Design and Optimization of a 3-Coil Inductive Link for Efficient Wireless Power Transmission

Abstract

Inductive power transmission is widely used to energize implantable microelectronic devices (IMDs), recharge batteries, and energy harvesters. Power transfer efficiency (PTE) and power delivered to the load (PDL) are two key parameters in wireless links, which affect the energy source specifications, heat dissipation, power transmission range, and interference with other devices. To improve the PTE, a 4-coil inductive link has been recently proposed. Through a comprehensive circuit based analysis that can guide a design and optimization scheme, we have shown that despite achieving high PTE at larger coil separations, the 4-coil inductive links fail to achieve a high PDL. Instead, we have proposed a 3-coil inductive power transfer link with comparable PTE over its 4-coil counterpart at large coupling distances, which can also achieve high PDL. We have also devised an iterative design methodology that provides the optimal coil geometries in a 3-coil inductive power transfer link. Design examples of 2-, 3-, and 4-coil inductive links have been presented, and optimized for 13.56 MHz carrier frequency and 12 cm coupling distance, showing PTEs of 15%, 37%, and 35%, respectively. At this distance, the PDL of the proposed 3-coil inductive link is 1.5 and 59 times higher than its equivalent 2- and 4-coil links, respectively. For short coupling distances, however, 2-coil links remain the optimal choice when a high PDL is required, while 4-coil links are preferred when the driver has large output resistance or small power is needed. These results have been verified through simulations and measurements.

Fig. 1

Lumped circuit models of (a) 4-coil and (b) conventional 2-coil inductive links for wireless power transfer. (c) Equivalent circuit of the reflected load on to the primary loop at resonance (for the sake of simplicity, R_s, which is a property of the driving circuitry, has been merged with R₂).

Fig. 2

Simulated (a) power transfer efficiency (PTE) and (b) power delivered to the load (PDL) for a 4-coil inductive link as a function of k₁₂ and d₂₃ when k₃₄ = 0.22 for the coils specified in Table I. V_s = 1 V and R_L = 100 Ω.

Fig. 3

Lumped circuit model of the 3-coil inductive link.

Fig. 4

Simulated (a) PTE and (b) PDL for a 3-coil inductive link as a function of k₃₄ and d₂₃ for the coils in Table I. V_s = 1 V and R_L = 100 Ω.

Fig. 5

(a) Optimal load quality factor, Q_L,PTE, needed to achieve the highest PTE vs. coils’ spacing in 2- and 3-coil inductive links (k₃₄ = 0.22, R_L = 100 Ω, and other parameters from Table I). (b) k₃₄ adjustments based on (25) to maintain the optimal PTE in a 3-coil link vs. R_L at d₂₃ = 5 cm. The 2-coil link only reaches the optimal PTE for a specific R_L = 200 Ω that satisfies (10).

Fig. 6

Iterative multi-coil inductive link design optimization flowchart.

Fig. 7

PTE measurement setups for inductive links: (a) Conventional method using a network analyzer, (b) direct method using a signal source and current and voltage probe via oscilloscope, (c) the new method using network analyzer with all the coils tuned at the carrier frequency and R_L connected.

Fig. 8

(a) Experimental setup for measuring the PTE and PDL in a 3-coil inductive link. (b) 3-coil inductive link model in the HFSS. Coil specifications are listed in Table I.

Fig. 9

(a) Experimental setup for measuring the PTE and PDL in a 4-coil inductive link. (b) 4-coil inductive link model in the HFSS. Coil specifications are listed in Table I.

Fig. 10

Comparison between measured, simulated (HFSS), and calculated (see section II) values of the (a) PTE and (b) PDL vs. d₂₃ for 2-, 3-, and 4-coil inductive links specified in the “Measurement” columns of Table I (V_s = 1 V).

Fig. 11

Calculated PTE and PDL vs. source resistance, R_s, for 2-, 3-, and 4-coil inductive links in the design example of Table I (V_s = 1 V, d₂₃ = 12 cm).

Fig. 12

(a) Comparison between calculated values of the PTE and PDL vs. d₂₃ for 2-, 3-, and 4-coil inductive links specified in Table II (V_s = 1 V, R_s = 0.5 Ω). (b) Comparison between calculated values of the PTE and PDL vs. R_s for 2-, 3-, and 4-coil inductive links for the IMD example of Table II (V_s = 1 V, d₂₃ = 1 cm).