Volume 15, Issue 8 p. 717-727
ORIGINAL RESEARCH
Open Access

A comprehensive design approach for a three-winding planar transformer

Shenli Zou,

Corresponding Author

Shenli Zou

Electric Power Conversion, Rivian Automotive, Inc, USA

Correspondence

Shenli Zou, Rivian Automotive, Inc., 1059 E Bedmar St, Carson, CA 90746, USA.

Email: slzou@terpmail.umd.edu

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Chanaka Singhabahu,

Chanaka Singhabahu

Maryland Power Electronics Laboratory (MPEL), Department of Electrical and Computer Engineering, Institute for Systems Research, University of Maryland, College Park, Maryland, USA

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Jianfei Chen,

Jianfei Chen

Maryland Power Electronics Laboratory (MPEL), Department of Electrical and Computer Engineering, Institute for Systems Research, University of Maryland, College Park, Maryland, USA

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Alireza Khaligh,

Alireza Khaligh

Maryland Power Electronics Laboratory (MPEL), Department of Electrical and Computer Engineering, Institute for Systems Research, University of Maryland, College Park, Maryland, USA

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First published: 23 February 2022

Abstract

In this paper, a new three-winding planar transformer design with the integrated leakage inductor is proposed for a triple-active-bridge converter. It enables two output voltage levels: a high voltage (HV) output port and a low voltage (LV) output port. The primary and secondary windings are split unevenly in both side legs while the tertiary winding is connected in parallel. The unique winding configuration enables: (i) enhanced efficiency with low volume; and (ii) suppressed parasitic capacitances. Detailed transformer reluctance and loss models are developed in the design process. The core geometry is optimized using a reluctance-model-based mathematical computation. Moreover, comprehensive high-fidelity simulations are conducted to analyse the trade-offs among parasitic capacitances, losses, and inductances. The customized core and the non-overlapping winding boards are assembled, characterized, and tested under various power flow conditions.

1 INTRODUCTION

Transformers play a vital role in power electronic systems to facilitate electrical energy transfer and provide galvanic isolation. A typical transformer is composed of a magnetic core, and two coupled windings that are connected to an input port and an output port [1]. However, with the increasing demand for highly compact and integrated power electronic interfaces, multi-winding transformers have gained great attention to achieve the electrical integration with fewer component counts and capability of providing additional operation modes [2, 3]. Compared to the two-winding transformer, multi-winding transformer enables higher power density, reduced cost, and flexibility in different operation modes. For instance, various DC-DC converters can be integrated through a multi-winding transformer [3-6], in order to reduce volume, cost, and enhance power conversion efficiency.

Research has been conducted in multi-winding transformers in the literature [7-10]. A split-winding transformer structure is proposed in [7] to realize the multi-port integration. The minimum leakage inductance is achieved through a mathematical model. The leakage magnetic field energy is computed to screen out all possible winding configurations. Compared with simply interleaving primary and secondary windings in two winding transformers, this method is able to realize the traversal of all the possible configurations while maintaining low winding losses. However, in this design, the leakage inductance cannot be large enough to account for the required shim inductance in the phase-shifted based and resonant converters. Meanwhile, since the system is operated at low power and low switching frequency, the parasitic capacitance caused by the interleaved winding structure is ignored in the transformer design; while our proposed design considers a gallium nitride (GaN) based design, where transformer parasitics play a vital role in achieving desired converter operation. Furthermore, a Litz-wire based integrated transformer using EE-shape core is proposed in [8]. The primary winding is located on one side of the EE cores while the secondary winding is placed on the other side. The tertiary winding is located above the secondary winding. The air gap between primary and secondary windings is utilized to ensure appropriate leakage inductances. However, the winding loss can be significant considering the monotonic magnetomotive force (MMF) distribution in each winding. Recently, a low-profile two-winding planar transformer is proposed in [9] using a split winding structure to reduce winding resistance while maintaining the required magnetizing inductance. The leakage inductance is controllable by adjusting the length of air gap or the cross-sectional area of the centre core leg. However, this proposed winding layer configuration is not applicable to a three-winding structure due to the unbalanced flux. In [10], a hand-wound three-winding transformer is proposed; however, the power rating and the performance is limited by the implementation of the Litz wires.

In addition, to achieve an optimal transformer design, prior efforts have been made using different analytical methods [11-13]. Using the concept of flux cancellation, an integrated transformer with leakage inductance is established and optimized in [14] based on the equivalent flux model. However, parasitic capacitances are not fully examined in this design process, which may lead to the distorted operation waveforms. In [15], a comprehensive approach considering the trade-off between the losses and footprint area is proposed for the PCB-integrated inductors and transformers. However, this approach cannot be used to design the integrated planar transformer with a three-winding structure due to the model limitations. Furthermore, the work in [16] discusses a systematic transformer design method using the genetic algorithm for medium-frequency applications, which satisfies all the design requirements with minimum iterations. However, this design approach might not be applicable to high-frequency wide bandgap GaN and SiC based converters.

In this work, a new three-winding planar transformer design is proposed for a three-port triple-active-bridge (TAB) converter. The primary and secondary windings of the transformer are split unevenly in both side legs. The reasons behind winding in two side legs are: (i) to compensate the magnetizing inductance reduction due to the proposed side-leg interleaved structure; (ii) to obtain a controllable leakage inductance; and (iii) to provide enough winding turns. The planar transformer with the proposed PCB winding configuration is utilized to improve the manufacturability, power density, and efficiency. A systematic transformer loss model, including both core and winding losses, is investigated. Magnetizing and leakage inductances are obtained from both the analytical model and simulation. In addition, a parasitic capacitance study is conducted. Consequently, a multi-objective optimization problem is formulated to optimize the integrated transformer design considering core geometry, losses, and inductances. The objective is to determine a set of core and winding specifications to achieve minimum transformer loss. It is worth mentioning that the traditional approach of using a three-winding transformer with a centre leg with twice width of the outer legs [4, 5] is not suitable in this case due to the inherently unbalanced flux distribution of the core. Finally, the optimal design is accomplished as a customized core, which is experimentally verified.

This manuscript is organized as follows: Section 2 discusses the basis of the three-winding transformer, including the reluctance model and study of the parasitic capacitance. Moreover, comprehensive high-fidelity simulations are conducted to analyse the trade-offs among parasitic capacitances, losses, and inductances. Thus, a transformer design optimization problem is formulated. The objectives are to minimize the total loss incurred in the transformer concerning the geometrical parameters and electrical parameters, and to achieve the smallest possible volume and weight. Section 3 presents the experimental results to validate the proposed transformer design. The Section 4 puts forward conclusions with relevant discussions.

2 INVESTIGATION OF THE THREE-WINDING TRANSFORMER

A conventional three-winding transformer [3] is composed of three non-interleaved windings across the centre leg using wire-wound configuration, as shown in Figure 1. However, this design has the following drawbacks: (i) the winding AC resistance R A C ${R_{AC}}$ is relatively large, leading to the increased loss with large amounts of winding currents, which significantly decreases the efficiency and may require a demanding thermal solution. More specifically, since the magnetomotive forces (MMFs) across each winding sum up in the end, the AC resistance would be substantially large in the middle point; (ii) the Litz wire-based winding configuration makes it difficult to achieve the leakage inductance control as it is highly sensitive to the relative displacement between primary and secondary windings, which is difficult to adjust precisely; (iii) the tertiary winding is made of copper bar and needs massive labour, making it difficult for manufacturing; (iv) the height of wire-wound transformer increases the volume of the system.

Details are in the caption following the image
The integrated transformer in [3] with the MMF distribution

A split winding structure using EE core is proposed to resolve the aforementioned issues, as shown in Figure 2, where the primary and secondary windings of the transformer are split unevenly in both side legs; and the two tertiary windings are connected in parallel to maintain the flux balance. Note that the primary and secondary windings are asymmetrically interleaved on two legs, which is extremely difficult to achieve through a wire-wound transformer due to the complexity of the winding routings. Furthermore, this split winding configuration can help achieve a controllable leakage inductance while maintaining the sufficient magnetizing inductance for the converter operation.

Details are in the caption following the image
The integrated planar transformer with three PCB winding boards

As shown in Figure 2, top two boards 1 and 2 are composed of the primary and secondary windings while all the tertiary windings are located in the bottom board 3, where the distances between the boards are denoted as G 1 ${G_1}$ and G 2 ${G_2}$ . The layer change for the same winding is realized by the vias, while both left and right PCB layers with the same vertical height share the same PCB board. The width a $a$ and height h $h$ of side legs can be adjusted to reduce the core loss while maintaining enough magnetizing inductance. The increase of the thickness b $b$ reduces the effective reluctance and core loss, however, it leads to a smaller window area. The width ratio k = c a $k\; = \frac{c}{a}\;$ between the center and side legs contributes to the core loss and the leakage inductance. The centre leg confines the leakage flux path, which is determined by the reluctance of the centre leg air gap. If the centre leg air-gap reluctance is large, less leakage flux will flow through it, resulting in smaller leakage inductance. Consequently, the leakage flux in the proposed magnetic structure is confined within the core instead of air. The confined flux can contribute to less radiated EMI and eddy current loss in the surrounding metals. With the increase in switching frequency (from 100 kHz to 500 kHz to 1 MHz), the reduction on radiated EMI and eddy current loss plays a key role in improving the system performance [17]. The coupling structure between the primary and secondary windings gives additional control freedom in the mitigation of the common mode (CM) noise.

2.1 The planar transformer loss model

2.1.1 The core loss model

Considering the asymmetrical structure of the integrated transformer, a comprehensive transformer core loss model based on the proposed winding structure is established to achieve more accurate results using the magnetic equivalent circuit. This core loss model includes the leakage flux path from both windings and air gap, while splitting the location of magnetic flux path from the side legs and the centre leg. Three current sources are considered to form the equivalent magnetic circuit, where the reluctance is obtained from each leg piece to improve the accuracy of the model.

In this design, the number of primary and secondary winding turns are equal while the winding distribution for left and right legs are different. As shown in Figure 3, primary and secondary windings are asymmetrically placed in both side legs to obtain controllable leakage inductance. The tertiary windings in the side legs are connected in parallel to reduce the overall resistance. Meanwhile, the cross-section areas of the side and centre legs are denoted as A 1 ${A_1}$ and A 2 ${A_2}$ in Figure 3. The relations among the winding turns are expressed as,
N p 1 + N p 2 = N p , N s 1 + N s 2 = N s , N p 1 = N s 2 , N p 2 = N s 1 \begin{equation} \def\eqcellsep{&}\begin{array}{l} {N_{p1}} + {N_{p2}} = {N_p},{N_{s1}} + {N_{s2}} = {N_s},\\[7pt] {N_{p1}} = {N_{s2}},\quad {N_{p2}} = {N_{s1}} \end{array} \end{equation} (1)
where N p 1 ${N_{p1}}$ represents the primary winding on the left column and N p 2 ${N_{p2}}$ represents the primary winding on the right column; N s 1 ${N_{s1}}$ represents the secondary winding on the left column and N s 2 ${N_{s2}}$ represents the secondary winding on the right column. Furthermore, N p 1 I p ${N_{p1}}{I_p}$ and N p 2 I p ${N_{p2}}{I_p}$ denote the MMFs of primary winding excitation across the left and right column, and so does for N s 1 I s ${N_{s1}}{I_s}$ and N s 2 I s ${N_{s2}}{I_s}$ . R a 1 ${R_{a1}}$ and R a 2 ${R_{a2}}$ represent the reluctances of the side leg and center leg, respectively. R g 1 ${R_{g1}}$ and R g 2 ${R_{g2}}$ represent the reluctances of the side leg air gap and centre leg air gap, respectively. R a 3 ${R_{a3}}$ denotes the equivalent reluctance of top and bottom core leg pieces. The reluctance expressions are related to the cross-sectional area of the core as,
R g 1 = l a i r μ 0 A 1 , R g 2 = l a i r μ 0 A 2 \begin{equation}{R_{{\rm{g}}1}} = \frac{{{l_{air}}}}{{{\mu _0}{A_1}}},\;\;{R_{{\rm{g}}2}} = \frac{{{l_{air}}}}{{{\mu _0}{A_2}}}\;\end{equation} (2)
R a 1 = l 1 μ A 1 , R a 2 = l 1 μ A 2 , R a 3 = l 2 μ A t p \begin{equation}{R_{{\rm{a}}1}} = \frac{{{l_1}}}{{\mu {A_1}}},\;\;{R_{{\rm{a}}2}} = \frac{{{l_1}}}{{\mu {A_2}}},\;{R_{{\rm{a}}3}} = \frac{{{l_2}}}{{\mu {A_{tp}}}}\end{equation} (3)
where l a i r ${l_{air}}$ , l 1 ${l_1}$ and l 2 ${l_2}$ are the magnetic paths of the air gap, side leg and top/bottom leg piece, and μ 0 ${\mu _0}$ is the permeability of the air. Assume N p 1 N p 2 , ${N_{p1}} \ge {N_{p2}},$ the flux direction is determined from the left leg to the center leg and right leg. It is worth mentioning that the center leg flux contributes to the leakage flux, which forms the leakage inductance of the transformer. Therefore, the total reluctance R t p ${R_{tp}}$ that is reflected to the primary side can be derived using the equivalent magnetic circuit in Figure 3,
R t p = f l , g e o , l a i r = R a 1 + R g 1 + 2 R a 3 + R g 2 + R a 2 2 R a 1 + 2 R g 1 + 4 R a 3 2 R a 1 + R a 2 + R g 2 + 2 R g 1 + 4 R a 3 \begin{eqnarray} {R_{tp}} &=& f\left( {l,geo,{l_{air}}} \right)\nonumber\\ &=& {R_{{\rm{a}}1}} + {R_{{\rm{g}}1}} + 2{R_{{\rm{a}}3}} + \frac{{\left( {{R_{{\rm{g}}2}} + {R_{{\rm{a}}2}}} \right)\left( {2{R_{{\rm{a}}1}} + 2{R_{{\rm{g}}1}} + 4{R_{{\rm{a}}3}}} \right)}}{{2{R_{{\rm{a}}1}} + {R_{{\rm{a}}2}} + {R_{{\rm{g}}2}} + 2{R_{{\rm{g}}1}} + 4{R_{{\rm{a}}3}}}}\nonumber\\ \end{eqnarray} (4)
where l $l$ is the magnetic path length, g e o $geo$ is the core geometry parameter, l a i r ${l_{air}}$ is the air gap length. 1 ${\emptyset _1}$ , 2 ${\emptyset _2}$ and 3 ${\emptyset _3}$ are the magnetic fluxes flowing through each leg. Since the flux is dominated by the air gap, the flux expression can be derived as,
1 = I p N p 1 R g 1 + N p 1 R g 2 + N p 2 R g 2 I s N s 1 R g 1 + N s 1 R g 2 + N s 2 R g 2 I t N t R g 1 + N t R g 2 I t N t R g 2 R g 1 R g 1 + 2 R g 2 \begin{eqnarray} {\emptyset _1} = \def\eqcellsep{&}\begin{array}{l} {I_p}\left( {{N_{p1}}{R_{g1}} + {N_{p1}}{R_{g2}} + {N_{p2}}{R_{g2}}} \right)\\[12pt] \quad -\, {I_s}\left( {{N_{s1}}{R_{g1}} + {N_{s1}}{R_{g2}} + {N_{s2}}{R_{g2}}} \right)\\[12pt] \displaystyle\frac{\quad -\, {I_t}\left( {{N_t}{R_{g1}} + {N_t}{R_{g2}}} \right) - {I_t}\left( {{N_t}{R_{g2}}} \right)} {{{R_{g1}}\left( {{R_{g1}} + 2{R_{g2}}} \right)}} \end{array} \end{eqnarray} (5)
2 = I p N p 1 N p 2 + I s N s 2 N s 1 I t N t + I t N t R g 1 + 2 R g 2 \begin{equation}{\emptyset _2} = \frac{{{I_p}\left( {{N_{p1}} - {N_{p2}}} \right) + {I_s}\left( {{N_{s2}} - {N_{s1}}} \right) - {I_t}{N_t} + {I_t}{N_t}}}{{{R_{g1}} + 2{R_{g2}}}}\;\end{equation} (6)
3 = I p N p 1 R g 2 + N p 2 R g 1 + N p 2 R g 2 I s N s 1 R g 2 + N s 2 R g 1 + N s 2 R g 2 I t N t R g 2 I t N t R g 1 + N t R g 2 R g 1 R g 1 + 2 R g 2 \begin{eqnarray} {\emptyset _3} = \def\eqcellsep{&}\begin{array}{l} {I_p}\left( {{N_{p1}}{R_{g2}} + {N_{p2}}{R_{g1}} + {N_{p2}}{R_{g2}}} \right)\\[12pt] \quad -\, {I_s}\left( {{N_{s1}}{R_{g2}} + {N_{s2}}{R_{g1}} + {N_{s2}}{R_{g2}}} \right)\\[12pt] \displaystyle\frac{\quad -\, {I_t}\left( {{N_t}{R_{g2}}} \right) - {I_t}\left( {{N_t}{R_{g1}} + {N_t}{R_{g2}}} \right)} {{{R_{g1}}\left( {{R_{g1}} + 2{R_{g2}}} \right)}}\end{array} \end{eqnarray} (7)
Details are in the caption following the image
The equivalent magnetic circuit of the integrated transformer
Therefore, the magnetizing and leakage inductances can be derived as,
L m = N p 1 1 | I s = I t = 0 + N p 2 2 | I s = I t = 0 I p = N p 1 2 + N p 2 2 R t p \begin{equation}{L_m} = \frac{{{N_{p1}}{\emptyset _{1|{I_s} = {I_t} = 0}} + {N_{p2}}{\emptyset _{2|{I_s} = {I_t} = 0}}}}{{{I_p}}} = \frac{{N_{p1}^2 + N_{p2}^2}}{{{R_{tp}}}}\;\end{equation} (8)
L l k = N p 1 1 | I s = I t = 0 + N p 2 3 | I s = I t = 0 N s 1 1 | I s = I t = 0 N s 2 3 | I s = I t = 0 I p \begin{eqnarray} \def\eqcellsep{&}\begin{array}{l} {L_{lk}} = {N_{p1}}{\emptyset _{1|{I_s} = {I_t} = 0}} + {N_{p2}}{\emptyset _{3|{I_s} = {I_t} = 0}}\\[7pt] \displaystyle\frac{\quad -\, {N_{s1}}{\emptyset _{1|{I_s} = {I_t} = 0}} - {N_{s2}}{\emptyset _{3|{I_s} = {I_t} = 0}}}{{{I_p}}}\end{array} \end{eqnarray} (9)
Consequently, the flux density for different magnetic pieces B i = μ i R i / l i ${B_i} = \mu {\emptyset _i}\;{R_i}/{l_i}$ can be examined. Since the Steinmetz equation is more accurately applicable for a sinusoidal waveform, therefore an equivalent frequency for calculating the core loss using Steinmetz equation should be determined for a triangular waveform in a TAB-based converter. This is derived using a method mentioned in [18] and presented as follows,
f e q = 1 2 B i 2 π 2 0 f s d B d t 2 d t = 8 f s π 2 \begin{equation}{f_{eq}} = \frac{1}{{2{B_i}^2{\pi ^2}}}\;\;\mathop \int \limits_0^{{f_s}} {\left( {\frac{{dB}}{{dt}}} \right)^2}dt = \frac{{8{f_s}}}{{{\pi ^2}}}\;\end{equation} (10)
Therefore, a more accurate core loss result for the integrated transformer is achieved using the proposed reluctance model,
P c o r e = V i A i ( B i ) α f e q β \begin{equation}{P_{core}} = \sum {V_i}{A_i}{({B_i})^\alpha }f_{eq}^\beta \end{equation} (11)
where V i ${V_i}$ is the volume for each piece and V i = V c $\sum {V_i} = {V_c}$ . As can be seen from Equations (10) and (11), the proposed core loss model is suitable for any switching frequency application. It is expected that at higher switching frequency that is, 1 MHz, the core loss will increase using the same volume and magnetic materials.

2.1.2 PCB winding loss

Regarding the PCB winding, the winding loss is mainly determined by the MMF distribution, which means that the winding layer structure needs to be carefully considered. The MMFs are suppressed using the interleaved winding structure, where the primary and secondary windings are asymmetrically placed in both side legs. For N p 1 = 9 , and N p 2 = 7 ${N_{p1}} = 9,{\rm{\;\;\;and\;}}{N_{p2}} = 7$ , the proposed winding structure along with the MMF distribution is demonstrated in Figure 4.

Details are in the caption following the image
One side leg winding configuration with MMF distribution

Moreover, only the bottom two layers have the non-interleaved windings in the left leg, and the top two layers in the right leg have non-interleaved windings. This kind of winding configuration takes the advantage of interleaving to reduce the winding loss while maintaining the flexibility of magnetizing and leakage inductances control.

Based on Dowell's assumptions for single winding per layer structure, the expression for total resistance R t o t a l ${R_{total}}$ of the α th ${\alpha ^{{\rm{th}}}}$ layer including R A C ${R_{AC}}$ and R D C ${R_{DC}}$ is derived in [19],
R t o t a l = x R D C 2 × sinh x + sin x cosh x cos x + 2 m 1 2 sinh x sin x cosh x + cos x {\fontsize{9.5}{11.5}{\selectfont{ \begin{eqnarray} {R_{total}} &=& \frac{{x{R_{DC}}}}{2}\nonumber\\ &&\times\,\left[ {\frac{{\sinh \left( x \right) + {\rm{sin}}\left( x \right)}}{{\cosh \left( x \right) - {\rm{cos}}\left( x \right)}} + {{\left( {2m - 1} \right)}^2}\frac{{\sinh \left( x \right) - {\rm{sin}}\left( x \right)}}{{\cosh \left( x \right) + {\rm{cos}}\left( x \right)}}} \right]\nonumber\\ \end{eqnarray}}}} (12)
where m $m$ and x $x$ are given by,
m = M M F α M M F α M M F α 1 , x = T h i c k n e s s o f P C B S k i n d e p t h \begin{eqnarray} m = \frac{{MMF\left( \alpha \right)}}{{MMF\left( \alpha \right) - MMF\left( {\alpha - 1} \right)}},x = \frac{{ThicknessofPCB}}{{Skindepth}}\nonumber\\ \end{eqnarray} (13)
The skin depth is dependent on the operation frequency of the winding current. At higher switching frequency, x $x$ in Equation (13) increases with the decreased skin depth. Thus, the winding configuration needs to be adjusted to ensure a low R t o t a l ${R_{total}}$ . This becomes critical when the switching frequency approaches to MHz level. Moreover, a lower MMF ratio m $m$ leads to a weaker proximity effect in the adjacent layers. Thus, this winding configuration can achieve a low MMF ratio for all the layers while maintaining a sufficient leakage inductance. Furthermore, the DC resistance of PCB copper trace is represented as,
R d c = ρ c o p p e r l s u r N A P C B \begin{equation}{R_{dc}} = \frac{{{\rho _{copper}}{l_{sur}}N}}{{{A_{PCB}}}}\end{equation} (14)
Therefore, the total winding resistance of primary winding [8] can be expressed as,
R e f f = 1 N p 1 N s 1 2 N × R t o t a l m = 1 + N p 1 N s 1 2 N × R t o t a l m = 2 \begin{eqnarray} {R_{eff}} &=& \left( {1 - \left| {\frac{{{N_{p1}} - {N_{s1}}}}{{2N}}} \right|} \right) \times {R_{total}}_{m\; = 1} + \left| {\frac{{{N_{p1}} - {N_{s1}}}}{{2N}}} \right|\nonumber\\ && \times\, {R_{total}}_{m\; = 2} \end{eqnarray} (15)

Meanwhile, the winding loss can be further reduced by settling the layer thickness less than the skin depth, which allows the effective cross-section area to be increased. Considering the high current rating, the tertiary windings can be split into two parts and wound around the side legs to maintain the flux balance.

2.2 The parasitic capacitance study

The parasitic capacitance of the planar transformer can lead to many issues, including the winding current/bridge voltage waveform distortion, unexpected voltage gain, increased EMI noise, and reduced power conversion efficiency. This is in particular of significant importance in wide bandgap GaN and SiC semiconductor-based converters, as the slew rate of turn-on and turn-off of switches is very high. The converter zero-voltage-switching operation is sensitive to the transformer parasitic capacitance. Thus, it is necessary to conduct a thorough study on the parasitic capacitance mitigation based on the proposed transformer structure. The simplified equivalent parasitic circuit is shown in Figure 5. The inter-winding capacitance refers to the parasitic capacitance between primary and secondary windings, which has little effect in distorting the waveforms; however, the intra-winding capacitance contributes to the waveform distortion.

Details are in the caption following the image
The simplified equivalent parasitic circuit of the proposed planar transformer with PCB windings
The parasitic capacitances are related to the following factors: (i) adjacent winding overlap surface area S $S$ , which directly determines the parasitic capacitance value. However, decreasing S , $S,$ increases the AC winding loss, where the current density distribution is affected by the proximity effect; (ii) distance between two winding layers, whereas the increasing distance leads to the larger leakage inductance and smaller parasitic capacitance; (iii) dielectric material property, which is usually FR4 material for PCB manufacturing with the ε r ${\varepsilon _r}$ of 4.3; (iv) winding configuration, which is related to the MMF distribution; and (v) core geometry. The increase of the cross-section area leads to reduced reluctance and lower core loss. On the other hand, it increases the winding loss as the width of the winding trace needs to be compromised. The formula for the capacitance between two parallel conductive plates is given by,
C o = ε r ε o S Δ h \begin{equation}{C_o} = {\varepsilon _r}\;{\varepsilon _o}\frac{S}{{\Delta h}}\end{equation} (16)
where ε o ${\varepsilon _o}$ is the permittivity of the air; ε r ${\varepsilon _r}$ is the relative permittivity of the dielectric material. If there is only one turn per layer, the turn-to-turn capacitance in the same layer is zero. The intra-winding capacitance is formed by the layer-to-layer effect, which can be expressed by,
C i n t r a , p r i = 4 N p 1 N p 2 C o , C i n t r a , s e c = 4 N s 1 N s 2 C o \begin{equation}{C_{intra,pri}} = \frac{{4\left( {{N_p} - 1} \right)}}{{N_p^2}}{C_o},{\rm{\;\;\;}}{C_{intra,sec}} = \frac{{4\left( {{N_s} - 1} \right)}}{{N_s^2}}{C_o}\end{equation} (17)

2.3 System level co-design

Considering all the aforementioned factors, a comprehensive system level transformer co-design is achieved. First, the turns ratio evaluation is conducted to investigate the relation between the parasitic capacitance and the circulating power, as shown in Figure 6. OBJ is denoted as the current objective function, which is three winding current RMS square summation. It is observed that both the objective function (formed by the circulating power) and the winding loss function are negatively related to the turns ratio. A high turns ratio between primary/secondary and tertiary windings is needed to integrate with different energy sources. For instance, the onboard charger and the auxiliary power module for electric vehicle applications can be integrated using the proposed structure: 400 V for HV output port-1 (secondary) and 12 V for LV output port-2 (tertiary). On one hand, higher step-down turns ratio help reduce the circulating energy in the tank. On the other hand, increasing turns ratio leads to increasing the parasitic capacitance due to the increased overlapping area. It is worth mentioning that although more winding turns lead to more winding resistance, considering the reduced winding current, the winding loss is in fact reduced. In other words, the control burden can be relieved with the high step-down turns ratio. Thus, the turns ratio 16:16:1 for the primary/secondary/tertiary is selected considering conduction loss and manufacturing capability, which can be realized by stacking two 8 layers PCBs. PCBs with more than 8 layers are not preferred due to the high manufacturing cost, especially for high-power applications.

Details are in the caption following the image
The turns ratio sweeps on the circulating power and winding loss

Apart from turns ratio, the overlapping area between adjacent layers contribute to the parasitic capacitance and winding loss. A series of simulation studies are conducted in ANSYS to analyse the relationship between the overlapping area, winding loss, magnetizing inductance, core loss, and parasitic capacitance. Windings with 5.5 mm PCB trace width with 3 oz copper thickness are selected in the study. The transformer 3D model for high fidelity simulation model is shown in Figure 7.

Details are in the caption following the image
The proposed transformer 3D model with high fidelity in ANSYS

A high-fidelity simulation is conducted, where the PCB trace model is directly extracted from the PCB layout software. The parameter variations on the PCB trace overlapping between the primary and secondary windings are achieved using the ANSYS optimetrics analysis. It is observed that the core loss is not varied in a large range with different overlapping displacements. However, with the decrease of the PCB overlapping area, the copper loss increases due to the non-negligible proximity effect while the parasitic capacitances are reduced. Moreover, the displacement range is not only determined by the PCB trace width, but also is related to the core geometry, where the minimum clearance requirement between the core and the winding board needs to be satisfied. The window area inherently confines the maximum trace width. To better understand the trade-offs, two cases of the PCB winding configurations are selected and manufactured for the laboratory testing, which are marked in red and green colour in Figure 8. The green colour case refers to the fully non-overlapping and the red colour case refers to the fully overlapping.

Details are in the caption following the image
The trace overlapping variation study (a) Winding loss and parasitic capacitances, (b) transformer loss and magnetizing inductance. The red and green colours represent the winding configuration with the overlapping and the non-overlapping structures, respectively

Furthermore, the trade-off between the trace overlapping displacement and the winding resistance needs to be analysed. Note that the AC resistance is determined by the effective conduction area, which is related to the current density. Figure 9 illustrates the FEA simulation results of the current density distribution in the PCB windings. It is observed that the current density increases when the non-overlapping-structure is implemented. As can be seen from Figure 9a, the split structure merits the parasitic capacitance because of the minimum overlapping area. However, the current vector is concentrated in the adjacent terminals between the primary and secondary windings, which results in lower effective conduction area and higher winding resistance. In Figure 9b, the current density is distributed along with all the sections, which leads to a lower winding resistance.

Details are in the caption following the image
The simulated current density distribution (a) in the non-overlapping winding structure, (b) in the overlapping winding structure

2.4 Transformer design optimization

Considering the proposed transformer performance model including loss, inductance, and parasitic capacitance, a multi-objective optimization process is conducted to achieve the optimal design. The fixed design parameters are winding turns, turns ratio, magnetizing and leakage inductances, as well as core materials. Given the operation frequency (100 kHz), PC95 from TDK is selected due to its lowest core loss density at 100 kHz. In order to identify the candidates in terms of loss, volume and weight, the tuning variables for the optimization process are selected as effective volume, air gap length, cross-sectional area, core geometry, magnetizing and leakage inductance, width and thickness of PCB winding, as well as winding layer distribution. The flowchart describing the transformer optimization process is shown in Figure 10.

Details are in the caption following the image
The flowchart of the optimal integrated transformer design
The objectives are to minimize the total loss incurred in the transformer considering geometrical and electrical parameters, and to achieve the smallest possible volume and weight. The constraints are imposed on the minimum window area requirement, maximum allowable flux density, and the requirement for the power transfer capability and magnetizing inductance value. The objective function is given by,
f V c , l a i r , A c , g e o , L m , L k , W p c b , T p c b , N p 1 , N p 2 , N s 1 , N s 2 = P l o s s P l o s s , m a x V V m a x w e i g h t w e i g h t m a x \begin{eqnarray} && f\left( {{V_c},{l_{air}},{A_c},geo,{L_m},{L_k},{W_{pcb}},{T_{pcb}},{N_{p1}},{N_{p2}},{N_{s1}},{N_{s2}}} \right)\nonumber\\ &&\quad =\, \frac{{{P_{loss}}}}{{{P_{loss,max}}}}\frac{V}{{{V_{max}}}}\frac{{weight}}{{weigh{t_{max}}}} \end{eqnarray} (18)

Figure 11a shows the 3D surface of magnetizing inductance with two independent variables from geometry parameters. Given the fixed value of air gap length, the requirement for the minimum magnetizing inductance applies an additional restriction for the transformer design, which helps define the optimal solution with air gap length iteration. The shim inductance design target is 18–20 μH from the power transfer requirement.

Details are in the caption following the image
The computed results (a) 3D surface of the magnetizing inductance concerning the side leg length and centre leg length, (b) core geometry dataset considering the core loss and magnetizing inductance

Thus, the core geometry dataset is computed using the optimization method, given different dimension constraints. As indicated, there is a trade-off among the volume, magnetizing inductance, and core loss. Due to the plotting variable limitations, two factors, core loss and magnetizing inductance, are plotted using the simplified winding model, as shown in Figure 11b. The selected core geometry has a balanced performance in core loss and magnetizing inductance. Given the desired magnetizing inductance range, the core volume is minimum compared to other adjacent core options.

2.5 Towards very high switching frequency operation

Increasing switching frequency further beyond 100 kHz can potentially reduce the core size of the transformer leading to a highly compact design. However, the winding loss at higher switching frequencies can be substantially increased. In a conventional centre-leg-wound transformer [8], the leakage inductance is achieved using the energy stored in the air gap between adjacent winding boards, as demonstrated in Figure 12. Thus, it is difficult to implement the interleaved winding structure as it significantly reduces the maximum achievable leakage inductance. Unlike the proposed transformer design, the conventional centre-leg-wound transformer cannot achieve an asymmetrical winding structure to maintain the desired leakage inductance.

Details are in the caption following the image
Centre-leg wound integrated three-winding transformer

To illustrate the effectiveness of the proposed three-winding transformer design at higher switching frequencies, a frequency sweep is conducted to analyse the AC winding resistance. The sweep ranges from 100 kHz to 1 MHz with a step size of a 100 kHz. Figure 13 shows the comparison between the proposed side-leg-wound transformer and the conventional centre-leg-wound transformer counterpart with similar specifications. The Y-axis units represent the percentage increase in AC resistance compared to the 100 kHz design.

Details are in the caption following the image
AC resistance variations under different operation frequencies

A significant increase in AC resistance is observed in the conventional centre-leg-wound transformer when increasing the switching frequency. This would affect heavily on the transformer conduction losses and thermal performance. Meanwhile, the proposed side-leg-wound transformer is able to keep the AC resistance variation minimal with the increased frequency due to the interleaved asymmetric winding structure. This result suggests that the proposed transformer design process is extendable to high frequency operation, that is, 500 kHz to 1 MHz.

3 EXPERIMENTAL VERIFICATIONS

The detailed geometrical parameters of the proposed transformer core are shown in Figure 14a. Given the customized core dimensions, two cases of the winding designs are achieved: non-overlapping and fully overlapping. The finished board thickness is around 4 mm with immersion silver technique, where the dielectric layer thickness is maximized considering the manufactory capability. The layer change terminals are minimized as they reduce the effective winding turns. The assembled integrated planar transformer is shown in Figure 14b. The copper bars are utilized as the spacers and connectors.

Details are in the caption following the image
The proposed integrated planar transformer (a) core dimension, (b) the assembled transformer

As can be seen from Figure 15, the tertiary winding board with 4 layers in parallel forms a "W" shape PCB trace, where the left leg winding is connected in parallel with the right leg to increase the ampacity. Moreover, since the adjacent layer is not utilized, the intra-winding capacitance is reduced in the tertiary winding.

Details are in the caption following the image
The PCB layout for the transformer windings

The impedance analyser Keysight E4990A with a wide frequency range of 20 Hz to 120 MHz is utilized to characterize the transformer. Both open and short circuit tests are conducted for the overlapping and non-overlapping winding boards.

One-layer tape-based air gap is employed to obtain the required leakage inductance. Thus, the parasitic capacitances, the leakage inductance, and the magnetizing inductance can be extracted using the equivalent model. With open circuits in both secondary and tertiary windings, C i n t r a ${C_{intra}}$ and L m + L k ${L_m} + {L_k}$ are measured across the primary winding. With short circuits in both secondary and tertiary windings, L k ${L_k}$ are measured across the primary winding. The measured results are summarized in Table 1.

TABLE 1. The measured parameters for the proposed winding boards
Type f r ( kHz ) ${f_r}\;( {{\bf{kHz}}} )$ L m ( mH ) ${L_m}\;( {{\bf{mH}}} )$ C i n t r a ( nF ) ${C_{intra}}\;( {{\bf{nF}}} )$ L k ( μ H ) ${L_k}\;( {{\bm{\mu H}}} )$
Non-overlapping 270 1.17 0.3 20
Overlapping 150 1.68 0.67 18.5

The measured intra-winding capacitances are consistent with the FEA based estimations. It is observed that higher parasitic capacitances are formed in the non-split winding board. The intra-winding capacitance is reduced to 0.3 nF in the split winding structure.

The three-winding transformer is tested with a GaN based three-port DC-DC converter, with one input power source and two output loads. It enables two output voltage levels: 400 V for HV output port-1 (secondary) and 12 V for LV output port-2 (tertiary). As shown in Figure 16, the tertiary winding current is measured as 39.3 A. The power distribution of this testing condition is: P H V ${P_{HV}}$  = 2095 W, P L V ${P_{LV}}$  = 290 W, where P H V ${P_{HV}}$ refers to the high voltage output port and P L V ${P_{LV}}$ refers to the low voltage output port. The HV load resistance is 47 Ω ${{\Omega}}$ and the LV load resistance is 0.33 Ω ${\;\Omega }$ . It is observed that there is some ringing in the tertiary bridge voltage, which is caused by the parasitic capacitance in the tertiary side.

Details are in the caption following the image
The steady state waveforms with the input power 2.5 kW (tertiary winding current RMS 39.3 A)

Moreover, the power conversion efficiency of the proposed transformer is measured using the Tektronix PA3000 power analyser. To analyse the transformer loss, a subtraction-based method is implemented. First, all winding current RMS values are measured. By subtracting the semiconductor loss and capacitor loss from the total power loss, the transformer efficiency is obtained, as shown in Figure 17.

Details are in the caption following the image
The efficiency measurement of the proposed transformer

The thermal images of the transformer and the hardware prototype operating in G2B mode with a power rating of 2.5 kW are shown below, which include the side-view of the transformer to capture the thermal distribution across all three transformer PCBs. In Figure 18a, the highest temperature of the proposed transformer is observed to be 39.1 °C located at the middle board of the transformer stack with the forced air cooling. The core temperature is observed to be 28.4 °C. In Figure 18b, the thermal image of the entire hardware prototype (top-view) is illustrated. The LV side circuit uses bottom-cooled switches without heatsink. The highest temperature is observed to be 33.9 °C at the LV side trace due to the ohmic losses induced by high currents.

Details are in the caption following the image
Thermal images of the hardware setup (a) transformer side-view, (b) setup top-view

Furthermore, a comprehensive comparison between the simulation and the experiment is investigated, as shown in Table 2. The transformer loss from the experiment is obtained through the loss breakdown as it is difficult to measure the winding and core loss separately. The transformer loss from the simulation is obtained through ANSYS, where the core loss is 10 W and the winding loss is 72 W. It can be observed that the error is less than 10%.

TABLE 2. The comparison between the simulation and the experiment with the non-overlapping winding boards
Total R A C ( m Ω ) ${R_{AC}}\;( {{\bm{m}\Omega }} )$ P c o r e ${P_{core}}$ + P w i n d i n g ( W ) ${P_{winding}}\;( {\bf{W}} )$ C i n t r a ( nF ) ${C_{intra}} ( {{\bf{nF}}} )$ L m ( μ H ) ${L_m}\;( {{\bm{\mu H}}} )$ L k ( μ H ) ${L_k}\;( {{\bm{\mu H}}} )$
Simu. 750 82 0.27 1240 22.1
Test 90 0.3 1170 20

Moreover, a comparative study of transformer loss between the proposed transformer design and other existing studies, as shown in Table 3. Note that the design space parameters including turns ratio, power rating, and volume in the multi-winding transformer and the optimization objective varies in different cases.

TABLE 3. The comparative study of transformer loss between the proposed transformer design and other existing studies
Case I (proposed transformer) Case II [7 ] Case III [8 ]
Transformer efficiency at peak power 96% 87% 96%
Transformer loss accuracy 9% NA 10%

4 CONCLUSIONS

In this work, a new three-winding planar transformer design is proposed, which can be used within any three-port isolated converter. It enables two output voltage levels with high step-down ratios. Detailed transformer reluctance and loss models are developed to synthesize a systematic design approach. Moreover, co-simulation is conducted to analyse the relationships among parasitic capacitances, losses, and inductances. The optimized three-winding transformer design is achieved considering the trade-off among the loss, magnetizing and leakage inductances, parasitic capacitance, and volume. The customized core and the non-overlapping winding board are assembled and tested. The proposed transformer is tested up to 2.5 kW with the peak efficiency of 98%. It is reported that the error between the simulation and the experiment is less than 10%. The proposed transformer design process is extendable to very high frequency operation, that is, 500 kHz to 1 MHz.

ACKNOWLEDGMENT

This work has been partially sponsored by the Maryland Innovation Initiative Grant, which is gratefully acknowledged.

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