Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications

13-2

REFERENCE

DATA

FOR ENGINEERS

Wideband Transformers

13-15

Core-Material Considerations

Design Example for Carrier Frequencies

High-Frequency Wideband Transformers

Pulse Transformers

13-17

Magnetic-Core Reactors

13-18

Rectifier-Filter Reactors

AC-Filter Reactors

Magnetic-Core Inductors

13-19

Audio-Frequency Inductors

Precision Adjustable Inductors

MAGNETIC-CORE TRANSFORMERS AND REACTORS

13-3

INTRODUCTION

Definition of Transformer and

Inductor

Magnetic-core transformers are static devices con-

taining magnetically coupled windings. They are used

in power systems to change values of voltage and current

at a single frequency. In communications circuits, often

over a wide band of frequencies, they are used to

provide direct-current isolation, signal splitting and

combining functions, specific current or voltage ratios,

impedance matching, and phase inversion.

The Institute of Electrical and Electronics Engineers,

Inc. (IEEE) has defined a transformer as follows:

“A

static device consisting of a winding, or two or more

coupled windings, with or without a magnetic core, for

introducing mutual coupling between circuits. Note:

Transformers

are

extensively used in electric power

systems to transfer power by electromagnetic induction

between circuits at the same frequency, usually with

changed values of voltage and current.”*

Magnetic-core inductors and reactors are static de-

vices containing one or more windings to introduce

inductance into an electric circuit. Reactors are used in

power circuits primarily to filter alternating current

from direct current. Inductors are used in communica-

tions systems primarily in frequency-selective circuits.

In this chapter, only those devices having magnetic

cores will be considered. The type of core material is

known as

soft

magnetic material, which is defined

as

ferromagnetic material which, once having been mag-

netized, is very easily demagnetized (Le., requires only

a slight coercive force to remove the resultant magnet-

ism). A ferromagnetic material usually has relatively

high values of specific permeability, and it exhibits

hysteresis. The principal ferromagnetic materials

are

iron, nickel, cobalt, and certain of their alloys.?

Transformer Types and

Frequency Ranges

The major types

of

transformers for both power and

communications applications are listed below, along

with the general operating frequencies for each type.

Power

Power transformers 50,

60,

and

400

Hz

Ferroresonant transformers

SO,

60,

and

400

Hz

Converter transformers

100

Hz to 150 kHz

Communications

Audio-frequency trans-

20

Hz

to

20

kHz

Carrier-frequency trans-

20

kHz to

20

formers

formers MHz

*

Reference

1.

t

Reference

2.

High-frequency trans-

Pulse transformers

formers

Inductor Types

Ranges

20

MHz to

1000

MHz

Repetition rates

to

4

MHz

and Frequency

The major types of reactors or inductors are rectifier-

filter reactors, alternating-current reactors, audio-

frequency inductors, and precision adjustable inductors

for filters. Inductors are used from

20

Hz to

1000

MHz

or higher.

Generalized Equivalent Circuit

for a Transformer

Fig. 1 shows the equivalent circuit for a generalized

transformer having two windings. Commonly accepted

nomenclature” is as follows:

a

=

turns ratio

=

N,/N,

Cp

=

primary equivalent shunt capacitance

C,

=

secondary equivalent shunt capacitance

E,

=

root-mean-square generator voltage

E,,,

=

root-mean-square output voltage

k

=

coefficient of coupling

1,

=

primary leakage inductance

1,

=

secondary leakage inductance

L,

=

primary inductance

R,

=

core-loss equivalent shunt resistance

R,

=

generator impedance

RI

=

load impedance

R,

=

primary-winding resistance

R,

=

secondary-winding resistance

POWER TRANSFORMERS

Power transformers operate from a low source imped-

ance at a low frequency. Depending on the source of

power, the frequency may vary as much as 25.5% at

SO

or

60

Hz, and as much as

?20%

at

400

Hz.

Types of Magnetic Cores

The magnetic cores used for power transformers are

usually

E

and

I

laminations stamped from silicon-iron

sheet when low cost is of primary importance. When

__

*

Reference

3.

Fig.

1.

Equivalknt network

of

a transformer.

minimum size or low

loss

is of greatest concern,

wound-cut “C” cores of oriented silicon steel or the

more expensive Supermendur could be considered.

Table

1

lists basic properties of soft magnetic

materials. Table 2 gives the maximum-flux-density

operating conditions for various core materials at 60

and

400

hertz. Two types of laminations are listed as

typical, although there are more types that are of both

a

higher and lower grade. The

0.014

M-6 material is of a

higher grade than the

0.0185

M-19 material, but the

cost of the former may be 50% more per pound than the

cost of the latter, depending on the lamination size

chosen. On the other hand, less of the better-grade

material is required for the same performance. In a

recent study,* it was shown that transformers and

reactors constructed of the higher-grade materials were

always smaller,

as

expected, but that in some cases the

total material cost

of

the structures having the better-

grade laminations was the lowest.

Wound-cut

‘‘e”

cores are wound in tape form on a

rectangular mandrel, impregnated, and cut into halves.

These halves are then banded around the wound trans-

former coil.

The sheet-form magnetic materials may also be made

in thin strip form and supplied as toroidal tape-wound

bobbin cores for high frequencies. The

79

permalloy in

0.000

125-inch tape thickness on a bobbin core may be

-

*

Reference

4.

Material

used at frequencies as high as 1 MHz. These cores are

not cut into halves.

Tables

1

and

2

make reference to “Metallic Glass.”

METGLAS? is Allied Corporation’s registered trade-

mark for amorphous alloys of metals. This material is

new to the list of available core materials. Its advantage

is low core

loss

and exciting volt-amperes.

It

is currently

manufactured in ribbon form with a nominal thickness

of

0.0011

inch and widths of

1.0

to

4.0

inches. The

material can be stamped into laminations, but the form

lends itself best to tape-wound cores. METGLAS

material was originally developed for low-frequency

power transformers at a commercially competitive price

compared with the standard Si-Fe material. The gen-

eral-purpose alloy with the formulation Fesl

B,,,,

Si3.,

Cz, known as Alloy 2605SC, is specified in Tables

1

and 2. Other alloys are available.

The approximate number of exciting volt-amperes is

largely dependendent on the air gap or equivalent air

gap in series with the magnetic path. The values

specified in Table 2 are for the material exclusive of the

air gap. Information on core loss and exciting volt-

amperes for specific lamination sizes may be obtained

from Thomas and Skinner.**

Similar information for cut-cores may be obtained

from catalogs of the Arnold Engineering

Co.

Initial

Permeability

t

Reference

5.

**

Reference

6.

Sheet Form

SiFe (Unoriented)

SiFe (Oriented)

50-50

NiFe

(Oriented)

79

Permalloy

Supermendur

Metallic Glass

(cO49

Fe49

Vd

(Fe81

B13.5

c2)

Bonded Powder

Permalloy Powder

Iron

Powder

Ferrite-MnZn

Ferrite-NiZn

TABLE

1.

PROPERTIES

OF

SOFT

MAGNETIC MATERIALS

400

1500

2000

12

000

to

100

000

800

2000

14

to

550

5

to

80

750

to

15

000

10

to

1500

,

Form

Specific

Gravity

Curie

Temp.

(“C)

Operating

Resistivity Frequency

20

16

8

to

11

23

16

3

10

3

to

5

3

to

5

7.65

8.25

8.74

8.15

7.32

4.5

to

5.2

3.7

to

5.3

740

360

450

980

370

450

770

100

to

300

150

to

450

47x104

50X

lo-‘

40X

lo-‘

55X

26X10-6

125X

60

to

1000

60

to

1000

60

to

1000

lk

to

75k

60

to

5000

60

to

lOOk

I

l.O

I

lokto200k

I

lo4

lOOk

to

lOOM

I

::

I

lek

to

2M

100

106

200k

to

lOOM

Sources:

Allegheny

Ludlum, Allied Corp.,

Armco,

Arnold Engineering, Indiana General, Magnetics

MAGNETIC-CORE TRANSFORMERS AND REACTORS

Freq

.

(Hz)

60

400

TABLE

2.

MAXIMUM-FLUX-DENSITY OPERATING CONDITIONS

FOR

CORE MATERIALS

AT

60

AND

400

HZ

Material

Thickness

(Inches)

0.0185

0.014

0.012

0.004

0.001

1

0.004

0.001

1

Core Material

M-19 Nonoriented

Laminations

M-6 Oriented

Laminations

Silectron

Wound-Cut Core

Supermendur

Wound-Cut Core

Metallic-Glass

Wound-Cut Core

Silectron

Wound-Cut Core

Supermendur

Wound-Cut Core

Metallic-Glass

Wound-Cut Core

Sources:

Allied

Corp.,

Arnold

Engineering,

U.S.

Steel

*

Exciting

VA

values

are

for

the

material

exclusive

of

the

air gap.

Design of Power Transformers

for Rectifiers

The design of transformers for rectifiers was chosen

as an example because it represents one of the more

difficult transformer design problems. The reason it is

difficult is that all parts of all windings

are

not operating

continuously with a sinusoidal current. The result is that

the capability of the transformer structure is not as fully

utilized as it would be if the transformer supplied a

nonrectified resistive load.

An

early paper by

R.

W.

Armstrong* gave the effective, or rms, values of voltag-

es and currents for the primary and secondary windings

of a transformer that provides the power for various

types of single-phase and polyphase rectification fol-

lowed by a reactor-input filter. Table

3

lists single-phase

rectifier transformer ratings for both inductive

(L)

and

resistive (R) filter inputs.

A

more comprehensive listing

of all the circuit parameters of these single-phase as

well as polyphase rectifier circuits is found in Chapter

14

of this book. Should the input to the filter be

capacitive, higher rms values of current appear in the

secondary winding, resulting in a higher volt-ampere

rating.

A

detailed analysis of the effect

of

the capacitor-

input filter on the transformer-winding voltage and

current requirements was made by

0.

H.

Schade in

1943."

More recent analyses have been made by

R.

Lee** and

N.

R.

Gr0ssner.t

__

*

Reference

7.

i

Reference

8.

?

Reference

9.

**

Reference

10.

Core Flux

Density

B,

(kG)

12

15

16

21

14

15

20

14

Approx.

Core Loss

(Wilb)

1

.o

0.65

1.1

0.14

10.0

7.0

1.6

13-5

Approx

.

Exciting

VA*

(VNlb)

3.3

0.83

4.0

0.16

15.0

30.0

1.82

The first step in designing a transformer

is

to

determine its volt-ampere

(VA)

rating.

In

the case of the

transformer for a rectifier,

where,

VAT

may be obtained from Table

3,

Edc'

is the sum of the output dc voltage

(Edc),

the

diode drop (Edd), and the reactor drop (Erd).

In the case of the bridge rectifier, the current passes

through two diodes

on

each half cycle, and it is

necessary to use the value of two diode drops in the

calculation of

Edc'.

At this point, it is handy to have a table of

VA

ratings

versus lamination sizes, such as Table

4.

Note the

constraints of the 60-Hz frequency and the

75

"C

winding temperature rise in

an

ambient of

75

"C. If a

lower frequency or temperature rise is required, then the

VA

average will be lower for a given structure, with

other parameters also being affected. It might also be

noted that if a bobbin type of construction is used on the

smaller structures instead of a layer-wound construction

with interlayer insulation, then up to

30%

more copper

may be used in a given structure, resulting in up to

30%

more

VA

average at the same frequency and temperature

rise. The above calculated

VA

rating may be used to

select a suitable structure from Table

4.

In order to determine the number of turns and wire

size of each winding, it is first necessary to determine

the voltage and current for each winding. Table

3

gives

the relationships between the rms voltages and currents

and the dc voltages and currents. The value of Edc'

13-6

REFERENCE

DATA

FOR ENGINEERS

TABLE

3.

*

SINGLE-PHASE RECTIFIER TRANSFORMER RATINGS*

*

Half-

Wave

R

Input

Full-Wave

,

Center-Tapped

R

Input

Ripple frequency

.

Ripple

V,,

. .

.

Ripple

V,,

total$.

. .

Primary

E,

.

. . .

Primary

I,

.

. .

Primary VA..

.

Secondary

E,.

. .

Secondary

I,

.

Secondary

VA

.

. .

.

Average

VAT

.

PIV per Diode.

. .

.

I,,

per Diode.

.

. .

.

I,

per Diode.

. .

,

.

I,,

per Diode

. . .

.

f

1.11

1.21

2.22

1.21

2.69

2.22

1.57

3.49

3.09

3.14

1

.oo

1.57

2f

0.471

0.482

1.11

1.23

l.llt

0.785

1.74

1.49

3.14

1.57

0.50

0.785

__

L

Input

2f

0.471

0.482

1.11

1

.oo

1.11

l.llt

0.707

1.57

1.34

3.14

1

.oo

0.50

0.707

Bridge

R

Input

2f

0.471

0.482

1.11

1.23

1.11

1.23

1.57

0.50

0.785

*

From

N.

R. Grossner,

Transformers and Electronic Circuifs

(New York: McGraw-Hill

Book

Co.,

1967).

**

Voltages, currents,

and

VA

are based on unity dc output voltage

and

current. Voltage drops

in

transformer, diode,

and

7

Secondary voltage

at

each side of center tap.

f

Includes second and third harmonics

of

ripple frequency

inductor are neglected.

calculated above is used for the dc voltage. The primary

voltage,

E,,,

is determined by the specified input volt-

age. The primary

rms

current,

I,,,

is determined as

follows:

I,,

=

[(VA) (Primary

VA)]/[(Efficiency)(E,,)]

The quantities “primary VA” and “efficiency” are

obtained from Tables

3

and

4,

respectively. The secon-

dary rms voltage,

E,,

and the secondary rms current,

I,,

are obtained from the following relationships:

E,

=

(Secondary

,?,)(Edc‘)

I,

=

(Secondary

Is)(Idc)

The quantities “Secondary

E,”

and “Secondary

I,”

are obtained from Table

3.

Now the number of turns in each winding can be

calculated. The number of primary-winding turns,

Np,

is obtained as follows:

Np

=

(E,,

X

105)/(4.44

X

f

X

A,

X

B,)

wherefis the frequency

of

the applied voltage, which is

assumed to be sinusoidal. If the applied voltage has

other than a sinusoidal waveform, then the

4.44

con-

stant must be changed. An ASTM standard explains

this.* The quantity

A,

is the area of the core, and

B,,,

is

-

*

Reference

11

the core flux density. If the metric unit the kilogauss

(kG) is used, as listed in Table

4,

then

A,

must be in

square centimeters. If

B,

is in kilolines per square inch,

then the units of

A,

must be square inches. The

A,

of

the structure selected from Table

4

may be computed by

squaring the specified tongue width (in the appropriate

units) and multiplying by the core manufacturer’s

recommended stacking factor. Although Table

4

struc-

tures are

all

square stacks (Le., the stack height equals

the tongue width), the stack heights are often increased

or decreased for a larger or smaller VA rating.

The number of secondary-winding turns,

N,,

is

obtained as follows:

N,

=

N,,(E,/E,,)[I

+

(Copper Regulation

/

loo)]

where “Copper Regulation” (in percent)

is

obtained

from Table

4.

The wire sizes for each winding are determined by

dividing the current calculated for the winding by the

current density specified in Table

4.

This determines the

cross-sectional area needed for the conductor. A wire

table, such as Table

5,

will give the bare area for each

wire size. This table also gives the thickness of insula-

tion necessary to support each layer of a given wire size

in the layer-wound construction, as well as the maxi-

mum diameter of the wire over its film insulation.

The next step is to design the coil that will result in

the configuration shown in Fig.

2.

This wound coil will

then be laminated to form the finished product as shown

in Fig.

3.

3

E,

n

2

m

1

T5

h

0

31

m

1

2

v)

75

Y4

0.237 20.3 14.2

3

480 73.2 0.88 6.6 32.6 0.63 0.182

31

3

87

%

0.441 40.0 14.4

3

040

80.9 1.47 8.7 22

1

.oo

0.32

m

100

1

0.750 72.5 14.6 2 580 84.5 2.3

11.0

15.1 1.49

0.46

2.91

1

.o

31

125

1%

1.825 163 14.8 2 220 88.6 4.7 16.2 9.9

138

1

3/s

2.66 229 14.8 2 130 90.2 6.2 19.0 8.3 3.88 1.44

ua

P

150

1

Y2

3.80 298 14.8 2

000

91

.O

8.1 21.8 7.3 5.05 1.75

2

175

1%

7.0

524 14.8

1

845 92.8 12.8 27.8 5.3 8.0 2.86

212 2% 15.3

1

050 14.8

1

550 94.7 22.6 37.4 3.6 14.2 5.18

U

250 2% 29.3

1

823 14.8

1

335

95.7

35.5

41.5 2.6 22.2 8.5

31

25

1

2% 68.8 3 551 14.8 935 96.5 49.8 79.2 2.23

31.1

26.6

c)

31

v)

TABLE

4.*

VA

RATINGS

vs

LAMINATION

SIZES-60

Hz,

75

"C

TEMPERATURE

RISE**

5

625

36

0.114 9.1 14.0 4 060 63.5 0.5 4.7 52 0.37 0.098

6

Lamination Tongue Flux Current

Effi-

Core Copper Copper Weight, lb

E-I

Width, Area VA Density, Density, ciency,

Loss,

Regulation,

Type in Product Average Kilogauss .Win2

%

Watts Watts

%

Iron Copper

*

Electm-Echnol.,

Vol.

67,

No.

1,

p.

61,

January,

1961.

Copyright C-M Technical Publications Corp.,

1961.

**

Table based on

29-gauge,

grain-oriented

(M6)

silicon steel, square stack. Exciting VNinput VA is

23.5

percent

(EI625)

to

12.7

percent

(EI251).

Operating temperature

=

75

"C

(amb)

+

75

"C (rise)

=

150

"C.

Copper weight will ordinarily be less than values in the table.

d

13-8

TABLE

5.

WIRE

TABLE

FOR

TRANSFORMER

DESIGN*

AWG

Size?

14

15

16

17

18

19

20

21

22

23

24

25

26

21

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

-

Nom.

Bare

Area

(in2

x

3.227

2.561

2.027

1.612

1.276

1.012

0.804

0.638

0.503

0.401

0.317

0.252

0.1986

0.1584

0.1247

0.1003

0.0785

0.0622

0.0503

0.0396

0.0312

0.0246

0.0196

0.0159

0.01257

0.00962

0.00755

0.00616

0.0049 1

0.00380

0.00314

Maximum Overall

DiaI

Single

Build

(inches)

0.0666

0.0594

0.0531

0.0475

0.0424

0.0379

0.0339

0.0303

0.0270

0.0243

0.0217

0.0194

0.0173

0.0156

0.0140

0.0126

0.0112

0.0100

0.0091

0.0081

0.0072

0.0064

0.0058

0.0052

0.0047

0.0041

0.0037

0.0033

0.0030

0.0026

0.0024

ter

Heavy

Build

(inches)

0.0682

0.0609

0.0545

0.0488

0.0437

0.0391

0.0351

0.0314

0.0281

0.0253

0.0227

0.0203

0.0182

0.0164

0.0147

0.0133

0.0119

0.0108

0.0098

0.0088

0.0078

0.0070

0.0063

0.0057

0.0051

0.0045

0.0040

0.0036

0.0032

0.0029

0.0027

Layer

Factor

0.90

0.89

0.88

0.87

0.86

0.85

Nominal

Resist.**

(a/looo

ft)

2.52

3.18

4.02

5.05

6.39

8.05

10.13

12.77

16.20

20.30

25.67

32.37

41.02

5 1.44

65.31

81.21

103.71

130.9

162.0

205.7

261.3

330.7

414.8

512.1

648.2

846.6

1079.2

1323.

1659.

2143.

2593.

Nominal

Weight

(lbi1000 ft)

12.44

9.87

7.812

6.213

4.914

3.900

3.099

2.459

1.937

1.546

1.223

0.970

0.7650

0.6101

0.4806

0.3866

0.3025

0.2398

0.1937

0.1526

0.1201

0.0949

0.07569

0.06 128

0.04844

0.03708

0.029 10

0.02374

0.01892

0.0 1465

0.01210

Minimum

Margin

m

(inches)

0.1875

0.1562

0.125

0.0938

0.0625

Kraft

Layer

Insulation

(inches)

~

0.0100

0.0070

0.0050

0.0020

0.0015

0.0013

0.0010

0.0007

0.0005

*

Data for this table are courtesy of NEMA (ref.

12)

and Phelps Dodge (ref.

13).

7

Square

or rectangular wire is recommended for wire sizes heavier than AWG

14.

**

Resistance values

are

at

20

"C.

In

designing the coil, one first selects the core tube

thickness

(1

in Fig.

2).

This thickness may vary from

0.025

to

0.050

inch for lamination stack heights

(p

in

Fig.

3)

of

0.5

to

2

inches. Next, calculate

the

coil-build

(a

in Fig.

3)

for each winding, using the number of turns

and wire sizes previously calculated.

Single build is not recommended for these sizes.

a

=

l.l[q(D

+

t)

-

t

+

t,]

where,

nl

is

the number

of

layers in the winding,

D

is the diameter of the insulated wire,

t,

is

the thickness

of

the insulation under and over Fig.

2.

Dimensions relating to coil mean length of turn

the winding. (MLT)

,

MAGNETIC-CORE TRANSFORMERS AND REACTORS

13-9

A,

=

core area

=

(gp)

k

o

=height

of

coil

=

coil-build

b

=toil

u,idth

g

=width

of

lamination

tongue

IC

=average

length

of

magnetic.flux

path

k

=stacking factor

=

0

90

for

14-mil lamination

=O

80

for

2-mil lamination

or

ribbon-wound core

m

=marginal

space given

in

Table

5

p =height

of

laminatinn stack

t

=thickness

of

interlayer

insulation

LL’

=width

of

core window

i

=window length tolerance

=

1116 Inch. total

Fig.

3.

Dimensions relating to

the

design of a transformer

coil-build

and

core.

The numeric

1.1

allows for a

10%

bulge factor. This

factor may be reduced, depending

on

the winding

equipment and methods of winding used. The total

coil-build should not exceed

85-90%

of the window

width.

Compute the mean length per turn (MLT) of each

winding from the geometry of the core and windings

(Fig.

2).

(MLT),

=

2(r

+

J)

+

2(s

+

J)

+

TTU~

(MLT),

=

2(r

+

J)

+

2(s

+

J)

+

.rr(2~l

+

(12)

where,

a,

is the build of the first winding,

a’

is the build of the second winding,

J

is the thickness of the winding form,

I

and

s

are

the winding-form dimensions.

Calculate the total length and resistance of each wind-

ing, and determine the

IR

drop and IZR loss for each

winding.

Make corrections,

if

required,

in

the

number

of

turns

of the windings to allow for the IR drops,

so

as to have

the required

E,.

Compute the core loses from the weight of the core and

Table

2

or reference

6.

Determine the percent efficiency

7

and voltage regu-

lation (VR) from

w,,

x

100

’

=

w,,,

+

(core

loss)

+

(copper loss)

For a more accurate evaluation of voltage regulation,

determine leakage-reactance drop

=

Idc

d,,

/27r,

and

add to the above (VR) the value of

IdCW~,/2TTEdc.

Here,

l,,

=

leakage inductance viewed from the secondary;

see “Methods of Winding Transformers” (in this

chapter) to evaluate

l,,

.

Bring out all terminal leads. Use the wire of the coil,

insulated with suitable sleevings, for all sizes of wire

heavier than 21. Use

7-30

stranded and insulated wire

for smaller sizes.

Effect of Duty Cycle on Design

If

a transformer is operated at different loads accord-

ing to a regular duty cycle, the equivalent volt-ampere

(VA) rating is

where (VA),

=

output during time

tl,

etc.

minute

off.

Example:

5

kilovolt-ampere output,

1

minute

on,

1

(5000)’(1)

+

(0)’(1)

=

5000/(2)”’

=

3535

volt-amperes

Methods of Winding

Transformers

The most common methods of winding transformers

are shown in Fig.

4.

Leakage inductance is reduced by

interleaving, Le., by dividing the primary or secondary

coil into two sections and placing the other winding

between the two sections. Interleaving may be accom-

plished by concentric and by coaxial windings, as

shown in Figs.

4B

and

C.

Reduction of leakage

inductance is computed from

10.6

N~(MLT) (2nc

+

U)

I,

=

n’b

X

lo9

where

I,

is the leakage inductance (referred to the

winding having N turns) in henrys and the dimensions

are in inches and to be the same for Figs.

4B

and C.

Means

of

reducing leakage inductance

are:

(A)

(B)

Reduce build of coil.

Minimize turns by using high-permeability

core.

13-10

SECONDARY

12)

t

PRIMARY

c

REFERENCE DATA FOR ENGINEERS

\

n=2

SECONDARY

bl

1-n-

C

T

I

l-

b+

B

[

-

I

(""[

t---b----l

D

Fig.

4.

Methods

of

winding transformers.

(C)

Increase winding width.

(D)

Minimize spacing between windings.

(E)

Use bifilar windings.

Means of minimizing capacitance are:

(A)

Increase dielectric thickness

t.

(B)

Reduce winding width

b

and thus area

A.

(C)

Increase number of layers.

(D)

Avoid large potential differences between wind-

ing sections, as the effect of capacitance is

proportional to applied potential squared.

Note:

Leakage inductance and capacitance require-

ments must be compromised in practice since corrective

measures

are

opposites.

Effective interlayer capacitance of a winding may be

reduced by sectionalizing it as shown in Fig.

4D.

This

can be seen from

C,

=

(4C1/3n1)(1

-

lhl)

where,

C,

=

effective capacitance in picofarads,

nl

=

number of layers,

CI

=

capacitance of one layer to another

A

=

area of winding layer

=

(MLT)b inches2,

t

=

thickness of interlayer insulation in inches,

E

=

dielectric constant

J

3

for paper.

=

0.225

A&

picofarads,

Dielectric Insulation and

Corona

For class

A

(Table 6), a maximum dielectric strength

of

40

volts/mil is considered safe for small thicknesses

of insulation. At high operating voltages, due regard

must be paid to corona that occurs before dielectric

breakdown and will in time deteriorate insulation and

cause dielectric failure. Best practice is to operate

insulation at least

25

percent below the corona starting

voltage. Approximate 60-hertz rms corona voltage

V

is

V

(in volts)

=

(34)

log

(loot)

log

800

where

t

=

total insulation thickness in inches. This may

be used as a guide in determining the thickness of

insulation. With the use of varnishes that require no

solvents, but solidify by polymerization, the bubbles

present in the usual varnishes

are

eliminated, and much

higher operating voltages and, hence, reduction in the

size of high-voltage units may be obtained. Epoxy resins

and some polyesters belong in this group. In the design

of high-voltage transformers, the creepage distance

required between wire and core may necessitate the use

of insulating channels covering the high-voltage coil, or

taping of the latter. For units operating at 10 kilovolts or

higher, oil insulation will greatly reduce creepage and,

hence, the size of the transformer.

Temperature and Humidity

Table 6 lists the standard classes of insulating

materials and their limiting operating temperatures.

Table

7

compares the properties of four high-tempera-

ture wire-insulating coatings.

Open-type constructions generally permit greater

cooling than enclosed types, thus allowing smaller sizes

for the same power ratings. Moderate humidity protec-

tion may be obtained by impregnating and dip-coating

or molding transformers in polyester or epoxy resins;

these units provide good heat dissipation but are not as

good in this respect as completely open transformers.

Protection against the detrimental effects of humidity

is commonly obtained by enclosing transformers in

hermetically sealed metal cases. This is particularly

important if very fine wire, high output voltage, or

direct-current potentials are involved. Heat conductivity

to the case exterior may be improved by the use of

asphalt or thermosetting resins as filling materials. Best

conductivity is obtained with high-melting-point silica-

filled asphalts or resins

of

the polyester or epoxy types.

Coils impregnated with these resins dissipate heat best,

since voids in the heat path may be eliminated.

Immersion in oil is an excellent means of removing

heat from transformers.

An

air space or bellows must be

provided to accommodate expansion of oil when heat-

ed.

FERRORESONANT

TRANSFORMERS

Ferroresonant transformers, also known as constant-

voltage transformers or ferroresonant voltage regula-

tors, make use of an alternating-current phenomenon

involving at least one magnetic component in combina-

tion with a suitable capacitor to provide stabilized

voltage to a load when the source voltage fluctuates.

A

MAGNETIC-CORE TRANSFORMERS

AND

REACTORS

13-11

TABLE

6.

CLASSIFICATION

OF

ELECTRICAL

INSULATING MATERIALSt

Limiting

Insulation

Temperature

(Hottest Spot)

Class Insulating Material in “C

0

Materials or combinations of materials such as cotton, silk, and paper without

impregnation*

90

Materials or combinations of materials such as cotton, silk, and paper when

suitably impregnated or coated

or

when immersed in a dielectric liquid’

Materials or combinations of materials such as mica, glass fiber, asbestos, etc.,

with suitable bonding substances*

130

F

Same as for Class

B

155

H

A

105

B

Materials or combinations of materials such as silicone elastomer, mica, glass

fiber, etc., with suitable bonding substances such as appropriate silicone resins* 180

*

220

Materials consisting entirely of mica, porcelain, glass, quartz, and similar

inorganic materials*

C

Over C

Over

220

*

(Other) materials or combinations of materials may be included in this class if by experience or accepted tests they can be

shown to have comparable thermal life at the temperature given in the right-hand column.

These temperatures are, and have been in most cases over a long period of time, benchmarks descriptive of the various classes

of insulating materials, and various accepted test procedures have been or are being developed for

use

in their identification. They

should not be confused with the actual temperatures at which these

same

classes of insulating materials may be used in the various

specific types of equipment nor with the temperatures on which specified temperature rise in equipment standards are based.

In the above definitions the words “accepted tests” are intended to refer to recognized test procedures established for the

thermal evaluation of materials by themselves or in simple combinations. Experience or test data, used in classifying insulating

materials, are distinct from the experience or test data derived for the use of materials in complete insulation systems. The thermal

endurance of complete systems may be determined by suitable test procedures.

A

material that is classified as suitable for a given temperature may be found suitable for a different temperature, either higher

or

lower, by an insulation system test procedure. For example, it has been found that some materials suitable for operation at one

temperature in air may be suitable for a higher temperature when used in a system operated in an inert gas atmosphere. Likewise

some insulating materials when operated in dielectric liquids will have lower or higher thermal endurance than in air.

It is important to recognize that other characteristics (in addition to thermal endurance) such as mechanical strength, moisture

resistance, and corona endurance are required in varying degrees in different applications for the successful use of insulating

materials.

+From “Insulation class ratings,”

IEEE Standard Dictionary

of

Electrical and Electronics Terms,

IEEE Std.

100-1972

magnetic component must have

a

magnetization charac-

teristic that is sharply nonlinear,

and

it must operate

above the “knee” of the characteristic, where

the

change in voltage

across

it is small compared

to

the

change

in

current through it.

A

set of design equations

for commonly used ferroresonant regulators and regu-

lated rectifiers

are

derived in

a

paper

by

Hart and

Kakalec.*

These equations

are

for the basic open-loop

type of ferroresonant voltage regulator.

A

more

recent development is the closed-loop, or

feedback-controlled, ferroresonant voltage regultor.?

Whereas the regulating function of the open-loop type

depends

on

the stability of the frequency of the source

and the magnetic characteristics of the core, the regulat-

ing function of the closed-loop type is dependent

on

the

voltage stability of the reference in the control circuit,

and also

on

the gain of the feedback loop. Regulation

better than

0.5%

for line, load, frequency,

and

temper-

ature changes can be attained. The circuit of reference

15

requires the use of a magnetic component, an

inductor, in the control circuit.

A

later development**

eliminates the need for this inductor

as

a separate

component by the use of a double-shunt feedback

ferroresonant transformer.

CONVERTER/INVERTER

TRANSFORMERS

The

IEEE$

defines a converter as a machine that

changes alternating-current power to direct-current

*

Reference

14.

t

Reference

15.

**

Reference 16

$

Reference

1.

Middleton W.M. (ed.) Reference Data for Engineers: Radio, Electronics, Computer and Communications

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