Submit manuscript...
International Journal of
eISSN: 2573-2838

Biosensors & Bioelectronics

Research Article Volume 2 Issue 2

Wireless power transfer (WPT) using strongly coupled magnetic resonance (SCMR) at 5.8 GHz for biosensors applications: a feasibility study by electromagnetic (EM) simulations

Donald YC Lie,1,2 BT Nukala,1 J Tsay,1 J Lopez,1 Tam Q Nguyen1,2

1Department of Electrical and Computer Engineering, Texas Tech University, USA
2Department of Surgerym Texas Tech University Health Sciences Centerm USA

Correspondence: Donald YC Lie, Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, TX, USA

Received: December 01, 2016 | Published: March 24, 2017

Citation: Lie D, Nukala BT, Tsay J, et al. Wireless power transfer (WPT) using strongly coupled magnetic resonance (SCMR) at 5.8 GHz for biosensors applications: a feasibility study by electromagnetic (EM) simulations. Int J Biosen Bioelectron. 2017;2(2):65–71. DOI: 10.15406/ijbsbe.2017.02.00019

Download PDF

Abstract

We report here a detailed 3-dimensional (3-D) electromagnetic (EM) simulation study on the feasibility of Wireless Power Transfer (WPT) using the strongly coupled magnetic resonance (SCMR) effect at 5.8 GHz for potential μm-scale biosensors applications. The tiny 110 μm x110 μm planar aluminum inductor coil is built on the silicon substrate as our miniaturized receiver coil, which has been designed and simulated by 3-D EM simulations and its EM data is consistent with the measured data from an advanced IBM/Global Foundries' 0.18 μm complimentary metal-oxide-semiconductor (CMOS) silicon-on-insulator (SOI) process technology. By using small relay coils for an optimized four-coil WPT system to reach the SCMR condition, EM simulations show that one can increase the wireless power transfer between the transmitter coil to the miniature receiver coil by about 300% to 400% over the traditional 2-coil inductive resonant system at the 5.8 GHz ISM band, making SCMR quite attractive for implantable bioelectronics and biosensors applications, such as on cochlear implants, capsule endoscopy and pacemakers. Our study features the smallest receiver coil (about 330 times smaller in area) than the previously reported smallest receiver coil used in inductive coupling for wireless power transfer.

Keywords: 3-d electromagnetic simulation; 5.8 ghz ism (industrial, scientific, and medical radio) band; Inductive power coupling; Resonant inductive coupling; Strongly coupled magnetic resonance; Wireless power transfer

Abbreviations

WPT: Wireless Power Transfer; SCMR: Strongly Coupled Magnetic Resonance; CMOS: Complimentary Metal-Oxide-Semiconductor; SOI: Silicon-on-Insulator; RF: Radio-Frequency; SCMR: Strongly Coupled Magnetic Resonance; GHz: Sub-Gigahertz; ISM: Industrial Scientific and Medical; CMOS: Complimentary Metal-Oxide-Semiconductor; SOI: Silicon-On-Insulator

Introduction

Inductive coupling has been studied for decades to realize efficient wireless power transfer (WPT). Typically the radio-frequency (RF) source drives a transmitting (TX) primary coil, creating a sinusoidally time-varying magnetic field, which induces a voltage across the terminals of a receiving (RX) secondary coil, and thus power is wirelessly transferred to the load. Two-coil inductive coupling is now routinely used to power up High-Frequency (HF) RF ID (Identification Card) tags and many commercial medical implantable devices, such as cochlear implants [1-3]. Wireless power transfer can also used in pacemaker where the primary coil is assumed to be on-body, while the secondary coil is assumed to be inside the human body and connected to a battery recharge system [4]. The experimental results shows that the power transfer efficiency is greater than 36.6 % by using WPT on the optimal coil configuration for capsule endoscopy [5]. Integrated implantable hearing devices such as cochlear implant can also benefit from efficient wireless power coupling between first and second coils [1,6]. Wireless powering of implantable devices can remove the need for bulky batteries, which may eliminate a serious health risk if periodic surgeries were to be needed to replace them. A common technique for increasing the voltage received by the load is to add a parallel capacitor to the secondary RX coil to form a resonant circuit at the operating frequency [3]. In 2007, Soljacic M et al. [3] experimentally demonstrated efficient non-radiative wireless power transfer over distances up to 8 times the radius of the coils using a 4-coil strongly coupled magnetic resonance (SCMR) system, and transferred 60 watts with ∼40% efficiency over distances in excess of 2 meters at around 10 MHz [7]. One would, therefore, expect a well-designed multi-coils inductive coupling WPT system with SCMR can extend the power transfer distance over the 2-coil system with the same power, at least at low MHz range [7]. Zhang et al. [8] & Kim et al. [9] analyzed the transfer characteristics of the WPT system architectures with multi-relay coils based on the circuit mode theory. Kim et al. [9] pointed out that either a coaxially arranged relay coil or a perpendicularly arranged relay coil can considerably improve the system power transfer efficiency. Zhong et al. [10] also analyzed the power transfer characteristics of multi-relay coils system using the circuit mode theory, where the coils are arranged coaxially, non-coaxially and circularly.

Recently, wireless power transfer is also being used at sub-gigahertz (GHz) frequency to capsule endoscope where compact self-resonant antennas are designed to realize the transcutaneous power transfer [11]. It is commonly believed that efficient WPT to implantable devices require RF transmission frequency in the low MHz range to avoid excess losses in tissues. Therefore, antenna sizes above a few cm are required, making implantable devices with integrated antennas inherently large and cannot be miniaturized further. However, recently, Poon A et al. [12] from Stanford University have convincingly shown that when the receiver dimension is much smaller than its depth inside the body, there exists an optimal frequency for WPT and this frequency is much higher and in the giga-Hertz (GHz) range [12]. In their work reported in [12] the receiver coil size is 2mm x 2mm on each side and it is a square copper loop, similar to the size of another impressive miniature RX coil design of 2mm x 2 mm by the same Stanford group that achieved a wireless power coupling of -33dB, very close to the theoretical WPT limit they calculated as at -31 dB [13]. This "Midfield" WPT proposed by [8] claims to enable miniature implantable sensors with millimeter sized coils at nearly any location in the body without batteries [14]. The same group has also shown by EM simulations that different body tissues may have an optimal frequency greater than 4 GHz for optimal WPT. Therefore, by considering higher GHz frequency range will reduce the implanted coil size, we have chosen the 5.8 GHz Industrial, Scientific and Medical (ISM) band frequency for our WPT system design for this study. In this work, however, we propose an even more miniaturized WPT system with a receiver coil of only 110 x 110 mm in size, which is ~330x smaller in area than the previously reported 2mm x 2mm RX coil by the Stanford's group. We kept the RX-TX distance at 1 mm to mimic the near-field scenario of an implantable device right underneath the skin. Note this distance may also be increased from 1 mm to 1 cm, depending upon the application of WPT for different medical devices.

In addition, we investigate a special case of inductive coupling, namely the 4-coil SCMR as proposed in [7,15] to improve WPT with two relay coils sandwiched between the TX-RX coils. In our previous work [15] we have achieved -26 dB power coupling for the 4-coil system with a miniature RX coil. We report here a more optimized 4-coil system that has achieved an impressive power coupling of -20.12 dB (i.e., ~ 1% WPT efficiency), which shows a 6-7 dB improvement over the traditional 2-coil system and also our previous work.

Materials and Methods

Two-coil resonant system design

WPT can be achieved by transferring the RF power over an air gap using coupled TX-RX coils in a resonant circuit. When two coils are tuned to be resonating at the same frequency, a highly efficient transfer of power can take place. The most common resonant transfer circuit consists of a series tuned transmitting circuit and a parallel tuned receiving circuit (i.e., the series-parallel system) as shown in Figure 1, where the on-chip load resistance of R4 = 232 Ω and R3 = 0.5 Ω (representing the minute trace resistance when the tiny receiver coil is placed on a silicon substrate as part of the integrated circuit, or a "chip") connect to an on-chip RX tuning cap C2. The system operates at the 5.8 GHz ISM band in our analysis. The designed two-coil system has a high Q TX coil of 3 mm in diameter, with 28 mm thick and 40 mm wide Cu metal, placed on the 1 mm thick FR4 substrate. The WPT efficiency depends on the coupling coefficient (k) between the two inductors and their quality factors (Q). Here k is dependent on the distance between the coils, the ratio of the sizes of the coils, the shape of each coil and the angle between them. The inductance L and quality factor Q simulations of the TX coil and the RX coil are performed in ANSOFT HFSS 3-D electromagnetic (EM) simulator by taking the silicon substrate model into account, which is similar to the substrate model of IBM/Global Foundries' 7RFSOI 0.18 mm CMOS SOI process that has high resistive silicon substrate of 50 µm in thickness. Here the RX coil is an on-chip planar inductor design mimicking the 7RFSOI design-kit inductor design on a lossy high resistivity silicon substrate with SOI to facilitate miniaturization in size and thickness for applications such as in cochlear implants. The L and Q values are extracted from the EM simulated Y-parameters using the equation 1 below [15,17]:

L= IM( 4 Y 11 Y 12 Y 21 + Y 22 ) ω Q= IM( 4 Y 11 Y 12 Y 21 + Y 22 ) RE( 4 Y 11 Y 12 Y 21 + Y 22 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOabaeqabaqcfaOaam itaiabg2da9maalaaabaGaamysaiaad2eacaGGOaWaaSaaaeaacaaI 0aaabaGaamywaSWaaSbaaKqbagaajugWaiaaigdacaaIXaaajuaGbe aacqGHsislcaWGzbWaaSbaaKqbGeaacaaIXaGaaGOmaaqcfayabaGa eyOeI0IaamywamaaBaaajuaibaGaaGOmaiaaigdaaKqbagqaaiabgU caRiaadMfadaWgaaqcfasaaiaaikdacaaIYaaajuaGbeaaaaGaaiyk aaqaaiabeM8a3baaaOqaaKqbakaadgfacqGH9aqpdaWcaaqaaiaadM eacaWGnbGaaiikamaalaaabaGaaGinaaqaaiaadMfadaWgaaqcfasa aiaaigdacaaIXaaabeaajuaGcqGHsislcaWGzbWaaSbaaKqbGeaaca aIXaGaaGOmaaqcfayabaGaeyOeI0IaamywamaaBaaajuaibaGaaGOm aiaaigdaaKqbagqaaiabgUcaRiaadMfadaWgaaqcfasaaiaaikdaca aIYaaajuaGbeaaaaGaaiykaaqaaiaadkfacaWGfbGaaiikamaalaaa baGaaGinaaqaaiaadMfadaWgaaqcfasaaiaaigdacaaIXaaabeaaju aGcqGHsislcaWGzbWaaSbaaKqbGeaacaaIXaGaaGOmaaqabaqcfaOa eyOeI0IaamywamaaBaaajuaibaGaaGOmaiaaigdaaeqaaKqbakabgU caRiaadMfadaWgaaqcfasaaiaaikdacaaIYaaabeaaaaqcfaOaaiyk aaaaaaaa@7833@ (1)

Figure 1: Series-parallel circuit model for our traditional 2-coil wireless power transfer (WPT) system.

where ω is the resonant frequency and IM and RE are the imaginary and real parts of the Y-parameter values, respectively. The simulated inductance of the TX coil design is 6.82 nH with a high Q of 67.2, as it can be fabricated off-chip with these feasible values. The RX on-chip planar inductor coil is on the realistic lossy silicon substrate and the complete stack design for the RX coil in IBM/GF 7RFSOI process is shown in Figure 2. The tiny 110 μm x110 μm planar aluminum inductor coil is built on the silicon substrate as our miniaturized receiver coil, which has been designed and simulated by 3-D EM simulations and its simulated EM data is found to be consistent when compared against the measured data from an advanced IBM/Global Foundries' 0.18 mm complimentary metal-oxide-semiconductor (CMOS) silicon-on-insulator (SOI) process technology. Series-parallel compensation architecture is chosen for the 2-coil resonant system used here. The circuit R’s and C’s are calculated knowing L’s and Q’s as shown from equations (2)-(7) [16]:

C1= 1 L1× ω 2   MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaam4qaiaaigdacqGH9aqpdaWcaaWdaeaapeGaaGymaaWdaeaa peGaamitaiaaigdacqGHxdaTcqaHjpWDpaWaaWbaaeqabaWdbiaaik daaaaaaiaacckaaaa@41BD@ (2)

C 2 = 1 L 2 × ω 2   MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaam4qamaaBaaajuaibaGaaGOmaaqabaqcfaOaeyypa0ZaaSaa a8aabaWdbiaaigdaa8aabaWdbiaadYeadaahaaqabKqbGeaacaaIYa aaaKqbakabgEna0kabeM8a39aadaahaaqabKqbGeaapeGaaGOmaaaa aaqcfaOaaiiOaaaa@4436@ (3)

RS=R1= L1/C1 /Q1  MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaamOuaiaadofacqGH9aqpcaWGsbGaaGymaiabg2da9maakaaa paqaa8qacaWGmbGaaGymaiaac+cacaWGdbGaaGymaaqabaGaai4lai aadgfacaaIXaGaaiiOaaaa@4340@ (4)

R2= L2/C2 /Q2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaamOuaiaaikdacqGH9aqpdaGcaaWdaeaapeGaamitaiaaikda caGGVaGaam4qaiaaikdaaeqaaiaac+cacaWGrbGaaGOmaaaa@3F6B@ (5)

R4= L2/C2 ×Q2  MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaamOuaiaaisdacqGH9aqpdaGcaaWdaeaapeGaamitaiaaikda caGGVaGaam4qaiaaikdaaeqaaiabgEna0kaadgfacaaIYaGaaiiOaa aa@41F5@ (6)

K 12 = M 12 × L1×L2    MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaam4sa8aadaWgaaqcfasaa8qacaaIXaGaaGOmaaWdaeqaaKqb a+qacqGH9aqpcaWGnbWdamaaBaaajuaibaWdbiaaigdacaaIYaaapa qabaqcfa4dbiabgEna0oaakaaapaqaa8qacaWGmbGaaGymaiabgEna 0kaadYeacaaIYaGaaiiOaaqabaGaaiiOaaaa@4824@ (7)

Figure 2: On-chip coil (RX coil) metal stack designed in IBM/GF 7RFSOI 0.18 μm SOI CMOS technology.

On the TX side, Vs in Figure 1 functions as an AC source. In a resonant system with high Q, this is a narrow band system with negligible high order harmonics under steady state. From [15,16], the input impedance can be easily shown as:

Z in =Rs+jωL1+ 1 jωC1 +R1+ Z re MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaamOwa8aadaWgaaqcfasaa8qacaWGPbGaamOBaaWdaeqaaKqb a+qacqGH9aqpcaWGsbGaam4CaiabgUcaRiaadQgacqaHjpWDcaWGmb GaaGymaiabgUcaRmaalaaapaqaa8qacaaIXaaapaqaa8qacaWGQbGa eqyYdCNaam4qaiaaigdaaaGaey4kaSIaamOuaiaaigdacqGHRaWkca WGAbWdamaaBaaajuaibaWdbiaadkhacaWGLbaapaqabaaaaa@4F31@ (8)

Where Zre is the reflected impedance to the TX side from the RX side. Taking mutual inductance model into account, the reflected impedance in a series-parallel compensation WPT system is given by equations (9)-(10):

Z re =  ω 2 M 12 2 jωL2+R2+[ 1 jωC2 +R3 ]R4   MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaamOwa8aadaWgaaqcfasaa8qacaWGYbGaamyzaaqcfa4daeqa a8qacqGH9aqpcaGGGcWaaSaaa8aabaWdbiabeM8a39aadaahaaqabK qbGeaapeGaaGOmaaaajuaGcaWGnbWdamaaDaaajuaibaWdbiaaigda caaIYaaapaqaa8qacaaIYaaaaaqcfa4daeaapeGaamOAaiabeM8a3j aadYeacaaIYaGaey4kaSIaamOuaiaaikdacqGHRaWkdaWadaWdaeaa peWaaSaaa8aabaWdbiaaigdaa8aabaWdbiaadQgacqaHjpWDcaWGdb GaaGOmaaaacqGHRaWkcaWGsbGaaG4maaGaay5waiaaw2faaiaadkfa caaI0aaaaiaacckaaaa@58BC@ (9)

 = ω 2 M 12 2 jωL2+R2+ R4×[ 1 jωC2 +R3 ] 1 jωC2 +R3+R4                          MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaaiiOaiabg2da9maalaaapaqaa8qacqaHjpWDpaWaaWbaaKqb GeqabaWdbiaaikdaaaqcfaOaamyta8aadaqhaaqcfasaa8qacaaIXa GaaGOmaaWdaeaapeGaaGOmaaaaaKqba+aabaWdbiaadQgacqaHjpWD caWGmbGaaGOmaiabgUcaRiaadkfacaaIYaGaey4kaSYaaSaaa8aaba WdbiaadkfacaaI0aGaey41aq7aamWaa8aabaWdbmaalaaapaqaa8qa caaIXaaapaqaa8qacaWGQbGaeqyYdCNaam4qaiaaikdaaaGaey4kaS IaamOuaiaaiodaaiaawUfacaGLDbaaa8aabaWdbmaalaaapaqaa8qa caaIXaaapaqaa8qacaWGQbGaeqyYdCNaam4qaiaaikdaaaGaey4kaS IaamOuaiaaiodacqGHRaWkcaWGsbGaaGinaaaaaaGaaiiOaiaaccka caGGGcGaaiiOaiaacckacaGGGcGaaiiOaiaacckacaGGGcGaaiiOai aacckacaGGGcGaaiiOaiaacckacaGGGcGaaiiOaiaacckacaGGGcGa aiiOaiaacckacaGGGcGaaiiOaiaacckacaGGGcaaaa@7BB8@ (10)

Therefore, the power transferred from the TX side to the RX side with a load of 232 Ω is:

P=Re{ Z re }. I 1 2   MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaamiuaiabg2da9iGackfacaGGLbWaaiWaa8aabaWdbiaadQfa paWaaSbaaKqbGeaapeGaamOCaiaadwgaaKqba+aabeaaa8qacaGL7b GaayzFaaGaaiOlaiaadMeapaWaa0baaKqbGeaapeGaaGymaaWdaeaa peGaaGOmaaaajuaGcaGGGcaaaa@4598@ (11)

Where I1 is the current in the primary circuit, i.e., on the transmitter (TX) side.

The series-parallel circuit model for the 2-coil system was simulated in the ANSOFT MAXWELL environment and also co-simulated with the ANSOFT SIMPLORER for the power transfer as shown in Figure 3.

Figure 3: 2-coil coupling optimization in ANSOFT SIMPLORER co-simulated with HFSS/MAXWELL achieved with the tuning capacitors C1 and C2 at a coil-to-coil distance of 1 mm, where the RX coil inductance is 0.64 nH and R2=1.1 Ω; C2=0.110 pF; R3=1.1 Ω; L1=6.82 nH; R4=1.5 Ω; C1=1.05pF; R1=232 Ω (Load); R5=0.5 Ω.

Results and Discussion

Two-coil resonant system em simulation results

The tuning caps for the TX and RX coils help the entire traditional 2-coil WPT system shown in Figures 1 & 3 to resonate at 5.8 GHz. The simulated maximum power coupling of the 2-coil system is shown in Figure 4. Simulated mutual inductance for 2-coil system is M12 = 2.81 pH and the k factor is calculated as    k 12 = M L1.L2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaaiiOaiaacckacaWGRbWdamaaBaaajuaibaWdbiaaigdacaaI Yaaapaqabaqcfa4dbiabg2da9maalaaapaqaa8qacaWGnbaapaqaa8 qadaGcaaWdaeaapeGaamitaiaaigdacaGGUaGaamitaiaaikdaaeqa aaaaaaa@4283@ =0.001305. Parameters of two-coil system are shown in Table 1. The complete EM simulation stack of the 2-coil system is shown in Figure 4. The simulated wireless power coupling from the TX coil to the RX coil is -26.29 dB at the resonance frequency of 5.8 GHz.

The B-field of the designed traditional and optimized 2-coil WPT system was simulated in 3-D EM ANSOFT HFSS and its distribution plot is shown in Figure 6. Most region/space around the 2-coil system is green in color and its intensity ranges from 7.10 x 10-4 T to 8.52 x 10-4 T. We need to point out here that the SCMR condition as proposed in Reference [7] is not only for a 4-coil WPT system; it could also be reached for a traditional 2-coil WPT system if it satisfies the condition for strong magnetic coupling regime. The condition for strong coupling regime is k ' 2 Γ A × Γ B >1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbaoaalaaaba Gaam4AaiaacEcadaahaaqcfasabeaacaaIYaaaaaqcfayaaiabfo5a hnaaBaaajuaibaGaamyqaaqcfayabaGaey41aqRaeu4KdC0aaSbaaK qbGeaacaWGcbaajuaGbeaaaaGaeyOpa4JaaGymaaaa@43AF@ , derived from the coupled mode (CM) theory [7]. The k’ and Γ are the coupling coefficient and the intrinsic decay rate, respectively, and they are functions of frequency from the CM theory as illustrated numerically below [7]:

k'= ωM 2 L1×L2 Γ= ω 2Q MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOabaeqabaqcfaOaam 4AaiaabEcacqGH9aqpdaWcaaqaaiabeM8a3jaab2eaaeaacaqGYaWa aOaaaeaacaqGmbqcfaIaaeymaKqbakabgEna0kaabYeajuaicaqGYa aajuaGbeaaaaaakeaajuaGcqqHtoWrcqGH9aqpdaWcaaqaaiabeM8a 3bqaaiaaikdacaWGrbaaaaaaaa@499D@

k'= ωM 2 L A × L B = 2π×5.8× 10 9 ×2.81× 10 12 2 0.68× 10 9 ×6.82× 10 9 =2.4E7 Γ A = ω 2 Q A = 2π×5.8× 10 9 2×67.2 =2.71E8 Γ B = ω 2 Q B = 2π×5.8× 10 9 2×8.57 =2.12E9 => k ' 2 Γ A × Γ B = (2.4E7) 2 2.71E8×2.12E9 =1.04E3<<1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaajuaGca WGRbGaae4jaiabg2da9maalaaabaGaeqyYdCNaaeytaaqaaiaabkda daGcaaqaaiaabYeadaWgaaqaaKqzadGaaeyqaaqcfayabaGaey41aq RaaeitamaaBaaabaqcLbmacaqGcbaajuaGbeaaaeqaaaaacqGH9aqp daWcaaqaaiaaikdacqaHapaCcqGHxdaTcaaI1aGaaiOlaiaaiIdacq GHxdaTcaaIXaGaaGimaSWaaWbaaKqbagqabaqcLbmacaaI5aaaaKqb akabgEna0kaaikdacaGGUaGaaGioaiaaigdacqGHxdaTcaaIXaGaaG imaSWaaWbaaKqbagqabaqcLbmacqGHsislcaaIXaGaaGOmaaaaaKqb agaacaaIYaWaaOaaaeaacaaIWaGaaiOlaiaaiAdacaaI4aGaey41aq RaaGymaiaaicdalmaaCaaajuaGbeqaaKqzadGaeyOeI0IaaGyoaaaa juaGcqGHxdaTcaaI2aGaaiOlaiaaiIdacaaIYaGaey41aqRaaGymai aaicdadaahaaqabeaajugWaiabgkHiTiaaiMdaaaaajuaGbeaaaaGa eyypa0JaaGOmaiaac6cacaaI0aGaamyraiaaiEdaaeaacqqHtoWrda WgaaqaaKqzadGaamyqaaqcfayabaGaeyypa0ZaaSaaaeaacqaHjpWD aeaacaaIYaGaamyuaSWaaSbaaKqbagaajugWaiaadgeaaKqbagqaaa aacqGH9aqpdaWcaaqaaiaaikdacqaHapaCcqGHxdaTcaaI1aGaaiOl aiaaiIdacqGHxdaTcaaIXaGaaGimamaaCaaabeqaaKqzadGaaGyoaa aaaKqbagaacaaIYaGaey41aqRaaGOnaiaaiEdacaGGUaGaaGOmaaaa cqGH9aqpcaaIYaGaaiOlaiaaiEdacaaIXaGaamyraiaaiIdaaeaacq qHtoWrdaWgaaqcfasaaiaadkeaaKqbagqaaiabg2da9maalaaabaGa eqyYdChabaGaaGOmaiaadgfadaWgaaqaaKqzadGaamOqaaqcfayaba aaaiabg2da9maalaaabaGaaGOmaiabec8aWjabgEna0kaaiwdacaGG UaGaaGioaiabgEna0kaaigdacaaIWaWaaWbaaeqabaqcLbmacaaI5a aaaaqcfayaaiaaikdacqGHxdaTcaaI4aGaaiOlaiaaiwdacaaI3aaa aiabg2da9iaaikdacaGGUaGaaGymaiaaikdacaWGfbGaaGyoaaGcba qcfaOaeyypa0JaeyOpa4ZaaSaaaeaacaWGRbGaai4jamaaCaaabeqa aKqzadGaaGOmaaaaaKqbagaacqqHtoWrdaWgaaqaaKqzadGaamyqaa qcfayabaGaey41aqRaeu4KdC0cdaWgaaqcfayaaKqzadGaamOqaaqc fayabaaaaiabg2da9maalaaabaGaaiikaiaaikdacaGGUaGaaGinai aadweacaaI3aGaaiykamaaCaaabeqaaKqzadGaaGOmaaaaaKqbagaa caaIYaGaaiOlaiaaiEdacaaIXaGaamyraiaaiIdacqGHxdaTcaaIYa GaaiOlaiaaigdacaaIYaGaamyraiaaiMdaaaGaeyypa0JaaGymaiaa c6cacaaIWaGaaGinaiaadweacqGHsislcaaIZaGaeyipaWJaeyipaW JaaGymaaaaaa@F4E8@

Therefore, this 2-coil WPT system is NOT in the strongly magnetic coupled regime 1 mm away at 5.8 GHz.

Figure 4: 2-coil 3-D EM simulated wireless power coupling at a 1 mm TX-RX coil distance.

Parameter (2-Coil System)

TTU Design Probe-Dielet

RX Coil Size # of Turns

110 mm x 110 mm 2 Turns

TX Coil Size (Diameter)# of Turns

3 mm 1 Turn

TX Q simulated

67.2

TX Coil L

6.82 nH

TX Coil C

0.110 pF

RX Coil

On Chip

RC Coil L

0.64 nH

RX Coil C

1.21 pF

RX LC Q

8.57

Spacing of the RX coil to TX coil

1 mm

Coupling Coeff. (k)

0.001305

Coupling Power in dB

-26.29

Table 1:Parameters summary for the designed 2-coil system, where the tiny RX coil is on-chip.

Figure 5: Our 2-coil system EM simulation setup in ANSOFT HFSS/MAXWELL.

Figure 6: 3-D EM simulated B-field of the designed 2-coil WPT system.

Four-coil scmr system design with em simulation results

The circuit for the corresponding 4-coil system design is shown in Figure 7. In this 4-coil system a series-parallel compensation architecture is used at the TX-RX sides similar to the 2-coil resonant system. The 2 relay coils, however, are inserted into the TX-RX coils to improve WPT without changing the TX coil and RX coil at all. Except for C1 and C2 that was also used in the 2-coil WPT system as shown in Figure 1, no tuning caps are used, especially no tuning cap for the 2 relay coils (i.e., the coils #2, #3 in Figure 7 sandwiched between the TX and RX coils). Other circuit component values in the TX and RX coils remain same as in the 2-coil system shown in Figure 1. Some key points we have found from EM simulations of the 4-coil system suggest that the parasitic resistance of the relay coils does not play a key role in this 4-coil system that has reached the SCMR condition, as will be described later. As we will show in this section, theoretical calculations using our EM simulated coupling data also indicates and confirms this optimized 4-coil SCMR system reaches the strongly coupled magnetic resonance regime, while the 2-coil system described earlier does not [7]. Neglecting the internal resistances for relay coils, the reflected impedance to TX side is given by equations (12)-(13):

      R ref 21 = { M 12 2 M 23 2 }× R ref 32    MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaaiiOaiaacckacaGGGcGaaiiOaiaacckacaWGsbWdamaaBaaa juaibaWdbiaadkhacaWGLbGaamOzaiaacckacaaIYaGaeyOKH4QaaG ymaaWdaeqaaKqba+qacqGH9aqpcaGGGcWaaiWaa8aabaWdbmaalaaa paqaa8qacaWGnbWdamaaDaaajuaibaWdbiaaigdacaaIYaaapaqaa8 qacaaIYaaaaaqcfa4daeaapeGaamyta8aadaqhaaqcfasaa8qacaaI YaGaaG4maaWdaeaapeGaaGOmaaaaaaaajuaGcaGL7bGaayzFaaGaey 41aqRaamOua8aadaWgaaqcfasaa8qacaWGYbGaamyzaiaadAgacaGG GcGaaG4maiabgkziUkaaikdaa8aabeaajuaGpeGaaiiOaiaacckaaa a@6046@ (12)

R ref 32 = { M 23 2 M 34 2 }×R4  MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbacbaaaaaaa aapeGaamOua8aadaWgaaqcfasaa8qacaWGYbGaamyzaiaadAgacaGG GcGaaG4maiabgkziUkaaikdaa8aabeaajuaGpeGaeyypa0JaaiiOam aacmaapaqaa8qadaWcaaWdaeaapeGaamyta8aadaqhaaqcfasaa8qa caaIYaGaaG4maaWdaeaapeGaaGOmaaaaaKqba+aabaWdbiaad2eapa Waa0baaKqbGeaapeGaaG4maiaaisdaa8aabaWdbiaaikdaaaaaaaqc faOaay5Eaiaaw2haaiabgEna0kaadkfacaaI0aGaaiiOaaaa@51C2@ (13)

Figure 7: Our optimized 4-coil SCMR series-parallel circuit model.

Each relay coil is 5 mm x 5 mm in size. As mentioned before, the TX coil in our 4-coil system is identical to the one shown in the 2-coil system with the same Q. The analytical analysis of the power transferred from TX coil to RX coil in this 4-coil SCMR system is more complicated than the 2-coil system and only the 3-D EM simulations data is shown below. The circuit is simulated in ANSOFT MAXWELL and co-simulated with ANSOFT SIMPLORER for wireless power transfer as shown in Figure 8.

Figure 8: 4-Coil coupling SCMR optimization in ANSOFT SIMPLORER co-simulated with 3-D HFSS /MAXWELL achieved with the tuning capacitors C1 and C2 where the distance from the relay coil #3 to the RX coil is at 1 mm spacing and the self-inductance value of Coil #2 and #3 is both 7.86 nH. Here R2=1.1 Ω; C2=0.110 pF; R3=1.1 Ω; L1=6.82 nH; R4=1.5 Ω; L2=0.64nH; C1=1.21pF; R1=232Ω; R5=0.5Ω; R6=R7=19 Ω.

The RX coil used for the optimized 4-coil SCMR system has exactly the same stack as the 2-coil system. The dielectric between the Coil #1 and Coil #2, and Coil #2 and Coil #3 is also the same FR4 substrate and has a thickness of 0.3 mm each. The circuit elements of the 4-coil system are calculated similar to the 2-coil system that we have shown before. The power coupling of the 4-coil system is simulated in 3-D HFSS and the result is shown in Figure 9. The complete stack setup of the 4-coil system is shown in Figure 10. Parameters for the 4-coil SCMR system are shown in Table 2. From the data presented here, the optimized 4-coil SCMR system improves power coupling by ~6.1 dB vs. the corresponding optimized traditional 2-coil WPT system as shown earlier. The simulated Q of each of the relay coil is 12.72 and the coil inductance is 7.86 nH. Calculated resistance of the coil is 22.5 Ω by using Eq. 4. Even if the relay coil were to have a very low Q of 2.86, which corresponds to a large parasitic resistance of 100 Ω, the simulated power coupling for the SCMR 4-coil system would be -20.42 dB, which still has a ~6 dB higher power coupling than the corresponding optimized 2-coil system. Please note that even though there are two additional relay coils inserted for the 4-coil system, the losses introduced by them are very minimal according to the EM simulations and they not only do not degrade but actually enhance the power transfer efficiency for the optimized 4-coil SCMR system. These sophisticated EM simulations show promising data for practical implementation of our 4-coil SCMR system. Now we will show the calculations for the optimized 4-Coil WPT system to see if it has reached the SCMR condition:

k'= ωM 2 L S × L D =6.02E9 Γ S = Γ D = ω 2 Q S = ω 2 Q D 2π×5.8× 10 9 2×12.72 =1.43E9 k ' 2 Γ S × Γ D = (6.02E9) 2 (1.43E9) 2 =17.704>1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaajuaGca WGRbGaae4jaiabg2da9maalaaabaGaeqyYdCNaaeytaaqaaiaabkda daGcaaqaaiaabYeadaWgaaqaaiaabofaaeqaaiabgEna0kaabYeada Wgaaqaaiaabseaaeqaaaqabaaaaiabg2da9iaaiAdacaGGUaGaaGim aiaaikdacaWGfbGaaGyoaaqaaiabfo5ahnaaBaaabaGaam4uaaqaba Gaeyypa0Jaeu4KdC0aaSbaaeaacaWGebaabeaacqGH9aqpdaWcaaqa aiabeM8a3bqaaiaaikdacaWGrbWaaSbaaeaacaWGtbaabeaaaaGaey ypa0ZaaSaaaeaacqaHjpWDaeaacaaIYaGaamyuamaaBaaabaGaamir aaqabaaaamaalaaabaGaaGOmaiabec8aWjabgEna0kaaiwdacaGGUa GaaGioaiabgEna0kaaigdacaaIWaWcdaahaaqcfayabeaajugWaiaa iMdaaaaajuaGbaGaaGOmaiabgEna0kaaigdacaaIYaGaaiOlaiaaiE dacaaIYaaaaiabg2da9iaaigdacaGGUaGaaGinaiaaiodacaWGfbGa aGyoaaGcbaqcfa4aaSaaaeaacaWGRbGaai4jaSWaaWbaaKqbagqaba qcLbmacaaIYaaaaaqcfayaaiabfo5ahnaaBaaabaGaam4uaaqabaGa ey41aqRaeu4KdC0aaSbaaeaacaWGebaabeaaaaGaeyypa0ZaaSaaae aacaGGOaGaaGOnaiaac6cacaaIWaGaaGOmaiaadweacaaI5aGaaiyk amaaCaaabeqaaKqzadGaaGOmaaaaaKqbagaacaGGOaGaaGymaiaac6 cacaaI0aGaaG4maiaadweacaaI5aGaaiykamaaCaaabeqcfawaaKqz adGaaGOmaaaaaaqcfaOaeyypa0JaaGymaiaaiEdacaGGUaGaaG4nai aaicdacaaI0aGaeyOpa4JaaGymaaaaaa@9785@  

k1= ωM 2 L S × L X =4.2E9 Γ S = ω 2 Q S = 2π×5.8× 10 9 2×12.72 =1.43E9 Γ X = ω 2 Q X = 2Π×5.8× 10 9 2×67.2 =2.71E8 k 1 2 Γ S × Γ X = (4.22E9) 2 1.43E9×2.71E8 =46.08>1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaajugibi aadUgacaqGXaGaeyypa0tcfa4aaSaaaeaajugibiabeM8a3jaab2ea aKqbagaajugibiaabkdajuaGdaGcaaqaaKqzGeGaaeitaKqbaoaaBa aabaqcLbsacaqGtbaajuaGbeaajugibiabgEna0kaabYeajuaGdaWg aaqaaKqzGeGaaeiwaaqcfayabaaabeaaaaqcLbsacqGH9aqpcaaI0a GaaiOlaiaaikdacaWGfbGaaGyoaaqcfayaaKqzGeGaeu4KdCucfa4a aSbaaeaajugibiaadofaaKqbagqaaKqzGeGaeyypa0tcfa4aaSaaae aajugibiabeM8a3bqcfayaaKqzGeGaaGOmaiaadgfajuaGdaWgaaqa aKqzGeGaam4uaaqcfayabaaaaKqzGeGaeyypa0tcfa4aaSaaaeaaju gibiaaikdacqaHapaCcqGHxdaTcaaI1aGaaiOlaiaaiIdacqGHxdaT caaIXaGaaGimaKqbaoaaCaaabeqaaKqzadGaaGyoaaaaaKqbagaaju gibiaaikdacqGHxdaTcaaIXaGaaGOmaiaac6cacaaI3aGaaGOmaaaa cqGH9aqpcaaIXaGaaiOlaiaaisdacaaIZaGaamyraiaaiMdaaKqbag aajugibiabfo5ahLqbaoaaBaaabaqcLbsacaWGybaajuaGbeaajugi biabg2da9KqbaoaalaaabaqcLbsacqaHjpWDaKqbagaajugibiaaik dacaWGrbqcfa4aaSbaaeaajugibiaadIfaaKqbagqaaaaajugibiab g2da9KqbaoaalaaabaqcLbsacaaIYaGaeuiOdaLaey41aqRaaGynai aac6cacaaI4aGaey41aqRaaGymaiaaicdajuaGdaahaaqabKqbafaa jug4aiaaiMdaaaaajuaGbaqcLbsacaaIYaGaey41aqRaaGOnaiaaiE dacaGGUaGaaGOmaaaacqGH9aqpcaaIYaGaaiOlaiaaiEdacaaIXaGa amyraiaaiIdaaOqaaKqbaoaalaaabaqcLbsacaWGRbGaaGymaKqbao aaCaaabeqaaKqzadGaaGOmaaaaaKqbagaajugibiabfo5ahLqbaoaa BaaabaqcLbsacaWGtbaajuaGbeaajugibiabgEna0kabfo5ahLqbao aaBaaabaqcLbsacaWGybaajuaGbeaaaaqcLbsacqGH9aqpjuaGdaWc aaqaaKqzGeGaaiikaiaaisdacaGGUaGaaGOmaiaaikdacaWGfbGaaG yoaiaacMcajuaGdaahaaqabeaajugWaiaaikdaaaaajuaGbaqcLbsa caaIXaGaaiOlaiaaisdacaaIZaGaamyraiaaiMdacqGHxdaTcaaIYa GaaiOlaiaaiEdacaaIXaGaamyraiaaiIdaaaGaeyypa0JaaGinaiaa iAdacaGGUaGaaGimaiaaiIdacqGH+aGpcaaIXaaaaaa@D516@  

k2= ωM 2 L D × L Y =3.9E9 Γ D = ω 2 Q D = 2π×5.8× 10 9 2×12.7 =1.4E9 Γ Y = ω 2 Q Y = 2π×5.8× 10 9 2×8.5 =2.12E9 k 1 2 Γ D × Γ Y = (3.9E9) 2 1.4E9×2.1E9 =5.1>1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaajuaGca WGRbGaaeOmaiabg2da9maalaaabaGaeqyYdCNaaeytaaqaaiaabkda daGcaaqaaiaabYeadaWgaaqaaiaabseaaeqaaiabgEna0kaabYeada WgaaqaaiaabMfaaeqaaaqabaaaaiabg2da9iaaiodacaGGUaGaaGyo aiaadweacaaI5aaabaGaeu4KdC0aaSbaaeaacaWGebaabeaacqGH9a qpdaWcaaqaaiabeM8a3bqaaiaaikdacaWGrbWaaSbaaeaacaWGebaa beaaaaGaeyypa0ZaaSaaaeaacaaIYaGaeqiWdaNaey41aqRaaGynai aac6cacaaI4aGaey41aqRaaGymaiaaicdalmaaCaaajuaqbeqaaKqz adGaaGyoaaaaaKqbagaacaaIYaGaey41aqRaaGymaiaaikdacaGGUa GaaG4naaaacqGH9aqpcaaIXaGaaiOlaiaaisdacaWGfbGaaGyoaaqa aiabfo5ahnaaBaaabaGaamywaaqabaGaeyypa0ZaaSaaaeaacqaHjp WDaeaacaaIYaGaamyuamaaBaaabaGaamywaaqabaaaaiabg2da9maa laaabaGaaGOmaiabec8aWjabgEna0kaaiwdacaGGUaGaaGioaiabgE na0kaaigdacaaIWaWaaWbaaeqabaqcLbmacaaI5aaaaaqcfayaaiaa ikdacqGHxdaTcaaI4aGaaiOlaiaaiwdaaaGaeyypa0JaaGOmaiaac6 cacaaIXaGaaGOmaiaadweacaaI5aaakeaajuaGdaWcaaqaaiaadUga caaIXaWaaWbaaeqajuaybaqcLbmacaaIYaaaaaqcfayaaiabfo5ahn aaBaaabaGaamiraaqabaGaey41aqRaeu4KdC0aaSbaaeaacaWGzbaa beaaaaGaeyypa0ZaaSaaaeaacaGGOaGaaG4maiaac6cacaaI5aGaam yraiaaiMdacaGGPaWaaWbaaeqabaqcLbmacaaIYaaaaaqcfayaaiaa igdacaGGUaGaaGinaiaadweacaaI5aGaey41aqRaaGOmaiaac6caca aIXaGaamyraiaaiMdaaaGaeyypa0JaaGynaiaac6cacaaIXaGaeyOp a4JaaGymaaaaaa@AB61@  

Therefore, our 4-coil WPT system (all coil couplings 1-2, 2-3, 3-4) is indeed in the SCMR regime according the calculations. Finally, the B-field of the optimized 4-coil SCMR system was simulated in 3-D EM simulation similar to the 2-coil system (Figure 6), and the result is shown in Figure 11. Most region/space around the 4-coil system is red in color and range from 1.56 x 10-3 T to 1.70 x 10-3 T, which is ~ 2x (or 6-7 dB) higher than the 2-coil case shown in Figure 6, suggesting the 4-coil system is indeed in a much strongly magnetically coupled regime, and the results are consistent with the SCMR calculations, and the ~6dB higher wireless power transfer from the S-parameter simulation data shown in (Figure 9).

Figure 9: Optimized 4-coil SCMR system 3-D EM simulated power coupling at 1 mm distance.


Figure 10: 4-coil SCMR system setup in ANSOFT HFSS/MAXWELL; TOP View (UP); Cross-section (DOWN).

Parameters: 4-Coil System

Probe-Dielet With Relay Coils

RX Coil Size and # of Turns

110 mm x100 mm; 2 Turns

TX Coil Size (Diameter)

3 mm

TX Coil Q simulated

67.2

TX Coil L

6.82 nH

TX Coil C

0.110 pF

Relay Coils #2, #3 size and # of turns

5 mm x 5 mm; 1 Turn

Relay Coils #2 and #3 inductance L

7.86 nH

RX Coil

On Chip

RX Coil L

0.64 nH

RX Coil C

1.21 pF

RX Coil LC Q

8.54

Spacing of RX coil to Relay Coil #2/TX Coil

1 mm/1.6 mm

Coupling Coefficients K34 and K14

0.004263/0.001643

Coupling Power (dB)

-20.19

Table 2: Parameters summary for the designed 4-coil SCMR system, where the tiny RX coil is on-chip.

Figure 11: 3-D EM simulated B-Field of the 4-coil SCMR system.

Conclusion

We have presented an efficient and promising WPT design using near-field inductive 4-coil SCMR on a miniature RX coil at the 5.8 GHz ISM band. Both 3-D EM S-parameter simulation and the B-field simulations have shown the tuned 4-coil SCMR system achieves a ~ 6-7 dB improvement over the corresponding optimal 2-coil system for WPT, and this considerably higher power transfer is also accomplished at a larger separation distance between the TX coil and the RX coil (i.e., 1.6 mm for the 4-coil SCMR system vs. 1 mm for the 2-coil traditional system). Therefore, we conclude a well-designed 4-coil SCMR system should outperform the corresponding 2-coil system by successfully transferring about four times more power wirelessly into the tiny RX on-chip coil, which is about 330 times smaller in area than the previously reported smallest RX coil [12,13] for WPT using inductive coupling. We expect a power-efficient miniaturized SCMR WPT system has the potential to enable critical advancement in areas such as novel implantable and wearable biosensors and bioelectronics [14].

Acknowledgement

The authors would like to thank the funding support from the Keh-Shew Lu Regents Chair Endowment at Texas Tech, and Texas Instruments (TI) for the TI-Texas Tech Analog System and Design (ASD) program. We also like to thank Ms. D. Wang, Dr. Ned Cahoon, Dr. A. Joseph and Dr. D. Harame at IBM/Global Foundries for the 7RFSOI design kit access and collaboration.

References

  1. T Nguyen, S Zupancic, DYC Lie (2012) Engineering Challenges in Cochlear Implants Design and Practice. IEEE Circuits and Systems Mag 12(4): 47-55.
  2. G Wang, W Liu, M Sivaprakasam, M Humayun, J Weiland (2005) Proc IEEE Int Symp Circuits Syst 3(12): 2743-2746.
  3. B Jiang, Joshua R Smith, Matthai Philipose, Sumit Roy, Kishore Sunder Rajan, et al. (2007) Energy Scavenging for Inductively Coupled Passive RFID Systems. IEEE Trans Instrum Meas 56(1): 118-125.
  4. Tommaso Campi, Silvano Cruciani, Federica Palandrani, Valerio De Santis, Akimasa Hirata, et al. (2016) Wireless power transfer charging system for AIMDs and pacemakers. IEEE Trans Microw Theory Techn 64(2): 633-642.
  5. Md Rubel Basar, Mohd Yazed Ahmad, Jongman Cho, Fatimah Ibrahim (2016) An improved resonant wireless power transfer system with optimum coil configuration for capsule endoscopy. Sensors and Actuators A: Physical 249: 207-216.
  6. JF Kasic, JR Easter (2006) Integrated implantable hearing device microphone and power unit.
  7. A Kurs (2007) Wireless Power Transfer via Strongly Coupled Magnetic Resonances. Science 317: 83-86.
  8. Z Fei, Steven A Hackworth, Weinong Fu, Chengliu Li, Zhihong Mao, et al. (2011) Relay Effect of Wireless Power Transfer Using Strongly Coupled Magnetic Resonances. IEEE Trans Magn 47(5): 1478-1481.
  9. JW Kim, HC Son, KH Kim, YJ Park (2011) Correction to “Efficiency Analysis of Magnetic Resonance Wireless Power Transfer With Intermediate Resonant Coil”. IEEE Antennas Wirel Propag Lett 10: 389-392.
  10. W Zhong, CK Lee, SYR Hui (2013) General Analysis on the Use of Tesla's Resonators in Domino Forms for Wireless Power Transfer. IEEE Trans Ind Electron 60(1): 261-270.
  11. K Ding, Y Yu, H Lin, J Xie (2016) Wireless Power Transfer at Sub-GHz frequency for Capsule Endoscope." Progress In Electromagnetics Research C 66: 55-61.
  12. ASY Poon, SO Driscoll, TH Meng (2010) Optimal Frequency for Wireless Power Transmission Into Dispersive Tissue. IEEE Trans Antenna and Propagation 58(5): 1739-1750.
  13. SO Driscoll, ASY Poon, TH Meng (2009) in IEEE ISSCC Dig Tech Papers 294-295.
  14. A Ma, ASY Poon (2015) Midfield Wireless Power Transfer for Bioelectronics. IEEE Circuits and Systems Magazine 15(2): 54-60.
  15. BT Nukala, J Tsay, DYC Lie, J Lopez, Tam Q Nguyen (2015) Proc 18th ICRTET-2015, Int Conf on Recent Trends in Eng and Tech, p. 26-29.
  16. CS Wang, GA Covic, OH Stielau (2004) Power transfer capability and bifurcation phenomena of loosely coupled inductive power transfer systems. IEEE Trans Ind Electronics 51(1): 148-157.
  17. Kenichi Okada, Kazuya Masu (2010) “Modeling of spiral inductors”. In Advanced Microwave Circuits and System 14: 291-312.
Creative Commons Attribution License

©2017 Lie, et al. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work non-commercially.