2021 IEEE 12th International Symposium on Power Electronics for Distributed Generation Systems (PEDG) | 978-1-6654-0465-5/21/$31.00 ©2021 IEEE | DOI: 10.1109/PEDG51384.2021.9494223
An Accurate Time Domain Analysis Based ZVS
Evaluation Tool for LLC Resonant Converters
Yuqi Wei
Department of Electrical
Engineering
University of Arkansas
Fayetteville, United States
yuqiwei@uark.edu
Abstract—LLC converters are popular in numerous
industrial applications owning to their high efficiency and soft
switching characteristics. Conventionally, the first harmonic
approximation (FHA) analysis method is used to perform the
zero-voltage switching (ZVS) analysis for LLC resonant
converter. However, the FHA method assumes that the LLC
resonant converter is always operating at resonant frequency
point so that the primary switch turn-off current is a constant
value during the whole operation range. When the LLC resonant
converter operating point is away from the resonant frequency,
considerable errors would exist, which will lead to unoptimized
deadtime design or ZVS failure. Therefore, in this article, a ZVS
evaluation tool is developed based on the time domain analysis,
the analysis results have much higher accuracy when compared
with the traditional FHA method, which can be used to guide the
analysis and design of the converter. Experimental validations
are presented.
Keywords—ZVS operation, LLC resonant converter, deadtime
analysis
I. INTRODUCTION
Owning to their high efficiency and wide soft switching
operation range characteristics, LLC resonant converters have
been widely adopted in numerous industrial applications [1][10]. Conventionally, the first harmonic approximation (FHA)
analysis method is adopted to perform the analysis and design
of LLC resonant converter [10]. In particular, to achieve the
zero-voltage switching (ZVS) operation for LLC resonant
converter, the following two conditions have to be met: 1)
necessary condition: the direction of the primary switch turnoff current should be able to discharge the energy stored in the
junction capacitor; 2) sufficient condition: the current value
and deadtime should be large enough to fully discharge the
capacitive energy. Incomplete ZVS (iZVS) will be achieved if
the deadtime is not large enough. Therefore, for LLC resonant
converter, the deadtime is an important parameter that needs to
be determined. However, conventional FHA analysis method
has considerable errors when the converter switching
frequency is away from the resonant frequency, which will
lead to miscalculation of the deadtime [11]. A too large
deadtime will cause the circuit current flows through the body
diode of the primary switch for a certain amount of time, which
will lead to the increase of converter conduction loss. On the
other hand, a too small deadtime will cause the loss of ZVS
Alan Mantooth
Department of Electrical
Engineering
University of Arkansas
Fayetteville, United States
operation, which will generate considerable electro-magnetic
interference (EMI) noises and switching losses. Therefore, an
accurate deadtime calculation mechanism is desired to find out
the minimum required deadtime under certain conditions.
The main purpose of this paper is to develop an accurate
ZVS evaluation tool based on time domain analysis. With the
aid of the developed evaluation tool, the optimized deadtime
can be calculated in less than one second. Therefore, the
proposed method has the advantages of high accuracy, fast, and
convenient, which can be used to guide the analysis and design
of LLC resonant converters.
Based on the analysis and experimental results, the required
deadtime for LLC converter varies with circuit operating
conditions significantly. Therefore, it is recommended that
variable deadtime should be applied for the converter for wide
operation conditions.
The remaining of this article is organized as follows.
Section II of this article reviews the traditional ZVS analysis
method for LLC converter and the deficiencies (inaccurate and
incomplete) of traditional method are pointed out. To
overcome these shortcomings, Section III discusses the
proposed complete and accurate ZVS analysis method for LLC
converter and an automatic evaluation tool is developed and
introduced. To prove the effectiveness of the developed tool,
experiment results under different scenarios are presented.
Finally, conclusions and the focus of future work are discussed.
II. TRADITIONAL ZVS ANALYSIS METHODS FOR LLC
RESONANT CONVERTER
The zero-voltage switching (ZVS) operation analysis for
LLC converter is of great importance for both the converter
design and performance. Traditionally, many assumptions are
made for the ZVS analysis of LLC converter. From the
converter level, the LLC converter is assumed to operate at
resonant frequency during the whole operation range. Thus, a
simplified current expression can be derived. Another
common assumption is that the junction capacitance for the
primary switch is constant at the input voltage. Based on the
above assumptions, the basic requirement for the ZVS
operation is that the inductive current during deadtime is large
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enough to fully discharge the energy stored in the junction
capacitance of primary switch.
However, the traditional ZVS analysis method does not
have satisfactory accuracy, which will lead to either
conservative design or ZVS failure. From the circuit parasitic
perspective, in addition to primary switch junction capacitance,
the transformer stray capacitance, printed circuit board (PCB)
stray capacitance, secondary rectifier diode junction
capacitance, and secondary rectifier diode reverse recovery
will all have influence on the ZVS performance of the primary
switch.
A. Method 1 (traditional ZVS analysis)
Fig. 1 demonstrates the circuit diagram of half-bridge
converter, the analysis is same for other topologies. Most of
the case, the leakage inductor of the transformer is acting as
the resonant inductor Lr to improve the converter power
density.
Fig. 1. Circuit diagram of LLC converter
Traditionally, the ZVS operation for LLC converter is
simply determined based on the current direction during
deadtime. Take the primary switch S2 for an example, the ZVS
operation can be achieved once the body diode of S2 conducts
during the deadtime. Fig. 2 shows the two possible cases of
the current direction during deadtime. Due to the very short
time period of deadtime, the magnetizing current during the
deadtime can be regarded as a constant current source. The
ZVS operation is achieved when the current direction is the
same as Fig. 2(a).
(b)
Fig. 2. Two possible cases for the magnetizing inductor
current during deadtime. (a) ZVS is achieved for S2; (b) ZVS
is lost for S2.
For this method, the circuit parasitics are not considered. In
practice, the current direction can be judged based on the
operation region of LLC converters. The ZVS operation is
achieved when the LLC converter is designed to operate at the
right side of the peak gain curve (the inductive region).
B. Method 2 (constant output capacitance of primary switch)
Although method 1 is very simple to use and can provide
guidance for LLC converter design, the accuracy is greatly
sacrificed by ignoring the circuit parasitics. The most
commonly used ZVS analysis method is to consider the
primary switch output capacitance into consideration as shown
in Fig. 3. The two conditions to ensure ZVS operation for
primary switch S2 can be described as: 1) the magnetizing
current direction during the deadtime should be able to
discharge the energy stored in the output capacitance of S2
Coss2; 2) the deadtime and current should be large enough to
fully discharge the energy stored in the output capacitance of
the primary switch.
S1
+
Vi
-
Cin
Fig. 3. ZVS analysis method by taking primary switch
junction capacitance into consideration
S2
ILm
(a)
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output capacitance as discussed in [12] should be adopted. Fig.
6 shows the ZVS analysis model for method 3.
Vi
 Coss(v )dv
Coss,eq = 0
Vi
(4)
Then, by substituting Eq. (4) into Eq. (3), the new design
guideline for LLC converter is shown below.
(5)
tdead ≥ 16 LmCoss,eqfr
Fig. 4. Operation waveform when the LLC converter
operating at resonant frequency
Traditionally, first harmonic approximation (FHA) method
is applied to analyze the ZVS performance of the converter.
For FHA, it is assumed that fs=fr. The voltage across the
magnetizing inductance is clamped by the output voltage, and
the magnetizing inductance current increases linearly. The
magnetizing inductor current during deadtime can be
expressed as
ILM =
NVoD NVo
=
2 Lmfs 4 Lmfr
(1)
where D is the duty cycle of primary switch, for frequency
controlled LLC converter, D=0.5 can be obtained.
Then, to satisfy the ZVS operation, the following inequality
should be satisfied.
(2)
ILM × tdead ≥ 2 ⋅ Coss ⋅Vi
where tdead is the dead time implemented for the primary halfbridge switches.
By substituting Eq. (1) into Eq. (2), an important design
guideline for LLC converter is derived. The magnetizing
inductance value and deadtime should satisfied the following
equation.
(3)
tdead ≥ 16 LmCossfr
From the above equation, one can observe that the output
capacitance Coss of the primary switch is a critical parameter
for converter design. Fig. 4 illustrates the typical relationship
between the drain-to-source voltage and the primary switch
output capacitance value. For this ZVS analysis method, the
output capacitance value when the drain-to-source voltage
equals input voltage Vi is selected and used in Eq. (3).
C. Method 3 (variable output capacitance of primary switch)
However, if we look at the converter operation waveform
during the deadtime as shown in Fig. 5, we can find out that
the voltage across the primary switch is varying during the
deadtime. From Fig. 4, with different VDS, the output
capacitance Coss is different. More specifically, a small VDS
value will lead to the increase of output capacitance Coss.
Therefore, if a constant output capacitance as shown in Fig. 6
is adopted, the calculated deadtime from Eq. (3) will be
insufficient to achieve ZVS operation for the primary switch.
Therefore, a modified output capacitance value is required to
take the variation of VDS into consideration. An equivalent
vGS
vDS
iLr
iD
Fig. 5. Operation waveform when the LLC converter during
deadtime.
Fig. 6. ZVS analysis model for method 3.
D. Method 4 (constant output capacitance of secondary
rectifier)
In addition to the primary switch output capacitance, the
secondary rectifier diode output capacitance will also affect
the ZVS operation of primary switch. In the scenario of fs<fr,
during the deadtime, the secondary rectifier diode is OFF and
the output capacitance of the diode will affect the ZVS
operation of primary switch [13]. If the output capacitance is
reflected to the transformer primary side, the equivalent circuit
model can be modified as shown in Fig. 7.
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F. Method 6 (reverse recovery of secondary rectifier diode)
In below resonant frequency operation region, although the
secondary rectifier diode current goes to zero naturally, a
certain amount of reverse recovery energy still exists. As
analyzed in [14], the secondary rectifier diode reverse
recovery will affect the ZVS operation of LLC converter. The
equivalent capacitance for the reverse recovery charge effect
can be approximately expressed as
Crr,eq =
Then, the ZVS operation criteria can be modified as follow
by taking the secondary rectifier diode output capacitance into
consideration.
(6)
ILM × tdead ≥ 2 ⋅ Coss ⋅ Vi+Cj ⋅Vo
For the full-bridge rectifier, by substituting the equivalent
junction capacitance Cj,eq into Eq. (6), the design guideline
can be derived as
Cj,eq
)
2N
(10)
Then, the ZVS analysis method by taking the secondary
rectifier reverse recovery effect into consideration can be
expressed as Eq. (11). The corresponding ZVS analysis circuit
model is shown in Fig. 9.
Fig. 7. ZVS analysis model for method 4.
tdead ≥ 8Lmfr(2Coss,eq+
Qrr
Vo
tdead ≥ 8 Lmfr(2Coss,eq+
Cj,eq+Crr,eq
)
2N
(11)
(7)
Similar to the primary switch, a constant output capacitance
value for the secondary rectifier diode is used for this analysis
method.
E. Method 5 (variable output capacitance of secondary
rectifier)
Similarly, the output capacitance for the secondary rectifier
diode is not constant since the voltage across the diode is
changing. Therefore, a linear charge equivalent capacitance
Cj1 can be adopted and the expressions for Cj1 and tdead are [5]
vD
 C( v )dv
Cj1 = 0
(8)
vD
tdead ≥ 8 Lmfr(2Coss,eq+
Cj1
)
2N
(9)
The equivalent ZVS analysis circuit model is shown in Fig.
Fig. 9. ZVS analysis model for method 6.
Nevertheless, with the penetration of wide band gap devices,
the Silicon Carbide (SiC) diode has no reverse recovery
energy loss. Thus, the reverse recovery effect can be ignored.
Due to the page limitation, the other ZVS analysis methods
are not discussed in this article.
III. ACCURATE AND COMPLETE ZVS ANALYSIS FOR LLC
CONVERTER
8.
Fig. 10 shows all the possible factors that will affect the
ZVS operation of the LLC converter. The rest includes the
transformer stray capacitance, printed circuit board (PCB)
stray capacitance, time domain analysis method, and gate
driver delays. The traditional FHA method ignores other
operating conditions, which makes its accuracy unacceptable
when the converter operating point is away from the resonant
frequency point.
Fig. 8: ZVS analysis model for method 5
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ViorVO

Ceq = 0
C oss( v )dv
ViorVo
(13)
The other parasitic capacitances can be obtained by using
measurement or simulation method. The impedance analyzer
or ANSYS Q3D can be used to extract the parasitic capacitors.
4) Results
Once all the required information are given, after clicking
the ‘calculate’ button, the circuit under certain conditions can
be obtained. Circuit current waveform, deadtime, turn-off
current, frequency, and calculation time are presented.
Fig. 10. ZVS analysis model in this article.
To improve the accuracy of FHA, the time domain based
method is utilized. The general principles for the time domain
modelling is based on the operation stages of the LLC
converter. The circuit can be mathematically expressed based
on KCL and KVL. Due to the page limitation, the details
regarding the time domain modelling process are not
presented. The method is same as the modelling method in
[15]. Please note that the LLC converter can also be modelled
using the method presented in [16, 17].
Fig. 11 shows the picture of the developed graphical user
interface (GUI) for the evaluation of LLC converter deadtime.
The operation of the evaluation tool can be divided into the
following steps.
1) Converter structure selection
LLC converter has different structures based on the inverter
and rectifier [18]. Users can select the structure based on the
application requirements.
2) Circuit parameters
The circuit parameters are required to calculate the primary
switch turn-off current, which is used to evaluate the ZVS
performance of the converter. In addition, the regulation type
should also be defined, which includes output voltage
regulation, output current regulation, and output power
regulation.
3) Circuit parasitic capacitance
The semiconductor junction capacitance is modelled as
follows. Please note that other model equation would also
work, small modification is required on the developed
evaluation tool.
Coss = k 4 ⋅ ek 3VDS + k 2 ⋅ ek 1VDS
(12)
The coefficients k1-k4 in Eq. (12) can be obtained by using
curve fitting tool and the data from manufacture datasheet.
Then, the equivalent junction capacitance of the
semiconductor is calculated as shown in Eq. (13) [12].
Fig. 11. Developed deadtime evaluation tool for LLC
converter.
Fig. 12 shows the results of an example.
Fig. 12. An example.
IV. EXPERIMENTAL RESULTS
To validate the effectiveness of the developed deadtime
evaluation tool, experimental results and analysis results are
compared.
The converter operating conditions are: RL=5 Ω/50 Ω,
Lr=38μH, Cr=66 nF, Lm=204 μH, N=4, Vo=25. Fig. 13 shows
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the theoretical required deadtime in below resonant frequency
region. Fig. 14 shows the experimental results by applying the
same deadtime, it can be seen that the ZVS operation is just
achieved for the primary switch, which is almost the minimum
required deadtime under this condition.
Fig. 13. Theoretical required deadtime the scenario of fs<fr.
the conduction of body diode or achieve ZVS operation for all
conditions.
Fig. 15. Theoretical required deadtime in the scenario of fs>fr.
vGS
vDS
iLr
iD
Fig. 16. Experimental results in the case of fs>fr and RL=50 Ω.
Fig. 14. Experimental results in below resonant frequency
region when input voltage equals 160 V and load resistance
equals 5 Ω.
Fig. 15 shows the theoretical results in above resonant
frequency region and Fig. 16 shows the corresponding
experiment results. It can be seen that in the scenario of fs>fr,
the required deadtime varies significantly with the circuit
operating conditions. Thus, it would be beneficial to use
variable deadtime instead of fixed deadtime to either minimize
If the same deadtime is applied during all the conditions, as
can be seen in Fig. 17, under heavy load conditions, the
deadtime is too large that the body diode of the primary switch
will start conducting, which will generate extra conduction
loss.
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[4]
Fig. 17. Experimental results in the case of fs>fr and RL=5 Ω.
V. CONCLUSIONS AND FUTURE WORK
In this paper, a ZVS evaluation tool for LLC converters
based on time domain analysis are discussed. The optimized
deadtime can be calculated accurately under different
scenarios. It can be concluded that the proposed method has the
advantages of high accuracy, fast, and convenient. The focus of
the future work is to determine the upper limit for the
deadtime. The developed evaluation tool can provide a
minimum deadtime, while an upper limit value for the
deadtime is also important for the analysis and design. The
ZVS operation can be lost if the deadtime is too large.
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