LLC inverter design procedure for induction heating with quantitative analysis of power transfer

Science & Technology Development Journal – Engineering and Technology, 4(1):738-746
Open Access Full Text Article Research Article
1Electrical and Electronic Engineering,
Cao Thang Technical College, Ho Chi
Minh City, Vietnam
2Faculty of Electrical and Electronics
Engineering, Ho Chi Minh City
University of Technology, Ho Chi Minh
City, Vietnam.
Correspondence
Thuong Ngo-Phi, Electrical and
Electronic Engineering, Cao Thang
Technical College, Ho Chi Minh City,
Vietnam
Email: ngophithuongbk@gmail.com
History
 Received: 27-7-2020 
 Accepted: 22-3-2021 
 Published: 31-3-2021
DOI : 10.32508/stdjet.v4i1.751 
Copyright
© VNU-HCM Press. This is an open-
access article distributed under the
terms of the Creative Commons
Attribution 4.0 International license.
LLC inverter design procedure for induction heating with
quantitative analysis of power transfer
Thuong Ngo-Phi1,*, NamNguyen-Quang2
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ABSTRACT
Induction heating has been an advanced process for industrial quenching applications, aiming
to increase the material's hardness to a desirable depth of penetration, with advantages such as
high energy conversion efficiency, clean, safe and especially localized heating. In this process, an
L coil with the right shape and size for the material to be heated will be normally used, and the
matching between the coil size and the quenched material has a great effect on heating perfor-
mance as well as the operation of the power converter, because it affects the airgap in the electro-
magnetic-thermal energy conversion system. Although induction heating has attracted a great
deal of attention in recent years, design consideration of inductance in resonant circuits for specific
requirements is still very limited. Specifically, there remains a need for a design process that uses the
transferred power and workhead size as inputs, in practice. In this paper, the operating principle of
an LLC resonant circuit for induction heating will be explained, from which a quantitative analysis
of the transferred power to the workhead will be performed to help design the resonant circuit. An
LLC circuit design procedure will be proposed, using the results from a quantitative analysis of the
transferred power and taking into account the physical cons traints of the workhead. In addition,
a simple technique for monitoring the soft-switching state of the power switches in a resonant in-
verter, based on monitoring the phase difference between the resonant capacitor voltage and the
resonant circuit voltage, is also proposed. The feasibility of the proposed design process and phase
tracking algorithm will be illustrated and verified through simulation and experiments on a 2 kW,
100 kHz LLC induction heating circuit for hardening hollow steel tubes up to 4 cm diameter.
Key words: Resonant inverters, Inductive power transmission, zero voltage switching
INTRODUCTION
Induction heating makes use of high frequency in-
verters, in which a resonant circuit is formed by a
work-head and a capacitor in series 1–4 or parallel
configuration5. The resonant inverter is responsible
for supplying a large current in the work-head, with
a heating load being represented as a resistor R in se-
ries or parallel with the coil. A resonant circuit is a
popular solution to implement zero voltage switch-
ing (ZVS) or zero current switching (ZCS), in order
to reduce switching losses 6,7. Series resonant cir-
cuitsmay be used for all-metal induction heating with
adaptive control8 or tundish induction heating with
modular multilevel converter9. However, a combina-
tion of series resonant and parallel resonant (specifi-
cally, an LLC circuit) could provide better efficiency
than a simple series resonant circuit6, especially in
higher short-circuit capability and lower input cur-
rent10. In6, the LLCwas used in parallel-loaded form,
in which the capacitor is in parallel with the primary
coil of a coupling transformer. Another research pro-
posed moving the Ls inductor to primary side of the
transformer, resulting in lower current in that induc-
tor10. However, only a calculation procedure for Ls
and C was proposed, with the assumption that the
value of L is already available. In addition, conditions
for ZVS on power switches have not been identified.
In this paper, a design procedure for LLC resonant cir-
cuits (in induction hardening) will be proposed, tak-
ing into account work-piece dimension and ZVS con-
ditions. A demonstration system of 2 kW, 100 kHz for
surface hardening will be designed, built and tested.
Simulations and experiments have been done to ver-
ify the proposed procedure.
BASIC ANALYSIS METHODOF THE
LLC RESONANT CIRCUIT
LLC oscillation
Figure 1 shows the proposed LLC resonant inverter,
supplied by a three-phase bridge rectifier and an LC
filter. The inverter is a H-bridge, supplying the reso-
nant circui ... 
Where ZLCR(jw) is the equivalent impedance of two
parallel branches, where L and R are in series in one
branch, and C forms the other branch. From (4) and
(7), capacitor voltage at series resonance (f0) can be
expressed as:
vc ( jw0) =
1 jQ
b
v1 (8)
From (8), phase difference4j between vc and v1 can
be calculated, as given in (9)
4j = ac tan(Q) (9)
As mentioned above, for a small j0, quality factor Q
should be large, normally larger than 6 in LLC cir-
cuits11. Therefore, at resonance, capacitor voltage
vc will be nearly 90o lagging with respect to input
voltage v1. For ZVS operation on power switches,
the operating frequency should be higher than reso-
nant frequency f0, and the closer to this resonant fre-
quency the more power can be transferred. However,
during the heating process, passive components may
change their inductances and capacitances, leading to
a change of resonant frequency. Then the phase dif-
ference Dj calculated in (9) may be used to monitor
resonant frequency, and circuit condition and main-
tain maximum power transfer.
INDUCTION HEATING COIL
INDUCTANCE
In design procedures, inductance value of the work-
head is normally given. However, the shape of work-
head depends on the work-piece, so inductance value
may be different among shapes. For radio-frequency
(RF) induction heating, the work-head is usually an
air-core solenoid, made by a copper tube to ease the
cooling process and account for skin effect, as illus-
trated in Figure 4.
Figure 4: Induction coil as single layer coil.
Figure 5: LLC inverter design procedure.
740
Science & Technology Development Journal – Engineering and Technology, 4(1):738-746
Work-piece should be put inside the solenoid or close
to solenoid.
An experimental formula 12 can be used to calculate
the inductance of the single layer solenoid:
L=
a2n2
0:228a+0:254b
mH (10)
Where a is the diameter of the solenoid, b is the length,
and n is the number of turns. These parameters de-
pend on the work-piece shape and area to be heated
up.
LLC INVERTER DESIGN PROCEDURE
A design procedure for LLC inverter has been pro-
posed, as presented by the flow chart in Figure 5. In-
put parameters for designing the RF induction heater
include: Desired dimension of the work-head (pa-
rameters a, b, and n), heating power P (depending on
heating temperature and time), DC link voltage, op-
erating frequency f0 (depending on skin depth), and
variation range of the quality factor of the work-head
and work-piece ([Qmin, Qmax)]. Below is a demon-
stration for the proposed design procedure with the
following parameters: a = 2.5 cm, b = 12 cm, n = 11
turns, P = 2 kW, f0 = 100 kHz, Qmin = 6, Qmax = 10,
and Vdc = 500 V.
Step 1: Calculation of work-head inductance L
By applying (10), work-head inductance can be deter-
mined as:
L=
0:0252112
0:2280:025+0:2540:12 = 2:09 mH (11)
L in (11) will be round up to L = 2.1 mH.
Step 2: Calculation of Ln and Ls:
From (5), ratio Ln can be calculated from quality fac-
tor Q and switching angle j0. For a given Ln, switch-
ing angle will be large for small values for Q. There-
fore, minimum quality factor Qmin will be used for
this calculation. On the other hand, switching an-
gle in LLC resonant circuits should be smaller than
20O 11, hence:
Ln = 6 tan(20o)1= 1:18 (12)
From this ratio and the inductance value calculated in
step 1, series inductance Ls can be determined:
Ls = 1:182:1 2:4 mH (13)
Step 3: Calculation of N
Fundamental component of the voltage applied to pri-
mary side of the transformer:
vin =
4Vdc
p
p
2
=
4500
p
p
2
= 450VRMS (14)
Transformer’s turns ratio should be selected so that a
high current can be supplied from the secondary side
of the transformer, in order not to create overvoltage
on the capacitor C. From (6), a variation range for
turns ratio (Nmin to Nmax) can be determined, corre-
sponding to the range of quality factor (Qmax toQmin),
to achieve the rated power Pmax:
N =
vuut v2in
L2inRPmax
"
1+

Ln+1
Q
2#
(15)
For the demonstration system, it has been found that
Nmax = 24 and Nmin = 19.3. Select N = 20.
Table. 1 summarizes all design parameters for the
demonstration system.
SIMULATION RESULTS AND
DISCUSSION
To verify the feasibility of the design, a SPICE simula-
tion will be done with the system schematic as shown
in Figure 6.
The circuit should have ZVS operation, which is eval-
uated by examining its switching waveforms (Fig-
ure 7) on MOSFETs, in the target frequency range.
Considering both current waveform (top graph) and
voltage waveform (bottom graph) of Q4 MOSFET, the
anti-parallel diode conducts before the gate-source
voltage reaches a threshold value, making drain-
source voltage slightly negative. Therefore, the MOS-
FET will be turn on at zero voltage, i.e. zero voltage
switching.
An advantage of the LLC circuit is the ability to draw
a smaller input current (output current from the in-
verter) compared to work-head current, as shown in
Figure 8. It can be seen that the work-head current is
sinusoidal at around 100 kHz, with amagnitude about
1.14 times themagnitude of the secondary current ILS
(bottom waveforms group). In top waveforms group,
the capacitor voltage is sinusoidal and almost 90 lag-
ging with respect to input voltage Vin. Therefore, the
designed LLC circuit has fulfilled requirements for si-
nusoidal output current, and ZVS on input switches,
allowing higher efficiency and better heating effect.
EXPERIMENTAL RESULTS AND
DISCUSSION
A prototype has been built to verify the ZVS opera-
tion and statusmonitoring with phase difference (Fig-
ure 9). In Figure 9a, a 380 V three-phase voltage was
supplied to the diode rectifier through an LC line fil-
ter, a DC link capacitor was used to reduce the voltage
ripple of the rectifier output. A standardH-bridgewas
741
Science & Technology Development Journal – Engineering and Technology, 4(1):738-746
Table 1: Design Parameters
Symbol Quantity Value
V Line – line Voltage 380 V (RMS)
P Power heating 2 kW
L Inductance 2.1 mH
Q Quality factor 6 : 10
fs Switching frequency 80 – 120 kHz
f0 Resonant frequency 100 kHz
Ls Series resonant inductance 2.4 mH
C Resonant capacitance 2.2 mF
N Transformer ratio 20 : 1
Figure 6: Simulation circuit in LTspice.
used to supply high frequency voltage to the match-
ing transformer, energizing the LLC resonant circuit.
The work-head was a solenoid made of copper tube
and was water-cooled. A Tiva C Launchpad (EK-
TM4C123GXL) was used to provide gating signals at
100 kHz to the power switches through gate drivers.
The work-piece is a 4 cm diameter steel tube as shown
in Figure 9b.
In Figure 10a, the MOSFET current (bottom wave-
form) and the MOSFET voltage (top waveform) are
in good agreement with corresponding waveform in
simulation. Although gate signal was not shown, ZVS
has been achieved in practice, according to the analy-
sis presented in section 5. Due to internal impedance
of power supply, impedance of the LC filter, and volt-
age drop on the rectifier, the available voltage at DC
link will be reduced at high current value, leading to
voltage dip as shown in Figure 10a.
In Figure 10b, filtered waveform of secondary voltage
v1 and capacitor voltage vc are shown, with nearly 90
phase lagging on capacitor voltage with respect to the
fundamental voltage, showing a near resonant work-
ing condition.
CONCLUSION
The paper has explained the operating principle of
an LLC resonant circuit in induction heating applica-
tions, with a quantitative analysis of power transferred
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Science & Technology Development Journal – Engineering and Technology, 4(1):738-746
Figure 7: ZVS turn on in MOSFET (top graph: IDS-Red, VGS – Blue, bottom graph: VDS – Blue)
Figure 8: LLC Circuit waveform
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Science & Technology Development Journal – Engineering and Technology, 4(1):738-746
Figure 9: Experimental Prototype
Figure 10: Experimental result.
to the work-head to help in design process. A design
procedure for the LLC circuit has also been proposed,
utilizing results from the quantitative power analysis
and taking into accountmechanical constraints on the
work-head. The effectiveness of the proposed design
procedure has been verified by simulations and exper-
iments.
LIST OF ABBREVIATIONS
LLC: Inductor – inductor – capacitor
ZVS: Zero voltage switching
ZCS: Zero current switching
RF: Radio - frequency
CONFLICT OF INTEREST
Theauthors confirm that they do not have any conflict
of interest in completing this paper.
AUTHORS’ CONSTRIBUTION
Thuong Ngo-Phi proposed the research idea, con-
ducted simulations and experiments.
Nam Nguyen-Quang contributed to the technical
background, hardware implementation, and proof
reading.
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Tạp chí Phát triển Khoa học và Công nghệ – Kĩ thuật và Công nghệ, 4(1):738-746
Open Access Full Text Article Bài Nghiên cứu
1Khoa Điện – Điện tử, Trường Cao đẳng
Kỹ thuật Cao Thắng, Hồ Chí Minh, Việt
Nam
2Khoa Điện - Điện tử, Trường Đại học
Bách khoa, ĐHQG-HCM, Việt Nam
Liên hệ
Ngô Phi Thường, Khoa Điện – Điện tử,
Trường Cao đẳng Kỹ thuật Cao Thắng, Hồ Chí
Minh, Việt Nam
Email: ngophithuongbk@gmail.com
Lịch sử
 Ngày nhận: 27-7-2020
 Ngày chấp nhận: 22-3-2021 
 Ngày đăng: 31-3-2021
DOI : 10.32508/stdjet.v4i1.751 
Bản quyền
© ĐHQG Tp.HCM. Đây là bài báo công bố
mở được phát hành theo các điều khoản của
the Creative Commons Attribution 4.0
International license.
Quy trình thiết kế bộ nghịch lưu LLC với phân tích định lượng về
công suất truyền
Ngô Phi Thường1,*, Nguyễn Quang Nam2
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TÓM TẮT
Gia nhiệt bằng đốt nóng cảm ứng đã là một quy trình tiên tiến cho các ứng dụng tôi trong công
nghiệp, nhằm tăng độ cứng của vật liệu đến một độ thấm sâu cho phép, với những ưu điểm như
hiệu suất chuyển đổi năng lượng cao, sạch, an toàn và đặc biệt là khả năng làm nóng từng phần
cho chi tiết cần tôi. Trong quá trình này, thông thường một cuộn dây L sẽ được sử dụng với hình
dạng và kích thước phù hợp với vật liệu cần gia nhiệt, sự phù hợp giữa kích thước cuộn dây L và
vật liệu tôi có ảnh hưởng lớn đến hiệu suất đốt nóng cũng như hoạt động của bộ biến đổi công
suất vì sẽ ảnh hưởng đến khoảng hở không khí của hệ thống chuyển đổi năng lượng điện-từ-nhiệt.
Mặc dù đốt nóng cảm ứng đã thu hút mạnh mẽ sự quan tâm trong những năm gần đây, nhưng
việc thiết kế điện cảm trongmạch cộng hưởng cho các yêu cầu cụ thể vẫn ít được xem xét. Cụ thể,
vẫn cần có một quy trình thiết kế sử dụng công suất yêu cầu và kích thước của cuộn đốt làm đầu
vào, trong thực tế. Trong bài báo này, nguyên lý hoạt động của một mạch cộng hưởng LLC dùng
cho đốt nóng cảm ứng sẽ được giải thích, từ đómột phân tích định lượng về công suất truyền đến
cuộn đốt sẽ được thực hiện để giúp thiết kế mạch cộng hưởng. Một quy trình thiết kế mạch LLC
sẽ được đề xuất, sử dụng các kết quả từ phân tích định lượng về công suất và có xét đến các ràng
buộc vật lý của cuộn đốt. Ngoài ra, một kỹ thuật đơn giản để giám sát trạng thái chuyển mạch
mềm của các khóa công suất trong mạch nghịch lưu cộng hưởng, dựa trên việc theo dõi lệch pha
giữa điện áp của tụ điện cộng hưởng và điện áp mạch cộng hưởng, cũng được đề xuất. Tính khả
thi của quy trình thiết kế và giải thuật theo dõi pha đề xuất sẽ đượcminh họa và kiểm chứng thông
qua mô phỏng và một mạch thực nghiệm đốt nóng cảm ứng LLC 2 kW, 100 kHz cho ứng dụng tôi
vật liệu thép rỗng ruột đường kính 4 cm.
Từ khoá: Nghịch lưu cộng hưởng, Truyền năng lượng cảm ứng, Chuyển mạch với điện áp bằng
không
Trích dẫn bài báo này: Thường N P, Nam N Q. Quy trình thiết kế bộ nghịch lưu LLC với phân tích 
định lượng về công suất truyền. Sci. Tech. Dev. J. - Eng. Tech.; 4(1):738-746.
746