Influences of Leakage Inductances in Integrated Transformer of Input-Series Flyback Converter

Abstract

In this paper, the influences of leakage inductances are investigated for the integrated transformer of an input-series flyback converter, in which each input-series circuit is based on the single-switch flyback topology. First, the configuration of this converter is introduced, and a novel multiple-inductor coupling model is proposed for its flyback integrated transformer. Second, the operational process of this converter is analyzed by considering the leakage inductances between the primary and secondary windings of its integrated transformer. Third, the influences of these leakage inductances are analyzed; on this basis, the essential design considerations of the flyback integrated transformer are summarized. Finally, an experimental prototype of this input-series converter is built. Based on this, the analysis is verified by the experimental comparisons among three flyback integrated transformers with various winding layouts.

1. Introduction

With the continuous development of power electronics techniques, more and more converters with medium or high input voltages (≥1000 V) are needed in various industry applications, especially in renewable energy and transportation applications [1,2,3]. In these converters, the high voltage issue of each component is the most urgent problem to be solved. The input-series structure is a valid scheme to solve the high voltage problem in the converters with medium or high input voltages, and voltage stress of each component in these converters can be reduced substantially as long as the input voltage sharing of each input-series circuit is achieved [4,5].

Generally, there are two basic input-series structures: one is the output-parallel strategy, as shown in Figure 1a, and the other one is the output-series strategy, as shown in Figure 1b. In addition to the input voltage sharing, output voltage and current sharing should also be ensured in these two kinds input-series converters [5,6,7]. In past years, many voltage or current sharing strategies have been implemented, and a good voltage or current sharing effect could be achieved for each converter [7,8,9,10,11,12]. These two basic input-series structures can be applied in various power applications, provided the suitable circuit topology is adopted in each input-series circuit. However, their output connections will become more complex when multiple outputs are required, so these two basic input-series structures are not suitable to apply in multiple-output applications.

Figure 1. Input-series structures. (a) Output-parallel strategy. (b) Output-series strategy. (c) Output-independent strategy. (d) Transformer-integration strategy.

Aiming at multiple-output applications, the output-independent strategy is applied in the input-series converters, as shown in Figure 1c. The input voltage sharing effect of these converters will be serious when the energies transferring through various output circuits are unbalanced, so the output-independent strategy can only be adopted in applications when the energies transferring through different output circuits are balanced [13,14,15,16].

In addition to the output-parallel, output-series, and output-independent strategies, the transformer-integration strategy can also be applied in the input-series converters, as shown in Figure 1d, where all input-series circuits enjoy a common integrated transformer, so the output circuits can be conveniently made in the secondary sides of this integrated transformer [17,18,19,20]. In these input-series transformer integration (ISTI) converters, natural input voltage sharing can be achieved, provided all input-series circuits are operating synchronously. The transformer-integration strategy can also be applied in various power applications, as long as the suitable circuit topology is adopted in each input-series circuit. Compared to the output-parallel or output-series strategies, the transformer-integration strategy is much more suitable to apply when the multiple-output circuits are required, which is a conventional requirement in low-power applications.

Recently, ISTI flyback converters have been investigated systematically in multiple-output low-power applications [18,19]. These investigations provided the following conclusions:

(1) The input voltage sharing of the ISTI flyback converter can be ensured naturally by the coupling relationships of the primary windings in the integrated transformer. The input voltage sharing effects will be achieved more efficiently as the coupling coefficients of the primary windings increase.

(2) Due to inevitable parameter errors, the absolute synchronous operation of all input-series circuits cannot be realized, so input voltage differences occur. The input voltage differences can be reduced through the special design of key parameters, especially the input filter capacitance in each input-series circuit.

(3) Input voltage sharing effects of the ISTI flyback converter cannot be affected by the components in the secondary sides of the integrated transformer. Influences of the coupling relationships among secondary windings in the integrated transformer mainly aim at multiple-output features, which are similar to those in the other traditional flyback converters with multiple-output circuits.

In each ISTI flyback converter, the integrated transformer is the main device, so its design and manufacture are very important. As shown in Figure 1d, there are N (N ≥ 2) primary windings and n (n ≥ 1) secondary windings in each integrated transformer, so the influences of the coupling relationships between two arbitrary windings should be clarified. Based on this, the layouts of these windings can be determined in the design process. Presently, the influences of the coupling relationships among primary windings have been clarified, as well as the coupling relationships among secondary windings. However, the influences of the coupling relationships between primary and secondary windings have not been clarified.

In each traditional flyback transformer, a leakage inductance is used to represent the coupling relationship between the single primary winding and the secondary winding. The energy of this leakage inductance is released by the absorbing circuit in the flyback converter, so additional power loss is introduced. Generally, this leakage inductance should be minimized to decrease the power losses of the flyback converter.

However, there are N primary windings and n secondary windings in the integrated-transformer of each ISTI flyback converter, so numerous leakage inductances are needed to represent the coupling between these primary and secondary windings, and the influences of these leakage inductances and their differences will be more complex. Therefore, the influences of these numerous leakage inductances should be clarified, especially their influences on the voltage sharing effects of each input-series circuit, which are the unique issues of each ISTI flyback converter.

Generally, the coupling relationship between two arbitrary windings should be represented by at least one leakage inductance, so N × n leakage inductances are needed to represent the coupling relationships between N primary windings and n secondary windings, which cannot be realized in the existing model of the flyback integrated transformer. Therefore, in this paper, a novel multiple-inductor coupling model is proposed for this flyback integrated transformer, through which the coupling relationships between primary and secondary windings are analyzed and the essential design considerations of the flyback integrated transformer are summarized.

The remainder of this paper is organized as follows. In Section 2, the ISTI flyback converter and the multiple-inductor coupling model of its integrated transformer are introduced. In Section 3, the operational process of this converter is analyzed based on the proposed model, where the leakage inductances between primary and secondary windings are considered. In Section 4, the influences of the leakage inductances are analyzed; based on this, the essential design considerations of the flyback integrated transformer are summarized. In Section 5, the analysis is verified by experimental comparisons among three flyback integrated transformers with various winding layouts. In Section 6, conclusions are provided.

2. ISTI Flyback Converter and Its Integrated Transformer

2.1. Configuration of the ISTI Flyback Converter

Figure 2 shows the configuration of the ISTI flyback converter, where each input-series circuit is based on the single-switch flyback topology, V_i and I_i are the input voltage and input current, V_i-1, …, V_i-N are the input voltages of the N input-series circuits, and V_o-1, …, V_o-n and I_o-1, …, I_o-n are the output voltages and output current of the n output-independent circuits.

Figure 2. Configuration of the ISTI flyback converter.

In the input-series circuits, there are identical components and parameters, including the input filter capacitors (C_i-1 = … = C_i-N), the switches (S₁, …, S_N), the turn numbers (N_p-1 = … = N_p-N), and the self-inductances (L_p-1 = … = L_p-N) of the primary windings (W_p-1, …, W_p-N) in the integrated transformer (T) and the absorbing circuits (R₁ = … = R_N, C₁ = … = C_N, and D₁, …, D_N).

In the output-independent circuits, the turn numbers (N_s-1, …, N_s-n) of secondary windings (W_s-1, …, W_s-n) in T, as well as the output rectifier diodes (D_o-1, …, D_o-n) and output filter capacitors (C_o-1, …, C_o-n), are designed according to the special output requirements.

2.2. Multiple-Inductor Coupling Model of Flyback Integrated Transformer

In the integrated transformer (T), there are N primary windings and n secondary windings, so the influences of the coupling relationships among these windings should be clarified. On this basis, the layouts of these windings can be determined in the design process. In previous investigations, the influences of the coupling relationships among primary windings have been clarified, as well as the coupling relationships among secondary windings. However, the influences of the coupling relationships between primary and secondary windings have not been clarified.

Generally, the coupling between two arbitrary windings should be represented by at least one leakage inductance, so N × n leakage inductances are needed to represent the coupling between N primary windings and n secondary windings, which cannot be realized in the existing model of the flyback integrated transformer.

To overcome the shortcomings of the existing model, a novel multiple-inductor coupling model is proposed for this flyback integrated transformer, as shown in Figure 3, through which the influences of the coupling relationships between primary and secondary windings are expected to be clarified. This novel model is introduced as follows.

Figure 3. Multiple-inductor coupling model of the flyback integrated transformer.

(1) The input voltage sharing effects of the ISTI flyback converter cannot be affected by the coupling relationships among the secondary windings of the integrated transformer, and the influences of the coupling relationships among secondary windings are mainly aimed at the multiple-output features, which are similar to those in the other traditional flyback converters with multiple-output circuits. Therefore, to simplify the analysis, an equivalent single secondary winding (W_s-1) is adopted in this model to represent the n secondary windings.

(2) In this model, the equivalent single secondary winding (W_s-1) is divided into N identical parts (W_s-11, …, W_s-1N), and they are used as the secondary windings of the ideal transformers (T_i-1, …, T_i-N). T_i-1, …, T_i-N are connected in parallel in the secondary sides, where their turn ratios are identical (N_p-1/N_s-1). D_o-11, …, D_o-1N are used as the output rectifier diodes.

(3) In this model, a coupled inductor (L_p-1 = … = L_p-N) is adopted to represent the coupling relationships among the N primary windings.

(4) In this model, the leakage inductances (L_lk-1, …, L_lk-N) are adopted to represent the coupling relationships between the N primary windings (W_p-1, …, W_p-N) and the equivalent single secondary winding (W_s-1), respectively.

3. Operational Process of ISTI Flyback Converter Considering the Leakage Inductances

Based on the model provided in Figure 3, the operational process of the ISTI flyback converter is analyzed as follows. To simplify the analysis, the following conditions are assumed: (1) this converter operates in discontinuous current mode (DCM); (2) this converter is composed of two input-series circuits (N = 2) and a single output circuit (n = 1); (3) in addition to the integrated transformer, all devices in this converter are ideal; (4) the asynchronous turning of S₁ and S₂ is not considered; (5) the input voltage differences between two input-series circuits are not considered (V_i-1 = V_i-2 = V_i/2); and (6) C₁, C₂, and C_o-1 are large enough, so the fluctuations of their voltages (V_C1, V_C2, and V_o-1) are ignored. During each switching period, there are the following four stages, where the main waveforms in each period are shown in Figure 4 and the equivalent circuit in each stage is shown in Figure 5.

Figure 4. Main voltage and current waveforms in each period.

Figure 5. Equivalent circuit in each stage. (a) Stage 1. (b) Stage 2. (c) Stage 3. (d) Stage 4.

Stage 1 (t₀~t₁): At t₀, S₁ and S₂ are turned on. After t₀, the coupled inductor (L_p-1 and L_p-2) is charged by the input voltages, so its current increases. In the absorbing circuits, D₁ and D₂ are turned off, while C₁ and C₂ are discharged through R₁ and R₂, respectively. In the output circuits, D_o-11 and D_o-12 are turned off, and I_o-1 is only provided by C_o-1. In this stage, the voltages in the primary or secondary sides of T_i-1 and T_i-2 are V_p-1 = V_i-1 = V_i/2, V_p-2 = V_i-2 = V_i/2, and V_s-11 = V_s-12 = N_s-1V_i/2N_p-1. At t₁, the current of these inductors increases to the peak value during the whole period, as shown in Equation (1):

$$i_{\mathrm{p}\text{-}1}\left(t_1\right)=i_{\mathrm{p}\text{-}2}\left(t_1\right)=i_{\mathrm{lk}\text{-}1}\left(t_1\right)=i_{\mathrm{lk}\text{-}2}\left(t_1\right)={\displaystyle {\int }_{t_0}^{t_1}\frac{V_{\mathrm{i}}}{L_{\mathrm{p}\text{-}\mathrm{es}}}}\mathrm{d}t$$

(1)

where i_p-1 (or i_p-2) and i_lk-1 (or i_lk-2) are the currents of L_p-1 (or L_p-2) and L_lk-1 (or L_lk-2), respectively; L_p-es = 2(1 + k₁₂)L_p-1 is the equivalent series inductance of L_p-1 and L_p-2; k₁₂ is the coupling coefficient between L_p-1 and L_p-2; and L_lk-1 (or L_lk-2) is much smaller than L_p-es, which are not considered here.

Stage 2 (t₁~t₂): At t₁, S₁ and S₂ are turned off, and their voltages (V_S1 and V_S2) increase immediately to V_i-1 + V_C1 and V_i-2 + V_C2, respectively. The durations of these processes are very small, which are not considered here.

After t₁, D_o-11 and D_o-12 are turned on, and the energies stored in L_p-1 and L_p-2 are transferred to the loads through T_i-1 and T_i-2, respectively. In the absorbing circuits, D₁ and D₂ are turned on, and the energies stored in L_lk-1 and L_lk-2 are transferred into C₁ and C₂, respectively. In this stage, V_s-11 = V_s-12= −V_o-1 and V_p-1 = V_p-2 = −N_p-1V_o-1/N_s-1; moreover, the expressions of i_p-1 (or i_p-2) and i_lk-1, i_lk-2 can be obtained in Equations (2) and (3), respectively.

$$i_{\mathrm{p}\text{-}1}\left(t-t_1\right)=i_{\mathrm{p}\text{-}2}\left(t-t_1\right)=i_{\mathrm{p}\text{-}1}\left(t_1\right)-{\displaystyle {\int }_{t_1}^t\frac{N_{\mathrm{p}\text{-}1}{V}_{\mathrm{o}\text{-}1}}{2N_{\mathrm{s}\text{-}1}{L}_{\mathrm{p}\text{-}\mathrm{ep}}}}\mathrm{d}t$$

(2)

$$\left\{\begin{array}{l}{i}_{\mathrm{lk}\text{-}1}\left(t-t_1\right)=i_{\mathrm{lk}\text{-}1}\left(t_1\right)-{\displaystyle {\int }_{t_1}^t\frac{N_{\mathrm{s}\text{-}1}{V}_{\mathrm{C}1}-N_{\mathrm{p}\text{-}1}{V}_{\mathrm{o}\text{-}1}}{N_{\mathrm{s}\text{-}1}{L}_{\mathrm{lk}\text{-}1}}}\mathrm{d}t\\ i_{\mathrm{lk}\text{-}2}\left(t-t_1\right)=i_{\mathrm{lk}\text{-}2}\left(t_1\right)-{\displaystyle {\int }_{t_1}^t\frac{N_{\mathrm{s}\text{-}1}{V}_{\mathrm{C}2}-N_{\mathrm{p}\text{-}1}{V}_{\mathrm{o}\text{-}1}}{N_{\mathrm{s}\text{-}1}{L}_{\mathrm{lk}\text{-}2}}}\mathrm{d}t\end{array}\right.$$

(3)

where L_p-ep = (1 + k₁₂)L_p-1/2 is the equivalent parallel inductance of L_p-1 and L_p-2.

At the end of this stage, i_lk-1 and i_lk-2 decrease to zero; D₁ and D₂ are then turned off accordingly.

Stage 3 (t₂~t₃): At t₂, i_lk-1 = i_lk-2 = 0. After t₂, C₁ (or C₂) is still discharged through R₁ (or R₂), and the decrease in i_p-1 (or i_p-2) is continuous. In this stage, V_p-1, V_p-2, V_s-11, and V_s-12 are fixed; however, V_S1 and V_S2 are changed into V_i-1 + V_p-1 and V_i-2 + V_p-2, respectively.

Stage 4 (t₃~t₄): At t₃, i_p-1 = i_p-2 = 0. After t₃, D_o-11 and D_o-12 are turned off, V_p-1 = V_p-2 = 0, V_s-11 = V_s-12 = 0, V_S1 = V_i-1 = V_i/2, V_S2 = V_i-2 = V_i/2, and I_o-1 is only provided by C_o-1.

At t₄, S₁ and S₂ are turned on again. After t₄, this converter will operate in the next period.

4. Design Considerations of Integrated Transformer Based on the Leakage Inductances

According to the operational process, the influences of leakage inductances (L_lk-1 and L_lk-2) between the primary windings (W_p-1 and W_p-2) and the equivalent single secondary winding (W_s-1) are analyzed in this section. Based on this, the essential design considerations of this flyback integrated transformer are summarized.

4.1. Influences of the Leakage Inductances

In stage 1, S₁ and S₂ are turned on, and the coupling relationships of two primary windings (W_p-1 and W_p-2) are represented by the coupled inductor (L_p-1 and L_p-2), by which the input voltage sharing of each input-series circuit is achieved. The leakage inductances (L_lk-1 and L_lk-2) are adopted to represent the coupling relationships between the primary windings (W_p-1 and W_p-2) and the equivalent single secondary winding (W_s-1), which are much smaller than the equivalent series inductance (L_p-es) of this coupled inductor, so the input voltage sharing process in this stage has almost no relationship with L_lk-1 (or L_lk-2).

In stage 2, the energies of L_lk-1 and L_lk-2 are transferred into C₁ and C₂, respectively, so the energies stored in C₁ and C₂ can be affected. During the whole switching period, the maximum voltages of S₁ and S₂ are equal to V_i-1 + V_C1 and V_i-2 + V_C2, respectively. Therefore, the voltage sharing effect of S₁ and S₂ can also be affected, which cannot be ensured even if a good input voltage sharing effect has been achieved (V_i-1 = V_i-2 = V_i/2).

In stage 3 and stage 4, the current of L_lk-1 (or L_lk-2) is zero, so there is almost no influence caused by L_lk-1 (or L_lk-2) in these stages.

Therefore, the analysis concerning the influence of the leakage inductances (L_lk-1 and L_lk-2) is implemented in stage 2 as follows, where the simplified equivalent circuit of the ISTI flyback converter in stage 2 is shown in Figure 6.

Figure 6. Simplified equivalent circuit of the ISTI flyback converter in stage 2 (V_s-11 = V_s-12 = −V_o-1 and V_p-1 = V_p-2 = −N_p-1V_o-1/N_s-1).

From operational process of the ISTI flyback converter, it can be obtained that, during the whole switching period, C₁ and C₂ are discharged through R₁ and R₂, respectively. Accordingly, the decrease in the energies of C₁ and C₂ during each switching period can be estimated using Equation (4).

$$\left\{\begin{array}{l}{E}_{\mathrm{C}1\text{-}}={\displaystyle \frac{V_{\mathrm{C}1}^2}{R_{1}f}}\\ E_{\mathrm{C}2\text{-}}={\displaystyle \frac{V_{\mathrm{C}2}^2}{R_{2}f}}\end{array}\right.$$

(4)

where f is the switching frequency.

In stage 2, the current of L_lk-1 and L_lk-2 will decrease to zero, and their current decreasing durations can be obtained from Equation (3), as shown in Equation (5).

$$\left\{\begin{array}{l}{T}_{\mathrm{lk}\text{-}1}={\displaystyle \frac{N_{\mathrm{s}\text{-}1}{L}_{\mathrm{lk}\text{-}1}{i}_{\mathrm{lk}\text{-}1}\left(t_1\right)}{N_{\mathrm{s}\text{-}1}{V}_{\mathrm{C}1}-N_{\mathrm{p}\text{-}1}{V}_{\mathrm{o}\text{-}1}}}\\ T_{\mathrm{lk}\text{-}2}={\displaystyle \frac{N_{\mathrm{s}\text{-}1}{L}_{\mathrm{lk}\text{-}2}{i}_{\mathrm{lk}\text{-}2}\left(t_1\right)}{N_{\mathrm{s}\text{-}1}{V}_{\mathrm{C}2}-N_{\mathrm{p}\text{-}1}{V}_{\mathrm{o}\text{-}1}}}\end{array}\right.$$

(5)

From Equations (3) and (5), the increase in the energies of C₁ and C₂ in stage 2 can be estimated using Equation (6), where T_lk-1 (or T_lk-2) is much smaller than T, so the energies released by R₁ and R₂ are not considered in the estimations.

$$\left\{\begin{array}{l}{E}_{\mathrm{C}1+}={\displaystyle {\int }_{t_1}^{t_1+T_{\mathrm{lk}\text{-}1}}{V}_{\mathrm{C}1}{i}_{\mathrm{lk}\text{-}1}\left(t-t_1\right)}\mathrm{d}t={\displaystyle \frac{N_{\mathrm{s}\text{-}1}{L}_{\mathrm{lk}\text{-}1}{V}_{\mathrm{C}1}{\left[i_{\mathrm{lk}\text{-}1}\left(t_1\right)\right]}^2}{2\left(N_{\mathrm{s}\text{-}1}{V}_{\mathrm{C}1}-N_{\mathrm{p}\text{-}1}{V}_{\mathrm{o}\text{-}1}\right)}}\\ E_{\mathrm{C}2+}={\displaystyle {\int }_{t_1}^{t_1+T_{\mathrm{lk}\text{-}2}}{V}_{\mathrm{C}2}{i}_{\mathrm{lk}\text{-}2}\left(t-t_1\right)}\mathrm{d}t={\displaystyle \frac{N_{\mathrm{s}\text{-}1}{L}_{\mathrm{lk}\text{-}1}{V}_{\mathrm{C}1}{\left[i_{\mathrm{lk}\text{-}1}\left(t_1\right)\right]}^2}{2\left(N_{\mathrm{s}\text{-}1}{V}_{\mathrm{C}1}-N_{\mathrm{p}\text{-}1}{V}_{\mathrm{o}\text{-}1}\right)}}\end{array}\right.$$

(6)

During the whole switching period, it is required that E_C1+ = E_C1- and E_C2+ = E_C2- Therefore, the relationships in Equation (7) can be obtained from Equations (4) and (6).

$$\left\{\begin{array}{l}{V}_{\mathrm{C}1}\left(V_{\mathrm{C}1}-{\displaystyle \frac{N_{\mathrm{p}\text{-}1}}{N_{\mathrm{s}\text{-}1}}}{V}_{\mathrm{o}\text{-}1}\right)={\displaystyle \frac{1}{2}}{R}_1{L}_{\mathrm{lk}\text{-}1}f{\left[i_{\mathrm{lk}\text{-}1}\left(t_1\right)\right]}^2\\ V_{\mathrm{C}2}\left(V_{\mathrm{C}2}-{\displaystyle \frac{N_{\mathrm{p}\text{-}1}}{N_{\mathrm{s}\text{-}1}}}{V}_{\mathrm{o}\text{-}1}\right)={\displaystyle \frac{1}{2}}{R}_2{L}_{\mathrm{lk}\text{-}2}f{\left[i_{\mathrm{lk}\text{-}2}\left(t_1\right)\right]}^2\end{array}\right.$$

(7)

In stage 2, the energies stored in L_lk-1 and L_lk-2 are absorbed by C₁ and C₂, so V_C1 > N_p-1V_o-1/N_s-1 and V_C2 > N_p-1V_o-1/N_s-1 should be achieved. Moreover, it is considered that i_lk-1(t₁) = i_lk-2(t₁), as shown in Equation (1). Therefore, it can be obtained from Equation (7) that, when the parameters R₁ = R₂ and C₁ = C₂ are fixed, V_C1 and V_C2 are determined by L_lk-1 and L_lk-2, which will increase as L_lk-1 and L_lk-2 increase, respectively.

In the ISTI flyback converter, the energies of L_lk-1 and L_lk-2 are released through the absorbing circuits, and the power losses caused by the leakage inductances (L_lk-1 and L_lk-2) can be estimated using Equation (8).

$$\left\{\begin{array}{l}{P}_{\mathrm{os}\text{-}\mathrm{lk}1}=E_{\mathrm{C}1+}f=E_{\mathrm{C}1\text{-}}f={\displaystyle \frac{V_{\mathrm{C}1}^2}{R_1}}\\ P_{\mathrm{os}\text{-}\mathrm{lk}2}=E_{\mathrm{C}2+}f=E_{\mathrm{C}2\text{-}}f={\displaystyle \frac{V_{\mathrm{C}2}^2}{R_2}}\end{array}\right.$$

(8)

It can be seen from Equation (8) that, when the parameters R₁ = R₂ and C₁ = C₂ are fixed, P_os-lk1 and P_os-lk1 will increase as V_C1 and V_C2 increase, respectively. Therefore, it can be concluded from Equations (7) and (8) that the power losses caused by the leakage inductances L_lk-1 and L_lk-2 are also determined by L_lk-1 and L_lk-2, which will also increase as L_lk-1 and L_lk-2 increase, respectively.

4.2. Essential Design Considerations of Flyback Integrated Transformer

The influences of leakage inductances (L_lk-1 and L_lk-2) can be summarized from two aspects: (1) the voltage sharing effect of the switches (S₁ and S₂) in various input-series circuits and (2) the power losses caused by the leakage inductances (L_lk-1 and L_lk-2) in two input-series circuits. They are summarized as follows.

(1) The input voltage sharing effect of each input-series circuit has almost no relationships with L_lk-1 and L_lk-2; however, the voltage sharing effect of S₁ and S₂ can be affected by L_lk-1 and L_lk-2. The maximum voltages of S₁ and S₂ are equal to V_i-1 + V_C1 and V_i-2 + V_C2, respectively. When a good input voltage sharing effect is achieved (V_i-1 = V_i-2 = V_i/2), the voltage sharing effect of C₁ and C₂ should be specifically considered. As shown in Equation (7), V_C1 and V_C2 are determined by L_lk-1 and L_lk-2, respectively, and V_C1 = V_C2 can be achieved when L_lk-1 = L_lk-2.

(2) The energies stored in L_lk-1 and L_lk-2 are transferred into C₁ and C₂ in stage 2, and these energies are released through R₁ and R₂, respectively, so the power losses caused by L_lk-1 and L_lk-2 should be considered, which are similar to the other traditional flyback converters. As shown in Equations (7) and (8), the power loss caused by L_lk-1 (or L_lk-2) will increase as V_C1 (or V_C2) increases, and V_C1 (or V_C2) will increase as L_lk-1 (or L_lk-2) increases.

From the influences of leakage inductances (L_lk-1 and L_lk-2), essential design considerations of the flyback integrated transformer can be summarized: (1) the difference between L_lk-1 and L_lk-2 should be suppressed to ensure a good voltage sharing effect of S₁ and S₂, where L_lk-1 = L_lk-2 is especially expected to be achieved; and (2) L_lk-1 and L_lk-2 should be minimized to reduce the power losses.

5. Experimental Verifications

5.1. Experimental Prototype

To verify the aforementioned analysis, a 1000 V/60 W experimental prototype of the ISTI flyback converter was built, as shown in Figure 7. This experimental prototype is composed of two input-series circuits (N = 2) and two output-independent circuits (n = 2), and each input-series circuit is based on the single-switch flyback topology. The main components and parameters of this experimental prototype are shown in Table 1.

Figure 7. Experimental prototype of the ISTI flyback converter.

Table 1. Components and parameters of the prototype.

Components or Parameters	Features or Values
Vi	1000 V (N = 2)
Vo-1, Vo-2	24 V (Vo-1 = Vo-2, n = 2)
Io-1, Io-2	1.5 A, 1 A
Ci-1, Ci-2	1200 V/0.1 μF (Ci-1 = Ci-2)
S1, S2	2SK1271 (f = 50 kHz)
Do-1, Do-2	MUR1560
Co-1, Co-2	50 V/1000 μF (Co-1 = Co-2)
R1, R2	15 kΩ (R1 = R2)
C1, C2	630 V/0.1 μF (C1 = C2)
D1, D2	BYV26G

Based on this prototype, three flyback integrated transformers (T₁, T₂, and T₃) with various typical layout schemes for the primary windings (W_p-1 and W_p-2) are designed for the experimental comparisons. The winding layouts of T₁, T₂, and T₃ can be obtained from their cross-sections, as shown in Figure 8, in which only half of the cross-section is given in each illustration, and the number marked on each turn represents its manufacturing sequence.

Figure 8. Cross-sections of the flyback integrated transformer. (a) The illustration of T₁. (b) The illustration of T₂. (c) The illustration of T₃.

In each flyback integrated transformer, the secondary windings (W_s-1 and W_s-2) are connected in parallel, and they are manufactured intensively to improve their coupling relationship. The layouts of W_s-1 and W_s-2 are identical in T₁, T₂, and T₃, which are not given in Figure 8. Moreover, the other common features of these integrated transformers are shown in Table 2, and the layout schemes of their primary windings (W_p-1 and W_p-2) are explained as follows.

Table 2. Common features of the integrated transformers.

Types or Parameters	Features or Values
Magnetic core	EI 40 (Ferroxcube)
Np-1, Np-2	72 (Np-1 = Np-2)
Ns-1, Ns-2	14 (Ns-1 = Ns-2)
Lp-1, Lp-2	1.36 mH (Lp-1 = Lp-2)
Layer number (Wp-1, Wp-2)	4

In T₁, W_p-1 and W_p-2 are connected in parallel. The four layers of W_p-1 and W_p-2 are divided into two parts, where W_s-1 and W_s-2 are rounded in the middle of these two parts.

In T₂, the layer-by-layer winding layout is selected for W_p-1 and W_p-2. The two layers of W_p-1 (or W_p-2) are divided into two parts, where W_s-1 and W_s-2 are rounded in the middle of these two parts. The two layers of W_p-1 are rounded near W_s-1 and W_s-2, and the two layers of W_p-2 are rounded in the innermost and outermost layers, respectively.

In T₃, W_p-1 and W_p-2 are connected in parallel, and they are made in the inner four layers. W_s-1 and W_s-2 are made in the outer layers.

The main parameters of these integrated transformers are measured by the LCR meter (Tonghui/TH2826), including the coupling coefficient (k₁₂) and the leakage inductances (L_lk-1 and L_lk-2). The measuring results are shown in Table 3. It can be obtained that (1) a high coupling coefficient has been achieved in each integrated transformer; (2) in T₁ (or T₃), there is almost no difference between L_lk-1 and L_lk-2, but there is an obvious difference between L_lk-1 and L_lk-2 in T₂; and (3) in T₃, L_lk-1 (or L_lk-2) is much larger than that in T₁ (or T₂).

Table 3. Measuring results of the integrated transformer.

T	T1	T2	T3
k12	0.998999	0.997627	0.999130
Llk-1	13 μH	11 μH	36 μH
Llk-2	13 μH	18 μH	35 μH

According to the aforementioned analysis, the following experimental results can be expected: (1) a good input voltage sharing effect will be achieved for this experimental prototype when any one of the integrated transformers is adopted; (2) when T₁ (or T₃) is adopted, there is almost no voltage difference between C₁ and C₂, so a good voltage sharing effect will be achieved between S₁ and S₂; (3) when T₁ (or T₂) is adopted, the voltages of C₁ and C₂ will be lower than those when T₃ is adopted; and (4) when T₁ (or T₂) is adopted, the power losses caused by the leakage inductances will be much lower, so the efficiency of the experimental prototype will be higher than when T₃ is adopted.

5.2. Experimental Results

The three flyback integrated transformers (T₁, T₂, and T₃) are used in this experimental prototype one by one, and the main experimental results are shown in Figure 9, Figure 10 and Figure 11 and Table 4.

Figure 9. Main waveforms of the prototype when T₁ is used. (a) Voltage and current of S₁. (b) Voltage and current of S₂. (c) Input voltages (V_i-1 and V_i-2). (d) Voltages of C₁ and C₂.

Figure 10. Main waveforms of the prototype when T₂ is used. (a) Voltage and current of S₁. (b) Voltage and current of S₂. (c) Input voltages (V_i-1 and V_i-2). (d) Voltages of C₁ and C₂.

Figure 11. Main waveforms of the prototype when T₃ is used. (a) Voltage and current of S₁. (b) Voltage and current of S₂. (c) Input voltages (V_i-1 and V_i-2). (d) Voltages of C₁ and C₂.

Table 4. Main measuring results.

T	T1	T2	T3
VC1	155 V	152 V	175 V
VC2	155 V	161 V	175 V
η	87.12%	87.01%	83.78%

Figure 9 shows the main experimental waveforms when T₁ is used, including the driving (v_gs1), voltage (v_ds1), and current (i_S1) of S₁; the driving (v_gs2), voltage (v_ds2), and current (i_S2) of S₂; the input voltages (V_i-1 and V_i-2) of two input-series circuits; and the voltages (V_C1 and V_C2) of two capacitors in the absorbing circuits. Figure 10 and Figure 11 show the main experimental waveforms when T₂ and T₃ are used. It can be seen from these waveforms that a good input voltage sharing effect has been achieved for this experimental prototype when any one of the integrated transformers is adopted.

Table 4 shows the main measuring results when T₁, T₂, and T₃ are used one by one, including the voltages (V_C1 and V_C2) of two capacitors in the absorbing circuits and the efficiency (η) of this experimental prototype.

From Figure 9d, Figure 10d and Figure 11d and Table 4, the following can be obtained: (1) when T₁ is used, there is almost no voltage difference between the two capacitors (C₁ and C₂) in the absorbing circuits; (2) when T₂ is used, an obvious voltage difference (V_C2 – V_C1 = 9 V) appears between C₁ and C₂; and (3) when T₃ is used, there is almost no voltage difference between C₁ and C₂, but the voltage of C₁ (or C₂) is much higher than that when T₁ (or T₂) is adopted. Moreover, it can also be obtained from Table 4 that, when T₁ (or T₂) is used, the efficiency of this experimental prototype is higher than when T₃ is adopted.

Therefore, it can be seen that the analysis concerning the influences of leakage inductances has been verified through the above experimental comparisons.

6. Conclusions

In this paper, the influences of leakage inductances between primary and secondary windings are investigated for the integrated transformer in an input-series flyback converter, in which each input-series circuit is based on the single-switch flyback topology. To represent the coupling relationship between primary and secondary windings, a novel multiple-inductor coupling model is proposed for the flyback integrated transformer. The operational process of this converter and the influences of the leakage inductances are analyzed based on this model, and the essential design considerations of the flyback integrated transformer are summarized as follows: (1) the difference in various leakage inductances should be suppressed as much as possible to achieve a good voltage sharing effect for the switches in different input-series circuits; and (2) the leakage inductances should also be reduced to decrease the power losses of this converter, which are similar to the other traditional flyback converters. The results of the investigation are verified by the experimental comparisons among three flyback integrated transformers with various winding layouts.