Flexible & Planar Implantable Resonant Coils for Wireless Power Transfer using Inkjet Masking Technique Ahmad Usman, Jo Bito, and Manos M. Tentzeris School of Electrical and Computer Engineering Georgia Institute of Technology, Atlanta, GA, USA ahmadusman@gatech.edu Abstract—In this paper, we present the design, fabrication and characterization of implantable coils, operating at 13.56 MHz ISM band for biomedical applications. Rogers RO 4003C substrate was used for the prototype of the implantable coil while Rogers RO 3850 flexible substrate was used for the external transmitter coil. The Inkjet masking technique was used for the patterning the planar coil on the flexible sub- strate. Wireless power transfer efficiency measurements were conducted in free space and water environments, varying the operating distance between the prototype coils from 5mm to 20mm, featuring transfer efficiencies upto 55% and 35% ,respectively. I. I NTRODUCTION The ability to fabricate biocompatible micro and nano scale devices has made biomedical implant devices a reality now-a-days. One of the key challenges associated with these implants is the long-term operational power availability. Earlier implants employed batteries to power themselves, which needed replacement involving invasive surgical procedures. One of the few earliest designs for wireless powering of implant devices were proposed in [1] and [2]. These designs employed inductively coupled implant coils to receive power from transmitter coils in close vicinity. The size and volume of these coils were major constraints for practical bio-implant applications. The amount of powered delivered was limited, while these devices also suffered from bio-compatibility issues, espe- cially in applications featuring very strict size constraints [3]. Various optimized Litz Wire coils and Printed Spiral Coils (PSCs) has been used to demonstrate wireless power transfer for implant applications as reported in [4] and [5]. The proposed optimized receiver and transmitter coils in [4] and [5] were fabricated on the same material substrates and involved the same fabrication technique. In this paper, we present a proof-of-concept demonstra- tion of wireless power transfer for implant applications using two magnetically coupled coils, fabricated on differ- ent substrates with each employing a different fabrication approach. We fabricated implantable receiver PSC on Rogers RO-4003C substrate using the milling process and a flexible transmitter PSC on Rogers Ultraslam 3850TM substrate, patterned using the inkjet masking technique. Section II gives a brief overview of the analytical modeling of the coils while Section III gives an overview of the parameters selected for the design along with simulation and measurement results. Section IV gives the conclusion of the work. II. ANALYTICAL MODELLING OF COIL PROTOTYPES A. Inductance Calculation For the calculation of the inductance (L) of the prototype coils, we employed the relationship given in [6]. L = μn 2 d avg b 1 2 [ln( b 2 γ )+ b 3 γ + b 4 γ 2 )] (1) where d avg = do+di 2 is the average diameter of the coil , γ = do-di do+di is the coil fill factor, n is the total number of turns, μ 0 is the relative permeability of air, while d o and d i are the outer and inner diameter of the coil. The values of b 1 , b 2 , b 3 and b 4 are 1.27 , 2.07, 0.18 and 0.13 for square shaped printed spiral coils [6]. B. Mutual Inductance and Coupling Coefficient Calcula- tion The mutual inductance between the coils can be calcu- lated using following relationship [4]. M = πμ 0 √ ab  ∞ 0 J 1 (x  a b )J 1 (x  b a )J 0 ( xζ √ ab )e ( -dx √ ab ) dx (2) where J 0 and J 1 are the bessel functions of first and second order respectively, ζ is lateral misalignment, d is the axial distance between the coils, and a and b are the outer radius of the implant and the flexible transmitter coil, respectively [4]. The coupling coefficient k can be calculated as k = M √ LtLt where L t and L r are the inductance of the trans- mitter and the receiver coils, respectively [4]. C. Resistance Calculation The overall resistance (R) of a printed spiral trace can be calculated by [7] R = R DC (1 + t c 2δ(1 + tc wc ) ) (3)