Using the variable width in a planar inductor on Kapton for optimizing its performance

Turkish Journal of Electrical Engineering & Computer Sciences http://journals.tubitak.gov.tr/elektrik/ Turk J Elec Eng & Comp Sci (2017) 25: 3798 – 3810 c TÜBİTAK ⃝ doi:10.3906/elk-1606-343 Research Article Using the variable width in a planar inductor on Kapton for optimizing its performance Hayet KHARBOUCH1,∗, Azzedine HAMID1 , Thierry LEBEY2 , Vincent BLEY2 , Léon HAVEZ2 , Celine COMBETTE2 1 Department of Electrical Engineering, Faculty of Electrical Engineering, University of Sciences and Technology of Oran, Oran, Algeria 2 Paul Sabatier University, Toulouse, France Received: 21.06.2016 • Accepted/Published Online: 25.02.2017 • Final Version: 05.10.2017 Abstract: In this paper, we examine the design of planar inductors and consider an expansion of the conductor to reduce its resistance. An increase in the number of turns increases the proximity effect, capacitive coupling, and skin effect. The resulting effect will translate into an increase in the area occupied by the inductor and a decrease in the inductors’ performances. In order to solve such difficulties, an alternative approach is to design tapered inductors. For the same electrical and geometrical characteristics, a tapered inductor occupies a larger area than a standard inductor. Our approach consists of designing a new concept regarding tapered planar inductors that occupy the same surface and maintain the same electrical characteristics as the standard planar inductor regarding the following topologies: circular, hexagonal, and square. The results obtained show that impedance is more important in the case of the tapered inductor. Higher impedance implies smaller current and hence smaller parasitic effects of the capacitance series and proximity effect. Key words: Passive components, integration, tapered planar inductor, ferrite 1. Introduction Nowadays, miniaturization of active and passive electronic components has become a wide research area [1]. It is an increasing trend to manufacture electronic equipment and accessories that represent high consumer products such as hard drives, mobile phones, and automotive industry such as avionics and ships. The aim of this interest in miniaturization is, on the one hand, to increase the number of functionalities on the same chip and, on the other hand, to reduce the cost by putting in place a system of mass production [2,3]. In a number of cases, hybrid systems offer facilities for volume reduction. However, passive components represent a holdback to miniaturization. Nowadays, inductance is a key component in the electronics arena and represents an important factor for its progress. Several models have been considered to improve its characteristics [4–7]. The model of tapered inductors improves the performance of the planar inductor. Indeed, in this specific model, we need to change the conductor’s width in order to reduce its resistance [8,9]. For a standard inductor in the absence of a magnetic circuit, the concentration of the magnetic field at the centre of the inductor generates a worse distribution of the current within the central inductor than for the peripheral inductor. For a tapered inductor, the distribution of the current in each turn of the spiral is homogeneous. This makes it possible to exploit the copper section optimally. It is evident that the current density is higher for the inner turns ∗ Correspondence: 3798 KHARBOUCH et al./Turk J Elec Eng & Comp Sci than for the outer turns, which could cause greater heating in the center; however, the resistance of each turn remains in accordance with the desired design [10]. In this work, we will focus on the design, manufacture, and characterization of planar inductor spirals on a magnetic layer. We consider two types of inductors: standard and tapered inductors. The second type of inductor is characterized by an increasing track width according to the radius. This approach is of particular interest to the inductor, as the total DC resistance will be effectively reduced to a given number of turns. Indeed, on the one hand, this will compensate for the variation of the resistance linked to the increase in conductor width of the inductor [11]. On the other hand, it will reduce the proximity and capacitive effects between turns. The gain is less perceptible because we have considered the same occupied space for all prototypes of inductors studied. This study has targeted the following topologies: circular, square, and hexagonal, which are represented in Figure 1. The parameters that have been taken into account in this study are topology, turns’ width, interturn distance, and thickness of the conductor [12,13]. The production and characterization took place in the Laboratory on Plasma and Conversion of Energy-UMR5213, Team MDCE, Toulouse, France. Figure 1. Different studied topologies: (a) circular, (b) hexagonal, and (c) square. 2. Characteristics of planar inductors In this section, we present the geometrical and electrical characteristics of standard and tapered inductors. 2.1. Geometrical parameters In Figure 2, we present a 3D representation of planar inductors made in this study. Our strategy is to keep the same area occupied by the inductors and calculate the electrical parameters in particular values of the series inductance and resistance. The various stages of implementation are detailed in Section 3. For a given shape, an inductor is specified by the number of turns n , turn width w , turn spacing s , thickness t of the conductor, total conductor length lt , average diameter davg , outer and inner diameters dout and din , as shown in Figure 1 [14]. The dimensions of the different topologies are as follows: dout = 10 mm , din = 1 mm , and n = 3. For a tapered inductor, w1 , w2 , and w3 are the widths of winding of each turn, as shown in Figure 2. The results of geometric parameters included in Table 1 are obtained for conductor material copper (Cu) and magnetic material N87. We note that the total lengths vary according to the topology. The square spiral has the largest value, the smallest circular spiral, hence the interest in calculating the value of the resistance for each topology. The total length of the inductor can be expressed as lt =ndavg N tan (π/N ) (1) 3799 KHARBOUCH et al./Turk J Elec Eng & Comp Sci Figure 2. 3D representation of planar inductors realized circular, hexagonal, and square. Table 1. Geometric parameters for standard and tapered inductors. Topology Circular Hexagonal Square lt (cm) 4.7 5.2 6.0 Tapered inductors w1/w2/w3 (mm) 0.3/ 0.6/ 0.9 0.3/0.6/ 0.9 0.3 /0.6/0.9 t (µm) 35 35 35 Standard inductors w (mm) 0.9 0.9 0.9 For a square inductor, N = 4 and for a hexagonal inductor, N = 6 . N is a big number for the circular inductor, where we get the expressions of the total length lt Eq. (2) [15]. lt = πN davg davg = (2) dout +din 2 (3) 2.2. Simplified physical model of a inductor on ferrite The model includes the series inductance Ls , series resistance (...truncated)