# Reconfigurable Interleaved LLC Resonant Converter Using Hybrid Modulation for Ultrawide Output Voltage Range

Tae-Seok Kang, Hyun-Gyu Koh, Yoo-Seop Kim, Yeong-Jun Choi

► To cite this version:

Tae-Seok Kang, Hyun-Gyu Koh, Yoo-Seop Kim, Yeong-Jun Choi. Reconfigurable Interleaved LLC Resonant Converter Using Hybrid Modulation for Ultrawide Output Voltage Range. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0278. hal-05082316

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# Reconfigurable Interleaved LLC Resonant Converter Using Hybrid Modulation for Ultrawide Output Voltage Range

Tae-Seok Kang, Hyun-Gyu Koh, Yoo-Seop Kim, Yeong-Jun Choi†

Department of Electrical Engineering, Jeju National University
102 Jejudaehak-ro, Jeju-si, Jeju-do 63243, Republic of Korea
Jeju, Republic of Korea

Tel.: +82 / (64) - 754.3677.

E-Mail: wpwn1207@jejunu.ac.kr, ko9003@stu.jejunu.ac.kr, rdgcw12@jejunu.ac.kr, †yeongjun.choi@jejunu.ac.kr

## Acknowledgements

This work was supported by the Industrial Strategic Technology Development Program (RS-2024-00409108, Development of Component Technology for High-Load Power Components) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) and supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2024-00405278).

## Keywords

«Electric Vehicle (EV)», «Electrolysis», «LLC resonant converter», «Modulation strategy», «Wide range operation».

## Abstract

Applications such as renewable energy, electric vehicle (EV) battery charger, EV electronic Components, energy storage system, and electrolyzer demand DC/DC converters with a wide voltage range. The LLC resonant converter is widely applied due to their high efficiency advantage. This paper proposes a reconfigurable interleaved LLC resonant converter with hybrid modulation for ultra-wide output voltage range applications. The proposed converter achieves three operating modes with extended voltage gain within a narrow frequency range by regulating the switching frequency and phase-shift angle. This allows the selection of a large magnetizing inductance and reduces circulating current and conduction losses. Additionally, the converter achieves zero voltage switching of the MOSFETs at full load. To verify the performance of the proposed converter, a 3.3kW rated converter with 400V input and 150V-800V output is designed.

## Introduction

Recent advancements in energy technology have led to increased interest in renewable energy, EV electronic Components, EV charging, energy storage systems, and electrolysis [1]-[4]. Since these applications have a wide voltage operating range, the DC/DC converter is required to operate over a wide voltage range while maintaining high power conversion efficiency [5],[6].

LLC resonant converter is widely used in high-efficiency applications due to their advantages such as a low number of components, high efficiency, high power density, zero-voltage switching (ZVS) of active switches, zero-current switching (ZCS) of rectifier diodes, and low electromagnetic interference (EMI) [7], [8].

The conventional LLC resonant converter achieves a wide output voltage range by regulating the switching frequency far from the resonant frequency. However, this approach decreases the efficiency of the converter [9]. To overcome this problem, many methods have been studied for modulation strategies, and structure reconfiguration.

Modulation strategies for generating the gating signal in LLC resonant converters include pulse frequency modulation (PFM), pulse width modulation (PWM), and phase-shift modulation (PSM). Using PFM achieves a wide output voltage range. However it increases the switching frequency range, which results in lower efficiency.

PWM is appropriate for a wide output voltage range because the output voltage is regulatable when the switching frequency matches the resonant frequency [10]. However, it requires additional components, and since the output voltage is regulated by the duty cycle of the primary-side switch, it is difficult to achieve ZVS and asymmetric current occurs [11], [12].
<figure><img src="image_2.png" /><figcaption>Fig. 1: Topology of the proposed interleaved LLC resonant converter.</figcaption></figure>

The PSM regulates the output voltage using the phase-shift angle between the switch legs at a fixed frequency [13], [14]. However, if the PSM is adopted on the primary-side, it is difficult to achieve ZVS of the lagging legs when the phase-shift angle is too large.

Another method is structure reconfiguration [15]-[18]. This method achieves high efficiency and a wide voltage gain range. In [15], [16], a modified structure is proposed that switches between half-bridge and full-bridge modes through a bidirectional switch. However, the half-bridge and full-bridge hybrid structure on the primary-side is appropriate for wide input voltage range applications. In [17], dual transformers are used to achieve a wide output voltage range. However, the switching frequency range is still wide. In [18], the output voltage is regulated by changing the transformer turns ratio through the secondary-side auxiliary switch, however the voltage gain range is not wide.

In this paper, a reconfigurable interleaved LLC resonant converter using PFM, PSM for ultra-wide output voltage range is proposed. The proposed converter operates in three modes under low and high output voltage conditions, via PSM and PFM strategies, thereby achieving an ultra-wide output voltage range within a narrow switching frequency range. Additionally, all switches achieve ZVS throughout the entire operating range, reducing circulating current and conduction loss on the primary-side, resulting in high efficiency.

## Circuit and operation principle

Fig. 1 shows the circuit of the proposed reconfigurable interleaved LLC resonant converter. In the primary-side, the switching network consists of main switches $S_1-S_8$ with body diodes, parasitic capacitances. The two resonant tanks have the same parameters, that is, the primary-side leakage inductors $L_{lkp1} =$

<figure><img src="image_3.png" /><figcaption>Fig. 2: Operation of the Proposed LLC resonant converter in three modes (a) LG mode (b) HG mode (c) UG mode.</figcaption></figure>

$L_{lkp2} = L_{lkp}$ of the isolated transformers $T_1$ and $T_2$, two magnetizing inductors $L_{m1} = L_{m2} = L_m$, and two resonant capacitors $C_{r1} = C_{r2} = C_r$. The transformers $T_1$ and $T_2$ have the primary-side windings of transformers $N_{p1} = N_{p2} = N_p$, the secondary-side windings of transformers $N_{s1} = N_{s2} = N_s$, and the turns ratio $n_1 = n_2 = n$. The secondary-side is reconfigured by adding two active switches $S_9$ and $S_{10}$ to the full-bridge rectifier. $D_1-D_4$ are rectifier diodes. $L_{lks1} = L_{lks2}$ are secondary-side leakage inductors of the transformers. To simplify the analysis, assume that $L_{lks1} + L_{lks2} = L_{lks}$.

This reconfigured structure allows for the regulation of the turns ratio and output voltage gain, as shown in Fig. 2. Fig. 2(a) shows the main operation of low gain (LG) mode, Fig. 2(b) shows the main operation of high gain (HG) mode, and Fig. 2(c) shows the main operation of ultra gain (UG) mode.
## A. Low gain (LG) mode

Fig. 3 shows the key waveforms from LG mode to HG mode of the proposed LLC resonant converter. In this mode, $S_9$, $S_{10}$ are always turned off. Under low output voltage conditions, switching frequency $f_s$ operates at resonant frequency $f_r$, and phase-shift angle $\phi_p$ regulates output voltage. $\phi_p$ is defined as the phase difference between the gating signals of the two switching networks $S_1$ - $S_4$ and $S_5$ - $S_8$ on the primary-side and has a range of $0 \le \phi_p < \pi$. In this case, $V_{ab1}$ and $V_{ab2}$ are not in-phase, so the secondary-side winding connections of transformers $T_1$, $T_2$ are regulated according to the polarity of $V_{NS1}$ and $V_{NS2}$. When $S_5$, $S_8$ are turned off, the polarity of $V_{ab2}$ becomes negative. Therefore, diode $D_2$ begins to conduct due to the forward bias voltage, and since the secondary winding is not connected in series, the output voltage decreases. The normalized voltage gain $M_1$ of the proposed converter is defined as follows:

$$M_1 = \frac{nV_o}{V_{in}} \qquad (1)$$

where $V_{in}$ is the input voltage, $V_o$ is the output voltage, and $n = N_p/N_s$.

## B. High gain (HG) mode

Fig. 4 shows the key waveforms of the proposed LLC resonant converter in HG mode. Under high output voltage conditions, the LLC resonant converter maintains a phase shift angle $\phi_p = 0$ and regulates the output voltage using the PFM with a 50% duty cycle, operates at $f_s < f_r$. Therefore, since $V_{ab1}$ and $V_{ab2}$ are in-phase, the two secondary windings always operate in series. In this mode, the effective turns ratio is modified to $N_p: 2N_s$ due to the series structure of the secondary windings. The modified turns ratio is expressed as

$$n_a = \frac{N_p}{N_{S1}+N_{S2}} = \frac{N_p}{2N_s} \qquad (2)$$

where $n_a = n/2$. The voltage gain is as follows:

$$M_2 = \frac{n_a V_o}{V_{in}} \qquad (3)$$

## C. Ultra gain (UG) mode

Fig. 5 shows the key waveforms from HG mode to UG mode of the proposed LLC resonant

<figure><img src="image_4.png" /><figcaption>Fig. 3: Key waveforms in LG mode to HG mode transition.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4: Key waveforms in HG mode.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5: Key waveforms in HG mode to UG mode transition.</figcaption></figure>

converter. To achieve the high output voltage condition in HG mode, the switching frequency is regulated within the range of $f_s < f_r$, however, the problem of circulating current exists. Therefore, a phase shift angle $\phi_s$ is used to further increase the output voltage within a narrow switching frequency range. $\phi_s$ is defined as the phase difference between the gate signals of the primary-side switching network $S_1$-S$_8$ and the secondary-side active switches $S_9$ and $S_{10}$. As the output voltage increases, $\phi_s$ increases. The operations of each switching step are shown in Fig. 6.
<figure><img src="image_7.png" /><figcaption>Fig. 6: Operation stages of the Proposed LLC resonant converter in UG mode (a) Stage 1[t₀, t₁], (b) Stage 2[t₁, t₂], (c) Stage 3[t₂, t₃], (d) Stage 4[t₃, t₄], (e) Stage 5[t₄, t₅].</figcaption></figure>

Stage 1[t₀, t₁]: At t₀, switches S₂, S₃, S₆, S₇ are turned off. Due to the negative leakage inductor current i<sub>lkp</sub>, the parasitic capacitors of S₁, S₄, S₅, S₈ are discharged, and the body diode begins to conduct, causing a positive voltage to be applied to the primary-side of the transformer. In addition, the drain-source voltages of S₁, S₄, S₅, S₈ decrease from V<sub>in</sub> to zero, which provides the ZVS turn-on condition. In this mode, energy is transferred from the primary-side to the secondary-side of the transformer and the secondary-side winding of the transformer is short-circuited by S₁₀ and D₄. Therefore, the leakage inductors L<sub>lkp</sub>, L<sub>lks</sub> begin to charge and the magnetizing inductor is applied with zero voltage (V<sub>Lm</sub> = 0 V). The secondary-side windings are in series and the currents i<sub>NS1</sub> and i<sub>NS2</sub> flowing through the windings are equal.

Stage 2[t₁, t₂]: At t₁, the parasitic capacitors of S₁, S₄, S₅, S₈ are fully discharged, so S₁, S₄, S₅, S₈ are realized ZVS turn-on. In this mode, i<sub>lkp</sub> increases in the positive direction. V<sub>Lm</sub> is still

fixed at zero and energy is transferred from the primary-side to the secondary-side. The UG mode equivalent circuit of the proposed converter considering leakage inductance is shown in Fig. 7. In stages 1 and 2, the resonant inductor current i<sub>r</sub> and the resonant capacitor voltage v<sub>Cr</sub> are expressed by (4) and (5) from the equivalent circuit.

$$i_r = i_{Cr} = C_r \frac{dv_{cr}}{dt} \quad (4)$$

$$v_{Lr} + v_{Lp-Lr} = (L_r + L_p - L_r) \frac{di_r}{dt} \quad (5)$$

where L<sub>r</sub> = L<sub>lkp</sub> + L<sub>m</sub> || (n<sup>2</sup>L<sub>lks</sub>), L<sub>p</sub> = L<sub>lkp</sub> + L<sub>m</sub>, L<sub>p</sub> - L<sub>r</sub> = L<sub>m</sub> - L<sub>p</sub> || (n<sup>2</sup>L<sub>lks</sub>). From (4) and (5), i<sub>r</sub>(t) and v<sub>Cr</sub>(t) are derived as follows:

$$i_r(t) = I_{r0} \cos[\omega_0(t - t_0)] + \frac{V_{in} - V_{Cr0}}{Z_0} \sin[\omega_0(t - t_0)] \quad (6)$$
<figure><img src="image_8.png" /><figcaption>Fig. 7: Equivalent circuit with secondary leakage inductance.</figcaption></figure>

$$v_{Cr}(t) = I_{r0}Z_{0} \sin[\omega_{0}(t - t_{0})] + (V_{cro} - V_{in}) \cos[\omega_{0}(t - t_{0})] \quad (7)$$

where the initial values ($t = t_0$) are $V_{Cr0}$ and $i_{r0}$, $Z_0 = \sqrt{\frac{L_r+(L_p-L_r)}{C_r}}$, $\omega_0 = \frac{1}{\sqrt{(L_r+L_p-L_r)C_r}}$.

Stage 3[$t_2, t_3$]: $S_{10}$ is turned off, which causes the parasitic capacitor to discharge and the body diode to begin conducting. At $t_2$, the voltage begins to increase as the energy charged in the leakage inductors $L_{lkp}$ and $L_{lks}$ discharges. This is similar to the principle of a conventional boost converter. $L_{lkp}$ and $C_r$ resonate as power is transferred to the load, and the magnetizing inductor current $i_m$ increases linearly due to the positive voltage applied to $L_m$ as follows:

$$V_{Lm} = L_m \frac{di_m}{dt} \quad (8)$$

Stage 4[$t_3, t_4$]: The parasitic capacitors of $S_9$ is fully discharged, thereby realizing the ZVS turn-on. In stages 3 and 4, $i_r$ is as (4) and $v_{Cr}$ are expressed as follows from the equivalent circuit in Fig. 7.

$$v_{Lr} = L_r \frac{di_r}{dt} = V_{in} - n_a V_o \sqrt{\frac{L_p-L_r}{L_p}} - v_{Cr} \quad (9)$$

where $n_a = 1/2n$.

From (4) and (9), $i_r(t)$ and $v_{Cr}(t)$ are expressed by (10) and (11).

$$i_r(t) = I_{r0} \cos[\omega_1(t - t_0)] - \frac{\left( V_{in} - n_a V_o \sqrt{\frac{L_p - L_r}{L_p}} - V_{cro} \right)}{Z_1} \sin[\omega_1(t - t_0)] \quad (10)$$

$$v_{Cr}(t) = \left( V_{in} - n_a V_o \sqrt{\frac{L_p - L_r}{L_p}} + Z_1 I_{r0} \sin[\omega_1(t - t_0)] + [V_{cro} - (V_{in} - n_a V_o \sqrt{\frac{L_p - L_r}{L_p}}) \cos[\omega_1(t - t_0)]] \right) \quad (11)$$

where $Z_1 = \sqrt{L_r/C_r}$, $\omega_1 = 1/\sqrt{L_r C_r}$.

Stage 5[$t_4, t_5$]: At $t_4$, the current flowing through the secondary winding of the transformer becomes zero. $L_m$ begins to participate in resonance with $L_{lkp}$ and $C_r$. $i_m$ increases and becomes equal to $i_r$, and the primary-side current of the transformer becomes zero. In this mode, the output filter capacitor $C_o$ supplies the load, and the primary-side energy is no longer transferred to the secondary-side. In this mode, $i_r$ is as (4) and $v_{Cr}$ are expressed as follows:

$$v_{Llkp} + v_{Lm} = (L_{lkp} + L_m) \frac{di_r}{dt} \quad (12)$$

From (4) and (12), $i_r(t)$ and $v_{Cr}(t)$ are expressed by (13) and (14).

$$i_r(t) = I_{r0} \cos[\omega_2(t - t_0)] + \frac{V_{in} - V_{cro}}{Z_2} \sin[\omega_2(t - t_0)] \quad (13)$$

$$v_{Cr}(t) = I_{r0}Z_2 \sin[\omega_2(t - t_0)] + V_{cro} - V_{in} \cos[\omega_2(t - t_0)] \quad (14)$$

where $Z_2 = \sqrt{\frac{L_{lkp}+L_m}{C_r}}$, $\omega_2 = \frac{1}{\sqrt{(L_{lkp}+L_m)C_r}}$.

# Design and gain analysis

## A. Voltage gain

In general, the design optimization of LLC resonant converters with a wide voltage range follows established design procedures [19]-[22]. In this procedure, the series resonant tank components $L_r$ and $C_r$, and the magnetizing inductance $L_m$ of the transformer are selected so that the circuit is designed for optimal performance over a wide voltage range. The equivalent circuit of the proposed LLC resonant converter is built by adopting the Fundamental Harmonic Approximation (FHA) method considering the secondary-side leakage inductor $L_{lks}$ in Fig. 7[23]. The ac equivalent resistance is defined as $R_{ac}$. The input voltage $v_d$ applied to the resonant tank is a square wave voltage
<figure><img src="image_9.png" /><figcaption>Fig. 8: Voltage gain curves.</figcaption></figure>

generated by the switching network. According to Fourier analysis, $v_d^F(t)$ is expressed as

$$v_d^F(t) = \frac{4V_{in}}{\pi} \sum_{m=1,3,5...}^{\infty} \frac{1}{m} \sin(\omega mt) \quad (15)$$

where $\omega = 2\pi f_s$.

The rms value of the fundamental component of $v_d^F(t)$ is $v_d^F$.

$$v_d^F = \frac{2\sqrt{2}}{\pi} V_{in}. \quad (16)$$

The rms value of the voltage $v_{RO}^F$ of an AC equivalent resistor is expressed as

$$v_{RO}^F = nV_{RI}^F = \frac{2\sqrt{2n}}{\pi} V_o. \quad (17)$$

The rms value of the fundamental component of the current corresponding to $i_{ac}$ is

$$I_{ac} = \frac{\pi I_o}{2\sqrt{2}}. \quad (18)$$

Therefore, the AC equivalent resistance is expressed as

$$R_{ac} = \frac{nV_{RI}^F}{\frac{1}{n}I_{ac}} = \frac{8n^2 V_o}{\pi^2 I_o} = \frac{8n^2}{\pi^2} R_o. \quad (19)$$

Quality factor Q is as follows:

$$Q = \frac{1}{R_{ac}} \times \sqrt{\frac{L_r}{C_r}}. \quad (20)$$

1) LG mode: In this mode, the converter regulates $\phi_p$ using the PSM at $f_s = f_r$. The relationship between duty cycle D and $\phi_p$ is as follows:

$$D\pi = \pi - \phi_p. \quad (21)$$

As a result, (16) is changed as follows:

<figure><img src="image_10.png" /><figcaption>Fig. 9: Control block diagram of the proposed LLC resonant converter</figcaption></figure>

$$v_{d\_rms}^F = \frac{2\sqrt{2}}{\pi} V_{in} \sin\left(\frac{\pi - \phi_p}{2}\right). \quad (22)$$

Through equations (17) and (22), the voltage gain is expressed as

$$M_{LG} = \frac{nV_o_{LG}}{V_{in}} = \frac{\sqrt{\frac{L_p}{L_p-L_r}} \sin\left(\frac{\pi-\phi_p}{2}\right)}{\sqrt{\left[1+\frac{2k+1}{k^2}\left(1-\frac{\omega_r^2}{\omega^2}\right)\right]^2 + \left[Q_n^e\left(\frac{\omega}{\omega_r}-\frac{\omega_r}{\omega}\right)\right]^2}} \quad (23)$$

$$\text{where } \omega_o = 1/\sqrt{L_r C_r}, R_{ac\_n}^e = \frac{8n^2}{\pi^2} \frac{L_p-L_r}{L_p} R_o, \\ Q_n^e = \frac{\sqrt{L_r/C_r}}{R_{ac\_n}^e}, k = \frac{L_m}{L_{lkp}}.$$

2) HG mode: In this mode, the converter adopts the PFM in the range $f_s \le f_r$, the same as the conventional LLC resonant converter, and the secondary windings of the transformer are connected in series, changing the turns ratio from n to $n_a$. The voltage gain is

$$M_{HG} = \frac{nV_o_{HG}}{V_{in}} = \frac{\sqrt{\frac{L_p}{L_p-L_r}}}{\sqrt{\left[1+\frac{2k+1}{k^2}\left(1-\frac{\omega_r^2}{\omega^2}\right)\right]^2 + \left[Q_{na}^e\left(\frac{\omega}{\omega_r}-\frac{\omega_r}{\omega}\right)\right]^2}} \quad (24)$$

$$\text{where } R_{ac\_na}^e = \frac{8n_a^2 L_p - L_r}{\pi^2 L_p} R_o, Q_{na}^e = \frac{\sqrt{L_r/C_r}}{R_{ac\_na}^e}.$$

3) UG mode: This mode regulates the phase shift angle using the PSM at the $f_s$ regulated in HG mode ($\phi = 0, 0 \le \phi_s < \phi_{s\_max}$). The relationship between duty cycle D and $\phi_s$ is as follows:

$$D\pi = \pi - \phi_s. \quad (25)$$

As a result, (17) becomes as follows:

$$v_{RO\_rms}^F = \frac{2n\sqrt{2}}{\pi} V_o \sin\left(\frac{\pi - \phi_s}{2}\right). \quad (26)$$

Through (16) and (26), the voltage gain is expressed as
<table><caption>Table I: Design specifications</caption><thead><tr><th>Symbol</th><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>V<sub>in</sub></td><td>Input voltage</td><td>400 V</td></tr><tr><td>V<sub>o</sub></td><td>Output voltage</td><td>150 V-800 V</td></tr><tr><td>P<sub>o</sub></td><td>Output power</td><td>3.3 kW</td></tr><tr><td>f<sub>s</sub></td><td>Switching frequency</td><td>60 kHz-100 kHz</td></tr><tr><td>f<sub>r</sub></td><td>Resonant frequency</td><td>100 kHz</td></tr><tr><td>L<sub>m1</sub>, L<sub>m2</sub></td><td>Magnetizing inductance</td><td>309.6 μH</td></tr><tr><td>L<sub>lkp1</sub>, L<sub>lkp2</sub></td><td>Primary leakage inductance</td><td>51.6 μH</td></tr><tr><td>C<sub>r1</sub>, C<sub>r2</sub></td><td>Resonant capacitance</td><td>49.08 nF</td></tr><tr><td>n<sub>1</sub>, n<sub>2</sub></td><td>Transformer turns ratio</td><td>2.66, 2.66</td></tr></tbody></table>

$$M_{UG} = \frac{nV_{o_{UG}}}{V_{in}} = \frac{2 \sqrt{\frac{L_p}{L_p-L_r} \frac{1}{\sin(\frac{\pi-\phi_s}{2})}}}{\sqrt{\left[1+\frac{2k+1}{k^2}\left(1-\frac{\omega^2}{\omega^2}\right)\right]^2 + \left[q_{na}^e\left(\frac{\omega}{\omega_r}-\frac{\omega_r}{\omega}\right)\right]^2}} \quad (27)$$

Fig. 8 shows the voltage gain curve versus normalized frequency $f_n$ ($= f_s/f_r$) and the operating range of the proposed LLC resonant converter in three modes. It achieves a ultrawide voltage range within a narrow switching frequency range.

## A. Control Strategy

The control block diagram of the proposed converter is presented in Fig. 9. If $f_s$ is equal to $f_{s\_max}$, the output voltage is regulated by $\phi_p$ using PSM. When the load voltage increases and $\phi_p = 0°$ is reached, it is fixed at this angle. If $f_s$ is lower than $f_{s\_max}$, the output voltage is regulated by PFM. When the load voltage increases, $f_s$ decreases until it reaches $f_{s\_min}$. If $f_s$ reaches its minimum value, it is fixed at $f_{s\_min}$. When the load voltage is increased further, $\phi_s$ increases until it reaches $\phi_{s\_max}$.

## Results of verification

To verify the performance of the proposed reconfigurable interleaved LLC resonant converter, MATLAB based PLECS simulation is used, and the circuit parameters are shown in Table 1. A 3.3 kW LLC resonant converter is designed to verify the performance of the proposed method. The rated input voltage $V_{in} = 400 V \pm 10 V$, output voltage $V_o = 150-800 V$, $n = 2.66$.

Fig. 10 shows the steady-state waveform in LG mode. In this mode, $S_9$, $S_{10}$ are always off. The

<figure><img src="image_11.png" /><figcaption>Fig. 10: Steady-state Waveforms in LG mode with $V_o = 160 V$ and $P_o = 648 W$. (a) soft-switching waveforms of $S_1$. (b) phase-shift modulation in LLC resonant converter.</figcaption></figure>

PSM is used to regulate $V_o$ when the output load operates under low voltage conditions. Therefore, it shows that $V_o = 160 V$ depending on $\phi_p$ at $f_s = 100$ kHz. As $\phi_p$ decreases, the output voltage $V_o$ increases. In this mode, ZVS operation for $S_1$ is achieved.

Fig. 11 shows the steady-state waveform of the HG mode. $S_9$, $S_{10}$ are on/off, and the PFM is used to regulate $V_o$ in this mode. Therefore, it shows that $V_o = 340 V$ according to $f_s = 80$ kHz at
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 11: Steady-state Waveforms in HG mode with $V_o = 340$ V and $P_o = 1340$ W. (a) soft-switching waveforms of $S_1, S_9$. (b) pulse frequency modulation in LLC resonant converter.</figcaption></figure>

$\phi_p = 0$. ZVS operation is achieved in both primary- and secondary-side switches.

Fig. 12 shows the steady-state waveform for UG mode. In this mode, the PSM is used to regulate $V_o$ when the output load operates under the maximum voltage condition. It shows that $V_o = 800$ V depending on $\phi_s$ at $f_s = 60$ kHz. ZVS operation is achieved in both primary- and secondary-side switches.

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 12: Steady-state Waveforms in UG mode with $V_o = 800$ V and $P_o = 3300$ W. (a) soft-switching waveforms of $S_1, S_9$. (b) phase-shift modulation in LLC resonant converter.</figcaption></figure>

## Conclusion

This paper proposes a reconfigurable interleaved LLC resonant converter using PFM, PSM for ultra-wide output voltage range applications. The proposed converter obtains three operation modes with extended output voltage gain range within a narrow frequency range by regulating the switching frequency and phase shift angle. To verify the converter, MATLAB based PLECS simulation is used in this paper. According to the verification results,
an ultrawide output voltage range of 150 V-800 V is achieved within a narrow switching frequency range of 60 kHz-100 kHz due to pulse frequency modulation and phase-shift modulation of the primary- and secondary-side. This allows for significant reductions in circulating current and conduction losses. In addition, ZVS operation of the power switch is achieved under various output voltage conditions. In future work, the effectiveness of the proposed converter will be demonstrated through efficiency analysis.

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