Unified Inductor Type Based Linear Resonant Hybrid Converter for Wide Voltage Range Applications

Abstract

Pulse frequency modulation (PFM) is widely used in LLC resonant converters. However, in wide voltage applications, the switching frequency range is very wide, which affects the performance of magnetic components and filters. In order to achieve wide voltage gain in a narrow frequency range, this paper proposes a unified inductor type based linear resonant hybrid converter (UITBLRHC). The resonant inductor and excitation inductor are unified, and the resonant tank with equal inductance ratio is achieved. Hence, the output voltage can be adjusted within a very narrow frequency range. In addition, the parameters and operating modes of the two inductors are exactly the same. Therefore, the types of inductors can be reduced, and the magnetic flux and heat distribution between the two inductors are more uniform. Finally, an 800 W prototype was built. The proposed solution can achieve twice the voltage gain within a frequency range of 1.25 times. The experimental results prove the reliability and validity.

1. Introduction

Isolated DC/DC converters are employed in many application scenarios, such as energy storage systems, vehicle-to-grid applications, and renewable energy DC grid systems [1,2,3]. As one of the popular isolated DC/DC topologies, due to the advantages of soft switching characteristics, electrical isolation, high efficiency, and high power density, LLC resonant converter topology has received widespread attention in academia and industry [4,5,6]. For the traditional LLC resonant converter, pulse frequency modulation (PFM) is used to regulate the output voltage. When the switching frequency approaches the resonant frequency, the efficiency of LLC is higher [7]. However, for working scenarios with a wide voltage range, the switching frequency of the LLC converter needs to be varied over a considerably wide frequency range, which makes it more difficult to design the magnetic components and driver circuits [8,9].

In order to improve the voltage regulation capacity within a narrow switching frequency range, many improvement methods have been proposed based on the traditional LLC converter. The main improved schemes can be categorized into the following three: (1) Improving modulation strategies. (2) Reconfiguring the structure of the primary or secondary side. (3) Changing the topology of the resonant tank. For the aspect of improving the modulation strategy, some hybrid control strategies, such as PFM-phase-shift (PFM-PS) modulation [10,11] and pulse width modulation (PWM) with fixed frequency [12], are adopted. A hybrid modulation method is used in a dual-transformer-based LLC converter in [10]. Two different control strategies are used: PFM in normal operation and phase-shift control in hold-up-time operation. Similar to [10], two extra active switches are utilized in [11] to adjust the output voltage through phase shift angle. In [12], a PWM-controlled strategy is applied to widen the voltage gain range by controlling the duty cycle of the additional switch. Although they improve the gain range by some degree, the modulation strategies, driving logic, and circuit design become more complex. Pulse width modulation or phase shift modulation with fixed switching frequency is proposed in [13] and [14]. However, the voltage gain derivation and ZVS analysis are relatively complex. The mode switching control can effectively extend the voltage regulation range [15]. By changing the driving logic, the converter can be switched between full-bridge and half-bridge modes. Although this method can obtain more than twice the voltage gain, it is relatively difficult to achieve smooth mode switching. In [16], the voltage regulation capacity is optimized by periodically switching operation modes. Especially when running in burst mode, it can solve the overvoltage problem under light load. However, the equivalent frequency is reduced, and a larger filter is required.

The reconfigurable structure, like switching the resonant converter structure between full-bridge and half-bridge mode in [17] and arranging the configurable capacitors in parallel or series in [18], also contributes to enhanced voltage regulation capability. In [19], the semiactive variable-structure rectifier (SA-VSR) can operate in both voltage-doubler rectifier (VDR) mode and voltage-quadrupler rectifier (VQR) mode, which makes the output voltage range be doubled. Although mode switching can double the range of voltage gain, the modes’ smooth transition control is still a problem. And the number of components is usually more. In [20], the auxiliary switch is added. However, the complexity of the control and drive logic is increased.

In terms of the topology of the resonant tank, changing the equivalent parameters of the resonant tank or the combination method of resonant elements is a viable approach to broaden the voltage gain range. Neither additional active devices nor complex modulation strategies need to be introduced, which is very simple for practical implementation. A linear resonant hybrid bridge converter is proposed in [21]. By changing the position of the resonant inductor and adding the hybrid bridge, the converter can be divided into HG mode and LG mode. In [22], a CLL resonant converter with a secondary-side resonant inductor is proposed to remove the circulating current and reduce loss. Despite the fact that the number of their components is few, the types of inductors are still categorized into two different types, resonant inductors and excitation inductors, as in traditional LLC converters. Overall, in traditional LLC resonant topologies, it is necessary to supply two different inductors. Two types of inductors mean that inductors also require a separate design. A multi-transformer structure is adopted in [23]. The various operation configurations can achieve good conversion efficiency. However, the utilization of the auxiliary transformer is relatively low, which leads to a low power density. In [8,24], a variable inductor is used in a half-bridge variable magnetizing inductance-controlled LLC resonant converter. By changing the inductance value of the variable inductor, the inductance ratio can be altered to improve the gain capability. However, in order to change the inductance value, a variable inductor requires additional excitation to be applied to the corresponding winding.

In order to achieve wide voltage gain within a narrow frequency range and unify the types of inductors, this paper proposes a unified inductor type based linear resonant hybrid converter (UITBLRHC). The two inductors of the resonant tank operate in the linear resonant hybrid mode with the identical inductance values and working states. The detailed advantages are as follows:

• The resonant inductor and excitation inductor are unified, and the resonant tank with equal inductance ratio is realized. The wide voltage gain can be achieved within a very narrow frequency range;
• The type of inductor in the resonant tank is reduced. In addition, compared with the traditional LLC resonant converters, the magnetic flux and heat distribution are more uniform.

The rest of this paper is organized as follows. Section 2 presents the topology structure of the proposed UITBLRHC converter and its operation principle. In Section 3, the key characteristics of the proposed converter are analyzed. In Section 4, the design considerations and processes are discussed and shown. In Section 5, an 800 W prototype is built to verify the analysis, and the experimental results are presented. Furthermore, a comparison is made. Finally, Section 6 concludes this paper.

2. Proposed Topology and Operation Principle

2.1. Topology of the Proposed UITBLRHC

The proposed unified inductor type based linear resonant hybrid converter (UITBLRHC) is shown in Figure 1. The input to the converter is a DC voltage source, V_in, and the output voltage is V_o. The primary side of the transformer is composed of a full-bridge structure with four switches. The midpoint A, B of each leg is connected to a resonant capacitor C_r in series with the power transformer. The secondary side is composed of two rectifier diodes; D₁&D₂; two linear resonant (L-R) inductors, L₁&L₂, with equal inductance value; and an output filter capacitor, C_f. The transformer turns ratio is defined as n: 1. The direction of the arrow in Figure 1 is the positive direction specified in this paper.

As shown in Figure 1, C_r resonates with two L-R inductors, L₁ or L₂, together constituting the resonant tank of the converter. Since L₁ or L₂ alternately presents linear or resonant characteristics, respectively, two L-R inductors have a unified function. The result is that the inductor types are unified and the equivalent inductance ratio $Ln=Lr/Lm$ equals one, making the converter obtain the capability of higher voltage gain.

2.2. Operation Principle

The typical operation waveform of the UITBLRHC converter is illustrated in Figure 2. V_in is the input voltage. i_D1&i_D2 are the currents of the rectifier diodes. i₁&i₂ are the currents of the L-R inductors. i_o is the output current. i_p is the primary side current. Define that L_r is the equivalent resonant inductor and L_m is the equivalent excitation inductor. Define C_eq as the equivalent resonant capacitor converted to the secondary side. Thus, L_r, L_m, C_eq, and the series-resonant frequency f_r can be expressed as follows:

$$\left\{\begin{array}{l}Lr=Lm=L1=L2\\ Ceq=Cr\times n^2\\ fr=1/2\pi \sqrt{LrCeq}\end{array}\right.$$

(1)

There are a total of eight stages in a complete operation period. Since the first and second half cycles are completely symmetrical, only the first half of the cycle will be analyzed as an example. The equivalent circuits of each stage are illustrated in Figure 3.

Stage 1 [t₀, t₁] [see Figure 3a]: Before t₀, S₂&S₃ are ON. i₁ and i₂ are equal in amplitude and opposite in polarity. C_r is in ternary resonance with both L₁ and L₂. Stage 1 begins at t₀ when S₂&S₃ are turned OFF and D₁ is turned ON. It should be noted that Stage 1 is within the deadband of S₁–S₄. Since the polarity of i_p is negative, i_p charges the output capacitors C_oss2,3 of S₂&S₃ and discharges C_oss1,4. When the voltages across C_oss1,4 are discharged to 0, the body diodes of S₁&S₄ are able to conduct, preparing for ZVS turn ON of S₁&S₄. i_r, v_Cr, i_m and i_p can be expressed as follows:

$$\left\{\begin{array}{cc}\hfill ir(t)& =i2(t)=-Im\cos \left[\omega r(t-t0)\right]\hfill \\ & +{\displaystyle \frac{Vin/n-Vo-VCr0/n}{Zr}}\sin \left[\omega r(t-t0)\right]\hfill \\ \hfill vCr(t)& =\left({\displaystyle \frac{Vin}{n}}-Vo\right)+Zr\left(-Im\right)\sin \left[\omega r(t-t0)\right]\hfill \\ & -\left({\displaystyle \frac{Vin}{n}}-Vo-{\displaystyle \frac{VCr0}{n}}\right)\cos \left[\omega r(t-t0)\right]\hfill \\ \hfill im(t)& =i1(t)=Im-{\displaystyle \frac{Vo}{Lm}}\left(t-t0\right)\hfill \\ \hfill ip(t)& =ir(t)/n=i2(t)/n\hfill \end{array}\right.$$

(2)

where −I_m is the initial value of the resonant current at t₀, and V_Cr0 is the initial value of the voltage at t₀, $\omega r=1/\sqrt{LrCeq}$, $Zr=\sqrt{Lr/Ceq}$.

Stage 2 [t₁, t₂] [see Figure 3b]: As the body diodes conduct, the voltages across both S₁ and S₄ are 0. At t₁, S₁&S₄ are turned ON with ZVS. The input and output port voltages of the resonant tank remain both constant; hence, i_r, v_Cr, i_m, and i_p have the same expression formulas as stage 1.

It should be noted that i_r is defined as the current of the equivalent resonant inductor. For example, L₂ is employed as a resonant inductor in stages 1 and 2, resulting in i₂ and i_r being identical. And i_m is defined as the current of the equivalent excitation inductor. Due to the voltage across L₁ being clamped by −V_o, L₁ is utilized as the excitation inductor, and i_m is equal to i₁.

Stage 3 [t₂, t₃]: At t₂, since the resonant current becomes positive, the polarity of i_p also turns positive. Apart from that, the working condition is the same as Stage 2. During this stage, i_m will decrease under the effect of −V_o and eventually reach a negative peak.

Stage 4 [t₃, t₄] [see Figure 3c]: At t₃, i₁ and i₂ are again equal in amplitude and opposite in polarity; thus, i_o and i_D1 are identical and equal to 0. D₁ is turned OFF with ZCS. C_r will be in ternary resonance with both L₁ and L₂ during this stage. Because of D₁ being OFF, the load is supplied by C_f. i_r, v_Cr, i_m, and i_p can be written as follows:

$$\left\{\begin{array}{cc}\hfill ir(t)& =Im1\cos \left[{\displaystyle \frac{\omega r}{\sqrt{2}}}(t-t3)\right]\hfill \\ & +{\displaystyle \frac{Vin/n-VCr1/n}{\sqrt{2}Zr}}\sin \left[{\displaystyle \frac{\omega r}{\sqrt{2}}}(t-t3)\right]\hfill \\ \hfill vCr(t)& ={\displaystyle \frac{Vin}{n}}+\sqrt{2}ZrIm1\sin \left[{\displaystyle \frac{\omega r}{\sqrt{2}}}(t-t3)\right]\hfill \\ & -\left({\displaystyle \frac{Vin}{n}}-{\displaystyle \frac{VCr1}{n}}\right)\cos \left[{\displaystyle \frac{\omega r}{\sqrt{2}}}(t-t3)\right]\hfill \\ \hfill im(t)& =-ir(t)=i1(t)=-i2(t)\hfill \\ \hfill ip(t)& =ir(t)/n\hfill \end{array}\right.$$

(3)

where I_m1 is the initial value of the current at t₃ and V_Cr1 is the initial value of the voltage at t₃.

3. Characteristics of the UITBLRHC

3.1. Voltage Gain Characteristic

Generally, fundamental harmonic approximation (FHA) is used in resonant converters to analyze the voltage gain characteristic. However, due to the high harmonic content of the current, FHA will lose accuracy. Therefore, time domain analysis (TDA) is applied in UITBLRHC. The normalized voltage gain of the resonant tank is defined as follows:

$$M={\displaystyle \frac{Vo}{Vin/n}}=nVo/Vin$$

(4)

To simplify the calculation, the phase is used to represent the time:

$$\left\{\begin{array}{l}\theta =\omega rt\\ \theta 0=\omega rt0=0\\ \theta 1=\omega rt3\\ \theta 2=\omega rt4\end{array}\right.$$

(5)

Therefore, Equations (2) and (3) can be written as follows:

$$(0\le \theta \le \theta 1)\left\{\begin{array}{cc}\hfill ir(t)& =-Im\cos \theta +{\displaystyle \frac{Vin/n-Vo-VCr0/n}{Zr}}\sin \theta \hfill \\ \hfill vCr(t)& =\left({\displaystyle \frac{Vin}{n}}-Vo\right)+Zr\left(-Im\right)\sin \theta \hfill \\ & -\left({\displaystyle \frac{Vin}{n}}-Vo-{\displaystyle \frac{VCr0}{n}}\right)\cos \theta \hfill \\ \hfill im(t)& =Im-{\displaystyle \frac{Vo}{\omega rLm}}\theta \hfill \end{array}\right.$$

(6)

$$(\theta 1<\theta \le \theta 2)\left\{\begin{array}{cc}\hfill ir(t)& =Im1\cos {\displaystyle \frac{\theta -\theta 1}{\sqrt{2}}}\hfill \\ & +{\displaystyle \frac{Vin/n-VCr1/n}{\sqrt{2}Zr}}\sin {\displaystyle \frac{\theta -\theta 1}{\sqrt{2}}}\hfill \\ \hfill vCr(t)& ={\displaystyle \frac{Vin}{n}}+\sqrt{2}ZrIm1\sin {\displaystyle \frac{\theta -\theta 1}{\sqrt{2}}}\hfill \\ & -\left({\displaystyle \frac{Vin}{n}}-{\displaystyle \frac{VCr1}{n}}\right)\cos {\displaystyle \frac{\theta -\theta 1}{\sqrt{2}}}\hfill \\ \hfill im(t)& =-ir(t)\hfill \end{array}\right.$$

(7)

The capacitor voltages and inductor currents are always continuous in two adjacent stages. The voltage and current are symmetrical for the half cycle. Thus, the boundary conditions can be obtained:

$$\left\{\begin{array}{c}Im=ir(t4)=-ir(t0)\\ VCr0=vCr(t0)=-vCr(t4)\\ Im1=ir(t3)=-im(t3)\end{array}\right.$$

(8)

When the output voltage is V_o and the output power is P_o, the equivalent load $R=V{o}^2/Po$ and the output current I_o can be expressed as follows:

$$Io={\displaystyle \frac{Vo}{R}}={\displaystyle \frac{Vo}{{\pi }^{2}Rac/8}}={\displaystyle \frac{8QVo}{Zr{\pi }^2}}$$

(9)

where R_ac is defined as $Rac=8R/{\pi }^2$. And Q is defined as $Q=Zr/Rac$, which can indicate light or heavy load conditions.

Meanwhile, i_o is also the sum of i₁ and i₂, and averaging i_o over the half cycle is I_o, which yields the following:

$$Io=\overline{io}={\displaystyle \frac{1}{Ts/2}}{\displaystyle {\int }_{t_0}^{t_4}[i1(t)+i2(t)]dt}$$

(10)

Since $i1=-i2$ during [t₃, t₄], the equation can be reduced to the following:

$${\displaystyle \frac{8QVo}{2Zr{\pi }^{2}fs}}={\displaystyle {\int }_{t_0}^{t_3}i1(t)dt+{\displaystyle {\int }_{t_0}^{t_3}i2(t)dt}}$$

(11)

During [t₀, t₃], i₂ is equivalent resonant current i_r, which charges and discharges the resonant capacitor C_r:

$${\displaystyle {\int }_{t_0}^{t_3}i2(t)dt}={\displaystyle {\int }_{t_0}^{t_3}ir(t)dt}=Ceq({\displaystyle \frac{Vcr1}{n}}-{\displaystyle \frac{Vcr0}{n}})$$

(12)

And i₁ is equivalent to the excitation current, i_m. As shown in Figure 4, the integral of i_m over t₀ to t₃ is the area of the green rectangle minus the area of the yellow triangle, so the following can be deduced:

$${\displaystyle {\int }_{t_0}^{t_3}i1(t)dt}={\displaystyle {\int }_{t_0}^{t_3}im(t)dt}=Im(t3-t0)-{\displaystyle \frac{\frac{Vo}{Lm}(t3-t0)(t3-t0)}{2}}$$

(13)

Define the base values of the normalization parameters as follows:

$$Vbase={\displaystyle \frac{Vin}{n}}; Zbase=Zr; Ibase={\displaystyle \frac{Vbase}{Zbase}};$$

(14)

The normalized variables are calculated by the following equation:

$$VxN={\displaystyle \frac{Vx}{Vbase}}; IxN={\displaystyle \frac{Ix}{Ibase}};$$

(15)

where the subscript x denotes the corresponding original variable, and xN denotes the normalized variable.

Therefore, by combining Equations (11)–(13) and normalizing the expression, the relationship between the charging of the resonant capacitor and the resonant current can be derived as follows:

$$\left(VCr1N-VCr0N\right)+ImN\theta 1-{\displaystyle \frac{M\theta 1^2}{2}}={\displaystyle \frac{8MQ\theta 2}{{\pi }^2}}$$

(16)

Combe Equations (4)–(8) and (14)–(16) and define the normalized frequency f_n as $fn=fs/fr$. By normalizing all the relevant equations, the system of Equation (17) can be obtained:

$$\left\{\begin{array}{l}ImN=Im1N\cos {\displaystyle \frac{\theta 2-\theta 1}{\sqrt{2}}}+{\displaystyle \frac{1-VCr1N}{\sqrt{2}}}\sin {\displaystyle \frac{\theta 2-\theta 1}{\sqrt{2}}}\\ VCr0N=(1-VCr1N)\cos {\displaystyle \frac{\theta 2-\theta 1}{\sqrt{2}}}-1-\sqrt{2}Im1N\sin {\displaystyle \frac{\theta 2-\theta 1}{\sqrt{2}}}\\ M\theta 1-ImN=-ImN\cos \theta 1+(1-M-VCr0N)\sin \theta 1\\ VCr1N=(1-M)-ImN\sin \theta 1-(1-M-VCr0N)\cos \theta 1\\ Im1N=-ImN\cos \theta 1+(1-M-VCr0N)\sin \theta 1\\ VCr2N=1+\sqrt{2}Im1N\sin {\displaystyle \frac{\theta 2-\theta 1}{\sqrt{2}}}-(1-VCr1N)\cos {\displaystyle \frac{\theta 2-\theta 1}{\sqrt{2}}}\\ (VCr1N-VCr0N)+ImN\theta 1-{\displaystyle \frac{M\theta 1^2}{2}}={\displaystyle \frac{8MQ\theta 2}{{\pi }^2}}\\ \theta 2=\omega rt4=\omega rTs/2=\pi /fn\end{array}\right.$$

(17)

Since the analytical solution for the voltage gain M is hard to find, the numerical solution of the system of Equation (17) is obtained with the help of computerized mathematical tools, and the gain curve is given by the graphical representation method. Figure 5 plots the normalized voltage gain versus the normalized frequency f_n under different loads. It can be seen that the proposed UITBLRHC converter can achieve a wide voltage gain range in a narrow frequency range.

3.2. Soft Switching Performance

According to the operation principle in the previous paper, due to being in the discontinuous conduction mode (DCM) at $fs<fr$, ZCS turn OFF can be realized for both secondary-side rectifier diodes.

Although theoretically, ZVS turn ON for all switches on the primary side can be achieved naturally since the impedance of the resonant tank is inductive. However, in practice, to achieve ZVS turn ON in the deadband of S₁–S₄, it is necessary to ensure that the excitation current discharges the output capacitors C_oss to 0. Therefore, a large excitation current, I_m, helps the ZVS implementation. Given that the duration of the deadband is small enough, the resonant tank is approximated as a current source, I_m. The equivalent excitation current I_m can be approximately expressed as follows:

$$Im={\displaystyle \frac{Vo}{4Lmfs}}$$

(18)

Considering the charge relationship of the output capacitors, it is essential to satisfy the following:

$$nImtdead-4CossVin\ge 0$$

(19)

Combing Equations (18) and (19), the ZVS condition can be obtained:

$$tdead\ge {\displaystyle \frac{16LmVinfsCoss}{nVo}}$$

(20)

It should be noted that this current is also the switch-off current of the complementary switches at the same time. Thus, the current should not be too large, or it will greatly increase the switch-off loss. Consequently, there is a trade-off to be considered in the actual design.

3.3. Magnetic Flux Analysis

The current waveforms of unified and non-unified resonant tanks are shown in Figure 6. It can be seen that for unified inductor type L-R inductors, the excitation current waveforms of L₁ and L₂ are the same, except for a 180-degree difference in phase. However, both amplitudes and waveforms are different for two types of separate inductors. From this perspective, the flux variations of two L-R inductors are the same, whereas the flux distribution of two types of separate inductors is not homogeneous, manifesting as higher in one and lower in the other.

The results of finite element analysis (FEA) simulations for the magnetic flux distribution are compared in Figure 7. Apart from the different waveforms of winding excitation, the parameters of the two structures are identical. The relation between the magnetic flux variations in the three cases is as follows:

$$\Delta B_{Lr}>\Delta B_{\mathrm{L}-\mathrm{R}}>\Delta B_{Lm}$$

(21)

where $\Delta B_{Lr}$, $\Delta B_{\mathrm{L}-\mathrm{R}}$, and $\Delta B_{Lm}$ are the flux variations of the L-R inductor, resonant inductor, and excitation inductor, respectively. When using the same core and winding, and both inductors are of the same inductance value, the flux distribution between two L-R-type inductors will be more uniform compared to the combination of an individual resonant inductor and an individual excitation inductor. Since the hysteresis loss is mainly caused by the maximum magnetic flux density B_m, the L-R-type inductors will also have a more uniform loss distribution.

4. Proposed Converter Design Considerations

Figure 8 shows the overall design flowchart for the proposed UITBLRHC. To demonstrate the design process in detail, an example of the design of an 800 W experimental prototype is also used in this section. The circuit parameters are listed as follows: input voltage V_in = 240–480 V, output voltage V_o = 110 V, rated output power P_o = 800 W, and resonant frequency f_r = 150 kHz.

4.1. Turns Ratio of the Transformer

Taking the resonant point as the normal operating point, it corresponds to the case of maximum input voltage. Defining V_norm = 480 V as the base input voltage at unit voltage gain. Hence, based on (4), the turns ratio n of the transformer can be designed as follows:

$$n={\displaystyle \frac{Vnorm}{Vo}}$$

(22)

In the practical design, the number of coil turns must be an integer in order to facilitate the fabrication of the transformer.

4.2. Factor Q

Although the FHA method loses some accuracy, it is still widely used in the design of resonant converters due to its simplicity. Only two degrees (Q and L_n) should be considered. Once both of them are selected, the parameters of the resonant tank can be directly solved. Therefore, this paper still adopts the FHA method to obtain the resonant parameters.

Since two identical L-R inductors serve as a resonant inductor and an excitation inductor, respectively, the inductor ratio L_n equals one. Consequently, there is only one degree that needs to be chosen. Given that the input voltage range is 240–480 V, the maximum voltage gain, therefore, is 2. The maximum value of the factor Q is determined by the following equation:

$$Q_{\max }={\displaystyle \frac{1}{L_n{M}_{\max }}}\sqrt{L_n+{\displaystyle \frac{{M_{\max }}^2}{{M_{\max }}^2-1}}}$$

(23)

It is worth noting that the FHA method will have a large error considering that the higher harmonic components account for more when the resonant converter operates away from the resonant frequency. Therefore, a certain margin should be left in the consideration of the maximum value of the voltage gain.

4.3. Resonant Tank

Once the factor Q is determined, the resonant parameters can also be obtained. The resonant parameters can be expressed as follows:

$$\left\{\begin{array}{l}L1=L2={\displaystyle \frac{4QVnor{m}^2}{{\pi }^3{n}^{2}frPo}}\\ Cr={\displaystyle \frac{\pi Po}{16QfrVnor{m}^2}}\end{array}\right.$$

(24)

After calculating the resonant parameters, it is also necessary to verify that the ZVS can be realized by substituting the inductance value into relation (20). Since a margin was left for the choice of factor Q in the previous section, the value of Q can be appropriately reduced if relation (20) is not satisfied.

5. Experimental Verification and Comparison

5.1. Experimental Prototype

An 800 W experimental prototype is built as shown in Figure 9, and relevant experiment tests are conducted on this platform to verify the validity of the proposed UITBLRHC. According to Formulas (22)–(24), the key parameters of the converter can be determined. The detailed parameters of UITBLRHC are listed in

Table 1. System parameters.

Symbol	Quantity	Value
Vin	Input Voltage	240–480 V
Vo	Output Voltage	110 V
Po	Rated Power	800 W
n	Transformer Ratio	28/6
fs	Switching Frequency	120–150 kHz
fr	Resonant Frequency	150 kHz
L1, L2	L-R Inductors	6.34 μH
Cr	Resonant Capacitor	11.2 nF
S1~S4	MOSFETs	IPW60R070CFD7
D1&D2	Diodes	STTH30AC06C

.

5.2. Experimental Results and Waveforms

The steady-state working waveforms of the proposed UITBLRHC under different input voltages are shown in Figure 10. Over a wide input voltage range of 240–480 V, the proposed UITBLRHC can operate effectively to maintain a constant output voltage. The case of different input voltages can be represented by the amplitude of v_AB. Additionally, the inductor currents i_L1 and i_L2 alternate between sinusoidal and linear, demonstrating linear resonant features. It is worth noting that from the voltage gain curves in Figure 5, the theoretical normalized frequencies are 1, 0.908, and 0.826 (with corresponding switching frequencies of 150, 136.2, and 123.9 kHz) for voltage gains of 1, 1.33, and 2, respectively. Meanwhile, the practical switching frequencies are 150, 136, and 124 kHz for identical output voltage when input voltages are 480, 360, and 240 V, respectively, which can match the theoretical values. This correspondence effectively proves the accuracy of the voltage gain analysis discussed in Section 3, based on the time-domain method.

Since the driver signals of S₁&S₄ or S₂&S₃ are identical and the duty cycle is fixed at 50%, the ZVS realization is the same for both bridge arms on the primary side. Hence, the ZVS waveforms of only one bridge arm (S₁&S₂) are shown in Figure 11. From Figure 11a–c, it can be seen that the drain source voltage v_DS of switches is reduced to zero before the rising of the driver signal under different input voltages. Consistent with theoretical analysis, all switches can achieve ZVS turn ON. Apart from this, Figure 11d–f also gives the ZVS realization for different load cases. It can be seen that even under light load conditions, UITBLRHC is able to achieve ZVS turn ON.

The dynamic waveform of load switching is shown in Figure 12. When the output current changes within twice the range (3.6–7.2–3.6 A), the output voltage is maintained at 110 V. Therefore, the proposed UITBLRHC has good performance in a wide-range application. From the dynamic waveform of switching between half load and full load, when the load change occurs, the output voltage can also be adjusted rapidly and held at 110 V.

The curves of measured conversion efficiency for different output power levels under input voltages of 240, 360, and 480 V are shown in Figure 13. Due to the soft switching capability, the proposed UITBLRHC has good performance. The peak efficiency can reach 95.85%.

5.3. Loss Breakdown

The losses breakdown of the theoretical calculation is shown in Figure 14. For the proposed UITBLRHC, all the MOSFETs are turned on with ZVS, and all the diodes are turned off with ZCS. Hence, turning-on losses of MOSFETs and reverse recovery losses of diodes are zero. The overall losses can be divided into seven parts, namely conduction loss, switches turn-on loss, switches turn-off loss, inductor core loss, inductor copper loss, transformer core loss, and transformer copper loss. Among them, the conduction loss of switches and the copper loss of magnetic components are relatively high. The overall trend is basically consistent with the measured results. And it can be seen that efficiency is indeed higher under heavy loads, which is due to the large circulating current in the converter during light loads.

5.4. Inductor Difference Analysis

In the experimental prototype, L₁ and L₂ are 6.55 and 6.48, respectively. When the inductance difference is low, the inductor current waveform is symmetrical and the power is evenly distributed, as shown in the experimental waveform in Figure 10.

When the inconsistency between inductors increases, the characteristics of the converter will also be affected to a certain extent. The full load operation simulation results with a 20% inductance difference are shown in Figure 15. Under steady-state conditions, the difference in RMS value of inductor currents is approximately 17%.

5.5. Comparison

The proposed UITBLRHC is compared here with the conventional full-wave rectifier LLC converter since they are both resonant converters and PFM is used to regulate the output voltage for both of them.

For LLC, the magnetizing inductor of the transformer is typically utilized as the excitation inductor L_m. Therefore, the value of inductance ratio L_n is generally at least greater than 3, which limits the voltage gain capability of LLC topology. In contrast, due to inductor unification, UITBLRHC with an equivalent inductance ratio of 1 is more suitable for application scenarios in a wide voltage range.

While LLC can achieve an inductance ratio of 1 by using an external excitation inductor and resonant inductor, utilizing unified L-R-type inductors leads to better balance in terms of magnetic flux, losses, and thermal distribution, as analyzed earlier in Section 3. And the proposed UITBLRHC is simpler to design as it only needs to design one type of inductor.

The transformer in full-wave rectifier LLC topology has a central tap, with each secondary winding only operating for half a cycle while the other winding does not transfer power simultaneously. This alternating operation mode of two windings leads to a waste of winding utilization. Additionally, the structure with a central tap also makes manufacturing more complex. Compared with the former, the transformer in UITBLRHC does not require a central tap. This design is not only simpler to manufacture but also allows the secondary winding to operate throughout the entire cycle, resulting in improved utilization of the winding.

The proposed UITBLRC is compared with the other resonant topologies, as shown in

Table 2. Comparison with other resonant converter topologies.

Topologies	Traditional Full Bridge LLC Converter with Full-Wave Rectifier	Phase-Shift Controlled LLC Converter [10,11]	LLC Converter with Additional Components [18]	Variable Inductance LLC Converter [8,23]	Proposed UITBLRC
Number of switches and diodes	4 MOSFETs + 2 Diodes	6 MOSFETs + 2 Diodes	6 MOSFETs + 2 Diodes	2 MOSFETs + 4 Diodes	4 MOSFETs + 2 Diodes
Additional components	-	2 MOSFETs	1 Switched capacitor + 2 MOSFETs + 2 Output capacitors	1 Variable inductor	-
Magnetic components	1 Resonant inductor + 1 Excitation inductor + 1 Transformer (center-tapped)	1 Resonant inductor + 1 Excitation inductor + 1 Transformer	1 Resonant inductor + 1 Excitation inductor + 1 Transformer	1 Variable inductor + 1 Transformer	2 L-R inductors + 1 Transformer
Inductor types	2	2	2	2	1
Modulation	PFM	PFM + PSM	PFM + PWM	PFM	PFM
Switching frequency range	Wide	Narrow	Wide	Variable	Narrow
Voltage regulation range	Narrow	Wide	Wide	Narrow	Wide
Input/output voltage	-	200–400 V/48 V	400 V/100–500 V	190–210 V/48 V	240–480 V/110 V

. Compared with other wide voltage range resonant topologies, the proposed converter has fewer components. Moreover, the voltage regulation range is wide, which can be realized in a narrow frequency range. In terms of magnetic components, the transformer does not require a center tap, and there is only one inductor type in the proposed topology, simplifying the design of the magnetic components.

6. Conclusions

In this paper, a UITBLRHC converter is proposed and explored. The proposed converter uses two types of inductors as unified L-R-type inductors. Therefore, because of a low equivalent inductance ratio, a wide voltage gain range over a narrow switching frequency range can be achieved. Based on time-domain analysis, the proposed converter is suitable for wide voltage range application due to its high voltage gain characteristic. In addition, under the unified inductor type, the magnetic flux and heat distribution of the L-R inductors are more balanced. Compared to a full-wave rectifier, the transformer optimizes its winding utilization and eliminates the center tap, simplifying the design. Experimental results verify the effectiveness and the feasibility of the proposed topology.