Modeling and Analysis of the Bendable Transformer

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 1 Modeling and Analysis of the Bendable Transformer Godwin Kwun Yuan Ho, Student, IEEE, Cheng Zhang, Student, IEEE, Bryan M.H. Pong, Senior, IEEE, and S. Y. Ron Hui, Fellow, IEEE  Abstract—This paper presents a study of a bendable transformer for wearable electronics. Printed on a thin and bendable film, this transformer is bendable to wrap around body limbs such as the forearm. A model using partial equivalent circuit theory (PEEC) has been developed to analyze the characteristic of an inductor and a bendable transformer. The mutual inductance and self-inductance for the bendable transformer over a range of bent curvatures have been calculated based on the model and compared favorably with measurements. Simulation and experimental results of applying the bendable inductor and transformer in DC-DC converters as a 5 V, 500 mA (USB) power supply are included to confirm the usefulness of the transformer and the validity of the model Index Terms—buck converter, flexible transformer, LLC resonant converter, wearable electronics I. INTRODUCTION earable electronics products like smart watches, hearing Waids, intelligent glasses, are becoming popular nowadays. Wearable electronic products appeared back in 1950s [1]. A good portable electronic product should be small in size and light in weight. A good wearable electronics product needs one more requirement: comfortable to wear. This requirement introduces a new challenge: physically flexible. Many flexible electronics components are available nowadays like flexible display, flexible solar cell, printed RFID, flexible lighting and others based on the application [2]-[7]. It was estimated that there were about 1500 research units working on flexible electronics in worldwide in 2010 [8]. However, there is a lack of flexible power converter. A bendable converter can be used in many wearable applications. For example, a bendable converter can be mounted into a jacket with a flexible film solar panel and converts power form solar energy. Another example is to have a bendable converter mounted into a belt fitted with batteries and turns the belt into a central power source for various portable devices. There can be many innovative applications but all will need a fundamental building block which is the bendable Mansuricpt received May 27, 2015; revised Aug 13, 2015; accepted Oct 29 ,2015. G. K. Y. Ho, C. Zhang, B. M. H. Pong and R. S. Y. Hui are with the Department of Electrical Engineering, the University of Hong Kong, Hong Kong ( kyho@eee.hku.hk, guszhang@hku.hk, mhp@eee.hku.hk, ronhui@eee.hku.hk ) . converter. Flexible electronics including passive components is needed for wearable electronics. For switched mode power supplies, inductor and transformer are essential passive components. Although non-isolated converter with inductor can fulfill the power conversion requirement of the wearable electronics, isolated converter is also needed for some applications such as medical application. Traditional magnetic core based inductor and transformers are not bendable. Although many researchers have worked to improve the thickness, power density and efficiency of planar transformer, not much work has been done on bendable transformer [8]-[11]. Inductor and coreless printed-circuit-board (PCB) transformer [12]-[16] is applicable to wearable electronics. It has the advantages of having no core loss and thus being suitable for high frequency operation. Based on resonant technique, it has been successfully demonstrated in signal and power transfer applications such as isolated gate drives [12] and planar converters [16]. The coreless PCB transformer technology has the significance of turning the traditional solid transformers into flat ones, making it possible for embedment in power semiconductor integrated circuits as confirmed in its industrial adoptions in isolated gate drive integrated circuits [17], [18]. Therefore, if fabricated on a flexible substrate, coreless PCB transformer offers an attractive solution to bendable electronics. However, not much work has been done on flexible inductor and transformer. The bendable converter for wearable electronics will closely contact the human body and there is concern whether there is adverse effect form EM radiation form the converter. A lot of works have been done on this issue as the mobile phone today is carried by millions of people already. The equipment is not only in close contact with body but also designed to radiate as a primary function. The ICNIRP [19] has collected extensive work and reported that there is no evidence on major medical effect on the human body for such low radiation. The SAR maximum value of exposure is 4 WKg-1, and the recommended occupational exposure is wind down 10 times to 0.44 WKg-1. Even so the radiation produced by a bendable converter of the present power level is unlikely to reach such a value. The shape of flexible inductor or transformer changes when it is bent. When the structure changes its parameters are also changed. It is important to know how these parameters will be changed and how these parameters will affect the switching 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 2 converter. Most converter works at high frequency in order to cope with the low inductance in coreless device. Resonant techniques have been incorporated in coreless PCB transformer technology since its inception [14], [15]. The inherent high leakage inductance of the coreless PCB converter can be used as resonant inductance in the LLC resonant converter [11], [20]-[22]. This paper presents two steps in the development of bendable coreless PCB transformers. Firstly, in order to study possible parameter changes, a bendable model is developed to study the inductor and transformer under different bending angle. Such model is based on the partial element equivalent circuit (PEEC) method [23]. Secondly, a bendable inductor is made and its inductance measured. It is then applied to a buck converter. On the other hand a bendable transformer is also made. It is then applied to an LLC converter. Both converters have a power rating of 5 V and 500 mA for a USB power supply. The modeling procedure is described in detail. Both simulation and experimental measurements of a hardware prototype are included to confirm the proposal. II. BENDABLE INDUCTOR AND TRANSFORMER MODELING A. Analysis by PEEC Theory Inductance equations for standard regular shapes have been well documented [24]-[30]. Simple expressions for regular shape inductances are very limited because the flexible winding structure has changeable shapes. A tool for complicated winding structure analysis is needed. Ruehli proposed the PEEC (Partial Element Equivalent Circuit) theory in 1970s [26]. The PEEC theory enables analysis of coupling among interconnections in three-dimensional multi-conductor electronics circuits. This theory states that the effective self-inductance of a winding and mutual inductance of two windings can be calculated by dividing a complex conductor structure into small discrete segments. Integral equations are applied to each elementary piece of the conductor to calculated inductances. Such versatile feature of the PEEC method makes it suitable to calculate self and mutual inductance of windings with complicated structures, including non-standard winding structures for wireless power transfer systems. Mutual inductance between each segment can be calculated by Neumann’s formula (2) where l and l′ are segments of the primary and secondary conductors. The effective mutual inductance of the elementary elements is 𝐿= 𝜇 ∫ 4𝜋 𝑙 ∫𝑙′ 𝑑𝑙∙𝑑𝑙′ (1) |𝑟−𝑟′| The self-inductance of a winding can be calculated similar to the effective mutual inductance as the winding is broken into small discrete segments. However, when integrating the same segment itself, the distance between itself vanishes to zero and results in infinity. Therefore, Rosa’s equation for self-inductance of a typical wire for rectangular cross section is used when integrating the same segment [31]. The effective self-inductance of the elementary elements is = 2𝑙 [𝑙𝑜𝑔 ( 2𝑙 𝛼+𝛽 ) + 0.5 + 0.2235(𝛼+𝛽) 𝑙 ] (10−6 ) (2) where l is the length of the straight segment, α is the width and β is the thickness. B. Bendable Inductor and Transformer Model A mathematical model for bendable inductor and transformer is established. Actually both are based on the same principle. An inductor is presented by a single winding and a transformer is presented by grouping two different separate windings at a specified location. Here a winding structure is divided into many small segments. Define a finite set W to represent the winding. Thus, each conductor segment of the winding is an element of W. Each segment is considered as a straight conductor and represented by a matrix with ⃑⃑⃑s and position vector ⃑⃑⃑ segment-current vector C Ps . The segment-current vector describes the conductor length and the current direction. The segment-position vector describes the conductor position. Such that ⃑⃑⃑𝑠 ⃑⃑⃑ 𝐖 = {𝑤|𝑤 ∈ [𝐶 𝑃𝑠 ]} (3) Here a straight wire is divided in to N segments, the set W has N elements, such that ⃑⃑⃑𝑠 ⃑⃑⃑ 𝑃𝑠 ] (4) 𝐖 = {𝑤1 , 𝑤2 , … , 𝑠𝑤𝑁 }, ∀𝑤𝑖 ∈ [𝐶 Fig. 1. Single turn coil in three-dimension. Figure 1 shows a single turn rectangular winding on an x-y plane in three dimensions. Define set Wrect1 to be the rectangular winding and C to be each straight conductor in Fig. 1, such that 𝐖𝐫𝐞𝐜𝐭𝟏 = 𝐂𝟏 ∪ 𝐂𝟐 ∪ 𝐂𝟑 ∪ 𝐂𝟒 (6) ⃑⃑⃑⃑⃑ Each set Ci has a conductor-current vector Cic and a conductor-position vector ⃑⃑⃑⃑⃑ Cip , such that ⃑⃑⃑⃑⃑𝑖𝑐 , 𝑃 ⃑⃑⃑⃑⃑𝑖𝑐 , 𝑃 ⃑⃑⃑𝑠 ⃑⃑⃑ ⃑⃑⃑⃑𝑖𝑐 ]: [𝐶 ⃑⃑⃑⃑𝑖𝑐 ] ∈ [𝐶 𝐂𝐢 = {[𝐶 𝑃𝑠 ]} (7) Each side of the rectangle winding is divided into N segments. The segment-current vectors in a straight conductor are the same because they all lie in the same straight line. However, they have different positions. Such that ⃑⃑⃑⃑⃑𝑖𝑐 , 𝑃 ⃑⃑⃑⃑⃑𝑖𝑠 ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑𝑖𝑠 ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑𝑖𝑠 ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑𝑖𝑐 ]} = {[𝐶 𝑃𝑖𝑠1 ], [𝐶 𝑃𝑖𝑠2 ], … , [𝐶 𝑃𝑠𝑖𝑁 ]} (8) 𝐂𝐢 = {[𝐶 where the segment-current vector is ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑𝑖𝑠 = 𝐶𝑖𝑐 𝐶 (9) 𝑁𝑖 Ni is the number of segments of Ci and the segment-position vector is ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑𝑖𝑠 ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑ 𝐶𝑖𝑐 + (2𝑖−1) + 𝐶 𝑃 𝑖𝑠𝑗 = 𝑃𝑖𝑐 − 2 2 (10) where i = 1,2, … Ni The mathematical model of the rectangle winding in Fig. 1 is established by compounding (5), (6) and (7). The total segments number Ntotal is equal to N1 + N2 + N3 + N4 . The rectangle winding in Fig. 1 is mathematically represented as 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ 𝐖𝐫𝐞𝐜𝐭𝟏 = {[𝐶 𝑠1 𝑃𝑠1 ], [𝐶𝑠2 𝑃𝑠2 ], … , [𝐶𝑠𝑁 𝑃𝑠𝑁𝑡𝑜𝑡𝑎𝑙 ]} ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ = {[𝐶 1𝑐 𝐶1𝑝 ], [𝐶2𝑐 𝐶2𝑝 ], [𝐶3𝑐 𝐶3𝑝 ], [𝐶4𝑐 𝐶4𝑝 ]} 𝐖𝐫𝐞𝐜𝐭𝟏 = 3 (a). Coil central angle = 0. (11) ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ [𝐶 1𝑠 𝑃1𝑠1 ], [𝐶1𝑠 𝑃1𝑠2 ], … , [𝐶1𝑠 𝑃1𝑠𝑁1 ], ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ [𝐶 2𝑠 𝑃2𝑠1 ], [𝐶2𝑠 𝑃2𝑠2 ], … , [𝐶2𝑠 𝑃2𝑠𝑁2 ], (12) ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ [𝐶 3𝑠 𝑃3𝑠1 ], [𝐶3𝑠 𝑃3𝑠2 ], … , [𝐶3𝑠 𝑃3𝑠𝑁3 ], ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ { [𝐶 4𝑠 𝑃4𝑠1 ], [𝐶4𝑠 𝑃4𝑠2 ], … , [𝐶4𝑠 𝑃4𝑠𝑁4 ] } Although the flat structure of the winding can be presented by the proposed model easily, a model suitable for a bent structure is not readily available. The segment-current vectors and segment-position vectors may change according to curvature of the bent winding. A method for developing a bendable transformer model is now explained. (b). Coil central angle = π/2. (c). Coil central angle = π. Fig. 4. Coil bending at different angles. Fig. 2. Bending coil at the side view. There are three steps to convert a flat winding model to a bent winding model with reference to Fig. 3. First, convert each segment of the flat winding into a starting point ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ Sstart and an ⃑⃑⃑⃑⃑⃑⃑⃑ ending point Send , such that ⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑ 𝑆𝑐 = 𝑃𝑠𝑡𝑎𝑟𝑡 (𝑥, 𝑦, 𝑧) 𝑆 𝑠𝑡𝑎𝑟𝑡 = 𝑆𝑝 − (13) 2 ⃑⃑⃑⃑𝑐 𝑆 Fig. 3. Geometry of a bending conductor. Figure 2 shows a side view of a bent winding. The bending of the winding is described by an arc of a circle. It should be noted that the method applies to any curved geometry in principle. Usually, the arc is described by its central angle and radius. When a winding is bent, the winding length is fixed and equal to the arc length L. Angle θ defines the bending and radius r is equal to L/θ. When the bending is increased, the central angle increases and radius decreases. Figure 4(a) shows the winding at central angle equals to 0 (i.e. the winding is flat). Figure 4(b) shows the winding bent with a central angle equals to π/2 and Fig. 4(c) shows the winding bent with a central angle π. ⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑ 𝑆 (14) 𝑒𝑛𝑑 = 𝑆𝑝 + 2 = 𝑃𝑒𝑛𝑑 (𝑥, 𝑦, 𝑧) Second, convert each point of the segments from a flat surface to a curved surface. Define point Pi (x, y, z) as a point on the flat surface and point Pi ′(x ′ , y ′ , z ′ ) as the same point after bending the transformer structure. When the wire is bent in a plane along the x-axis, the new x-coordinate of each point remains unchanged. The distance between each point on the plane remains unchanged after the transformer is bent. Such that the arc length L’ at point Pi ′ is equal to the y-coordinate of point Pi (x, y, z) in Fig. 3. Arc length L is equal to the length of the winding at x-axis. Angle θ is equal to the bending angle. The transformation functions from point Pi (x, y, z) to point Pi ′(x ′ , y ′ , z ′ ) are 𝑥′ = 𝑥 (15) 𝑦 ′ ′) 𝑦 = 𝑟 𝑠𝑖𝑛(𝜃 = 𝑟 𝑠𝑖𝑛( ) (16) 𝑦 𝑟 𝜃 𝑧 ′ = 𝑧 + 𝑟 𝑐𝑜𝑠(𝜃 ′ ) − 𝐻 = 𝑧 + 𝑟 𝑐𝑜𝑠 ( ) − 𝑟 𝑐𝑜𝑠( ) 𝑟 2 (17) where H is the vertical displacement between the original plane and circle center. Third, create the winding segments of the bent transformer from the new points produced in the second step. The segments of the bent winding model become ⃑⃑⃑⃑⃑ 𝑆𝑐 ′ = ⃑⃑⃑⃑⃑⃑⃑⃑⃑ 𝑆𝑒𝑛𝑑 ′ − ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ 𝑆𝑠𝑡𝑎𝑟𝑡 ′ (18) ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ 𝑠𝑡𝑎𝑟𝑡 ′ 𝑒𝑛𝑑 ′+𝑆 ⃑⃑⃑⃑⃑𝑝 ′ = 𝑆⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ (19) 𝑆 2 In order to establish the mathematical model of the bent winding in Fig. 3, these steps are applied to the model of the same winding before bending. Define the set WFrect as the flat winding and WBrect as the bent winding in Fig. 3 such that 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 4 C. Calculation of self-inductance In the previous section, a mathematical model is established ⃑⃑⃑s ⃑⃑⃑ Ps ]} represents a for each winding. A set W = {w: w ∈ [C ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ winding. Set W1 = {[C1s1 ⃑⃑⃑⃑⃑⃑⃑ P1s1 ], [C1s2 ⃑⃑⃑⃑⃑⃑⃑ P1s2 ], … , [C 1sN1 P1sN2 ]} is the winding of the inductor. The self-inductance of the winding is calculated by applying (1) and (2) to the set W1 , such that 𝑁1 (24) 𝐿𝑠𝑒𝑙𝑓 = ∑𝑁1 𝑖=1 ∑𝑗=1 𝑓(𝑖, 𝑗) 𝑓(𝑖, 𝑗) = 2𝑙 [ 𝑙𝑜𝑔 ( + 2𝑙 ⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑ 𝐶 1𝑠𝑖 ∙𝐶 1𝑠𝑗 ⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑ |𝑃 1𝑠𝑖 −𝑃 1𝑠𝑗 | ) + 0.5 𝛼+𝛽 0.2235(𝛼+𝛽) ] (10−6 ) 𝑓𝑜𝑟 𝑖 ≠𝑗 (25) 𝑓𝑜𝑟 𝑖 = 𝑗 { 𝑙 where l is the length of the straight segment, α is the width and β is the thickness. D. Calculation of mutual inductance of two windings Define the set W1 to be the primary winding and W2 = ⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ {[C2s1 ⃑⃑⃑⃑⃑⃑⃑ P2s1 ], [C 2s2 P2s2 ], … , [C2sN1 P2sN2 ]} to be the secondary winding. The mutual inductance is calculated by applying (1) to the set W1 and W2 , such that 𝐿𝑚𝑢𝑡𝑢𝑎𝑙 = ⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑⃑ 𝑁2 𝐶1𝑠𝑖 ∙𝐶2𝑠𝑗 ∑𝑁1 𝑖=1 ∑𝑗=1 |𝑃 ⃑⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑⃑ 1𝑠𝑖 −𝑃 2𝑠𝑗 | (26) III. BENDABLE INDUCTOR AND TRANSFORMER Bendable inductors and coreless PCB transformers have been built to verify the mathematical model. The primary and secondary conductors are represented by two segment sets in MATLAB. The inductors are same as the primary side of the transformer. The mutual inductance and self-inductance are calculated by applying the primary and secondary segment sets into (25) and (26). Six inductors and twelve transformers have been built to verify the model. The specifications of the bendable and coreless PCB transformers and inductors are listed in Appendix I. A. Bendable Inductor There are two groups of inductors. This first group of inductor has winding dimension of 100 mm × 40.25 mm. There are thee inductors in this group. The turns number of them are 16, 18 and 20. Inductor L1, L2 and L3 are equal to the primary side of Tx1, Tx2 and Tx3 respectively. The secondary group of inductor has winding dimensions of 65 mm × 26mm. There are three inductors in the secondary group. The turns number of them are 22, 24 and 26. Inductor L4, L5 and L6 are equal to the primary side of Tx7, Tx8 and Tx9 respectively. The calculated and measured self-inductance values of the bendable inductance at flat are shown in Table I. The calculated and measured self-inductance with the bending angle is shown in Fig. 5 and Fig. 6. The bending angle of the transformer is fixed by supporters which are printed by 3D printer and shown in Fig. 7. The calculated results are in good agreement with the measurements within a tolerance of 1.5 %. Errors mainly arise from manufacturing tolerance. In practice, every segment direction, size and position have discrepancies between the model and the physical coil. The overall inductance is calculated by integrating all elementary inductances by PEEC theory. TABLE I SELF- INDUCTANCE OF THE BENDABLE CORELESS PCB TRANSFORMER/ INDUCTOR LIE FLAT Calculated Measured Error L1 (16T, 1 layer) L2 (18T, 1 layer) L3 (20T, 1 layer) 19.23 μH 20.89 μH 21.77 μH 19.22 μH 20.93 μH 21.93 μH -0.052 % 0.19 % 0.73 % L4 (22T, 2 layers, 11 turns per layer) L5 (24T, 2 layers, 12 turns per layer) L6 (26T, 2 layers, 13 turns per layer) 22.67 μH 22.75 μH 0.35 % 23.96 μH 23.99 μH 0.13 % 24.67 μH 24.82 μH 0.31 % 22 Self-inductance ( μH) ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑ 𝐖𝐅𝐫𝐞𝐜𝐭 = {[𝐶 (20) 𝑠1 𝑃𝑠1 ], [𝐶𝑠2 𝑃𝑠2 ], … , [𝐶𝑠𝑁 𝑃𝑠𝑁 ]} Step 1: Apply (7) and (8) to set WFrect , such that [𝑃𝑠𝑡𝑎𝑟𝑡1 (𝑥, 𝑦, 𝑧) 𝑃𝑒𝑛𝑑1 (𝑥, 𝑦, 𝑧)], [𝑃 (𝑥, 𝑦, 𝑧) 𝑃𝑒𝑛𝑑2 (𝑥, 𝑦, 𝑧)], } (21) 𝐖𝐅𝐫𝐞𝐜𝐭.𝐒𝐭𝐞𝐩𝟏 = { 𝑠𝑡𝑎𝑟𝑡2 …, [𝑃𝑠𝑡𝑎𝑟𝑡𝑁 (𝑥, 𝑦, 𝑧) 𝑃𝑒𝑛𝑑𝑁 (𝑥, 𝑦, 𝑧)] Step 2: Apply equations (9)-(10) to set WFrect.Step1 to convert the flat winding to bent winding with central angle equals to θ. Arc length L is equal to the length of the winding at x-axis. [𝑃𝑠𝑡𝑎𝑟𝑡1 ′(𝑥 ′ , 𝑦 ′ , 𝑧 ′ ) 𝑃𝑒𝑛𝑑1 ′(𝑥 ′ , 𝑦 ′ , 𝑧 ′ )], [𝑃 ′(𝑥 ′ , 𝑦 ′ , 𝑧 ′ ) 𝑃𝑒𝑛𝑑2 ′(𝑥′, 𝑦′, 𝑧′)], }(22) 𝐖𝐅𝐫𝐞𝐜𝐭.𝐒𝐭𝐞𝐩𝟐 = { 𝑠𝑡𝑎𝑟𝑡2 …, [𝑃𝑠𝑡𝑎𝑟𝑡𝑁 ′(𝑥 ′ , 𝑦 ′ , 𝑧 ′ ) 𝑃𝑒𝑛𝑑𝑁 ′(𝑥′, 𝑦′, 𝑧′)] Step 3: Apply (11) and (12) to set WFrect.Step3 , such that bent winding set WBrect is 𝐖𝐁𝐫𝐞𝐜𝐭 = 𝐖𝐅𝐫𝐞𝐜𝐭.𝐒𝐭𝐞𝐩𝟑 ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ ⃑⃑⃑⃑⃑⃑⃑ = {[𝐶𝑠1 ′ 𝑃𝑠1 ′] , [𝐶 (23) 𝑠2 ′ 𝑃𝑠2 ′] , … , [𝐶𝑠𝑁 ′ 𝑃𝑠𝑁 ′]} 21.5 L1, 16Turns, 1Layer (Measured) 21 L1, 16Turns, 1Layer (Calculated) 20.5 20 L2, 18Turns, 1Layer (Measured) 19.5 L2, 18Turns, 1Layer (Calculated) 19 18.5 L3, 20Turns, 1Layer (Measured) 18 0 0.5 1 1.5 2 2.5 3 3.5 Bending angle (rad) L3, 20Turns, 1Layer (Calculated) Fig. 5. Self-inductance against bending angle of the first group. 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 5 Self-inductance ( μH) 25 L4, 22Turns, 2Layers (Measured) 24.5 24 L4, 22Turns, 2Layers (Calculated) 23.5 23 L5, 24Turns, 2Layers (Measured) 22.5 L5, 24Turns, 2Layers (Calculated) 22 L6, 26Turns, 2Layers (Measured) 21.5 0 0.5 1 1.5 2 2.5 3 3.5 Bending angle (rad) L6, 26Turns, 2Layers (Calculated) Fig. 8. Layout of the Coreless PCB Transformer. Fig. 6. Self-inductance against bending angle of the second group. Fig. 9. Bendable transformer prototype. B. Bendable Transformer There are two groups of transformers. The first group has bigger windings. Transformer Tx1 to Tx6 is the first group with 100 mm × 40.25 mm in dimension. Each transformer has two windings. There are three types of windings in this transformer group: 16 turns each layer, 18 turns each layer, and 20 turns each layer. Transformer Tx1 to Tx3 have the same turns ratio 1:1 but different number of turns. The primary turns to secondary turns ratios of Tx1 is 16:16, Tx2 is 18:18 and Tx3 is 20:20. Transformer Tx4 to Tx6 have different turns ratio. The primary to secondary turns ratio of Tx4 is 16:20, Tx5 is 16:18 and Tx5 is 18:20. Transformer Tx7 to Tx12 is the second group with small windings. The winding dimensions are 65 mm × 26mm. There are three types of winding in this transformer group: 22 (2 layers, 11 turns per layer, 0.1 mm gap), 24 (2 layers, 12 turns per layer, 0.1 mm gap), 26 (2 layers, 13 turns per layer, 0.1 mm gap). Tx7 to Tx9 have the same turns ratio 1:1 but different number of turns. The primary turn to secondary turn of Tx1 is 22:22, Tx2 is 24:24 and Tx3 is 26:26. Transformer Tx10 to Tx12 have different turns ratio. The primary to secondary turns ratio of Tx10 is 22:26, Tx11 is 22:24 and Tx12 is 24:26. The layout of the transformer Tx10 is shown in Fig. 8. The bendable transformer windings are made of thin copper strips that are printed on a flexible substrate. This method provides the flexibility for bending the transformer structure. Two prototype are shown in Fig. 9. The calculated and measured mutual inductance values of the bendable transformer at flat are shown in Table II. The calculated and measured mutual inductance with the bending angle is shown in Fig. 10 to Fig. 13. The calculated agree well with the measurements within a tolerance of 1.5 %. TABLE II MUTUAL-INDUCTANCE OF THE BENDABLE CORELESS PCB TRANSFORMER LIE FLAT Calculated 18.65 μH 20.26 μH 21.20 μH 19.53 μH 19.30 μH 20.58 μH 21.61 μH 22.81 μH 23.46 μH 22.28 μH 22.10 μH 23.06 μH Tx1 Tx2 Tx3 Tx4 Tx5 Tx6 Tx7 Tx8 Tx9 Tx10 Tx11 Tx12 Measured 18.72 μH 20.37 μH 21.29 μH 19.65 μH 19.41 μH 20.74 μH 21.54 μH 22.84 μH 23.63 μH 22.33 μH 22.10 μH 23.16 μH Error 0.38 % 0.54 % 0.42 % 0.61 % 0.57 % 0.78 % -0.32 % 0.13 % 0.72 % 0.22 % 0% 0.43 % 21.5 Mutual inductance ( μH) Fig. 7. Support for fixing the bendable angle. 21 20.5 Tx1 (Measured) 20 Tx1 (Calculated) 19.5 Tx2 (Measured) 19 Tx2 (Calculated) 18.5 Tx3 (Measured) 18 Tx3 (Calculated) 17.5 0 0.5 1 1.5 2 2.5 3 3.5 Bending angle (rad) 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 6 Fig. 10. Mutual inductance of Tx1 to Tx3 (same turns ratio in the first group). Mutual inductance ( μH) 21 20.5 20 Tx4 (Measured) Tx4 (Calculated) 19.5 inductance, Lp is the primary self-inductance, Ls is the secondary inductance and K is the magnetic coupling factor. The variations of the mutual inductance and self-inductance change of the coreless PCB transformer Tx10 versus the bending angle θ are showed in Fig. 15(a) to 15(c). The equivalent transformer model parameters are shown in Fig. 15(d) to 15(e). Tx5 (Measured) 19 Tx5 (Calculated) Tx6 (Measured) 18.5 Tx6 (Calculated) 18 0 0.5 1 1.5 2 2.5 3 3.5 Bending angle (rad) Fig. 11. Mutual inductance of Tx4 to Tx6 (different turns ratio in the first group). Fig. 14. Equivalent transformer model. Mutual inductance ( μH) 24 23.5 23 Tx7 (Measured) 22.5 Tx7 (Calculated) 22 Tx8 (Measured) 21.5 Tx8 (Calculated) 21 (a). Primary self-inductance. (b). Secondary Self-inductance (c). Mutual inductance. (d). Leakage inductane. Tx9 (Measured) 20.5 Tx9 (Calculated) 20 0 0.5 1 1.5 2 2.5 3 3.5 Bending angle (rad) Fig. 12. Mutual inductance of Tx7 to Tx9 (same turns ratio in the second group). Mutual inductance ( μH) 23.5 23 22.5 Tx10 (Measured) Tx10 (Calculated) 22 Tx11 (Measured) 21.5 Tx11 (Calculated) Tx12 (Measured) 21 Tx12 (Calculated) 20.5 0 0.5 1 1.5 2 2.5 3 (e). Magnetizing inductance. (f). Np/Ns. Fig. 15. Inductance against bending angle. 3.5 Bending angle (rad) Fig. 13. Mutual inductance of Tx10 to Tx12 (different turns ratio in the second group). C. Analysis of Bendable Inductor and Transformer An equivalent transformer model is shown in Fig. 14. The magnetizing inductance, leakage inductance and equivalent turns ratio are 𝐿 (27) 𝐾= 𝑚 √ 𝐿𝑝 𝐿𝑠 𝐿𝑚𝑎𝑔 = 𝐾 2 𝐿𝑝 𝐿𝑙𝑒𝑎𝑘 = 𝐿𝑝 (1 − 𝐾 2 ) 𝑁𝑝 𝑁𝑠 = 𝐿𝑠 𝐿𝑚 (28) (29) (30) Figures 15(a) to 15(c) show the variations of the primary self-inductance, secondary self-inductance and mutual inductance, respectively, with the bending angle. The inductance variations of the inductors and transformers are found to be within 5 % of their respective inductance values obtained when the winding is flat. Figure 15(d) and 15(e) show the leakage inductance and magnetizing inductance respectively. The leakage inductance and magnetizing inductance change could affect resonant frequency in resonant power converter. Figure 15(f) shows the turns ratio change, which is within 0.5 %. The changing of the turns ratio affects the voltage gain in the power converter. These changes should be handled by the feedback controller in the power converter. where Lmag is the magnetizing inductance, Lleak is the leakage 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 IV. EXPERIMENTAL RESULT ON BENDABLE CONVERTER 7 Fig. 17. Simplify Buck Converter circuit. Two practical 26 V to 5 V, 500 mA (USB 2.0 standard) converters are built to verify the bendable inductor and transformer model. Seven Li Polymer batteries each with 3.7 V are used in series as the power source. A buck converter is built with the bendable inductor and an LLC resonant converter is built with the bendable transformer. The inductor in the buck converter is used as the primary winding of the transformer in the LLC converter for better comparison. Figure 16 shows the LLC resonant converter prototype used in this paper. Fig. 18. Buck converter waveforms (Ch1: Switching node; Ch2: Inductor current). 5.35 (a). LLC converter with bendable transformer. 5.3 Vout (V) 5.25 5.2 5.15 5.1 5.05 5 0 1 2 3 Bending angle (rad) Fig. 19. Vout against bending angle (Buck converter). Fig. 16. Bendable transformer prototype. A. A Buck Converter with Bendable Inductor A buck converter with bendable inductor L4 is. The design of the prototype is based on the bendable inductor and transformer model established in this paper. A simplified circuit is shown in Fig. 17.This buck converter is designed to operate at critical mode at full load. The switching frequency of the buck converter is 175 kHz. Figure 18 shows the waveform of the buck converter. It shows that the buck converter is operating at critical mode. Figure 19 shows the output voltage of the buck converter against the different bending angle at fixed duty cycle. The output voltage increases by 6 % at bending angle equal to π B. LLC Resonant Converter with Bendable Transformer An LLC converter is built to verify the bendable transformer model. Non-resonant converter topology usually requires high switching frequency for transformer with low magnetizing inductance. Also, the leakage inductance has to be minimized for high performance. However, bendable transformer has low magnetizing inductance and high leakage inductance. The LLC resonant converter topology can operate at a lower switching frequency with low magnetizing inductance transformer. Also, the inherent leakage inductance of the bendable transformer is used as the resonant inductance in the LLC resonant converter. Fig. 20. Simplify LLC Converter circuit. The design of the prototype is based on the bendable transformer model established in this paper. A simplified circuit with equivalent bendable transformer model is shown in 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 8 Fig. 20. Figure 21 shows the measured waveforms of the prototype and Fig. 22 shows the simulation waveforms. VSw is the voltage input of the resonant tank. VSw shows the switching frequency of the converter. IL is the primary resonant tank current. Figures 21 and 22 show that the experimental results match well with the simulation. Fig. 21. Prototype waveforms at flat (Ch1: VSw; Ch2: Id2, Ch3: Id1; Ch4: IL). Vout (V) Fig. 23. Prototype waveforms when bent (Ch1: VSw; Ch2: Id2, Ch3: Id1; Ch4: IL). 5.1 5.09 5.08 5.07 5.06 5.05 5.04 5.03 5.02 5.01 5 4.99 0 1 2 3 Bending angle (rad) Fig. 24. Vout against bending angle at fixed frequency (LLC converter). Fig. 22. Simulation waveforms (Top: VSw; Middle: IL; Bottom: Id1, Id2). Figure 23 shows the measured waveforms of the prototype with bending angle equals to π at the same switching frequency. The calculated resonant frequency of the prototype is 134 kHz at the flat and 141 kHz at the bending angle equal to π. The resonant frequency drifts by 5 % when the transformer is bent. Although this frequency drifted is not obvious in the waveform, the output voltage change is considerable. Figure 24 shows the output voltage of the prototype against different bending angles at fixed frequency of 134 kHz. The output voltage increases by 1.78 % at bending angle equal to π. The gain of the LLC resonant converter is fixed by resonant tank parameter and switching frequency. In a non-bendable LLC resonant converter, the resonant tank parameter is fixed and the output voltage is controlled by the switching frequency. However, the resonant tank parameter of the bendable LLC resonant converter changes with the bending angle. This change should be handled by appropriate feedback control in the converter. C. Buck Converter with Bendable Inductor v.s. LLC converter with Bendable Transformer Figure 25 shows the efficiency of the buck converter and LLC converter against the loading. For better comparison, the buck converter inductor has the same inductance as the primary winding in the LLC converter. The energy efficiency of the buck converter at 26 V input and the output of 5 V and 500 mA is 43 %. The energy efficiency of the LLC prototype at the same power rating is 63.4 %. The energy loss is mainly caused by losses in the bendable transformer and inductor. The winding traces of the bendable transformer and inductor in the prototypes are very thin. The efficiency of the LLC converter increases when the loading is increased. This is because when the load increases, the LLC converter frequency decreases to maintain regulation. This moves the operation point closer to the resonant frequency. On the other hand, the buck converter efficiency decreases with load. It shows that conduction loss dominates. However, they have comparable efficiencies and LLC converter works better at high load. 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 9 70% Efficiency 60% [5] 50% Buck Converter 40% 30% LLC converter 20% [6] 10% 0% 0.1 0.2 0.3 0.4 0.5 Output Current (A) [7] Fig. 25. Efficiency against output current. V. CONCLUSION In this paper, two milestones are established. A model for bendable inductor and transformer model based on PEEC theory is established and bendable buck converter and LLC resonant converter are built. The bendable transformer is made by printing thin copper tracks on a flexible substrate. A model is introduced such that the conductor of each winding is represented by a set of segment-current and segment-position vectors. A three-step procedure to turn a flat winding model into a bent model is presented. The bendable transformer model shows that both mutual inductance and self-inductance decrease when the transformer is bent by a reasonable amount. The leakage inductance and magnetizing inductance variation are small in this structure as compared with the flat transformer inductance. Based on the inductor and bendable transformer model, a buck converter with bendable inductor and an LLC resonant converter with bendable transformer are built successfully. Both converters have the same power rating of 5 V and 500 mA. The investigation shows that the leakage inductances and the magnetizing inductance can be incorporated as part of the resonant circuit. 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Ho ( S' 11) was born in Hong Kong, in 1985.He received the B.Eng degree in electrical engineering from the University of Hong Kong, Hong Kong SAR, in 2010 and the M.Phil degree in power electronics form the University of Hong Kong, in 2013. He is currently working toward the Ph.D. degree in the Department of Electrical and Electronic Engineering, The University of Hong Kong. Cheng Zhang(S' 13) was born in China, in 1990. He received the B.Eng. degree with first class honors in electronic and communication engineering from the City University of Hong Kong, Kowloon, Hong Kong SAR, in 2012, and is currently working toward the Ph.D. degree in the Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam, Hong Kong. His current research interests include designs and optimizations for wireless power transfer applications. Bryan M.H. Pong (M'84-SM'96) was born in Hong Kong. He received his BSc degree in Electronic and Electrical Engineering from the University of Birmingham in the U.K. in 1983. In 1987 he received his PhD degree in Power Electronics from Cambridge University, also in the U.K. He was a principal engineer and engineering manager at ASTEC which has become Artesyn Embedded Technologies today. Now he is an Associate Professor at the Electrical & Electronic Engineering Department of Hong Kong University of. His research interests focus on switching power supply. In particularon topics including synchronous rectification, EMI issues, design optimization of power converters, planar and bendable power converters. He has also co-invented a number of patents. S. Y. Ron Hui (F’03) received the Ph.D. degree from Imperial College London, London, U.K., in 1987. He is currently the Chair Professor of power electronics at The University of Hong Kong (HKU), Pokfulam, Hong Kong, and Imperial College London. At HKU, he holds the Philip Wong Wilson Wong Endowed Professorship in electrical engineering. He has published more than 200 technical papers, including more than 170 refereed journal publications and book chapters. More than 50 of his patents have been adopted by industry. Dr. Hui is an Associate Editor of the IEEE Transactions on Power Electronics and the IEEE Transactions on Industrial Electronics. Since 2013, he has been an Editor of the IEEE 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2015.2500606, IEEE Transactions on Power Electronics Manuscript ID TPEL-Reg-2015-05-0873.R1 11 Journal of Emerging and Selected Topics in Power Electronics. He has been appointed twice as an IEEE Distinguished Lecturer by the IEEE Power Electronics Society in 2004 and 2006. He served as one of the 18 Administrative Committee members of the IEEE Power Electronics Society and was the Chairman of its Constitution and Bylaws Committee from 2002 to 2010. He received the Excellent Teaching Award in 1998. He won an IEEE Best Paper Award from the IEEE IAS Committee on Production and Applications of Light in 2002, and two IEEE Power Electronics Transactions Prize Paper Awards for his publications on Wireless Battery Charging Platform Technology in 2009 and on LED system theory in 2010. His inventions on wireless charging platform technology underpin key dimensions of Qi, the world's first wireless power standard, with freedom of positioning and localized charging features for wireless charging of consumer electronics. In November 2010, he received the IEEE Rudolf Chope R&D Award from the IEEE Industrial Electronics Society, the IET Achievement Medal (The Crompton Medal) and was elected to the Fellowship of the Australian Academy of Technological Sciences & Engineering. Appendix I CORELESS PCB TRANSFORMER SPECIFICATIONS First Group Transformer (same turns ratio): Tx1 Tx2 Primary turns: 16T, 1 layer (L1) 18T, 1 layer (L2) Secondary turns: 16T, 1 layer 18T, 1 layer Primary outer rectangle dimension: Secondary outer rectangle dimension: 100 mm × 40.25 mm 100 mm × 40.25 mm Conductor cross section dimension: 0.5 mm × 0.01735 mm (0.5 oz) 0.5 mm 0.1 mm Distance between conductors Distance between primary and secondary layer: Tx3 20T, 1 layer (L3) 20T, 1 layer First Group Transformer (different turns ratio) : Tx4 Tx5 Tx6 Primary turns: 16T. 1 layer 16T, 1 layer 18T, 1 layer Secondary turns: 20T, 1 layer 18T, 1 layer 20T, 1 layer 100 mm × 40.25 mm Primary outer rectangle dimension: Secondary outer rectangle dimension: 100 mm × 40.25 mm Conductor cross section dimension: 0.5 mm × 0.01735 mm (0.5 oz) Distance between conductors 0.5 mm Distance between primary and secondary layer: 0.1 mm Second Group Transformer (2 layer, same turns ratio ): Primary turns: Tx7 Tx8 Tx9 22T, 2 layers, 11 turns per layer (L4) 22T, 2 layers, 11 turns per layer 26 (2 layers, 13 turns per layer) Primary outer rectangle dimension: 24T, 2 layers, 12 turns per layer (L5) 24T, 2 layers, 12 turns per layer) 65 mm × 26 mm Secondary outer rectangle dimension: Conductor cross section dimension: 65 mm × 26 mm 5 mm × 0.01735 mm (0.5 oz) Distance between conductors 0.5 mm Distance between primary and secondary layer: 0.1 mm Secondary turns: 26 (2 layers, 13 turns per layer) Second Group Transformer (2 layer, different turns ratio ): Tx10 Tx11 Tx12 Primary turns: 22 (2 layers, 11 turns per layer) 24T, 2 layers, 12 turns per layer Secondary turns: 26 (2 layers, 12 turns per layer) 22T, 2 layers, 11 turns per layer (L6) 24T, 2 layers, 13 turns per layer Primary outer rectangle dimension: 26T, 2 layers, 16 turns per layer 65 mm × 26 mm Secondary outer rectangle dimension: 65 mm × 26 mm Conductor cross section dimension: 5 mm × 0.01735 mm (0.5 oz) Distance between conductors 0.5 mm Distance between primary and secondary layer: 0.1 mm 0885-8993 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.