Proceedings of the 11th WSEAS International Conference on CIRCUITS, Agios Nikolaos, Crete Island, Greece, July 23-25, 2007
26
Circuits Analysis of Inductive Heating-Device with Half-Bridge
Resonated Inverter
HSU CHUN-LIANG
E.E Department of Saint John’s University
No. 499, Sec. 4, Tang-kin Rd. Taipei County, Taiwan
REPUBLIC OF CHINA
+886-2-28013131 #6500, liang@mail.sju.edu.tw
Abstract: - Since Farady’s Low of Electrolysis was presented in 1831 in which magnetic inductive phenomenon was
implemented in heating facilities, the inductive heating technique has been studied popularly by many scholars all over the
world. Today the inductive heating facilities have been applied in many manufacturing tools of many fields in Taiwan, and
this promoted research in this field directing to higher power, higher frequency, and higher efficiency as well. This study
was pilot study for practical design of resonated heating circuit with half-bridge resonated inverter, especially some critical
factors when considering the loading features including its primary theory, skin effects, permeance, conductance, and
loading features. Finally, in this study, we made a completed analysis about current flowed in resonated inverter circuits at
every key step when IGBT switching to get most efficient power. With this pilot-study, we would implement it into our
further advanced research in high-power heating facilities with Half-Bridge Resonated Inverter.
Key-Words: -Inductive Heating, Half-bridge Resonated Inverter, IGBT, Operating Frequency, Soft-switching Point,
Working Objects( cooking vessels).
1. Introduction
Owing to the progress of semi-conductor components in
recent decades, more power elements could be applied in
products of higher-power device. So as well the increase of
endurance of voltage and ampere of components prompted
the rapid development of power electronics field. That
leads to higher frequency, response, and efficiency
performance of a larger capacity heating device. The
inductive heating method which uses rectifiers and high
frequency inverter to convert 60Hz AC input current into
20~40KHz high frequency energy output to supply the
inductive coils which would generate the inductive eddy
current so as to heat the pan over coils. [1]
Nowadays the power electronic technique is to
implement the electronics into huge power circuits or
systems. So to speak, it’s a process how to deal with power
transformation with semiconductor components. Not with
standing the improvement with parameter as voltage,
current, dv/dt, di/dt, and switching feature, yet there were
many choke points such as lack of ways of up-grade
running frequency. That led to add capacities, conductors,
and some auxiliary switches in circuits, and led to
improper size of products and in-application controlled
frequency, and finally the new generation electronic
heating facility.
technique was initiated.[2]
Sum up, the purpose of this study is to design a high
power stable heating device with safety and intelligence.
Generally speaking, An intelligent and stable high power
magnetic inductive heating facility with IGBT as
switching components would provide well protection for
driver circuit to avoid damage of components even under
any troubleshooting including incorrect programming, and
this performance would be the motivation of this study. [7]
Since magnetic inductive heating facility belongs to
application of high frequency electronic power
components which combine of both inerter and technique
of switching so as to convert low frequency DC power into
high frequency AC power. Finally, crossing the coils
with changed magnetic field and generating eddy current
on the surface of cooking vessels, in the process, through
coupled magnetic field to convert electric energy into
magnetic energy, further more convert magnetic energy
into heat transferred to loads to accomplish heating effect.
But in this paper, we only consider system circuits
viewpoint as a pilot study and analyzed the circuit
operation for further study of practical circuit design.
2.1 Inductive Heating Primary Theories
Inductive heating mainly based on electrical-magnetic
inductive phenomenon presented by Faraday in 1831, in
which interpreted that the change of magnetic field would
generate electricity, and if a loop of conductor existed in a
change magnetic field could produce inductive electrical
field that would induce inductive electromotive force and
inductive current in this loop as in fig. 2-1. In an area
surrounded by closed loop, if magnetic field occurred to
Fig 2-1 Basics of electrical-magnetic inductive field
Supposed that we put a conductor in a changing
Proceedings of the 11th WSEAS International Conference on CIRCUITS, Agios Nikolaos, Crete Island, Greece, July 23-25, 2007
magnetic field that was changed based on time interval, the
density of line of magnetic force would change, and
according to Lenz’s law the conductor would generate
inductive current to against the change of the density of
line of magnetic force, consequently, this generated current
was called eddy current as shown in fig. 2-2.
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equivalent circuit with only one coil of secondary winding
coils, and the conception was transferred into fig 2-5. Z L is
the resistance of working object (pans on inductive-heating
facilities).
Fig 2-4 Equivalent circuit model of transformer
Fig 2-5 Equivalent circuit model of inductive-heating
Fig 2-2 Basics of eddy current
Furthermore, according to Ampere’s circuital law the
strength of constructed magnetic field surrounding the long
electrical conductor was positive ratio to the scale of
current flowing in the conductor while negative ratio to the
distance with the conductor. According to the Ampere’s
right-handed screw rule, we can easily know the direction
of magnetic field, so if we wanted to get direction-changed
magnetic field, there must be direction-changed current
flow in the conductor. Fig 2-3 was the inductive heating
conception. The heating coils would flow through
high-frequency, direction-changed AC current to generate
direction-changed magnetic field. The direction of
magnetic field would continuously stepping after AC
current, When working objects were located in this
magnetic field and was affected by the direction-change of
magnetic field, moving electronics in working objects
would be inductive by field and generate circulated
movement to generate opposite magnetic field to against or
offset coils’ magnetic field according to the Lenz’s law.
This movement of moving electronics was called eddy
current. Since there was resistance in working objects,
working objects would generate heat when eddy current
flowed inside the objects. The power produced in objects
could be figured out according to Joule’s Law as
Pv = ρ J 2 , ρ was resistance constant and J was current
density.
The parameters of loading usually are affected by those
factors as shape of heating coils, the distance between coils
and working objects (pans), the materials of working
objects, conductance rate of working objects, permeance
rate of working objects, and the operating frequency f of
the system. The heating coils are also affected by
inductance value, coil length, and the permeance constant
and area of coils. In fig 2-.6, the system considered the
equivalent resistance and coupling factor M of heating
coils. RL could be gained from depth of skin-effect of
eddy current.
RL =
ρ
= K ρ µt f
δ
2-1
Fig 2-6 Equivalent circuit considered with coils resistance
and coupling constant
In fig 2-7, an equivalent circuit was primary winding
coils equivalent to secondary winding coils. Leq is
equivalent inductance and Req is equivalent resistance.
Leq = L1 −
( wM ) 2 L2
= L1 − A2 L2
2
RL + ( wL) 2
2-2
( wM ) 2 RL
= r − A 2 RL
2
RL + ( wL ) 2
2-3
Req = L1 −
A=
wM
2-4
2
RL + (wL2 ) 2
Figure 2-3 Basics of inductive heating
2.2 Inductive-heating equivalent circuit
The equivalent circuit is almost the same as the
transformer equivalent circuit, and the transformer
equivalent circuit was shown in figure 2-4. The difference
between them is that the secondary winding coils of
inductive-heating circuit can be considered as transformer
Fig 2-7 Equivalent circuit from second winding to primary
2.3 Structure of Inverter
Fig 2-8 was shown the inverter circuit of this system,
which was a half-bridge resonated structure. The main
Proceedings of the 11th WSEAS International Conference on CIRCUITS, Agios Nikolaos, Crete Island, Greece, July 23-25, 2007
circuit topology of inductive-heating can be equivalent to
RLC resonated circuit as shown in fig 2-9. The resonated
frequency of RLC resonated circuit was f 0 , Z 0 was the
resistance feature, and Q was quality factor. The three
values can be calculated as following
1
f0 =
Lr
Cr
2π
Z0 =
Q=
28
2.4 Simulation and Analysis of Circuits of
Inverter
In this system, a half-bridge resonated inverter was
designed as circuit structure as Fig 2.11. The relationship
between driving signal of Gate of IGBT and loading
current i L was shown as fig 2.12. There were eight
function models of this circuit structure analysis shown as
following:
Lr
Cr
Z0
R
S1
C
Fig 2-51 Half-bridge resonated inverter circuit structure
R
L
S2
C
Fig 2-8 Half-bridge resonated structure
Fig 2-9 RLC equivalent circuit of half-bridge series
resonance
Fig 2-62 Relationship between gate driving signal and
loading current i L
Fig 2-10 was relationship between the ratio of system
operated frequency fs over resonated frequency f o and
output power. From the figure, we could obviously infer
that different quality factor Q would cause quite different
curve of output power. The lower was Q value, the
smoother was the output power curve, and that meant if we
want to gain high sensitivity output power, the Q value
must be high. And only when switching frequency was
equal to resonated frequency, we could gain the largest
output power.
Function Model1: t0~t1
S1 on S2 off under this model
Loop1: Input capacity Ci charged to Lr and C2 through S1
Loop2: Resonated capacity C1 charged to Lr and C2
through S1
As shown in fig 2-13, Ci and C1 charged to Lr, C2, and
Cs2. Resonated capacity Cs2. would be charged to Vin, so
the voltage of S2 would decrease down to input voltage Vm
Lr and C2 were at collecting energy condition while iL was
at positive and gradually increasing.
Fig 2-13 Function Model 1 of Inverter Operation
Fig 2-40 the relationship between
fs
f o and output power
Function Model1:t1~t2
S1 off, and S2 off under this model
Loop1: input capacity Ci charged to Lr and C2 through Cs2.
Loop2: resonated capacity C1 charged to Lr and C2 through
Proceedings of the 11th WSEAS International Conference on CIRCUITS, Agios Nikolaos, Crete Island, Greece, July 23-25, 2007
Cs1.
Loop3: snubber capacity Cs2 discharged to Lr and C2 down
to 0
As shown in fig 2-14, at the moment of S1 off, the
current originally flowed through S1 would change the path
to flowed through Cs1. The resonated capacity Cs1 would be
charged up to Vin, and Cs2 also discharged to Lr and C2.
Inductance was at collecting energy condition while iL
would continuously increase.
Fig 2-14 Function Model 2 of Inverter Operating
Function Model 3:t2~t3
S1 off, and S2 off under this model
Loop 1: resonated inductance Lr charged to
29
Fig 2-16 Function Model 4 of Inverter Operating
Function Model 5:t4~t5
S1 off and S2 on under this model
Loop 1: input capacity Ci charged to Lr and C1 through S2
Loop 2: resonated capacity C2 charged to Lr through S2
As shown in fig 2-17, S2 kept on until the energy in
inductance released out entirely while iL became zero. At
this moment inductance changed its polarity again, Ci and
C2 provided with energy to Lr. At this moment inductance
began to install energy and current iL increased forward
negative polarity.
C i through
C1
Loop 2: resonated capacity C1 charged to Lr and C2 through
D2
As shown in fig 2-15, at this moment Cs2 had discharged
entirely and Cs1 had charged to the level of Vin and this
condition led to open circuit, thus, iL began to decrease
gradually and a negative slop occurred. According to
Lenz’s Law, the inductance would against the change and
the polarity on it would reverse as well as release energy
through the built-in diodes D2 and C1 in IGBT. Because D2
was on, between collector and emitter of S2 would generate
soft switching point, and S1 would be clipped at voltage
level of input voltage Vin.
Fig 2-17 Function Model 5 of Inverter Operating
Function Model 6:t5~t6
S1 off and S2 off under this model
Loop 1: input capacity Ci would charge to Lr, C1, and Cs2
Loop 2: resonated capacity C2 would charge to Lr, C1, and
Cs2
Loop 3: snubber capacity Cs1 would charge to Lr, C1, and
Cs2
As shown in fig 2-18, S2 was off at this moment, and
originally charged path to Lr through S2 had been changed
through Cs2, thus, Cs2 began to charge up to Vin while Cs1
discharged to 0. Current ir continuously increased forward
reversed direction.
Fig 2-15 Function Model 3 of Inverter Operating
Function Model 4:t3~t4
S1 off and S2 on under this model
Loop 1: resonated inductance Lr charged to Ci through C1
and S2
Loop 2: resonated inductance Lr charged to C2 through S2
As shown in fig 2-16, S2was on in this model and S2 was
switching while D2 was on, so S2 was switching in
Zero-voltage
switching.
The
inductance
would
continuously release energy, but the release energy path
would change through S2.
Fig 2-18 Function Model 6 of Inverter Operating
Function Model 7:t6~t7
S1 and S2 were off under this model.
Loop 1: resonated inductance Lr would charge to Ci and C1
through D1.
Loop 2: resonated capacity C2 would charge to Ci and C1
through D1.
As shown in fig 2-19, at this moment Cs2 had been
charged to full charged and was at off condition, thus the
Proceedings of the 11th WSEAS International Conference on CIRCUITS, Agios Nikolaos, Crete Island, Greece, July 23-25, 2007
inductance polarity would reverse according to Lenz’s Law
and began to release energy. Its path of releasing energy
was from D1 to C1 and C i . Owing to D1 being on condition,
there was a soft-switching point between the collector and
emitter of S1 and S2 was clipped at voltage level of Vin.
+
Cs1
C1
R
Ci
g1
Lr
S1
a
D1
b
Cs2
C2
g2
D2
S2
-
Fig 2-19 Function Model 7 of Inverter Operating
Function model 8:t7~t0
S1 on and S2 off under this model
Loop 1: resonated inductance Lr would charge to Ci and C1
through S1.
Loop 2: resonated capacity C2 would charge to Ci and C1
through S1.
As shown in fig 2-20, S1 was switching at the moment
when D1 was on and that meant S1 was in Zero-voltage
switching. At this moment, inductance continuously
discharged until iL became 0, and then the system would
come to model 1 and the circuit would repeatedly operate
from model 1 to 8.
Fig 2- 70 Function Model 8 of Inverter Operating
1. Conclusion
The induced eddy current on working object will
centralize on over the surface, and the higher frequency
operated in heating coils is, the more obviously the eddy
current centralizes over the surface. This phenomenon
was called Skin Effect.
Regarding with all kind of magnetic materials, it was
not necessary for them to be magnetic at any temperature.
Generally speaking, there was a threshold temperature,
and above this temperature, atoms magnetic torque was
completely out of order because of briskly movement of
atoms under high temperature. On the other hand, under
this temperature, atoms magnetic torque was in order
sequence, so objects would be self-magnetic and became
iron-magnetic feature.
Permance rate represented the degree of
magnetization for magnetic materials or sensitivity of
reaction of materials to out magnetic field. The chemical
components of materials and alloy, heat-processing,
frozen-processing, and temperature all will affect on the
permance. As for iron-magnetic materials, the strength of
30
inductive magnetic field on the surface would increase
following the permance increase.
The higher was the frequency and the less was the
distance between working object and heating coils, the
more obvious was the close effect. At the time, the
generated eddy current would reinforce magnetic lines
density through area of conjunction of both, and the
heating capability was increased gradually. But it was
worthwhile to pay attention to skin effect that would only
affect the spread of eddy current in working object rather
than the scale of eddy current affected by close effect.
There were two factors that made the temperature of
coils rise up, one was the loss during current flowing
through coils, and the other was radiation heat produced
by working objects when heating. we could learn the
influence causing by the gap on equivalent inductance
and resistance of working object. That was if the distance
increased, the equivalent inductance would increase but
resistance decrease.
If we wanted to gain the same output current with
different materials of heating coils, the inductivity. If the
system operated under higher frequency, the sensitivity of
output current would be high e heating facility system
must operate under higher frequency.
2. Reference
[1] E. J. Davies, P.G. Simpson, “Induction heating
Handbook”, Mcgraw-Hill Book Company Ltd., London,
1979.
[2] “Induction Heating System Topology Review”,
Fairchild Semiconductor, 2000
[3] S. Llorente , F. Monterde , Burdio, J.M. Burdio , J.
Acero, “ A comparative study of resonant inverter
topologies used in induction cookers”, Power Electronics
Conference and Exposition, 2002. APEC 2002.
Seventeenth Annual IEEE , pp:1168 - 1174 vol.2
[4] Zhiqin Shu , Quaicoe , J.E., ”A PWM current source
inverter for medium - frequency induction heating
applications”, Electrical and Computer
Engineering ,1993, pp.:84 - 87 vol.1
[5] Koertzen, H.W.; van Wyk, J.D.; Ferreira, J.A. ,”Design
of the Half-Bridge Series Resonant Converter for
Induction Cooking” ,Power Electronics Specialists
Conference, pp.729 - 735 vol.2
[6] Bayindir, N.S.; Kukrer, O.; Yakup, M., “DSP-based
PLL-controlled 50-100 kHz 20 kW high-frequency
induction heating system for surface hardening and
welding applications”, Electric Power Applications, 2003,
pp.365 – 371
[7] Hirota, I.; Omori, H.; Nakaoka, M., “Performance
evaluations of single-ended quasi-load resonant inverter
incorporating advanced-2nd generation IGBT for soft
switching”, Industrial Electronics, Control,
Instrumentation, and Automation, 1992. pp.223 - 228
vol.1