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

1. Introduction

With the continuous development of power electronics technique, more and more converters with medium or high input voltages (≥1000V) are needed in various industry applications, especially in the 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 an 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, the output voltage and current sharing should also be ensured in these two kinds input-series converters respectively [5,6,7]. In the past years, many voltage or current sharing strategies have been implemented, and a good voltage or current sharing effect can 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 the multiple-output is required, so these two basic input-series structures are not suitable to be applied in the multiple-output applications.

Aiming at the 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 the 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 made in secondary sides of this integrated-transformer conveniently [17,18,19,20,21,22]. In these input-series transformer-integration (ISTI) converters, the 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 strategy, the transformer-integration strategy is much more suitable to be applied when the multiple output circuits are required, which is a conventional requirement in the low power applications.

Recently, the ISTI flyback converters have been investigated systematically in the multiple-output low power applications [18,20]. The investigations show that: input voltage sharing of the ISTI flyback converters can be achieved through the coupling relationships of primary windings in the integrated-transformer, and the input voltage sharing effect cannot be affected by the components in secondary sides of the integrated-transformer. In these ISTI flyback converters, there are multiple primary and secondary windings in each integrated-transformer, influences of the coupling relationships between arbitrary two windings should be clarified, based on which, layouts of these windings can be determined in the design process. Presently, influences of the coupling relationships among primary windings have been clarified, as well as the coupling relationships among secondary windings. However, influences of the coupling relationships between primary and secondary windings have not been clarified.

In each flyback integrated-transformer, there are multiple primary and secondary windings, so numerous leakage inductances are needed to represent the coupling between each primary winding and each secondary winding, which cannot be realized in the existing model of the flyback integrated-transformer. Therefore, a novel multiple inductors coupling model is proposed for this flyback integrated-transformer in this paper, through which the coupling relationships between primary and secondary windings are analyzed, and 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 multiple inductors coupling model of its integrated-transformer are introduced. In Section 3, operational process of this converter is analyzed, where the leakage inductances between primary and secondary windings are considered. In Section 4, the leakage inductances influences are analyzed, based on which, essential design considerations of the flyback integrated-transformer are summarized. In Section 5, the analysis is verified by the experimental comparisons among three flyback integrated-transformers with various windings layouts. In Section 6, the conclusion is given.

2. ISTI Flyback Converter and Its Integrated-Transformer

2.1. Configuration of the ISTI Flyback Converter

Figure 2 shows 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 input voltages of the N (N≥2) input-series circuits, V_o-1, …, V_o-n and I_o-1, …, I_o-n are output voltages and output current of the n (n≥1) output-independent circuits.

In the input-series circuits, there are the identical components and parameters, including the input filter capacitors (C_i-1=…=C_i-N), the switches (S₁, …, S_N), the turns number (N_p-1=…=N_p-N) and the self-inductances (L_p-1=…=L_p-N) of 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 turns number (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 Inductors Coupling Model of Flyback Integrated-Transformer

In [18,20], the input voltage sharing effects of various flyback ISTI converters are investigated. These investigations can be concluded as follows.

(1) The N primary windings of T are considered as a coupled-inductor, by which input voltage sharing of the N input-series circuits is ensured naturally, provided all switches are turning synchronously. The input voltage sharing will be achieved more efficiently as the coupling coefficients of this coupled-inductor increase.

(2) Due to the inevitable parameters errors, the absolute synchronous turning of S₁, …, S_N cannot be realized, so the input voltage differences occur among various input-series circuits, which will increase as the parameters errors increase. The input voltage differences can be reduced through special design of the key parameters, especially the input filter capacitances (C_i-1, …, C_i-N).

(3) Input voltage sharing effects of the N input-series circuits cannot be affected by the components in secondary sides of T. Influences of the coupling relationships among secondary windings of T are similar to those in the other traditional flyback converters with multiple output circuits, which are not the specific problems in each ISTI flyback converter.

From the above conclusions, it can be obtained that: the flyback integrated-transformer is a main device, so its design and manufacturing are very important.

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

Generally, the coupling between arbitrary two 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 inductors coupling model is proposed for this flyback integrated-transformer, as shown in Figure 3, through which influences of the coupling relationships between primary and secondary windings are expected to be clarified. This novel model is introduced as follows.

(1) Influences of the coupling relationships among secondary windings are not considered. To simplify the analysis, the equivalent single secondary winding (W_s-1) is adopted to represent the n secondary windings.

(2) The single secondary winding (W_s-1) is divided into N identical parts (W_s-11, …, W_s-1N), and they are made 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 turns ratio are identical (N_p-1/N_s-1), and D_o-11, …, D_o-1N stand for the output rectifier diodes.

(3) A coupled-inductor (L_p-1=…=L_p-N) is adopted to represent the coupling relationships among the N primary windings.

(4) 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 in Figure 3, 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 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 shorn in Figure 5.

Stage 1 (t₀~t₁): At t₀, S₁ and S₂ are turned on. After t₀, the coupled-inductor (L_p-1, L_p-2) is charged by the input voltages, so its current increases. In the absorbing circuits, D₁ and D₂ are turning off, C₁ and C₂ are discharged through R₁ and R₂ respectively. In the output circuits, D_o-11 and D_o-12 are turning off, and I_o-1 is only provided by C_o-1. In this stage, the voltages in primary or secondary side 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).

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

(1)

where i_p-1 (or i_p-2) and i_lk-1 (or i_lk-2) are the current 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. Duration of these processes are very small, which are not considered here.

After t₁, D_o-11 and D_o-12 are turning 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 turning 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.

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

(2)

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

(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, and then, D₁ and D₂ are 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 decreasing of i_p-1 (or i_p-2) is continuous. In this stage, V_p-1, V_p-2 and V_s-11, 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 turning 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, L_lk-2) between the primary windings (W_p-1, W_p-2) and the equivalent single secondary winding (W_s-1) are analyzed in this section, based on which, the essential design considerations of this flyback integrated-transformer are summarized.

4.1. Analysis of the Leakage Inductances Influences

For the ISTI flyback converter, the input voltage sharing of each input-series circuit is achieved by the coupling of primary windings in the integrated-transformer, and this input voltage sharing process occurs when all switches are turning on. 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 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 1, S₁ and S₂ are turning on, and the coupling relationships of two primary windings (W_p-1, W_p-2) are represented by the coupled-inductor (L_p-1, L_p-2). The leakage inductance L_lk-1 (or L_lk-2) is much smaller than the equivalent series inductance (L_p-es) of this coupled-inductor, so the input voltage sharing process in this stage have almost no relationship with L_lk-1 (or L_lk-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 of leakage inductances (L_lk-1, L_lk-2) influences 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.

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 energies decreasing of C₁ and C₂ during each switching period can be estimated in Equation (4).

$$\left\{\begin{array}{l}{E}_{\mathrm{C}1-}={\displaystyle \frac{V_{\mathrm{C}1}^{2}T}{R_1}}\\ E_{\mathrm{C}2-}={\displaystyle \frac{V_{\mathrm{C}2}^{2}T}{R_2}}\end{array}\right.$$

(4)

where T is the switching period.

It can be obtained from Equation (4) that: when the parameters (R₁=R₂ and C₁=C₂) are fixed, the power losses caused by the absorbing circuit in each input-series circuit is determined by V_C1 (or V_C2), which will increase as V_C1 (or V_C2) increases.

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).

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

(5)

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

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

(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).

$$\left\{\begin{array}{l}{V}_{\mathrm{C}1}\left(V_{\mathrm{C}1}-{\displaystyle \frac{N_{\mathrm{p}-1}}{N_{\mathrm{s}-1}}}{V}_{\mathrm{o}-1}\right)={\displaystyle \frac{R_1{L}_{\mathrm{lk}-1}{\left[i_{\mathrm{lk}-1}\left(t_1\right)\right]}^2}{2T}}\\ V_{\mathrm{C}2}\left(V_{\mathrm{C}2}-{\displaystyle \frac{N_{\mathrm{p}-1}}{N_{\mathrm{s}-1}}}{V}_{\mathrm{o}-1}\right)={\displaystyle \frac{R_2{L}_{\mathrm{lk}-2}{\left[i_{\mathrm{lk}-2}\left(t_1\right)\right]}^2}{2T}}\end{array}\right.$$

(7)

In stage 2, the energies stored in L_lk-1 and L_lk-2 are absorbed by C₁ and C₂, so it should be achieved that: V_C1>N_p-1V_o-1/N_s-1 and V_C2>N_p-1V_o-1/N_s-1. 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.

4.2. Essential Design Considerations of Flyback Integrated-Transformer

From the leakage inductances influences, essential design considerations of the flyback integrated-transformer can be summarized from two aspects: 1) voltage sharing effects of the switches (S₁, S₂); and 2) power losses caused by the absorbing circuit in each input-series circuit. They are summarized as follows.

(1) 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) after optimal design of the coupling between primary windings, the voltage sharing effect of C₁ and C₂ should be considered specially. As shown in Equation (7), V_C1 and V_C2 are determined by the leakage inductances (L_lk-1 and L_lk-2), and V_C1=V_C2 can be achieved when L_lk-1=L_lk-2. Therefore, to achieve a good voltage sharing effect of S₁ and S₂, the difference between L_lk-1 and L_lk-2 should be suppressed, and L_lk-1=L_lk-2 is expected to be achieved especially.

(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 these energies should be reduced, which is similar to the other flyback converter. As shown in Equations (4) and (7), the power losses caused by the absorbing circuits 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. Therefore, the leakage inductances (L_lk-1 and L_lk-2) should be reduced to decrease the power losses caused by the absorbing circuits.

5. Experimental Verifications

5.1. Experimental Prototype

To verify the aforementioned analysis, a 1000 V experimental prototype of the ISTI flyback converter is built, as shown in Figure 7. This experimental prototype is composed of two input-series circuits (N=2) and two output-independent circuit (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.

Based on this prototype, three flyback integrated-transformers (T₁, T₂ and T₃) with various typical layout schemes of the primary windings (W_p-1, W_p-2) are designed for the experimental comparisons. Windings 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.

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

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 windings 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, 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, however, 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).

According to the aforementioned analysis, the experimental results can be expected that: 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 absorbing circuits will be much lower, so the efficiency of the experimental prototype will be higher than that 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, Figure 11 and Table 4.

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, V_i-2) of two input-series circuits, and the voltages (V_C1, 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, V_C2) of two capacitors in the absorbing circuits, and the efficiency (η) of this experimental prototype.

It can be obtained from Figure 9d, Figure 10d, Figure 11d and Table 4 that: 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, however, 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 that when T₃ is adopted.

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

6. Conclusion

In this paper, influences of the 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 inductors coupling model is proposed for the flyback integrated-transformer, operational process of this converter and the leakage inductances influences are analyzed based on this model, and the essential design considerations of flyback integrated-transformer are summarized: 1) the difference of various leakage inductances should be suppressed as much as possible to achieve a good voltage sharing effect of the switches in different input-series circuits; and 2) the leakage inductances should be reduced to decrease the power losses of this converter. The investigating results are verified by the experimental comparisons among three flyback integrated-transformers with various windings layouts.