Research Article A 25kW, 25kHz Induction Heating Power...

Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2013 Article ID 584129 10 pageshttpdxdoiorg1011552013584129

Research ArticleA 25 kW 25 kHz Induction Heating Power Supply for MOVPESystem Using L-LC Resonant Inverter

Mangesh Borage and Sunil Tiwari

Power Supplies and Industrial Accelerator Division Raja Ramanna Centre for Advanced Technology Indore 452013 India

Correspondence should be addressed to Mangesh Borage mbbrrcatgovin

Received 25 April 2013 Accepted 25 June 2013

Academic Editor Jose Pomilio

Copyright copy 2013 M Borage and S Tiwari This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A topology named L-LC resonant inverter (RI) for induction heating (IH) applications takes most of the merits of the conventionalseries and parallel resonant schemes while eliminating their limitations In this paper fundamental frequency AC analysis of L-LCRI is revisited and a new operating point is suggested featuring enhanced current gain and near in-phase operation as comparedto the conventional operating point An approximate analysis of the circuit with square-wave voltage source is also describedhighlighting the effect of auxiliary inductor on the source current waveform The analysis also leads to an optimum choice of theauxiliary inductance The requirements of the metal organic vapour phase epitaxy (MOVPE) system in which a graphite susceptoris required to be heated to 1200∘C demanding a 25 kW 25 kHz IH power supply the configuration of developed IH system andexperimental results are presented

1 Introduction

The induction heating (IH) [1] is commonly used for heattreatment of metals (hardening tempering and annealing)heating prior to deformation (forging swaging upsettingbending and piercing) brazing and soldering shrink fittingcoating melting crystal growing cap sealing sinteringcarbon vapor deposition epitaxial deposition and plasmageneration IH is a noncontact methodThe heat is generatedonly in the part not in the surrounding area except byradiation The location of the heating can be defined to aspecified area on the metal component thereby achievingaccurate and consistent results As heating occurs in theobject itself IH is considered more efficient than alternativemethods

An IH system comprises a basic induction power sourcewhich provides the required power output at the requiredpower frequency complete with matching components aninduction coil assembly a method of material handling andsomemethod of cooling Generally full-bridge or half-bridgeresonant inverters (RIs) are most commonly used as thepower supplies for IH The equivalent model of an IH coil

with work piece can be represented in simplified form by anequivalent inductance (119871eq) and resistance (119877eq) as shownin Figure 1 If the IH coil is directly fed from a supply theratio of apparent to real power will be large Therefore theIH coil is properly compensated by capacitors and additionalinductors in suitable configuration so that minimum reactivepower is drawn from the source Additionally to match theload voltage-current requirements to the available sourcea matching network is required The matching is normallyachieved with the help of an isolation transformer of suitableturns ratio

Based on the connection of compensating capacitor withthe IH coil the two most commonly used RI topologies areas follows

(1) Series resonant inverter (SRI) the compensatingcapacitor is placed in series with the IH coil and itis fed by a voltage source [2ndash6]

(2) Parallel resonant inverter (PRI) the compensatingcapacitor is placed in parallel with the IH coil and itis fed by the current source [7ndash11]

2 Advances in Power Electronics

Leq Req

Figure 1 Equivalent circuit representation of an IH coil

The analysis of these circuits has been performed in greatdetails and the comparative assessment is also reported in theliterature [12 13]

A topology named L-LC RI has been proposed for IHapplications [14ndash21] which takes most of the merits ofSRI and PRI while eliminating their limitations It operateswith input dc voltage source thereby eliminating bulkyinput current smoothening inductor It offers high currentgain which in turn reduces the current rating of the sec-ondary winding of matching transformer and the feeder tocoil

Metal organic vapour phase epitaxy (MOVPE) [22] is ahighly controlled method for the deposition of semiconduc-tor epitaxial layers and heterostructures which are requiredfor the development of several optoelectronic and electronicdevices The process of MOVPE involves a vapour phasereaction betweenmetalorganic compound and a hydride gaswhich are transported to a heated (around 1200∘C) graphitesusceptor resulting in a growth of the desired material IH isone of the preferred methods for noncontact heating of thesusceptor

The paper aims to investigate the characteristics of L-LC RI for an application demanding a 25 kW 25 kHz IHpower supply to heat graphite susceptor to 1200∘C in aMOVPE system for the growth of nitride semiconductorsbeing developed at our Institute Section 2 describes ACanalysis of L-LC CN and investigates various characteristicswhen the converter is operated at the resonant frequencyThe suggested operating point is different than the previouslyproposed operating point which provides enhanced currentgain with smaller auxiliary inductance and results in nearin-phase operation Section 3 describes the operation ofhigh-119876 L-LC compensating network (CN) with square-wavevoltage source leading to an optimum choice of the auxiliaryinductor The requirements description and design of thepractical system are discussed in Section 4 Experimentalresults are presented in Section 5

2 Analysis of L-LC CN

Figure 2 shows the L-LC RI Input dc source 119881119889could be

an unregulated source (obtained with single-phase or three-phase diode rectifier and filter) or could be a regulatedvoltage source (obtained with single-phase or three-phasediodeSCR rectifier and filter or another front-end switch-mode regulator) In the former case regulation of the powerto the work piece should be done in the RI stage usingfrequency variation [23 24] fixed-frequency pulse widthmodulation (PWM) [25ndash27] or pulse density modulation(PDM) [28 29] In the latter case the output control canbe done by varying 119881

119889 providing easy control of the output

S1 D1 S3 D3

S2 D2 S4 D4

Vd

La

Tr

C

Leq

Req

+minus

Figure 2 Circuit diagram of L-LC RI for IH application

La

Leq

Req

C

Figure 3 Equivalent circuit diagram of L-LC RI for analysis

power over a wide range However two cascaded converterstend to reduce the overall efficiency

The following analysis based on the fundamental fre-quency approximation examines the important characteris-tics of L-LC topology In an equivalent circuit of L-LC CNshown in Figure 3 input voltage source is assumed to be asinusoidal voltage source whose rms value is equal to therms value of the fundamental component of the square-waveexcitation Following definitions are made for the analysis

Angular resonant frequency

120596119900= 2120587119891

119900=

1

radic119871eq119862 (1)

Normalized operating frequency

120596119899=120596

120596119900

(2)

where 120596 = 2120587119891 is the angular operating frequency and 119891 isthe operating or switching frequency

Characteristic Impedance

119885119899= radic

119871eq

119862 (3)

Circuit 119876

119876 =

120596119900119871eq

119877eq=119885119899

119877eq (4)

Inductance ratio

120574 =119871119886

119871eq (5)

Advances in Power Electronics 3

1 2 3 4 5 6 7 8 9 1000

01

02

03

04

05

06

07

08

09

10

120596n =1

Q = 20

Q = 15

Q = 10Q = 5

120574

I Leq

N

(a)

1 2 3 4 5 6 7 8 9 10minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Q = 5 120596n = 1

Q = 10 120596n = 1

Q = 15 120596n = 1

Q = 20 120596n = 1

Q = 5 120596n = 120596o c

Q = 20 120596n = 120596o c

120574

120601(d

eg)

(b)

Figure 4 The plots of 119868119871eq119873

(a) and 120601 (b) as a function of 120574 for different values of 119876 at two operating points

The expression for normalized current in coil and nor-malized source current (or the current in inductor 119871

119886) can

be respectively derived as

119868119871eq119873

=

119868119871eq

119881119889119885119899

=2radic2

120587

1

(1119876) (1 minus 1205962

119899

120574) + 119895 [120596119899(1 + 120574) minus 1205963

119899

120574]

119868119871119886119873=

119868119871119886

119881119889119885119899

=2radic2

120587

(1 minus 1205962

119899

) + 119895120596119899(1119876)

(1119876) (1 minus 1205962

119899

120574) + 119895 [120596119899(1 + 120574) minus 1205963

119899

120574]

(6)

Next the salient characteristics of the converter operatingat the proposed operating point 120596

119899= 1 are investigated

leading to the following observations(1)

100381610038161003816100381610038161003816119868119871eq119873

100381610038161003816100381610038161003816120596119899=1

=2radic2

120587

119876

radic1198762 + (1 minus 120574)2

(7)

For 119876 ≫ |(1 minus 120574)|

100381610038161003816100381610038161003816119868119871eq119873

100381610038161003816100381610038161003816120596119899=1

asymp2radic2

120587 (8)

(2)

10038161003816100381610038161003816119868119871119886119873

10038161003816100381610038161003816120596119899=1

=2radic2

120587

1

radic1198762 + (1 minus 120574)2

(9)

1206011003816100381610038161003816120596119899=1

= ang119868119871119886119873

10038161003816100381610038161003816120596119899=1

= minustanminus1 (120574 minus 1

119876) (10)

05 06 07 08 09 10 11 12 13 14 150

5

10

15

20

25

Q = 5

Q = 10 Q = 20

Q = 15

120596n = 120596o c

120574 = 5

H

120596n

Figure 5 The plots of119867 as a function of 120596119899

for 120574 = 5

The source current at 120596119899= 1 is also seen to be inductive for

all values of 120574 gt 1 and the phase angle is function of 119876 and120574 If 120574 = 1 the source current is always in-phase with voltage

Figure 4(a) shows the plot of 119868119871eq119873

as a function of 120574 fordifferent values of 119876 When the converter is operated at 120596

119899=

1 119868119871eq119873

is seen to be relatively insensitive to 120574 particularlyat high values of 119876mdasha typical operating condition in an IHapplication

Figure 4(b) shows the plot of 120601 as a function of 120574 Thesource current lags the applied square-wave voltage 120596

119899=

1 While this lagging current is beneficial for zero-voltage-switching (ZVS) of the semiconductor switches it can beanticipated that a higher value of 120601 results in higher source


Cs

LaLeq

Req

is

(a)

C

LaLeq

Req

is

h

s1

(b)

La

s1 s1

is1 is1

Q2ReqQ2Req

(c)

La

h

ih

(d)

Figure 6 (a) Equivalent circuit for L-LC RI for analysis with V119904

(b) Equivalent circuit redrawn with V119904

decomposed into V1199041

and Vℎ

(c)Approximate equivalent circuit for fundamental frequency (d) Approximate equivalent circuit for harmonics frequencies

current causing more conduction loss in the switches It isevident from the plots of Figure 4(b) that 120601 is small foroperation at 120596

119899= 1 particularly for operation with high

119876 Therefore the source current and conduction loss in theswitches will be smaller at this operating point

The current gain of the CN119867 is given by

119867 =

119868119871eq119873

119868119871119886119873

=1

(1 minus 1205962119899

) + 119895120596119899(1119876)

(11)

which can further be simplified at 120596119899= 1 as

|119867|120596119899=1= 119876 (12)

Figure 5 shows the plot of 119867 as a function of 120596119899for 120574 = 5

and different values of 119876 Maximum current gain (equal to119876) is observed for operation at the proposed operating point120596119899= 1The characteristics and design of L-LC RI for IH applica-

tions operating at120596119899= 120596119900 119888= radic(1 + 120574)120574 have been reported

extensively in the literature [15ndash21] At this operating point

|119867|120596119899=120596119900 119888

=119876120574

radic1198762 + 120574 (1 + 120574)

(13)

For 119876 ≫ 120574 |119867|120596119899=120596119900 119888

asymp 120574 which is less than theoreticalmaximum value given by (12) at the proposed operatingpointThus as also shown in Figure 5 the proposed operatingpoint of L-LC RI results in the enhanced current gainFurther the expression for 120601 at the conventional operatingpoint can be written as

1206011003816100381610038161003816120596119899=120596119900 119888

= tanminus1(minus120574

119876radic1 + 120574

120574) (14)

Theplots of (14) as a function of 120574 are shown in Figure 4(b) for119876 = 5 and 119876 = 20 It can be seen that phase angle is smallerat the proposed operating point than the conventional oper-ating point thereby resulting in less conduction loss in theswitches

3 Behaviour of L-LC CN with Square-WaveVoltage Source

Analysis based on the fundamental frequency approximationpresented in Section 2 suggests that the converter whenoperated at 120596

119899= 1 offers highest current gain and small

phase angle between source voltage and current resultingin low reactive power loading and low conduction loss inthe semiconductor devices of the square-wave inverter Theanalysis presented in Section 2 assumes sine wave voltagesource at the input In practice the input voltage is a square-wave generated by operating switches 119878

1ndash1198784in Figure 2 at

50 per cent duty cycle In this section the behaviour of L-LC resonant inverter for operation at 120596

119899= 1 with square-

wave voltage source examined Equivalent circuit for L-LCRI for analysis with square-wave voltage source is shown inFigure 6(a) The source voltage V

119904can be defined as

V119904(119905) = 119881

119889sdot sign (sin (120596

119900119905)) (15)

V119904can be decomposed into its fundamental component V

1199041

and harmonics Vℎas

V119904(119905) = V

1199041(119905) + V

ℎ(119905) =

4119881119889

120587sin (120596

119900119905) + Vℎ(119905) (16)

From (15) and (16)

Vℎ(119905) = 119881

119889sdot sign (sin (120596

119900119905)) minus

4119881119889

120587sin (120596

119900119905)

= 119881119889minus4119881119889

120587sin (120596

119900119905) for 0 le 119905 le

119879119904

2

= minus119881119889minus4119881119889

120587sin (120596

119900119905) for

119879119904

2le 119905 le 119879

119904

(17)

wherein 119879119904is the switching period Thus equivalent circuit

of Figure 6(a) can be redrawn as Figure 6(b) wherein V119904

decomposed into v1199041and Vℎ


t

s(t)

ih(t)

is(t) is1(t)

(a)

t

s(t)

ih(t)

is(t) is1(t)

(b)

t

is(t)

120574 = 1

120574 = 2

120574 = 3

120574 = 5

120574 = 7

120574 = 10

(c)

Figure 7 Typical calculated waveforms of V119904

(119905) 1198941199041

(119905) 119894ℎ

(119905) and 119894119904

(119905) for low-119876 (119876 = 1 120574 = 1) (a) and high-119876 (119876 = 50 120574 = 1) (b) operationThe effect of 120574 on the waveform of 119894

119904

(119905) is illustrated by the calculated waveforms in (c) for 119876 = 50

Equivalent impedance (119885eq) of the 119871eq 119877eq and 119862

resonant circuit at 120596119899= 1 is given by

10038161003816100381610038161003816119885eq10038161003816100381610038161003816120596119899=1

= 119877eq119876radic1 + 1198762 asymp 119877eq119876

2 for 119876 ≫ 1 (18)

Further for high-119876 resonant circuit in IH applications 119885eqcan be approximated to be zero for all operating points otherthan 120596

119899= 1 Under this assumption equivalent circuit for

Figure 6(b) can be decoupled for operation at 120596119899= 1 and

at harmonic frequencies as shown in Figures 6(c) and 6(d)respectively Assuming 119877eq119876

2

≫ 120596119900119871119886 equivalent circuit at

120596119899= 1 can further be simplified as shown in Figure 6(c)

With this simplification the circuit can be analyzed forfundamental and harmonic frequencies separately to findout individual source current and then be added to find outresultant source current An expression for 119894

119904can be derived

as

119894119904(119905) = 119894

1199041(119905) + 119894

ℎ(119905)

1198941199041(119905) =

4119881119889

1205871198762119877eqsin (120596

119900119905)

119894ℎ(119905) =

119881119889

119871119886

(119905 minus119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for 0 le 119905 le119879119904

2

= minus119881119889

119871119886

(119905 minus3119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for119879119904

2le 119905 le 119879

119904

(19)

Figure 7(a) shows the calculated waveforms for the operationof the circuit under low-119876 condition It can be easily noticedthat 1198941199041(119905) being inversely proportional to 119876 is significantly

larger than 119894ℎ(119905) for low-119876 values Therefore resulting 119894

119904(119905)

is also nearly sinusoidal Under this condition the predic-tions of the ac analysis (Section 2) are reasonably accurateHowever under high-119876 condition as shown in Figure 7(b)amplitude of 119894

1199041(119905) is much smaller than 119894

ℎ(119905) Therefore

119894119904(119905) is nearly the same as 119894

ℎ(119905) and is highly nonsinusoidal

Under this condition the predictions of Section 2 tend to beerroneous Since the analysis of Section 2 does not accountfor harmonics the actual peak and rms values of 119894

119904calculated


by (3) are significantly more than those predicted by (9)This will result in degradation of the current gain from itsvalue predicted by (12) However the amplitude and rmsvalue of 119894

ℎ(119905) can be controlled by choosing a proper value

of 119871119886 Figure 7(c) shows the calculated waveform of 119894

119904(119905) for

different values of 120574 when 119876 = 50 Since the rms valueof 119894ℎ(119905) can be reduced by increasing the value of 119871

119886 the

degradation in the current gain can be corrected to someextent by choosing higher value of 120574 Figure 8 shows the plotsof current gain as a function of 119876 for different values of 120574 Aplot of the current gain predicted by (12) is also shown fordirect comparisonThe figure also shows the evolution of thecurrent gain at the conventional operating point predicted by(13) for 120574 = 1 and 120574 = 5 It is noticed that the actual currentgain at the proposed operating point is higher than that at theconventional operating point

Thephysical size of an inductor depends on its value peakcurrent and rms current Since peak and rms value of 119894

119904(119905)

decreases with increasing 119871119886 it is intuitive to expect that the

physical size of 119871119886will first reduce as 119871

119886increased reach a

minimum and subsequently increase with further increase in119871119886 To obtain a value of 119871

119886resulting in minimum size the

following term is defined as its normalized size index

119870119871119886

=

119871119886119868119904pk119868119904rms

119871eq119868119871eqpk119868119871eq rms (20)

Figure 9 shows the plots of (20) for different values of 119876 Itis seen that for high-119876 applications 119871

119886should typically be 5

times 119871eq

4 System Description

MOVPE is a highly controlled method for the deposition ofsemiconductor epitaxial layers and heterostructures whichare required for the development of several optoelectronicand electronic devices The process of MOVPE involves avapour phase reaction between metalorganic compound anda hydride gas which are transported to a heated (around1200∘C) graphite susceptor resulting in a growth of thedesired material A power supply is required to heat graphitesusceptor (50mm diameter and 20mm length) to 1200∘C ina quartz reactor of 80mm diameter

41 Work Coil and Resonant Capacitor While recommendedcoil design practices suggest that the coil should be as closeto the susceptor and the coil length should be larger thanthat of the susceptor [1] physical dimensions of the susceptorand the reactor force the inner diameter of the coil to be100mm Further since a stainless steel showerhead withnozzles for flowing gases into the reactor is attached to oneend of the reactor the maximum length of the coil is alsolimited to 50mm The coil is made up of hollow copperconductor The number of turns conductor diameter and itswall thickness are optimized considering various parameterslike coil resistance power loss electrical efficiency requiredcooling water flow rate and pressure drop The designed coilhas 4 turns of hollow copper conductor with 38 inch ODand SWG 19 wall thickness The coil resistance is estimated

0

10

20

30

40

50

0 10 20 30 40 50

Curr

ent g

ain

From (12)

Q

120574 = 1 120596n = 120596o c

120574 = 5 120596n = 120596o c

120574 = 1 120596n = 1

120574 = 15 120596n = 1

120574 = 2 120596n = 1120574 = 3 120596n = 1

120574 = 4 120596n = 1

120574 = 5 120596n = 1

Figure 8 The plots of current gain as a function of 119876 for differentvalues of 120574 at the at the proposed operating point 120596

119899

= 1 andconventional operating point 120596

119899

= 120596119900 119888

1 2 3 4 5 6 7 8 9 100

001

002

003

004

005

006

007K

La

Q = 15

Q = 20

Q = 25

Q = 30

120574

Figure 9 The plots of (20) showing the variation of 119870119871119886

as afunction of 120574 for different values of 119876

to be 113mΩ and coil inductance is 270 120583H The operatingfrequency of 25 kHz has been fixed to ensure uniform heatingof the susceptor (the skin depth of graphite is nearly 17mm at25 kHz) Equivalent resistance ofwork piece is estimated to be166mΩ The coil is designed to carry a maximum of 1000Arms

A bank of 6 conduction-cooled capacitors of 3 120583F eachhas been used as the resonant capacitor 119862 These capacitorsare mounted on a cold plate which in turn is water cooledHowever only 5 capacitors are used to get the resonantfrequency of 25 kHz The capacitor bank is kept very close tothe coil to reduce the circulating path

42 Power Circuit A schematic circuit diagram of the powercircuit is shown in Figure 10 which can broadly be dividedinto three sections front-end-three phase diode rectifier withfilter a dc-dc converter and the L-LC RI In addition to


PD

Ref phaseIntegral controller

VCO and driver

Set temperaturePID controllerIntegral controller

PWM and driver

Tempsensor

Front-end rectifier DC-DC converter L-LC RI

415 V

50 H

zAC

mai

ns LeqC

Req

La

TrD4

D3

Cdb

Rdb

S1

S2

D1

D2

S3

S4

Cb

Lb

Sb

Cf

Lf

Db

Ls

Cs1Cs2

Ds2

Ds1

Ds3

Process controller module

Figure 10 The power circuit and the control block diagram of a 25 kHz 25 kW induction heating power supply using L-LC RI for MOVPEsystem The process controller shown for the completeness is not used in the laboratory testing of the system

these the actual power circuit also consists of breakers EMIfilter and inrush-current-limiting circuit in the rectifier stageHowever these are not shown in Figure 10 for clarity

The input to the power supply is 415V 50Hz and 3-phaseac The values of filter inductor (119871

119891) and capacitor (119862

119891) in

the input rectifier section are 22mH and 3mF respectivelygiving the cut-off frequency of 70Hz

It is seen in Section 2 that the L-LC RI exhibits desiredbehaviour only when it is operated at 120596

119899= 1 Therefore

variation of switching frequency for output power control isnot permitted Therefore fixed-frequency control methodssuch as pulse width modulation (PWM) or the quantizedcontrol methods such as pulse density modulation can beused However the soft-switching operation of the switchesin RI stage may not be guaranteed over the entire operatingrange and the quantized control methods such as PDMresult in discrete output levels and also have limited range ofoutput power control If on the other hand input voltage tothe RI stage is controlled output power control over a widerrange and operational flexibility can be ascertained Demeritsof this scheme namely requirement of an intermediate dc-dcconverter stage and reduction of overall conversion efficiencyare sacrificed for aforementioned advantages

A dc-dc buck converter is chosen as the intermediate dc-dc converter stage IGBT 119878

119887and diode119863

119887constitute themain

switching cell A passive loss-less snubber circuit (composedof snubber inductor 119871

119904 capacitors 119862

1199041 1198621199042 and diodes 119863

1199041

1198631199042 and 119863

1199043) is used to limit switching losses in this stage

It is worthwhile to note that apart from the careful choice ofthe component values described in [30] an equal attentionto several practical aspects [31] such as forward recovery ofsnubber diodes and stray inductances is also important foreffective snubber action Inductor 119871


119887 119862119887119889 and

resistor 119877119887119889

constitute a high-frequency damped low-passfilter

Two half-bridge IGBT modules SKM100GB123D areused to realize the H-bridge in the inverter section feeding

Figure 11 The photograph of the developed induction heatingpower supply The graphite susceptor heated to 1200∘C is shown inthe inset

square-wave voltage to the high-frequency isolation trans-former The transformer 119879

119903having 1 1 turns ratio has been

developed using 7 pairs of EE80 core with 7 turns of theprimary winding and 7 turns of the secondary windingWhile the primary is wound using 02 times 50mm copper foiloxygen-free high conductivity hollow copper conductor isused for water-cooled secondary winding The results forFigure 9 suggest that the additional resonant inductor 119871

119886

should approximately be 5 times 119871eq for high-119876 operationTherefore in the present system 119871

119886= 135 120583H is chosen

The transformer leakage inductance is estimated to be 5 120583HThe additional 85 120583H inductance is realized by running thesecondary turns around auxiliary gapped core (2 pairs ofEE80) following the configuration suggested in [32]

A capacitor has been placed in series with the transformerprimary (not shown in Figure 10) to prevent the transformersaturation in the event of unsymmetrical excitation Table 1


(1)

(2)

T

2gt

(a)

(1) (2)

T

T

2gt

(b)

(1) (2)

TT2gt

(c)

(1) (2)

TT2gt

(d)

Figure 12 Experimental waveforms (a) V119904

(trace 1 200Vdiv) and 119894119904

(trace 2 25 Adiv) 119909-scale 5 120583sdiv (b) Waveforms at turn-on IGBTcollector-to-emitter voltage (trace 1 200Vdiv) and gate-to-emitter voltage (trace 2 10Vdiv) 119909-scale 500 nsdiv (c) Waveforms at turn-off IGBT collector-to-emitter voltage (trace 1 200Vdiv) and gate-to-emitter voltage (trace 2 10Vdiv) 119909-scale 500 nsdiv (d) V

119904

(trace 1200Vdiv) and the voltage across the work coil (trace 2 200Vdiv) 119909-scale 10 120583sdiv

Table 1 Component values and device part numbers used in thesystem

Component ValuePart number119871119891

22mH119862119891

3mF119871119887

300 120583H119862119887

30120583F119862119887119889

150120583F119877119887119889

22Ω119871119904

5120583H1198621199041

003 120583F1198621199042

033 120583F119871119886

135120583H119862 15120583F1198631199031

-1198631199036

VUO 82119878119887

-119863119887

SKM100GAR123D1198781

-1198784

and1198631

-1198634

SKM100GB123D two modules1198631199041

1198631199042

1198631199043

DSEI 31 times 100

summarizes the values of the components and part numbersof the semiconductor devices used in the system

43 Control Circuit The input dc voltage to the square-waveinverter is controlled to regulate the susceptor temperatureThe block diagram of overall control system is also shownin Figure 10 A thermocouple-type temperature sensor andprocess PID controller module are planned to be used forprogramming and controlling susceptor temperature Theoutput of PID module acts as the reference for the innercontrol loop to control the input dc voltage to the square-waveinverter by controlling the duty ratio of the buck converterAn additional phase control loop is employed to maintain

the tune-in condition of the RI stage against the slow driftof resonant frequency over varied operating conditions andtimeThis loop senses the phase of the inverter output currentusing a phase detector PD The output of the controllerdrives a voltage controlled oscillator (VCO) that adjusts theswitching frequency of the inverter in such a way that theinverter output current lags the voltage slightly

5 Results

The photograph of the developed induction heating powersupply being tested in laboratory to heat a graphite susceptoris shown in Figure 11The graphite susceptor heated to 1200∘Cin air is shown in the inset

The inverter output voltage V119904 (trace 1 200Vdiv) and

current waveforms 119894119904 (trace 2 25Adiv) are shown in

Figure 12(a) The nature of current waveform matches withthe predicted waveform given in Figure 7 The waveforms ofcollector-to-emitter (trace 1 200Vdiv) and gate-to-emitter(trace 2 10Vdiv) voltage of an IGBT in H-bridge inverterduring turn-on and turn-off transitions are shown in Fig-ures 12(b) and 12(c) respectively demonstrating the soft-switching Figure 12(d) shows the waveforms of V

119904(trace 1

200Vdiv) and the voltage across the work coil (trace 2200Vdiv) showing that only fundamental component ofinput square-wave voltage has been passed to the work coil

6 Conclusion

The paper reports the various issues in the developmentof an IH power supply for MOVPE application using L-LC RI The fundamental frequency ac analysis of L-LC RIis revisited and it is shown that the converter exhibitsenhanced current gain and near-unity power factor operationwhen operated at the resonant frequency Further analysis of


the circuit with square-wave voltage source highlights theeffect of the auxiliary inductor on the source current wave-form leading to the optimum choice for the value of auxiliaryinductor The requirements of MOVPE system demanding a25 kW 25 kHz IH power supply to heat a graphite susceptorto 1200∘C the configuration of developed IH system andexperimental results are presented thereby demonstratingthe suitability of L-LC RI operating at its resonant frequencyfor this application

References

[1] C A Tudbury Basics of Induction Heating vol 1 Library ofCongress Catalog Number 60-8958 1960

[2] IMillan JM Burdıo J Acero O Lucıa and S Llorente ldquoSeriesresonant inverter with selective harmonic operation applied toall-metal domestic induction heatingrdquo IET Power Electronicsvol 4 no 5 pp 587ndash592 2011

[3] O Lucıa J M Burdio I Millan J Acero and D PuyalldquoLoad-adaptive control algorithm of half-bridge series resonantinverter for domestic induction heatingrdquo IEEE Transactions onIndustrial Electronics vol 56 no 8 pp 3106ndash3116 2009

[4] P K Jain J R Espinoza and S B Dewan ldquoSelf-startedvoltage-source series-resonant converter for high-power induc-tion heating and melting applicationsrdquo IEEE Transactions onIndustry Applications vol 34 no 3 pp 518ndash525 1998

[5] H P Ngoc H Fujita K Ozaki and N Uchida ldquoPhase anglecontrol of high-frequency resonant currents in a multipleinverter system for zone-control induction heatingrdquo IEEETransactions on Power Electronics vol 26 no 11 pp 3357ndash33662011

[6] F Forest E Laboure F Costa and J Y Gaspard ldquoPrinciple ofa multi-loadsingle converter system for low power inductionheatingrdquo IEEE Transactions on Power Electronics vol 15 no 2pp 223ndash230 2000

[7] R Bonert and J D Lavers ldquoSimple starting scheme for a parallelresonance inverter for induction heatingrdquo IEEE Transactions onPower Electronics vol 9 no 3 pp 281ndash287 1994

[8] E J Dede V Esteve J Garcia A E Navarro E Maset and ESanchis ldquoAnalysis of losses and thermal design of high-powerhigh-frequency resonant current fed inverters for inductionheatingrdquo in Proceedings of the 19th International Conference onIndustrial Electronics Control and Instrumentation pp 1046ndash1051 November 1993

[9] E J Dede J Jordan J V Gonzalez J Linares V Esteve and EMaset ldquoConception and design of a parallel resonant converterfor induction heatingrdquo in Proceedings of the 6th Annual AppliedPower Electronics Conference and Exposition (APEC rsquo91) pp 38ndash44 March 1991

[10] E J Dede J Jordan J A Linares et al ldquoOn the design ofmedium and high power current fed inverters for inductionheatingrdquo inProceedings of the IEEE Industry Applications SocietyAnnual Meeting pp 1047ndash1053 October 1991

[11] V Chudnovsky B Axelrod and A L Shenkman ldquoAn approx-imate analysis of a starting process of a current source parallelinverter with a high-Q induction heating loadrdquo IEEE Transac-tions on Power Electronics vol 12 no 2 pp 294ndash301 1997

[12] L Hobson and D W Tebb ldquoTransistorized power supplies forinduction heatingrdquo International Journal of Electronics vol 59no 5 pp 543ndash552 1985

[13] F P Dawson and P Jain ldquoA comparison of load commutatedinverter systems for induction heating and melting applica-tionsrdquo IEEE Transactions on Power Electronics vol 6 no 3 pp430ndash441 1991

[14] G L Fischer and H-C Doht ldquoInverter system for inductivetube welding utilizing resonance transformationrdquo in Proceed-ings of the 29th Institute for Advanced Study (IAS) AnnualMeeting pp 833ndash840 October 1994

[15] J Espi E Dede A Ferreres and R Garcia ldquoSteady-statefrequency analysis of the L-LC resonant inverter for inductionheatingrdquo in Proceedings of the IEEE International Power Elec-tronics Congress Technical Proceedings (CIEP rsquo96) pp 22ndash281999

[16] J M Espi E J Dede E Navarro E Sanchis and A FerreresldquoFeatures and design of the voltage-fed L-LC resonant inverterfor induction heatingrdquo in Proceedings of the 30th Annual IEEEPower Electronics Specialists Conference (PESC rsquo99) pp 1126ndash1131 July 1999

[17] J M Espı and E J Dede ldquoDesign considerations for threeelement L-LC resonant inverters for induction heatingrdquo Inter-national Journal of Electronics vol 86 no 10 pp 1205ndash12161999

[18] S Chudjuarjeen A Sangswang andC Koompai ldquoAn improvedLLC resonant inverter for induction-heating applications withasymmetrical controlrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 7 pp 2915ndash2925 2011

[19] E J Dede J Gonzalez J A Linares J Jordan D Ramirez and PRueda ldquo25-kW50-kHz generator for induction heatingrdquo IEEETransactions on Industrial Electronics vol 38 no 3 pp 203ndash2091991

[20] S Dieckerhoff M J Ryan and R W De Doncker ldquoDesignof an IGBT-based LCL-resonant inverter for high-frequencyinduction heatingrdquo in Proceedings of the IEEE Industry Applica-tions Conference and 34th IAS Annual Meeting pp 2039ndash2045October 1999

[21] J M E Huerta E J D G Santamarıa R G Gil and J Castello-Moreno ldquoDesign of the L-LC resonant inverter for inductionheating based on its equivalent SRIrdquo IEEE Transactions onIndustrial Electronics vol 54 no 6 pp 3178ndash3187 2007

[22] KNishida SHaneda KHaraHMunekata andHKukimotoldquoMOVPE of GaN using a specially designed two-flow horizon-tal reactorrdquo Journal of Crystal Growth vol 170 no 1-4 pp 312ndash315 1997

[23] Y-S Kwon S-B Yoo and D-S Hyun ldquoHalf-bridge seriesresonant inverter for induction heating applications with load-adaptive PFM control strategyrdquo in Proceedings of the 14th annualApplied Power Electronics Conference and Exposition (APECrsquo99) pp 575ndash581 March 1999

[24] H W Koertzen J D Van Wyk and J A Ferreira ldquoCom-parison of swept frequency and phase shift control for forcedcommutated series resonant induction heating convertersrdquo inProceedings of the Conference Record of the IEEE IndustryApplications and 30th IAS Annual Meeting pp 1964ndash1969October 1995

[25] J M Burdıo L A Barragan F Monterde D Navarro andJ Acero ldquoAsymmetrical voltage-cancellation control for full-bridge series resonant invertersrdquo IEEE Transactions on PowerElectronics vol 19 no 2 pp 461ndash469 2004

[26] L Grajales and F C Lee ldquoControl system design andsmall-signal analysis of a phase-shift-controlled series-resonantinverter for induction heatingrdquo in Proceedings of the IEEE PowerElectronics Specialist Conference pp 450ndash456 1995


[27] L Grajales J A Sabate K R Wang W A Tabisz and FC Lee ldquoDesign of a 10 kW 500 kHz phase-shift controlledseries-resonant inverter for induction heatingrdquo in Proceedingsof the 28th Annual Meeting of the IEEE Industry ApplicationsConference pp 843ndash849 October 1993

[28] N A Ahmed ldquoHigh-frequency soft-switching AC conversioncircuit with dual-mode PWMPDM control strategy for high-power IH applicationsrdquo IEEE Transactions on Industrial Elec-tronics vol 58 no 4 pp 1440ndash1448 2011

[29] V Esteve E Sanchis-Kilders J Jordan et al ldquoImproving theefficiency of IGBT series-resonant inverters using pulse densitymodulationrdquo IEEE Transactions on Industrial Electronics vol58 no 3 pp 979ndash987 2011

[30] C-J Tseng and C-L Chen ldquoPassive lossless snubbers for dcdcconvertersrdquo in Proceedings of the 13th Annual Applied PowerElectronics Conference and Exposition (APEC rsquo98) pp 1049ndash1054 February 1998

[31] M Borage and S Tiwari ldquoOn the development of 30 kVA430 Hz sine wave inverter for DC accelerator applicationrdquo inProceedings of the Indian Particle Accelerator Conference (InPACrsquo11) IUAC New Delhi India February 2011

[32] A Kats G Ivensky and S Ben-Yaakov ldquoApplication of inte-grated magnetics in resonant convertersrdquo in Proceedings of theIEEE 12th Applied Power Electronics Conference pp 925ndash930February 1997

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Leq Req

Figure 1 Equivalent circuit representation of an IH coil

The analysis of these circuits has been performed in greatdetails and the comparative assessment is also reported in theliterature [12 13]

A topology named L-LC RI has been proposed for IHapplications [14ndash21] which takes most of the merits ofSRI and PRI while eliminating their limitations It operateswith input dc voltage source thereby eliminating bulkyinput current smoothening inductor It offers high currentgain which in turn reduces the current rating of the sec-ondary winding of matching transformer and the feeder tocoil

Metal organic vapour phase epitaxy (MOVPE) [22] is ahighly controlled method for the deposition of semiconduc-tor epitaxial layers and heterostructures which are requiredfor the development of several optoelectronic and electronicdevices The process of MOVPE involves a vapour phasereaction betweenmetalorganic compound and a hydride gaswhich are transported to a heated (around 1200∘C) graphitesusceptor resulting in a growth of the desired material IH isone of the preferred methods for noncontact heating of thesusceptor

The paper aims to investigate the characteristics of L-LC RI for an application demanding a 25 kW 25 kHz IHpower supply to heat graphite susceptor to 1200∘C in aMOVPE system for the growth of nitride semiconductorsbeing developed at our Institute Section 2 describes ACanalysis of L-LC CN and investigates various characteristicswhen the converter is operated at the resonant frequencyThe suggested operating point is different than the previouslyproposed operating point which provides enhanced currentgain with smaller auxiliary inductance and results in nearin-phase operation Section 3 describes the operation ofhigh-119876 L-LC compensating network (CN) with square-wavevoltage source leading to an optimum choice of the auxiliaryinductor The requirements description and design of thepractical system are discussed in Section 4 Experimentalresults are presented in Section 5

2 Analysis of L-LC CN

Figure 2 shows the L-LC RI Input dc source 119881119889could be

an unregulated source (obtained with single-phase or three-phase diode rectifier and filter) or could be a regulatedvoltage source (obtained with single-phase or three-phasediodeSCR rectifier and filter or another front-end switch-mode regulator) In the former case regulation of the powerto the work piece should be done in the RI stage usingfrequency variation [23 24] fixed-frequency pulse widthmodulation (PWM) [25ndash27] or pulse density modulation(PDM) [28 29] In the latter case the output control canbe done by varying 119881

119889 providing easy control of the output

S1 D1 S3 D3

S2 D2 S4 D4

Vd

La

Tr

C

Leq

Req

+minus

Figure 2 Circuit diagram of L-LC RI for IH application

La

Leq

Req

C

Figure 3 Equivalent circuit diagram of L-LC RI for analysis

power over a wide range However two cascaded converterstend to reduce the overall efficiency

The following analysis based on the fundamental fre-quency approximation examines the important characteris-tics of L-LC topology In an equivalent circuit of L-LC CNshown in Figure 3 input voltage source is assumed to be asinusoidal voltage source whose rms value is equal to therms value of the fundamental component of the square-waveexcitation Following definitions are made for the analysis

Angular resonant frequency

120596119900= 2120587119891

119900=

1

radic119871eq119862 (1)

Normalized operating frequency

120596119899=120596

120596119900

(2)

where 120596 = 2120587119891 is the angular operating frequency and 119891 isthe operating or switching frequency

Characteristic Impedance

119885119899= radic

119871eq

119862 (3)

Circuit 119876

119876 =

120596119900119871eq

119877eq=119885119899

119877eq (4)

Inductance ratio

120574 =119871119886

119871eq (5)


1 2 3 4 5 6 7 8 9 1000

01

02

03

04

05

06

07

08

09

10

120596n =1

Q = 20

Q = 15

Q = 10Q = 5

120574

I Leq

N

(a)

1 2 3 4 5 6 7 8 9 10minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Q = 5 120596n = 1

Q = 10 120596n = 1

Q = 15 120596n = 1

Q = 20 120596n = 1

Q = 5 120596n = 120596o c

Q = 20 120596n = 120596o c

120574

120601(d

eg)

(b)




119886) can


119868119871eq119873

=

119868119871eq

119881119889119885119899

=2radic2

120587

1

(1119876) (1 minus 1205962

119899

120574) + 119895 [120596119899(1 + 120574) minus 1205963

119899

120574]

119868119871119886119873=

119868119871119886

119881119889119885119899

=2radic2

120587

(1 minus 1205962

119899

) + 119895120596119899(1119876)

(1119876) (1 minus 1205962

119899

120574) + 119895 [120596119899(1 + 120574) minus 1205963

119899

120574]

(6)




100381610038161003816100381610038161003816119868119871eq119873

100381610038161003816100381610038161003816120596119899=1

=2radic2

120587

119876

radic1198762 + (1 minus 120574)2

(7)

For 119876 ≫ |(1 minus 120574)|

100381610038161003816100381610038161003816119868119871eq119873

100381610038161003816100381610038161003816120596119899=1

asymp2radic2

120587 (8)

(2)

10038161003816100381610038161003816119868119871119886119873

10038161003816100381610038161003816120596119899=1

=2radic2

120587

1

radic1198762 + (1 minus 120574)2

(9)

1206011003816100381610038161003816120596119899=1

= ang119868119871119886119873

10038161003816100381610038161003816120596119899=1


119876) (10)

05 06 07 08 09 10 11 12 13 14 150

5

10

15

20

25

Q = 5

Q = 10 Q = 20

Q = 15

120596n = 120596o c

120574 = 5

H

120596n


for 120574 = 5





119899=

1 119868119871eq119873



119899=



Cs

LaLeq

Req

is

(a)

C

LaLeq

Req

is

h

s1

(b)

La

s1 s1

is1 is1

Q2ReqQ2Req

(c)

La

h

ih

(d)




and Vℎ






119867 =

119868119871eq119873

119868119871119886119873

=1

(1 minus 1205962119899

) + 119895120596119899(1119876)

(11)


|119867|120596119899=1= 119876 (12)





|119867|120596119899=120596119900 119888

=119876120574

radic1198762 + 120574 (1 + 120574)

(13)

For 119876 ≫ 120574 |119867|120596119899=120596119900 119888


1206011003816100381610038161003816120596119899=120596119900 119888


119876radic1 + 120574

120574) (14)











V119904(119905) = 119881

119889sdot sign (sin (120596

119900119905)) (15)


1199041


V119904(119905) = V

1199041(119905) + V

ℎ(119905) =

4119881119889

120587sin (120596

119900119905) + Vℎ(119905) (16)

From (15) and (16)

Vℎ(119905) = 119881

119889sdot sign (sin (120596

119900119905)) minus

4119881119889

120587sin (120596

119900119905)

= 119881119889minus4119881119889

120587sin (120596

119900119905) for 0 le 119905 le

119879119904

2

= minus119881119889minus4119881119889

120587sin (120596

119900119905) for

119879119904

2le 119905 le 119879

119904

(17)





t

s(t)

ih(t)

is(t) is1(t)

(a)

t

s(t)

ih(t)

is(t) is1(t)

(b)

t

is(t)

120574 = 1

120574 = 2

120574 = 3

120574 = 5

120574 = 7

120574 = 10

(c)


(119905) 1198941199041

(119905) 119894ℎ

(119905) and 119894119904


119904




10038161003816100381610038161003816119885eq10038161003816100381610038161003816120596119899=1

= 119877eq119876radic1 + 1198762 asymp 119877eq119876

2 for 119876 ≫ 1 (18)





2





as

119894119904(119905) = 119894

1199041(119905) + 119894

ℎ(119905)

1198941199041(119905) =

4119881119889

1205871198762119877eqsin (120596

119900119905)

119894ℎ(119905) =

119881119889

119871119886

(119905 minus119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for 0 le 119905 le119879119904

2

= minus119881119889

119871119886

(119905 minus3119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for119879119904

2le 119905 le 119879

119904

(19)



119904(119905)







119904calculated





119904(119905) for


119886 the



119904(119905)







119870119871119886

=

119871119886119868119904pk119868119904rms

119871eq119868119871eqpk119868119871eq rms (20)



times 119871eq




0

10

20

30

40

50

0 10 20 30 40 50

Curr

ent g

ain

From (12)

Q

120574 = 1 120596n = 120596o c

120574 = 5 120596n = 120596o c

120574 = 1 120596n = 1

120574 = 15 120596n = 1

120574 = 2 120596n = 1120574 = 3 120596n = 1

120574 = 4 120596n = 1

120574 = 5 120596n = 1


119899


119899

= 120596119900 119888

1 2 3 4 5 6 7 8 9 100

001

002

003

004

005

006

007K

La

Q = 15

Q = 20

Q = 25

Q = 30

120574







PD


VCO and driver


PWM and driver

Tempsensor


415 V

50 H

zAC

mai

ns LeqC

Req

La

TrD4

D3

Cdb

Rdb

S1

S2

D1

D2

S3

S4

Cb

Lb

Sb

Cf

Lf

Db

Ls

Cs1Cs2

Ds2

Ds1

Ds3






119891) in



119899= 1 Therefore



119887and diode119863




1199041 1198621199042 and diodes 119863

1199041

1198631199042 and 119863




119887 119862119887119889 and

resistor 119877119887119889







119886


119886= 135 120583H is chosen




(1)

(2)

T

2gt

(a)

(1) (2)

T

T

2gt

(b)

(1) (2)

TT2gt

(c)

(1) (2)

TT2gt

(d)


(trace 1 200Vdiv) and 119894119904


119904




22mH119862119891

3mF119871119887

300 120583H119862119887

30120583F119862119887119889

150120583F119877119887119889

22Ω119871119904

5120583H1198621199041

003 120583F1198621199042

033 120583F119871119886

135120583H119862 15120583F1198631199031

-1198631199036

VUO 82119878119887

-119863119887

SKM100GAR123D1198781

-1198784

and1198631

-1198634


1198631199042

1198631199043

DSEI 31 times 100




5 Results





119904(trace 1


6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 2 3 4 5 6 7 8 9 1000

01

02

03

04

05

06

07

08

09

10

120596n =1

Q = 20

Q = 15

Q = 10Q = 5

120574

I Leq

N

(a)

1 2 3 4 5 6 7 8 9 10minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Q = 5 120596n = 1

Q = 10 120596n = 1

Q = 15 120596n = 1

Q = 20 120596n = 1

Q = 5 120596n = 120596o c

Q = 20 120596n = 120596o c

120574

120601(d

eg)

(b)




119886) can


119868119871eq119873

=

119868119871eq

119881119889119885119899

=2radic2

120587

1

(1119876) (1 minus 1205962

119899

120574) + 119895 [120596119899(1 + 120574) minus 1205963

119899

120574]

119868119871119886119873=

119868119871119886

119881119889119885119899

=2radic2

120587

(1 minus 1205962

119899

) + 119895120596119899(1119876)

(1119876) (1 minus 1205962

119899

120574) + 119895 [120596119899(1 + 120574) minus 1205963

119899

120574]

(6)




100381610038161003816100381610038161003816119868119871eq119873

100381610038161003816100381610038161003816120596119899=1

=2radic2

120587

119876

radic1198762 + (1 minus 120574)2

(7)

For 119876 ≫ |(1 minus 120574)|

100381610038161003816100381610038161003816119868119871eq119873

100381610038161003816100381610038161003816120596119899=1

asymp2radic2

120587 (8)

(2)

10038161003816100381610038161003816119868119871119886119873

10038161003816100381610038161003816120596119899=1

=2radic2

120587

1

radic1198762 + (1 minus 120574)2

(9)

1206011003816100381610038161003816120596119899=1

= ang119868119871119886119873

10038161003816100381610038161003816120596119899=1


119876) (10)

05 06 07 08 09 10 11 12 13 14 150

5

10

15

20

25

Q = 5

Q = 10 Q = 20

Q = 15

120596n = 120596o c

120574 = 5

H

120596n


for 120574 = 5





119899=

1 119868119871eq119873



119899=



Cs

LaLeq

Req

is

(a)

C

LaLeq

Req

is

h

s1

(b)

La

s1 s1

is1 is1

Q2ReqQ2Req

(c)

La

h

ih

(d)




and Vℎ






119867 =

119868119871eq119873

119868119871119886119873

=1

(1 minus 1205962119899

) + 119895120596119899(1119876)

(11)


|119867|120596119899=1= 119876 (12)





|119867|120596119899=120596119900 119888

=119876120574

radic1198762 + 120574 (1 + 120574)

(13)

For 119876 ≫ 120574 |119867|120596119899=120596119900 119888


1206011003816100381610038161003816120596119899=120596119900 119888


119876radic1 + 120574

120574) (14)











V119904(119905) = 119881

119889sdot sign (sin (120596

119900119905)) (15)


1199041


V119904(119905) = V

1199041(119905) + V

ℎ(119905) =

4119881119889

120587sin (120596

119900119905) + Vℎ(119905) (16)

From (15) and (16)

Vℎ(119905) = 119881

119889sdot sign (sin (120596

119900119905)) minus

4119881119889

120587sin (120596

119900119905)

= 119881119889minus4119881119889

120587sin (120596

119900119905) for 0 le 119905 le

119879119904

2

= minus119881119889minus4119881119889

120587sin (120596

119900119905) for

119879119904

2le 119905 le 119879

119904

(17)





t

s(t)

ih(t)

is(t) is1(t)

(a)

t

s(t)

ih(t)

is(t) is1(t)

(b)

t

is(t)

120574 = 1

120574 = 2

120574 = 3

120574 = 5

120574 = 7

120574 = 10

(c)


(119905) 1198941199041

(119905) 119894ℎ

(119905) and 119894119904


119904




10038161003816100381610038161003816119885eq10038161003816100381610038161003816120596119899=1

= 119877eq119876radic1 + 1198762 asymp 119877eq119876

2 for 119876 ≫ 1 (18)





2





as

119894119904(119905) = 119894

1199041(119905) + 119894

ℎ(119905)

1198941199041(119905) =

4119881119889

1205871198762119877eqsin (120596

119900119905)

119894ℎ(119905) =

119881119889

119871119886

(119905 minus119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for 0 le 119905 le119879119904

2

= minus119881119889

119871119886

(119905 minus3119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for119879119904

2le 119905 le 119879

119904

(19)



119904(119905)







119904calculated





119904(119905) for


119886 the



119904(119905)







119870119871119886

=

119871119886119868119904pk119868119904rms

119871eq119868119871eqpk119868119871eq rms (20)



times 119871eq




0

10

20

30

40

50

0 10 20 30 40 50

Curr

ent g

ain

From (12)

Q

120574 = 1 120596n = 120596o c

120574 = 5 120596n = 120596o c

120574 = 1 120596n = 1

120574 = 15 120596n = 1

120574 = 2 120596n = 1120574 = 3 120596n = 1

120574 = 4 120596n = 1

120574 = 5 120596n = 1


119899


119899

= 120596119900 119888

1 2 3 4 5 6 7 8 9 100

001

002

003

004

005

006

007K

La

Q = 15

Q = 20

Q = 25

Q = 30

120574







PD


VCO and driver


PWM and driver

Tempsensor


415 V

50 H

zAC

mai

ns LeqC

Req

La

TrD4

D3

Cdb

Rdb

S1

S2

D1

D2

S3

S4

Cb

Lb

Sb

Cf

Lf

Db

Ls

Cs1Cs2

Ds2

Ds1

Ds3






119891) in



119899= 1 Therefore



119887and diode119863




1199041 1198621199042 and diodes 119863

1199041

1198631199042 and 119863




119887 119862119887119889 and

resistor 119877119887119889







119886


119886= 135 120583H is chosen




(1)

(2)

T

2gt

(a)

(1) (2)

T

T

2gt

(b)

(1) (2)

TT2gt

(c)

(1) (2)

TT2gt

(d)


(trace 1 200Vdiv) and 119894119904


119904




22mH119862119891

3mF119871119887

300 120583H119862119887

30120583F119862119887119889

150120583F119877119887119889

22Ω119871119904

5120583H1198621199041

003 120583F1198621199042

033 120583F119871119886

135120583H119862 15120583F1198631199031

-1198631199036

VUO 82119878119887

-119863119887

SKM100GAR123D1198781

-1198784

and1198631

-1198634


1198631199042

1198631199043

DSEI 31 times 100




5 Results





119904(trace 1


6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Cs

LaLeq

Req

is

(a)

C

LaLeq

Req

is

h

s1

(b)

La

s1 s1

is1 is1

Q2ReqQ2Req

(c)

La

h

ih

(d)




and Vℎ






119867 =

119868119871eq119873

119868119871119886119873

=1

(1 minus 1205962119899

) + 119895120596119899(1119876)

(11)


|119867|120596119899=1= 119876 (12)





|119867|120596119899=120596119900 119888

=119876120574

radic1198762 + 120574 (1 + 120574)

(13)

For 119876 ≫ 120574 |119867|120596119899=120596119900 119888


1206011003816100381610038161003816120596119899=120596119900 119888


119876radic1 + 120574

120574) (14)











V119904(119905) = 119881

119889sdot sign (sin (120596

119900119905)) (15)


1199041


V119904(119905) = V

1199041(119905) + V

ℎ(119905) =

4119881119889

120587sin (120596

119900119905) + Vℎ(119905) (16)

From (15) and (16)

Vℎ(119905) = 119881

119889sdot sign (sin (120596

119900119905)) minus

4119881119889

120587sin (120596

119900119905)

= 119881119889minus4119881119889

120587sin (120596

119900119905) for 0 le 119905 le

119879119904

2

= minus119881119889minus4119881119889

120587sin (120596

119900119905) for

119879119904

2le 119905 le 119879

119904

(17)





t

s(t)

ih(t)

is(t) is1(t)

(a)

t

s(t)

ih(t)

is(t) is1(t)

(b)

t

is(t)

120574 = 1

120574 = 2

120574 = 3

120574 = 5

120574 = 7

120574 = 10

(c)


(119905) 1198941199041

(119905) 119894ℎ

(119905) and 119894119904


119904




10038161003816100381610038161003816119885eq10038161003816100381610038161003816120596119899=1

= 119877eq119876radic1 + 1198762 asymp 119877eq119876

2 for 119876 ≫ 1 (18)





2





as

119894119904(119905) = 119894

1199041(119905) + 119894

ℎ(119905)

1198941199041(119905) =

4119881119889

1205871198762119877eqsin (120596

119900119905)

119894ℎ(119905) =

119881119889

119871119886

(119905 minus119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for 0 le 119905 le119879119904

2

= minus119881119889

119871119886

(119905 minus3119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for119879119904

2le 119905 le 119879

119904

(19)



119904(119905)







119904calculated





119904(119905) for


119886 the



119904(119905)







119870119871119886

=

119871119886119868119904pk119868119904rms

119871eq119868119871eqpk119868119871eq rms (20)



times 119871eq




0

10

20

30

40

50

0 10 20 30 40 50

Curr

ent g

ain

From (12)

Q

120574 = 1 120596n = 120596o c

120574 = 5 120596n = 120596o c

120574 = 1 120596n = 1

120574 = 15 120596n = 1

120574 = 2 120596n = 1120574 = 3 120596n = 1

120574 = 4 120596n = 1

120574 = 5 120596n = 1


119899


119899

= 120596119900 119888

1 2 3 4 5 6 7 8 9 100

001

002

003

004

005

006

007K

La

Q = 15

Q = 20

Q = 25

Q = 30

120574







PD


VCO and driver


PWM and driver

Tempsensor


415 V

50 H

zAC

mai

ns LeqC

Req

La

TrD4

D3

Cdb

Rdb

S1

S2

D1

D2

S3

S4

Cb

Lb

Sb

Cf

Lf

Db

Ls

Cs1Cs2

Ds2

Ds1

Ds3






119891) in



119899= 1 Therefore



119887and diode119863




1199041 1198621199042 and diodes 119863

1199041

1198631199042 and 119863




119887 119862119887119889 and

resistor 119877119887119889







119886


119886= 135 120583H is chosen




(1)

(2)

T

2gt

(a)

(1) (2)

T

T

2gt

(b)

(1) (2)

TT2gt

(c)

(1) (2)

TT2gt

(d)


(trace 1 200Vdiv) and 119894119904


119904




22mH119862119891

3mF119871119887

300 120583H119862119887

30120583F119862119887119889

150120583F119877119887119889

22Ω119871119904

5120583H1198621199041

003 120583F1198621199042

033 120583F119871119886

135120583H119862 15120583F1198631199031

-1198631199036

VUO 82119878119887

-119863119887

SKM100GAR123D1198781

-1198784

and1198631

-1198634


1198631199042

1198631199043

DSEI 31 times 100




5 Results





119904(trace 1


6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










t

s(t)

ih(t)

is(t) is1(t)

(a)

t

s(t)

ih(t)

is(t) is1(t)

(b)

t

is(t)

120574 = 1

120574 = 2

120574 = 3

120574 = 5

120574 = 7

120574 = 10

(c)


(119905) 1198941199041

(119905) 119894ℎ

(119905) and 119894119904


119904




10038161003816100381610038161003816119885eq10038161003816100381610038161003816120596119899=1

= 119877eq119876radic1 + 1198762 asymp 119877eq119876

2 for 119876 ≫ 1 (18)





2





as

119894119904(119905) = 119894

1199041(119905) + 119894

ℎ(119905)

1198941199041(119905) =

4119881119889

1205871198762119877eqsin (120596

119900119905)

119894ℎ(119905) =

119881119889

119871119886

(119905 minus119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for 0 le 119905 le119879119904

2

= minus119881119889

119871119886

(119905 minus3119879119904

4) minus

4119881119889

120587120596119900119871119886

sin(120596119900119905 minus

120587

2)

for119879119904

2le 119905 le 119879

119904

(19)



119904(119905)







119904calculated





119904(119905) for


119886 the



119904(119905)







119870119871119886

=

119871119886119868119904pk119868119904rms

119871eq119868119871eqpk119868119871eq rms (20)



times 119871eq




0

10

20

30

40

50

0 10 20 30 40 50

Curr

ent g

ain

From (12)

Q

120574 = 1 120596n = 120596o c

120574 = 5 120596n = 120596o c

120574 = 1 120596n = 1

120574 = 15 120596n = 1

120574 = 2 120596n = 1120574 = 3 120596n = 1

120574 = 4 120596n = 1

120574 = 5 120596n = 1


119899


119899

= 120596119900 119888

1 2 3 4 5 6 7 8 9 100

001

002

003

004

005

006

007K

La

Q = 15

Q = 20

Q = 25

Q = 30

120574







PD


VCO and driver


PWM and driver

Tempsensor


415 V

50 H

zAC

mai

ns LeqC

Req

La

TrD4

D3

Cdb

Rdb

S1

S2

D1

D2

S3

S4

Cb

Lb

Sb

Cf

Lf

Db

Ls

Cs1Cs2

Ds2

Ds1

Ds3






119891) in



119899= 1 Therefore



119887and diode119863




1199041 1198621199042 and diodes 119863

1199041

1198631199042 and 119863




119887 119862119887119889 and

resistor 119877119887119889







119886


119886= 135 120583H is chosen




(1)

(2)

T

2gt

(a)

(1) (2)

T

T

2gt

(b)

(1) (2)

TT2gt

(c)

(1) (2)

TT2gt

(d)


(trace 1 200Vdiv) and 119894119904


119904




22mH119862119891

3mF119871119887

300 120583H119862119887

30120583F119862119887119889

150120583F119877119887119889

22Ω119871119904

5120583H1198621199041

003 120583F1198621199042

033 120583F119871119886

135120583H119862 15120583F1198631199031

-1198631199036

VUO 82119878119887

-119863119887

SKM100GAR123D1198781

-1198784

and1198631

-1198634


1198631199042

1198631199043

DSEI 31 times 100




5 Results





119904(trace 1


6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119904(119905) for


119886 the



119904(119905)







119870119871119886

=

119871119886119868119904pk119868119904rms

119871eq119868119871eqpk119868119871eq rms (20)



times 119871eq




0

10

20

30

40

50

0 10 20 30 40 50

Curr

ent g

ain

From (12)

Q

120574 = 1 120596n = 120596o c

120574 = 5 120596n = 120596o c

120574 = 1 120596n = 1

120574 = 15 120596n = 1

120574 = 2 120596n = 1120574 = 3 120596n = 1

120574 = 4 120596n = 1

120574 = 5 120596n = 1


119899


119899

= 120596119900 119888

1 2 3 4 5 6 7 8 9 100

001

002

003

004

005

006

007K

La

Q = 15

Q = 20

Q = 25

Q = 30

120574







PD


VCO and driver


PWM and driver

Tempsensor


415 V

50 H

zAC

mai

ns LeqC

Req

La

TrD4

D3

Cdb

Rdb

S1

S2

D1

D2

S3

S4

Cb

Lb

Sb

Cf

Lf

Db

Ls

Cs1Cs2

Ds2

Ds1

Ds3






119891) in



119899= 1 Therefore



119887and diode119863




1199041 1198621199042 and diodes 119863

1199041

1198631199042 and 119863




119887 119862119887119889 and

resistor 119877119887119889







119886


119886= 135 120583H is chosen




(1)

(2)

T

2gt

(a)

(1) (2)

T

T

2gt

(b)

(1) (2)

TT2gt

(c)

(1) (2)

TT2gt

(d)


(trace 1 200Vdiv) and 119894119904


119904




22mH119862119891

3mF119871119887

300 120583H119862119887

30120583F119862119887119889

150120583F119877119887119889

22Ω119871119904

5120583H1198621199041

003 120583F1198621199042

033 120583F119871119886

135120583H119862 15120583F1198631199031

-1198631199036

VUO 82119878119887

-119863119887

SKM100GAR123D1198781

-1198784

and1198631

-1198634


1198631199042

1198631199043

DSEI 31 times 100




5 Results





119904(trace 1


6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










PD


VCO and driver


PWM and driver

Tempsensor


415 V

50 H

zAC

mai

ns LeqC

Req

La

TrD4

D3

Cdb

Rdb

S1

S2

D1

D2

S3

S4

Cb

Lb

Sb

Cf

Lf

Db

Ls

Cs1Cs2

Ds2

Ds1

Ds3






119891) in



119899= 1 Therefore



119887and diode119863




1199041 1198621199042 and diodes 119863

1199041

1198631199042 and 119863




119887 119862119887119889 and

resistor 119877119887119889







119886


119886= 135 120583H is chosen




(1)

(2)

T

2gt

(a)

(1) (2)

T

T

2gt

(b)

(1) (2)

TT2gt

(c)

(1) (2)

TT2gt

(d)


(trace 1 200Vdiv) and 119894119904


119904




22mH119862119891

3mF119871119887

300 120583H119862119887

30120583F119862119887119889

150120583F119877119887119889

22Ω119871119904

5120583H1198621199041

003 120583F1198621199042

033 120583F119871119886

135120583H119862 15120583F1198631199031

-1198631199036

VUO 82119878119887

-119863119887

SKM100GAR123D1198781

-1198784

and1198631

-1198634


1198631199042

1198631199043

DSEI 31 times 100




5 Results





119904(trace 1


6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(1)

(2)

T

2gt

(a)

(1) (2)

T

T

2gt

(b)

(1) (2)

TT2gt

(c)

(1) (2)

TT2gt

(d)


(trace 1 200Vdiv) and 119894119904


119904




22mH119862119891

3mF119871119887

300 120583H119862119887

30120583F119862119887119889

150120583F119877119887119889

22Ω119871119904

5120583H1198621199041

003 120583F1198621199042

033 120583F119871119886

135120583H119862 15120583F1198631199031

-1198631199036

VUO 82119878119887

-119863119887

SKM100GAR123D1198781

-1198784

and1198631

-1198634


1198631199042

1198631199043

DSEI 31 times 100




5 Results





119904(trace 1


6 Conclusion




References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article A 25kW, 25kHz Induction Heating Power...

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