chhaapptteerr-5 design of heating coil of an induction...

CChhaapptteerr-5

DESIGN OF HEATING COIL OF AN

INDUCTION HEATER/ COOKER

This chapter is based on the published articles,

1. D. Sinha, A. Bandyopadhyay, P. K. Sadhu and N. Pal, Computation of

Inductance and AC Resistance of a Twisted Litz-Wire for High Frequency

Induction Cooker, in the proceeding of IEEE sponsored International

Conference on “Industrial Electronics, Control & Robotics” (IECR 2010) at

NIT, Rourkela, India, 2010. (Awarded the best paper)

2. Dola Sinha, Atanu Bandyopadhyay, Pradip Kumar Sadhu and Nitai Pal,

Optimum Construction of Heating Coil for Domestic Induction Cooker, in

the proceeding of International Conference on Modelling, Optimization and

Computing (ICMOC 2010), AIP, at NIT, Durgapur, India, P.P. 439–444,

2010.

Design of Heating Coil of an Induction Heater/ Cooker 60

In this chapter, analytical expressions are derived for determining AC resistance

and inductance of the heating coil used in an induction heater / cooker. Results are

presented varying different parameters of the induction heating system.

5.1. Introduction

The design and optimization of heating coil is very important for the analytical

analysis of high frequency inverter fed induction cooker. Moreover, accurate

prediction of high frequency winding loss is necessary. The eddy current loss

includes skin effect loss and proximity effect loss. Brief discussions on three kind

of losses i.e., skin effect loss, proximity effect loss and end and edge effect loss are

made below.

(a) Skin effect: The skin effect occurs when a sinusoidal current flowing

through a conductor and creates a sinusoidal magnetic flux within the

conductor which is perpendicular to conductor axis (refer to Fig. 5.1). This

magnetic flux produces eddy current which flows in the opposite direction

that of the main current flowing through the conductor. It also reduces the

net current at the centre of the conductor and the current decreases

exponentially from outer surface of the conductor to its centre. For a solid

conductor skin depth is the depth of penetration of which current is flowing

as derived in Kraus and Fleisch (1999). This skin depth is the function of

frequency, permeability and conductivity of the conductor materials. Skin

depth is normally expressed as 1f

, where, f is the operating

frequency, is the permeability of the conducting material, is the

conductivity of the conducting material. For copper conductor

0.066f

meter. Eddy current increases with the increase in frequency, as

a result conduction loss also increases.


Conductor Current

Eddy CurrentFlux

Conductor

Fig.5.1: Skin effect in a conductor

(b) Proximity effect: It occurs due to the generation of magnetic field among

the adjacent conductors. In the induction cooker spiral shaped heating coil

is used (refer to Fig. 5.2). In that case proximity effect further divided into

internal proximity effect and external proximity effect. Internal proximity

effect is the effect of the other current within the bundle and external

proximity effect is the effect of current in other bundles.

Fig.5.2: Cross-sectional view of spiral coil

(c) End and edge effects: The temperature profiles along the work piece’s

length and width are affected by a distortion of electromagnetic field (emf)

in its end and edge areas. Those field distortions and corresponding

distributions of induced currents and power densities are referred to as end

and edge effects. These effects and the field distortion caused by them are

primarily responsible for non-uniform temperature profiles in cylindrical,


rectangular and trapezoidal shaped work pieces. Suppose, a slab is placed

initially in a uniform magnetic field. If the slab’s length and width are

much larger than its thickness, the emf in the slab can be viewed as an area

consisting of three zones i.e., central area, transverse edge effect area and

longitudinal end effect area. In the central area, the emf distribution

corresponds to the field in the infinite plate. Basically, end and edge effects

have a two-dimensional space distribution excluding only the zone of three-

edge corners where the field is three dimensional and the corresponding

field distribution is the result of mixture of the end and edge effects. For

many practical applications, the separate study of end and edge effects is of

great engineering interest.

5.2. Factors considered for construction of heating coil

Following factors have been considered for construction of heating coil.

Type of wire: It may be solid wire or multi stranded litz wire. At high

frequency, the skin effect loss will be more in case of solid wire. Thus for

energy efficient induction cooker, the heating coil may be made by multi

stranded litz wire.

Shape of wire: It can be round or rectangular cross sectional wire or it may be

foil coil. At round cross sectional wire the current flows uniformly through

the whole cross section. But in case of rectangular or foil coil current density

is more at the corner or edge section.

Size of strand: From the litz wire manufacturer’s manual at the frequency

range of 20 to 50 kHz, the strand size lie between 30 to 36 AWG. Three

different strand sizes, such as 30, 33 and 36 AWG have been considered in

the present study.

Number of turns of spiral coil: It depends on the size of the heating coil. It is

varied from 30 to 60 in the present study and optimal value is chosen.

Number of twist per feet: The stranded litz wire is twisted so that each

strand can possess both azimuthal and radial transposition. For thick wire


number of twist can be 12 twists per feet and for thinner wire it may be up to

200 twists per feet.

Operating frequency: Induction cooker operates at the frequency range of 4

kHz to 50 kHz. For different strand size and number of strands suitable

operating frequency will be different and it is to be determined in an optimal

sense.

5.3. Inductance Calculation:

Important electrical parameters of a coil include resistance, inductance and

capacitance. Calculation of all these parameters is essential for designing a coil. A

methodology based on self Geometrical Mean Distance (GMD) for calculating

inductance of a litz wire is made, which is discussed in the next sub-section.

5.3.1. Inductance of a multiple stranded litz wire

Consider a round conductor consisting of a group of n parallel round strands

carrying phasor currents 1 2, ,......... nI I I , whose sum equal to zero. Distances of these

strands from a remote point P are indicated as 1 2, ,......... nD D D . The mutual flux

linkages ( ij ) as reported by Kothari and Nagrath (2003) in the ith strand due to

current in jth strand is given by,

72 10 ln jij j

ij

DI

D

(5.1)

The flux linkages in ith strand due to its own current (i.e., self linkages, ii ) is as

follows:

7'2 10 ln ,i

ii ii

DIr

(5.2)

Considering the symmetry condition,

ii iD = r = 0.7788r , (5.3)

where, r is the radius of each strand expressed in meter.

Therefore, the total flux linkages ( i ) in ith strand for ‘n’ no. of strands is

expressed as :


1

n

i ii ijjj i

(5.4)

1 271 2i

1 1 2 2

1 1 1 1ln ln ............... ln .............. ln 2 10

ln ln ................ ln .......... ln

i ni i ii in

i i n n

I I I ID D D D

I D I D I D I D

(5.5)

Since, the sum of total strand current is zero. Thus,

7i 1 2

1 2

1 1 1 1 2 10 ln ln ............... ln .............. lni ni i ii in

I I I ID D D D

(5.6)

Let us assume that uniform current flows through each strand and shares nI

amount of current.

7i

1 2 3

1 2 10 ln...... ........i i i ii in

In D D D D D

(5.7)

7i 1

1 2 3

12 10 ln /....... ....... n

i i i ii in

I Wb T mD D D D D

(5.8)

Therefore, the inductance of ith strand ( )iL is given by,

i

iLI

n

(5.9)

Since, there is ‘n’ no. of strands present in a litz wire conductor, the average

inductance AvgL of the conductor can be written as:

1 2 ................. nAvg

L L LLn

(5.10)

Now, the total inductance ( )stL of the conductor will be

2

7st 1

1 2 3

12 10 ln /....... ....... ni i i ii in

L H mD D D D D

(5.11)

The total number of strands ‘n’ is calculated by using the expression, 23 3 1n x x , where x is the no. of layers( Nagrath and Kothari, 2003). Fig. 5.3

shows a schematic cross sectional view of a litz wire having 3-layers and 19-

strands of equal radii. Therefore, the self GMD sD for a 3-layered and 19-

stranded litz wire can be obtained as follows (refer to Fig. 5.3):


16 12 19 19

19 19 1919

7, 1, 8,1, 1, 1,7 1 8

s i i ii i ii i i

D r D D D

, (5.12)

Or, sD = 3.793697r (5.13)

Therefore, the inductance of the coil will be

7 12 10 ln H/msts

LD

(5.14)

1

2

3

4

5

6

7

89

10

11

12

131415

16

17

18

19

Fig. 5.3: A schematic diagram showing a 3-layer stranded litz wire.


5.3.2. Inductance of a flat spiral shaped coil

From the Wheeler’s formula (Wheeler, 1928), inductance of the flat spiral coil as

shown in Fig. 5.4 is obtained using the expression mentioned below. 2 2

,8 11c

N RLR W

(5.15)

where, N = total number of turns,

R = mean radius of the spiral coil (in inches) = 00.5( )R c ,

W = depth of the spiral coil (in inches)

= outer radius –inner radius = 0( )R c

Now, the total inductance of the coil can be obtained as

st cL l L L , (5.16)

where, l is the total length of the spiral coil.

(a) (b)

Fig. 5.4: Schematic diagram of a flat spiral coil: (a) overall look, (b) internal

dimensions.

5.4. Length of a flat spiral shaped coil

The total length of the spiral coil is given by the expression

0l N c R (5.17)

where, c is the inner radius and 0R is the outer radius of the spiral coil. The

minimum and maximum values of 0R can be calculated as, 0 (min) bR c N d

S

2c

d


and 0 (max) ( )bR c N d S , respectively. Where, bd is the bundle diameter of the

litz wire and S is the intermittent space between the windings.

5.4.1. Effect of twist on the length of strand

The distance a strand travels is longer when it is twisted than when it goes straight.

The effect of twisting on the length of strand is illustrated in Fig. 5.5. It shows a

single cylinder shell of length equal to the pitch, unwound to show flat on the page.

With simple twisting, each strand will stay within one such shell of a radius br and

thus will be longer than the overall bundle by a factor of

p

rpp

l bd22 2

cos1

(5.18)

where, dl is the untwisted length of the strand per turn, br is the bundle radius of

litz wire, p is the pitch (i.e., vertical lift of the wire per turn after twisting) and

90 , being the helix angle by which the strand is twisted.

Fig. 5.5: The effect of twisting on the length of the strand.

Let us consider that a total of M number of twisting to be given in the wire

for a strand having effective length of , i.e., ll M p . Therefore, the total

untwisted length of a strand (considering constant effective length) may be

obtained using the relationship mentioned below.

221 btot d d

l rl M l l l pp

(5.19)

θ dl

br2

p


It has been found in the literature of litz wire that normally for thick wire 12 turns

per feet and for thinner wires 100 to 200 turns per feet of twisting are preferred.

5.5. Effect of twist on the bundle diameter

The overall bundle diameter bd depends on the strand packing factor ( aK ), which

is expressed below.

b

ea A

AK (5.20)

where, bA is the overall bundle area ( 2 4b bA d ) and eA is the sum of cross

sectional areas of all the strands with each strand area taken perpendicular to the

bundle but not perpendicular to the strand (as shown in Fig. 5.6).

Fig. 5.6: Cross sectional view of a strand after twisting.

Thus, the area of each strand is taken at a different angle, to the strand axis,

resulting in an elliptical area, as shown in Fig. 5.6. For the purpose of simplicity,

the packing factor aK is assumed to be constant and independent of the pitch.

However, the bundle diameter increases with twisting. Now, consider the situation

when a bundle of n strands are twisted. In the bundle cross section, each strand

area becomes elliptical at an angle as shown in Fig. 5.6. Note that at different

radii, have different values. Cross sectional area perpendicular to the strand can

be calculated as below.

cos,, escs AA (5.21)

where, ,s cA is the cross sectional area of the strand perpendicular to the strand and

, s eA is the cross sectional area of the strand perpendicular to the bundle axis.

Strand Axis

Bundle Axis

As, e As, c


Since, aK is independent of pitch,

,. s ca u

b

n AK

A (5.22)

where, ubA is the overall bundle area when there is no twisting.

Therefore, the total cross sectional area of the strand perpendicular to each strand

is calculated as follows. 2

,.4

uu b

c s c a b adA n A K A K

(5.23)

where, ubd is bundle diameter without twisting. In a twisted bundle, cA can be

calculated as:

, ,1

n

c s e i ii

A A cos

(5.24)

This can be approximated as: 2

0

cos( ) 2 bd

c aA K r dr (5.25)

Combining (5.22) and (5.23) bundle diameter with twisting can be found

2 2

214

u sb b

a

ndd dK p

(5.26)

Substituting in ubd ,

2u sb

a

nddK

(5.27)

Therefore, bundle diameter with twisting can be obtained as:

2 2 2

214

s sb

a a

nd nddK K p

(5.28)

5.6. Resistance calculation

The DC power loss of a single strand can be calculated as:

2,s

214

totdc s c

s

lP Id

(5.29)


where, sI is the rms current in each strand.

In the cross section of a twisted bundle, DC power loss per unit area can be

obtained as follows.

2,

2 4,

16dc sunit a s c totdc

s e s

a

P K I lP A dK

(5.30)

Integrating the DC power loss over the bundle can result in the total DC power loss

as given below. 2 2

220

2 14

bdunit u s

dc dc dca

ndP P rdr PK p

(5.31)

where, udcP is DC loss of the bundle without twisting.

Now, the DC resistance ( dcR ) of the twisted bundle is given by 2 2

2 2

4 14

c tot sdc

s a

l ndRnd K p

(5.32)

where, 2

4 uc totdc

s

l Rnd

represents the DC resistance without twisting.

5.6.1. AC Resistance of multi-stranded litz wire

In this section, an attempt is made to relate AC resistance with the skin effect

factor ( sy ). If a conductor is composed of one or more concentric circular

elements, then the centre portion of the conductor will be enveloped by a greater

magnetic flux than those on the outside. Consequently, the self induced emf will be

greater towards the centre of the conductor, thus, causing the current density to be

less at the centre than the conductor surface. This extra concentration at the surface

is known as skin effect. It results in an increase in the effective resistance of the

conductor. The skin effect factor ( sy ) is expressed as:

4

4192s

ss

xyx

(5.33)

where, 7

2 8 10ss

dc

f kxR

(5.34)


where, f is frequency (Hz), sk is factor determined by conductor construction,

( sk =1 for circular, stranded, compacted and sectored) and dcR is the DC resistance

at normal operating temperature. Therefore, sy depends on two parameters, DC

resistance dcR and operating frequency f .

Now, the AC resistance at normal temperature can be calculated as:

1ac dc sR R y (5.35)

Moreover, dcR varies with the number of twist of the stranded litz wire.

Therefore, it is essential to obtain a value of number of twist for which acR

becomes minimal at a constant operating frequency. To achieve the same, it is

considered that

0acdRdp

, 1 0dc sdor R ydp

(5.36)

, 1 0dc ss dc

dR dyor y Rdx dp

(5.37)

Now, combining the equations (5.33) through (5.37), optimal value of AC

resistance may be obtained using the expression:

27 3

227 2

384 8 10

8 10

dcac

dc

f RR

f R

(5.38)

5.7. Sample Calculations and Discussions

An attempt is made to obtain inductance and AC resistance of a heating coil for

domestic application induction cooker operating at a high frequency. The heating

coil is made up of litz wire having multiple strands and multiple layers. The

material is considered to be copper. For the strand size 36 AWG, operating

frequency 38.512 kHz and number of twist equals to 140 per feet is used here.

Table 5.1 shows the physical dimensions of a twisted litz wire. The inductances for

different litz wire construction are presented in Table 5.2.


Table 5.1: Dimensions of the twisted litz coil for four physical set-ups.

An attempt has also been made to make a comparative study among different litz

wire construction in different frequency range. In order to minimize AC resistance

of a litz wire, an attempt is made to test the variation of AC resistances due to

twisting. For the purpose of which AC resistances of litz wires having different

strand dimensions and number of strands are studied by varying the number of

twist per feet offered to the coil. It has been observed that AC resistances for any

strand size exponentially decay for the number of twist more than 30 per feet (refer

to Fig. 5.7(a)). The similar experiment has been conducted by varying the strand

size and number of strands. This study was made for a constant operating

frequency (38.512 kHz). The variation of AC resistances with the number of twist

per feet was found to be similar in nature for different number of strands (refer to

Fig. 5.7). Very low value of AC resistance is observed for the value of 200 twists

(No. of Layers, No. of Strands) Physical parameters (1, 4) (2, 7) (3, 19) (4, 37)

Radius of a strand, sr (mm) 0.0635 0.0635 0.0635 0.0635

Number of spiral turns, N 52 52 52 52

Inner radius of the spiral coil, c (m) 0.02175 0.02175 0.02175 0.02175

Outer radius of the spiral coil, 0R

(m) 0.054404 0.062842 0.094385 0.131574

Bundle dia. of the litz wire, db(m) 0.000314 0.000395 0.000698 0.001056

Intermittent space between the

winding of spiral coil, S (m) 0.000314 0.000395 0.000698 0.001056

Mean radius of the spiral coil, R

(m) 0.038077 0.042296 0.058067 0.076662

Packing Factor (Ka) 0.686413 0.77778 0.76 0.755102

Width of spiral coil, W (m) 0.032654 0.041092 0.072635 0.109824

Total length of spiral coil ltot (m) 13.65688 15.90561 26.9285 45.63579

GMD of the coil, Ds (mm) 0.109 0.138 0.241 0.338

Insulation thickness for each strand

(mm) 0.0133 0.0133 0.0133 0.0133


per feet and above for each of the cases. However, keeping in mind the physical

constraints of constructing a twisted litz wire, 140 twists per feet have been

considered in the design of an induction cooker.

Table 5.2: Inductance of the multi-layered, spiral shaped twisted litz coil.

1 layer,

4 strands

2 layers,

7 strands

3 layers,

19 strands

4 layers,

37 strands

Inductance for strands per unit length

of the coil, ( / )stL H m 1.824 1.777 1.666 1.598

Total inductance of strands for the

entire length of coil = ( )tot stl L H 22.66 24.468 30.99 38.309

Inductance for spiral coil, cL (µH) 231.92 239.464 275.04 317.65

The total inductance of the heating

coil, st cL = L +L (µH)totl 254.58 263.93 306.036 355.96

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

10 40 70 100 130 160 190

No. of twist per feet

AC

resis

tanc

e (o

hm)

36 AWG33AWG30AWG

(a) 1-layered, 4-stranded


0

2

4

6

8

10

12

14

10 35 60 85 110 135 160 185

No. of twists per feet

AC

Res

istan

ce (O

hm)

36AWG33AWG30AWG

(b) 2-layered, 7-stranded

0

2

4

6

8

10

12

14

1 31 61 91 121 151 181


AC

Res

istan

ce (O

hm)

36 AWG33 AWG30 AWG

(c) 3-layered, 19-stranded


0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.0045

0.005

10 40 70 100 130 160 190


AC

resis

tanc

e (o

hm)

36AWG33AWG30AWG

(d) 4-layered, 37-stranded

Fig. 5.7: AC resistance variation with the number of twist for (a) 1-layered, 4-

stranded, (b) 2-layered, 7-stranded, (c) 3-layered, 19-stranded and (d) 4-layered,

37-stranded litz wire.

AC resistances were found to be increasing with the increase in operating

frequency as shown in Fig 5.8. The experiment has been conducted by varying the

strand size and number of strands and taken 40 twist per feet. Table 5.3 shows the

inductances of different litz wire constructions for different AWG of the strand. It

is important to note that inductance of a litz coil increases due to twisting. It has

also been noticed that variation of inductances with strand dimension is more for

the twisted litz coils and the value of inductance increases as the strand dimension

reduces (refer to Table 5.3). It may have happened due to the increase in bundle

diameter after twisting and increased length of the spiral coil for keeping effective

length to be equal to that of the coil before twisting.


0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

0.0007

0.0008

1 6 11 16 21 26 31 36 41 46

Frequency (kHz)

AC

resis

tanc

e (o

hm)

36AWG33AWG30AWG


0

2

4

6

8

10

12

14

16

18

1 6 11 16 21 26 31 36 41 46

Frequency (kHz)

AC

Res

istan

ce (O

hm)

36AWG33AWG30AWG



0

0.00005

0.0001

0.00015

0.0002

0.00025

1 6 11 16 21 26 31 36 41 46

Frequency (kHz)

AC

Res

istan

ce (O

hm),

30 &

33A

WG

0

2

4

6

8

10

12

14

Res

istan

ce (O

hm),

36A

WG

33AWG30AWG36 AWG


0

0.00005

0.0001

0.00015

0.0002

0.00025

1 6 11 16 21 26 31 36 41 46

Frequency (kHz)

AC

resis

tanc

e (o

hm)

36AWG33AWG30AWG


Fig. 5.8: AC resistance variation with the operating frequency for (a) 1-layered, 4-

stranded, (b) 2-layered, 7-stranded, (c) 3-layered, 19-stranded and (d) 4-layered,

37-stranded litz wire.


An attempt was made to test the variation of inductance of heating coil due to

twisting. For the purpose of which inductance of litz wires having different strand

dimensions and number of strands are studied by varying the number of twist per

feet offered to the coil. It has been observed that inductance for 36 AWG and 33

AWG strand size to some extent increases for the number of twist (refer to Fig.

5.9) and significantly increases for strand size 30 AWG. This study was made for a

constant operating frequency (38.512 kHz). The variation of inductance with the

number of twist per feet was found to be similar in nature for different number of

strands (refer to Fig. 5.9).

Table 5.3: Inductance of multi-stranded litz wire with different strand

dimension.

Inductance (L in H ) of litz wire 36 AWG 33 AWG 30 AWG Litz wire

Untwisted Twisted Untwisted Twisted Untwisted Twisted

4-stranded 254.405 254.58 271.37 271.78 301.562 302.523

7-stranded 263.632 263.93 288.346 289.048 329.25 330.905

19-stranded 304.99 306.036 355.58 358.075 433.82 440.02

37-stranded 353.54 355.96 430.678 436.69 550.236 565.748

250260270280290300310320330340350

10 30 50 70 90 110 130 150 170 190


Indu

ctan

ce in

uH

36 AWG

33 AWG

30 AWG

(a) 1-layer, 4 stranded,


250270290310330350370390410430

10 30 50 70 90 110 130 150 170 190


Indu

ctan

ce in

uH

36 AWG

33 AWG

30 AWG

(b) 2 layer, 7 stranded,

250

350

450

550

650

750

850

950

10 30 50 70 90 110 130 150 170 190


Indu

ctan

ce in

uH

36 AWG33 AWG

30 AWG

(c) 3 layer, 19 stranded,


250

450

650

850

1050

1250

1450

1650

10 30 50 70 90 110 130 150 170 190


Indu

ctan

ce in

uH

36 AWG

33 AWG

30 AWG

(d) 4 layer, 37 stranded,

Fig. 5.9: Inductance variation with the number of twist for multi-layered stranded

(a) 1-layered, 4-stranded, (b) 2-layered, 7-stranded, (c) 3-layered, 19-stranded and

(d) 4-layered, 37-stranded litz wire.

5.8 Optimization of number of strand in litz wire and operating

frequency regarding skin depth

The skin depth is acceptable up to limit for which the current density is 37% of the

surface current density. This skin depth ( ) is the function of frequency (f),

absolute permeability ( 0 ) and conductivity ( ) of the conductor materials and

usually expressed as

0

1f

(5.39)

For copper conductor, 0.066f

meter. Therefore, the effect of eddy current

increases with frequency and as a result, conduction loss also increases. The

maximum frequency can be approximately estimated at the characteristic point of

individual strand where the skin depth is equal to the radius of strand rst.


So, at max , stf f r and max 20

1

st

fr

(5.40)

At very low frequency, both solid and litz wire have same resistance and it is

named as dc resistance. When the frequency gradually increases, the solid wire

experiences the impact of skin effect but litz wire experiences nothing or a very

low impact of skin effect. This is the characteristics point of bundle wire, when the

radius of the solid wire or the equivalent bundle wire ( a ) is equal to the skin depth.

So, at min , f f a and min 20

1fa

(5.41)

The operating frequency should be between minf and maxf . According to Lotfi and

Lee (1993), the maximum beneficial operating frequency of litz wire will be

min max.opf f f (5.42)

Domestic induction cooker operates at the frequency range of 4 kHz to 50 kHz. For

a particular strand diameter, number of strand can be varied for getting suitable

bundle radius operating at a suitable frequency. Nine types of optimum

constructions of litz wire can be chosen at the frequency range of 4 kHz to 50 kHz

shown in Table 5.4. The inductance and AC resistance for different number of

twist has been shown in Table 5.5 and Table 5.6 and plotted in Figs. 5.10 and 5.11,

respectively.

Table 5.4: Optimum operating frequency for different litz wires.

Wire size Strand

radius (mm)

Number of

strands

Bundle

radius (mm)

Optimum operating

frequency (kHz)

7 0.762 45.127

19 1.27 27

37 1.78 19.32

61 2.29 15

30AWG

0.127

91 2.794 12.3

37 1.26 38.512

61 1.62 30

33 AWG

0.09 91 1.98 24.5

36 AWG 0.0635 91 1.397 49.23


Table- 5.5: Comparison of inductance (μH) among different wire configuration.

Wire configuration (AWG/No. of strands) No. of

twist 30/91 30/61 30/37 30/19 30/7 33/61 33/37 33/91 36/91 10 177.4 155.0 134.1 114.0 95.9 127.4 113.4 142.6 119.1 20 184.7 159.1 136.1 114.8 96.1 128.9 114.2 145.3 120.1 30 196.9 165.8 139.4 116.0 96.4 131.5 115.4 149.8 121.8 40 214.2 175.4 144.1 117.9 96.9 135.0 117.2 156.2 124.2 50 237.2 187.9 150.2 120.2 97.4 139.6 119.4 164.5 127.3 60 266.0 203.5 157.7 123.1 98.1 145.3 122.3 174.9 131.1 70 301.2 222.4 166.8 126.6 99.0 152.2 125.6 187.3 135.7 80 343.4 244.8 177.4 130.6 99.9 160.2 129.5 202.0 141.0 90 393.2 271.0 189.7 135.2 101.0 169.4 134.0 219.1 147.1 100 451.3 301.1 203.8 140.4 102.3 179.9 139.0 238.6 154.1 120 594.9 374.6 237.5 152.8 105.1 205.1 151.0 285.9 170.6 150 890.0 522.4 303.8 176.5 110.6 254.0 173.9 379.6 202.4 180 1299.0 723.0 391.5 207.1 117.4 318.2 203.4 505.1 243.7 200 1645.3 890.6 463.6 231.6 122.8 370.6 227.1 609.0 277.1

Table -5.6: Comparison of AC resistance (Ω) among different wire configuration.

Wire configuration (AWG/No. of strands) No. of twist 30/91 30/61 30/37 30/19 30/7 33/61 33/37 33/91 36/91

10 2E-03

7E-04

2E-04

6E-05 8E-06

8E-05 3E-05

2E-04 2E-05

20 0.148 0.055 0.017 0.004 0.001 0.006 0.002 0.014 0.001 30 1.667 0.741 0.230 0.049 0.006 0.078 0.025 0.207 0.020 40 3.790 3.110 1.357 0.311 0.036 0.526 0.161 1.369 0.136 50 3.189 4.694 3.907 1.241 0.144 2.161 0.698 4.468 0.631 60 1.975 3.940 5.885 3.338 0.454 5.458 2.210 7.328 2.168 70 1.170 2.687 5.742 6.143 1.174 8.580 5.150 7.357 5.529 80 0.708 1.750 4.539 8.110 2.565 9.355 8.816 5.798 10.294 90 0.443 1.147 3.315 8.411 4.778 8.212 11.439 4.177 14.193

100 0.287 0.767 2.371 7.531 7.626 6.495 12.028 2.942 15.418 120 0.131 0.367 1.232 4.982 12.775 3.695 9.384 1.489 12.151 150 0.048 0.142 0.511 2.427 13.387 1.608 4.914 0.599 6.204 180 0.021 0.063 0.237 1.234 9.586 0.766 2.542 0.273 3.127 200 0.013 0.039 0.150 0.815 7.210 0.490 1.686 0.171 2.046


150

300

450

600

750

900

1050

1200

1350

1500

1650

10 40 70 100 130 160 190


Indu

ctan

ce (μ

H)

30/91 30/6130/37 30/1930/7 33/6133/37 33/9136/91

Fig. 5.10: Characteristic of inductance with number of twist per feet.

0

2

4

6

8

10

12

14

16

0 20 40 60 80 100 120 140 160 180 200


AC

Res

ista

nce

(ohm

)

30/91 30/61

30/37 30/19

30/7 33/6133/37 33/91

36/91

Fig. 5.11: Characteristic of AC resistance with number of twist per feet.


5.9. Summary:

Value of maximum load resistance should be such that the circuit remains under-

damped or oscillatory for a variable loads like household appliances. Therefore, the

effective resistance of the primary will contain the contribution from the bar,

inductor and reflected resistance from the secondary side. In the proposed scheme,

resistance of pan or vessel is placed on the secondary of the induction coil. Its

reflected resistance in the primary side will obviously be very low. As a result, the

effective primary resistance will be small. Therefore, it will fulfill the condition of

under-damped oscillation i.e., 2 4LRC

. It is shown that inductance increases with

the increase of number of twist per feet. In case of 30 AWG and 91 strands,

inductance increases rapidly, it may not be suitable for real implementation.

Finally, resistance and inductance values are considered to be 0.69Ω and 119μH,

respectively considering 33AWG litz wire having 37 numbers of circular strands

with 30 spiral turns and 50 no. of twists applied per feet of the wire.

***************

chhaapptteerr-5 design of heating coil of an induction...

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