled Circuits

Circuits without an iron core, where only a portion of the flux produced by one coil links another

Cannot be characterized by turns ratios

They are characterized by self- and mutual inductances

Loosely Coupled Circuits

Expressed by coefficient of coupling

Air-core

Ferrite-core transformers

General inductive circuit coupling

Loosely Coupled Circuits

Self-induced voltage in a coil is

v = L di/dt

Mutually induced voltage of a coil is

v = M di/dt

M is mutual inductance between coils

Loosely Coupled Circuits

In each coil

Induced voltage is the sum of its self-induced voltage

Plus voltage mutually induced due to the current in the other coil

Loosely Coupled Circuits

Coefficient of coupling, k

Describes degree of coupling between coils

Mutual inductance depends on k:

Loosely Coupled Circuits

Coupled impedance is


	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
	Coil (winding) on side of the transformer to which we apply power is called primary


	Coil on side to which we connect the load is called the secondary


	Iron-core transformers
		Generally used for low-frequency applications (such as audio and power)
	Iron core provides an easy path for magnetic flux


	Two basic construction types
		Core and shell
	Each type uses laminated sheets of metal to reduce eddy currents


	Air-core and ferrite-core types
		Used for high-frequency applications (such as radio frequencies)


	These do not have high hysteresis and eddy-current losses of iron-core transformers
	Ferrite
		Increases coupling between coils while maintaining low losses


	Transformer may be used to change 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
		Coils are tightly coupled
		Otherwise loosely coupled
	All transformer operations are described by Faraday’s law


	If we apply Faraday’s law, where N is the number of turns and f is the flux, then


	Ratio of primary voltage to secondary voltage
		Equal to ratio of the number of turns


	Turns ratio (or the transformation ratio)
		a = N_p/N_s
	Also, e_p/e_s = a


	A step-up transformer
		Secondary voltage is higher than the primary voltage (a < 1)
	A step-down transformer
		Secondary voltage is lower (a > 1)


	In an ideal transformer
		Power in equals power out (η = 100%)
	Ratios of the current are


	If voltage is stepped up
		Current is stepped down, and vice versa


	A load impedance Z_L connected directly to a source is seen as Z_L
	Impedance will be seen by the source differently
		If a transformer is connected between the source and the load


	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


	Using a transformer
		We can match loads to sources (such as amplifiers)
	Relates to the maximum power theorem discussed in a previous section


	Transformers are rated in terms of voltage and apparent power
	Rated current can be determined from these ratings


	By dividing the apparent power rating by the voltage rating
		Rated current is determined, regardless of the power factor


	Used to convert the incoming 120 V source to voltage levels required by circuit
	Some have a multi-tapped secondary winding to provide different voltages for different applications


	Typically, an incoming voltage is
		Stepped down
		Rectified
		Smoothed by a filter
		Passed through a voltage regulator


	Transformers are used at generating stations to raise voltage for transmission
		This lowers losses in the transmission lines
	At the user end
		Voltage is stepped down


	Transformers have a split secondary
		This permits both 120-V and 240-V loads to be supplied from the same transformer
	For residential use
		Single phase is used


	Transformers are sometimes used to isolate equipment
	Isolation transformers are often used to make measurements involving high voltages


	They can also ensure that a grounded metal chassis is not connected to a hot wire


	Readings can be made on an oscilloscope
		Must have a grounded lead without shorting circuit components across ground connections by using a 1:1 transformer


	A transformer can be used to raise or lower apparent impedance of a load
	Impedance matching
		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