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Coupling Coefficient Measurement Method with Simple Procedures

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Coupling Coefficient Measurement Method with Simple Procedures energies Article Coupling Coefficient Measurement Method with Simple Procedures Using a Two-Port Network Analyzer for a Multi-Coil WPT System Seon-Jae Jeon and Dong-Wook Seo * Department of Radio Communication Engineering, Korea Maritime and Ocean University (KMOU), 727 Taejong-ro, Yeongdo-gu, Busan 49112, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-51-410-4427 Received: 10 September 2019; Accepted: 16 October 2019; Published: 17 October 2019 Abstract: In this paper, we propose a measurement method with a simple procedure based on the definition of the impedance parameter using a two-port network analyzer. The main advantage of the proposed measurement method is that there is no limit on the number of measuring coils, and the method has a simple measurement procedure. To verify the proposed method, we measured the coupling coefficient among three coils with respect to the distance between the two farthest coils at 6.78 and 13.56 MHz, which are frequencies most common for a wireless power transfer (WPT) system in high-frequency band. As a result, the proposed method showed good agreement with results of the conventional S-parameter measurement methods. Keywords: coupling coefficient; impedance matrix; multiple coils; mutual inductance; scattering matrix; transfer impedance; wireless power transfer 1. Introduction The conventional wireless power transfer (WPT) system with two coils has obvious limits; the system is very sensitive to the transmission distance and alignment between the coils [1,2]. To resolve these problems, adaptive or tunable matching networks have been adopted [3,4], and a transmitting module not with a single coil, but with multiple coils has been also introduced into the WPT system [5,6]. Especially, the magnetic beamforming, which focuses magnetic fields from the multiple transmitting coils to the receiving coil, has recently attracted lots of attention. For an ideal multi-coil WPT system, the coupling coefficients among transmitting coils should be zero, but in reality, they are not. The non-zero coupling coefficient among transmitting coils is one of the major causes of deterioration of the power transfer efficiency (PTE) in the magnetic beamforming. To minimize the effect of non-zero coupling coefficients, the phase and magnitude of signals input to transmitting coils should be adjusted to the optimum values that are estimated from the measured coupling coefficients among coils. The adjustment makes the all current of transmitting coils in phase, and results in a maximum receiver current and maximum PTE [5,6]. Therefore, the accurate and simple procedures for measurement of the coupling coefficient among multiple coils is essential for implementing the magnetic beamforming of a multi-coil WPT system. For a WPT system with an operating frequency of a low-frequency (LF) band such as 110 to 205 kHz, the coupling coefficient (or mutual inductance) is usually measured by an LCR meter [7] or an impedance analyzer [8]. On the other hand, in a high-frequency (HF) band such as 6.78 or 13.56 MHz, most coils have a frequency-dependent characteristic due to the effect of ac resistance and parasitic elements. Therefore, a vector network analyzer is commonly used to measure the coupling coefficient in HF bands [9]. In the case of multi-coil WPT systems, the measurement issue arises primarily from Energies 2019, 12, 3950; doi:10.3390/en12203950 www.mdpi.com/journal/energies Energies 2019, 12, 3950 2 of 10 Energies 2019, 12, x FOR PEER REVIEW 2 of 10 the common vector network analyzer (VNA) having only two ports. Although a multiport VNA can measure thethe couplingcoupling coe coefficientfficient among amon ag greatera greater number number of coils,of coils, it is it still is still only only available available for coils for withcoils equalwith equal or less or than less thethan number the number of ports. of ports. In thisthis paper,paper, wewe simulatesimulate the the e effectffect of of inaccurately inaccurately measured measured coupling coupling coe coefficientsfficients on on the the PTE PTE of aof multi-coil a multi-coil WPT WPT system, system, and and propose propose a method a method to readily to readily measure measure the coupling the coupling coefficients coefficients among multipleamong multiple coils using coils a two-portusing a two-port VNA based VNA on based the definition on the definition of the impedance of the impedance matrix. In matrix. addition, In thisaddition, measurement this measurement method can method overcome can overcome the limitation the limitation of the performance of the performance of a multi-port of a multi-port VNA for moreVNA coilsfor more than coils the number than the of number ports. We of ports. verify We the validityverify the of validity the proposed of the methodproposed from method the results from thatthe results the proposed that the method proposed has the method same performance has the same as conventionalperformance measurement as conventional methods measurement according tomethods distance. according to distance. 2. Effect Effect of Inaccurate Coupling CoeCoefficientfficient onon PTEPTE ofof aa Multi-CoilMulti-Coil WPTWPT SystemSystem In this section, section, we we simulate simulate the the PTE PTE of of a amult multi-coili-coil WPT WPT system system with with magnetic magnetic beamforming beamforming by byapplying applying inaccurate inaccurate coupling coupling coefficient coefficient informat informationion to to examine examine the the importance importance of of an accurateaccurate coupling coecoefficientfficient measurement.measurement. Consider the multiple-input single-outputsingle-output (MISO) WPT system configuredconfigured as four transmitting coils and a single receiving coil, where all transmittingtransmitting coils are modeled as an inductance of 1.1 µμH and a parasiticparasitic resistance of 0.40.4 ohm.ohm. Additionally, we assume that all couplingcoupling coecoefficientsfficients amongamong transmitting coilscoils are fixedfixed to 0.05, and coupling co coeefficientsfficients between transmitting and receiving coils are also fixedfixed toto 0.05.0.05. The assumption that all coupling coecoefficientsfficients among transmitting coils are the same for all transmitting coils is didifficultfficult to realizerealize in practice,practice, but this assumption is eeffectiveffective in simulating thethe PTE PTE of of a multi-coil a multi-coil WPT WPT system, system, because because the input the signals input ofsignals all transmitting of all transmitting resonators haveresonators the same have value the same when value the magnetic when the beamforming magnetic beamforming algorithm isalgorithm applied. is Figure applied.1 shows Figure the 1 schematicshows the diagram schematic of thediagram MISO WPTof the system MISO forWPT circuit syst simulationem for circuit using simulation the Keysight’s using ADS the (AdvancedKeysight’s DesignADS (Advanced System). Design System). MUTIND P_AC C PORT1 C_Tx1 L Num=1 C=c L_Tx1 Mutua l Z=50 Ohm L=L M_Tx1_Rx Pac=polar(dbmtow(0),0) R=Rp K=k_Tx_Rx Freq=freq M=k_Tx_Rx*L Inductor1="L_Tx1" Inductor2="L_Rx" MUTIND P_AC C PORT2 C_Tx2 L Mutua l Num=2 C=c L_Tx2 M_Tx2_Rx Z=50 Ohm L=L K=k_Tx_Rx R=Rp Pac=polar(dbmtow(0),0) M=k_Tx_Rx*L Vout Freq=freq Inductor1="L_Tx2" C R L Inductor2="L_Rx" C_Rx RL L_Rx C=c R=3 Ohm L=L MUTIND R=Rp C P_AC Mutua l PORT3 C_Tx3 L C=c L_Tx3 M_Tx3_Rx Num=3 K=k_Tx_Rx Z=50 Ohm L=L R=Rp M=k_Tx_Rx*L Pac=polar(dbmtow(0),0) Inductor1="L_Tx3" Freq=freq Inductor2="L_Rx" MUTIND P_AC C M_Tx3_Tx4 C_Tx4 L Mutua l PORT4 M_Tx4_Rx K=k_Tx_Tx Num=4 C=c L_Tx4 M=k_Tx_Tx*L L=L K=k_Tx_Rx Z=50 Ohm M=k_Tx_Rx*L Inductor1="L_Tx3" Pac=polar(dbmtow(0),0) R=Rp Inductor2="L_Tx4" Inductor1="L_Tx4" Freq=freq Inductor2="L_Rx" Figure 1. Schematic diagram of a a multiple-input multiple-input single-output single-output (MISO) wireless power transfer (WPT) system for the advanced designdesign systemsystem (ADS)(ADS) circuitcircuit simulation.simulation. To apply magnetic beamforming to the MISO WPT system, the voltage of transmitting coils must be given by [6]: Energies 2019, 12, 3950 3 of 10 Energies 2019, 12, x FOR PEER REVIEW 3 of 10 To apply magnetic beamforming to the MISO WPT system, the voltage of transmitting coils must be given by [6]: ω2 T ! bbf f =+!2MMMTM bfb, f viTTZT ! (1) !v T = ZT + R i T , (1) RRR wherewhereM is M the is mutualthe mutual inductance inductance matrix matrix between between the transmittingthe transmitting and and receiving receiving coils; coils;RR is R theR is the total total b f bf ! i T resistanceresistance of theof the receiving receiving resonator; resonator;i T Tisthe is the transmit transmit current current and and is proportionalis proportional to toM M; and; andZ TZ is is thethe inter-coupling inter-coupling matrix matrix among among transmitting transmitting coils coils and and isis constructedconstructed asas thethe couplingcoupling coecoefficientsfficients (or (or mutual inductances)inductances) amongamong transmittingtransmitting coils. coils. That That is, is, the the amplitude amplitude and and phase phase of theof the transmit transmit voltagevoltage is dominantly is dominantly determined determined by couplingby coupling coe fficoefficientcient information. information. Therefore, Therefore, the the more more accurate accurate thethe coupling coupling coe coefficientfficient is, theis, the more more accurately accurately the the transmit transmit voltage voltage for for the the magnetic magnetic beamforming beamforming is is obtained.obtained. By applyingBy applying the the coupling coupling coe fficoefficientcient with with error error term term to the to the magnetic magnetic beamforming, beamforming, we simulatedwe simulated the PTEthe PTE degradation degradation of the of MISO the WPTMISO system WPT atsystem 13.56 MHz.at 13.56 The MHz. simulated The simulated results are shownresults inare Figure shown2. in WhenFigure the exact2. When coupling the exact coeffi couplingcient of 0.05coefficient is used of for 0. the05 is beamforming, used for the beamforming, the PTE achieves the about PTE achieves 77%.
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