A Multi-Cycle Q-Modulation for Dynamic Optimization of Inductive Links

Abstract

This paper presents a new method, called multi-cycle Q-modulation, which can be used in wireless power transmission (WPT) to modulate the quality factor (Q) of the receiver (Rx) coil and dynamically optimize the load impedance to maximize the power transfer efficiency (PTE) in two-coil links. A key advantage of the proposed method is that it can be easily implemented using off-the-shelf components without requiring fast switching at or above the carrier frequency, which is more suitable for integrated circuit design. Moreover, the proposed technique does not need any sophisticated synchronization between the power carrier and Q-modulation switching pulses. The multi-cycle Q-modulation is analyzed theoretically by a lumped circuit model, and verified in simulation and measurement using an off-the-shelf prototype. Automatic resonance tuning (ART) in the Rx, combined with multi-cycle Q-modulation helped maximizing PTE of the inductive link dynamically in the presence of environmental and loading variations, which can otherwise significantly degrade the PTE in multi-coil settings. In the prototype conventional 2-coil link, the proposed method increased the power amplifier (PA) plus inductive link efficiency from 4.8% to 16.5% at (R_L = 1 kΩ, d₂₃ = 3 cm), and from 23% to 28.2% at (R_L = 100 Ω, d₂₃ = 3 cm) after 11% change in the resonance capacitance, while delivering 168.1 mW to the load (PDL).

I. Introduction

Near-field wireless power transmission (WPT) has been utilized for contactless powering in a wide variety of applications. Charging mobile devices and electric vehicles are the leading applications for WPT by significantly improving the user experience, ease of use, and convenience [1]–[9]. Implantable microelectronic devices (IMDs) form another key category of devices that is significantly benefiting from advancements in WPT. Because eliminating the transcutaneous interconnects and large batteries that would otherwise be needed to operate IMDs over extended periods is necessary to reduce their invasiveness and improve patient safety [10]–[16].

Most IMDs have strict power restrictions to limit heat dissipation in the coils/tissue, exposure to electromagnetic field, and interference with other devices [17]–[21]. Such WPT systems need to have sufficient power delivered to the load (PDL), while maintaining high power transfer efficiency (PTE) [18]. Considerable attention has been paid to maximizing PTE in 2-, 3-, and 4-coil inductive links by optimizing the geometry of the coils [18], [22]–[27]. The PTE between the conventional 2-coil links degrades with load variation because the PTE is affected by the loaded quality factor (Q) of the receiver (Rx) LC-tank [28]. On the other hand, the 3- and 4-coil inductive links offer additional degrees of freedom to transform any given load to the optimal loading condition that maximizes the PTE, at the cost of increased size and complexity of the Rx. Furthermore, dynamic optimization during system operation is difficult, if not impossible, because the load matching in the 3-and 4-coil links require adjusting the geometry and mutual coupling of the coils. Other methods for the load transformation using L, π, and T-match networks have been presented also [29], [30]. While any load can be transformed to the optimal value, the limitations of size, complexity, additional power loss, and inability to react dynamically still remain.

More recently, there have been efforts to modulate the load using DC-DC converters in order to increase the Q-factor of the Rx coil in the 2-coil links [31], [32]. However, these systems cannot automatically find the optimal matching conditions to maximize the PTE and only compensate load variations in a limited range due to inherent limitations of the DC-DC converters. The Q-modulation technique, which was first introduced in [33], adaptively transforms the Rx loading to dynamically maximize the PTE in 2-coil inductive links during operation. While the fully-integrated Q-modulation power management application-specific integrated circuit (ASIC) in [33] successfully improved the PTE for a wide range of load variations, implementation of that method using commercial off-the-shelf (COTS) components would be difficult. Because in the Q-modulation technique in [33], the Rx LC-tank is chopped very rapidly, twice for every power carrier period, requiring sophisticated synchronization between the current in the Rx LC-tank and the timing of chopping switch.

Digital control of the duty cycle in [33] needs a clock rate much faster than the power carrier frequency, e.g. 100 times faster for 2% resolution in duty cycle control. Alternatively, analog control of the duty cycle would require accurate charge pump with adjustable output to set the duty cycle of the switching pulses, which adds to the complexity of the circuit needed to generate the switching pulses. This would limit the use of higher power carrier frequencies in the inductive links that utilize Q-modulation technique. If the timing of chopping switch is not properly synchronized with the carrier, the Q-modulation in [33] could degrade the PTE, while the method presented in this paper is considerably more robust.

In addition to the load variation in the Rx LC-tank, the PTE is also highly dependent on how well the transmitter (Tx) and Rx tank circuits are tuned at the operating frequency, f_p, because the inductive link is often adversely affected by the parasitic capacitance of the surrounding tissue environment or the process variations, which can significantly degrade the PTE, particularly when the Q-factor is high [28], [34]. Several adaptive tuning methods for the Rx LC-tank have been proposed by employing a variable LC-tank to compensate for variations in the Rx resonance capacitance [35]–[39]. Such adaptive Rx LC-tank tuning techniques would be important in Q-modulation because chopping the Rx LC-tank can affect its resonance frequency, and it needs to be continuously compensated along with matching the load impedance with that of the inductive link to maximize the PTE.

In this paper, we demonstrate a new Q-modulation method that can span across multiple carrier cycles without requiring complex circuits and sophisticated synchronization between the current in the receiver LC-tank and the timing of coil switching. As such, the new multi-cycle Q-modulation technique is easy to implement in either COTS or ASIC platforms, regardless of the power carrier frequency. We have combined the proposed multi-cycle Q-modulation with automatic resonance tuning (ART), for the first time, in a prototype utilizing COTS components, such as a rectifier, regulator, analog switch, capacitor bank, and microcontroller (MCU), as shown in Fig. 1. The series Rx LC-tank is composed of L₃ and C₃+ΔC_ART with its parasitic resistance, R₃, and it is assumed that the Rx LC-tank is always resonant at f_p because ΔC_ART is adaptively adjusted to maintain the resonant condition via ART operation. The power amplifier (PA) can be modeled with a sinusoidal voltage source, V_S, plus its output impedance, R_S. The Tx LC-tank is composed of L₂, C₂, and the series resistance, R₂. The mutual inductance, M₂₃, is decided by the coupling coefficient, k₂₃, and the Tx and Rx coil inductances, L₂ and L₃. We have also derived the governing equations over the new multi-cycle Q-modulation technique using a lumped circuit model, and verified them via simulation and measurements. The ART combined with multi-cycle Q-modulation keeps the PTE of the inductive link at its peak dynamically by simultaneously matching the load and tuning the Rx LC-tank at the carrier frequency, f_p. In section II, the lumped model and analysis of the proposed multi-cycle Q-modulation method are introduced in a 2-coil inductive link. The theoretical calculation, simulation, and measurement results of the multi-cycle Q-modulation inductive link are depicted in section III. The control algorithm for the multi-cycle Q-modulation and ART combination are presented in section IV. Implementation and experimental results are described in section V, followed by concluding remarks.

Fig. 1.

Block diagram of a multi-cycle Q-modulation with automatic resonance tuning (ART), which adaptively transforms any arbitrary load to the optimal loading and tunes the Rx LC-tank at the carrier frequency for continuous operation at the highest PTE.

II. Modeling and Analysis of Multi-Cycle Q-Modulation

Fig. 2a shows a lumped model of the proposed multi-cycle Q-modulation inductive link along with its switching waveforms in Fig. 2b. The parasitic components are not considered in the lumped model of the proposed Q-modulation inductive link in Fig.2 to avoid the complex analysis. In the conventional 2-coil inductive link, the PTE can be derived as [25],

$${\eta }_{2-\mathit{coil}}=\frac{{k_{23}}^2{Q}_2{Q}_{3L}}{1+{k_{23}}^2{Q}_2{Q}_{3L}}\cdot \frac{Q_{3L}}{Q_L},$$ (1)

where k₂₃ = M₂₃/(L₂L₃)^0.5, Q₂ = ωL₂/R₂, and Q_3L = Q₃Q_L/(Q₃+Q_L), in which ω=2πf_p, Q₃ = ωL₃/R₃ and Q_L = R_L / ωL₃. The high quality factors of Q₂, Q₃, and Q_3L are desirable to achieve high PTE in a 2-coil inductive link. During coil optimization, Q₂ and Q₃ are decided by their geometrical limitation and carrier frequency, and Q_3L is limited by the load resistance. The Q-modulation technique proposed in this paper modulates the loaded Q-factor, Q_3L, in the Rx coil by the switched L₃C₃-tank to transform R_L into optimal equivalent load, R_opt, for optimization of the 2-coil inductive link. Two control parameters are employed to achieve the highest PTE in the multi-cycle Q-modulation technique: 1) the switching time, T_on, and 2) the switching period, T_np, both of which are multiple times longer than the carrier period, T_p = 1/f_p. The SC signal closes or opens a switch with its ON resistance of R_SW to modulate the load, R_L, and maximize the voltage across the load, V_L, and consequently the received power.

Fig. 2.

(a) The circuit model of the proposed multi-cycle Q-modulation with ART inductive link. (b) Voltage and current waveforms, controlled by T_on and T_np.

The equivalent circuit of Fig. 2a is shown in Fig. 3a, in which ω = 2πf_p, R₂₂ = R_S + R₂, V_S(t)=E₀cos(ωt), and C₃′ = C₃ + ΔC_ART. The equivalent resistance, R₃₃, is R₃ + R_SW for 0 ≤ t < T_on, and R₃+R_L for T_on ≤ t < T_np where R_SW is the ON resistance of the SC switch (R_SW ≪ R_L). V₂₃ and V₃₂ in the equivalent circuit can be found from,

$$V_{23}=-jw{M}_{23}{I}_3,$$ (2)

$$V_{32}=jw{M}_{23}{I}_2.$$ (3)

The reflected impedance onto the primary side, Z_ref, can be derived from,

$$Z_{\mathit{ref}}=\frac{V_{23}}{I_2}=\frac{{\left(w{M}_{23}\right)}^2}{jw{L}_3+\frac{1}{jw{C}_3}+R_{33}}.$$ (4)

Fig. 3.

(a) Equivalent circuit of lumped model in Fig. 2a. (b) Simplified equivalent circuit seen from the primary (Tx) side at resonance. The secondary (Rx) side is maintained because of its effect on the transient mode calculations.

Assuming that L₂ and C₂ on the primary (Tx) side are tuned at f_p, the equivalent circuit seen from the primary and secondary sides can be simplified to what is shown in Fig. 3b. When L₃C₃-tank is also tuned at f_p, the primary current, I₂, and the secondary reflected voltage, V₃₂, in the steady-state condition can be calculated as,

$$I_2=\frac{V_S}{R_{22}+\frac{w^2{M_{23}}^2}{R_{33}}},$$ (5)

$$V_{32}=\frac{jw{M}_{23}{V}_S}{R_{22}+\frac{w^2{M_{23}}^2}{R_{33}}}\cdot$$ (6)

Therefore, the steady-state current in the Rx, I₃(t), can be derived by Kirchhoff’s voltage law (KVL),

$$V_{32}(t)=L_3\frac{d{I}_3(t)}{\mathit{dt}}+\frac{1}{C_3\prime }{\displaystyle \underset{0}{\overset{t}{\int }}{I}_3}(\tau )d\tau +I_3(t)\cdot R_{33}=E_1\sin (wt),$$ (7)

$$E_1=\frac{w{M}_{23}{E}_0}{R_{22}+\frac{w^2{M_{23}}^2}{R_{33}}}\cdot$$ (8)

Since R₃₃ is either R₃+R_SW or R₃+R_L during Q-modulation we substitute E₁ with E_close and E_open, which imply the steady-state amplitudes of I₂(t) for 0 ≤ t < T_on and T_on ≤ t< T_np, respectively. When SC is closed, the Rx circuit would be underdamped due to its small parasitic resistance and (7) can be solved by summing the particular integral (9) and the complementary function (10),

$$I_{3P,\mathit{close}}(t)=\frac{E_{\mathit{close}}}{R_3+R_{SW}}\sin (wt),$$ (9)

$$I_{3C,\mathit{close}}(t)=e^{-\alpha t}(A_1\cos (wt)+A_2\sin (wt)),$$ (10)

$$I_{3,\mathit{close}}(t)=I_{3C,\mathit{close}}(t)+I_{3P,\mathit{close}}(t),$$ (11)

where α = (R₃+R_SW)/2L₃. Considering the initial condition from t = 0⁻, where SC is opened, the secondary steady-state current during 0 ≤ t < T_on can be found from,

$$I_{3,\mathit{close}}(t)=\left[\frac{E_{\mathit{close}}}{R_3+R_{SW}}(1-e^{-\alpha t})+\frac{E_{\mathit{open}}}{R_3+R_L}{e}^{-\alpha t}\right]\sin (wt).$$ (12)

When SC is open at t = T_on⁺, the energy stored in the L₃C₃-tank is transferred to R_L. Since the load has a relatively large resistance compared to R_SW, the circuit condition is normally over-damped and the solution for (7) takes the form of,

$$I_{3,\mathit{open}}(t)=B_1{e}^{s_1(t-T_{on})}+B_2{e}^{s_2(t-T_{on})}+\frac{E_{\mathit{open}}}{R_3+R_L}\sin (w(t-T_{on}))$$ (13)

where,

$$s_{1,2}=\frac{-(R_3+R_L)}{2L_3}\pm \sqrt{{\left\{\frac{(R_3+R_L)}{2L_3}\right\}}^2-\frac{1}{L_3{C_3}^{\text{'}}}},$$ (14)

$$B_1=\frac{-V_C\left({T_{\mathit{on}}}^{-}\right)}{L_3(s_1-s_2)}+\frac{s_1\times I_{3.\mathit{close}}\left({T_{\mathit{on}}}^{-}\right)}{s_1-s_2},$$ (15)

$$B_2=\frac{V_C\left({T_{\mathit{on}}}^{-}\right)}{L_3(s_1-s_2)}-\frac{s_2\times I_{3.\mathit{close}}\left({T_{\mathit{on}}}^{-}\right)}{s_1-s_2}.$$ (16)

The two initial conditions, I_3,close(T_on⁻) = 0 and V_C(T_on⁻), which is the voltage across C₃′ at t = T_on⁻, that are needed to solve (13) can be iteratively calculated from (12) by utilizing the new initial condition from (13) in the transient state.

Although the transient waveforms of I_3,close(t) and I_3,open(t) can be derived from (11) and (13), the transient voltages reflected onto the secondary side, E_close(t) and E_open(t), are also affected by the LCR components on both primary and secondary sides while both L₂C₂- and L₃C₃-tanks are tuned at f_P. It is necessary to solve the overall transient equation derived from Fig. 3a to extract the exact waveforms for E_close(t) and E_open(t),

$$M_{23}\frac{d{I}_2(t)}{dt}=L_3\frac{d{I}_3(t)}{dt}+\frac{1}{C_3\text{'}}{\displaystyle \underset{0}{\overset{t}{\int }}{I}_3(\tau )d\tau +I_3(t)\cdot R_{33},}$$ (17)

$$V_S\sin (wt)=L_2\frac{d{I}_2(t)}{dt}+\frac{1}{C_2}{\displaystyle \underset{0}{\overset{t}{\int }}{I}_2}(\tau )d\tau +I_2(t)\cdot R_{22}+M_{23}\frac{d{I}_3(t)}{dt}.$$ (18)

Since (17) and (18) create a 4^th order differential equation, we estimate the transient voltage for E_close(t) and E_open(t) in this paper, when the overall system is in the over-damped condition,

$$E_{\mathit{close}}(t)=E_{\mathit{close}}(1-e^{-\alpha t})+E_{\mathit{open}}{e}^{-\alpha t},$$ (19)

$$E_{\mathit{open}}(t)=E_{\mathit{open}}(1-e^{-\alpha (t-T_{on})})+E_{\mathit{close}}{e}^{-\alpha (t-T_{on})},$$ (20)

where α = (R_S+R₂)/2L₂.

Assuming that the Tx and Rx LC-tanks are fully resonated, V_S and I₂ are in-phase because the reflected load in (4) has only the real part. The estimated transient voltage for E_close(t) and E_open(t) are used to calculate V_S output power in the transient state. Since power is only delivered to the load when SC is open T_on ≤ t < T_np, the PDL and V_S (source) output power for the multi-cycle Q-modulation can be derived from,

$$P_{L,Q\mathrm{mod},\mathit{average}}=\frac{R_L}{T_{np}}{\displaystyle \underset{T_{on}}{\overset{T_{np}}{\int }}{I}_{3,\mathit{open}}}{(t)}^{2}dt,$$ (21)

$$P_{Vs,\mathit{close},\mathit{rms}}=V_{S,\mathit{rms}}\times I_{2,\mathit{close},\mathit{rms}}=\frac{V_s}{\sqrt{2}}\times \sqrt{\frac{{\displaystyle \underset{0}{\overset{T_{on}}{\int }}{\left[\frac{E_{\mathit{close}}(t)}{wM}\sin (wt)\right]}^{2}dt}}{T_{on}}},$$ (22)

$$P_{Vs,\mathit{open},\mathit{rms}}=V_{S,\mathit{rms}}\times I_{2,\mathit{open},\mathit{rms}}=\frac{V_S}{\sqrt{2}}\times \sqrt{\frac{{\displaystyle \underset{T_{on}}{\overset{T_{np}}{\int }}{\left[\frac{E_{\mathit{open}}(t)}{wM}\sin (wt)\right]}^{2}dt}}{T_{np}-T_{on}}},$$ (23)

$$P_{Vs,Q\mathrm{mod},\mathit{average}}=\frac{T_{on}\times P_{Vs,\mathit{close},\mathit{rms}}+\left(T_{np}-T_{on}\right)\times P_{Vs,\mathit{open},\mathit{rms}}}{T_{np}},$$ (24)

where P_{L,Qmod,average} is the PDL, P_Vs,close,rms is the power drained from V_S for 0 ≤ t < T_on, P_Vs,open,rms is the power drained from V_S for T_on ≤ t< T_np, and P_{Vs,Qmod,average} is the average power drained from V_S. Moreover, the PA + link efficiency can be calculated as,

$${\eta }_{Q\mathit{mod}}\%=100\times P_{L,\mathit{Q}\mathit{mod},\mathit{average}}/P_{Vs,\mathit{Q}\mathit{mod},\mathit{average}}.$$ (25)

The proposed Q-modulation boosted Q_3L equal to Q₃ during t < T_on, and the boosted energy is stored in the Rx LC-tank although the power is not transferred to the load compared to the conventional 2-coil inductive link without the Q-modulation, which transfer the continuous inductive power to the load with relatively low Q_3L due to low Q_L. The stored energy in the Rx LC-tank is transferred to the load during T_np−T_on, to achieve the modulated loaded quality factor, Q_3L,_eq, which can be found from Q_3L,eq = Q₃Q_L,eq/(Q₃+Q_L,eq), where Q_L,eq = ωL₃/R_opt, and R_opt = (1−T_on/T_np)R_L.

III. Verification of Theoretical Model of Multi-Cycle Q-Modulation

The key parameters used in calculation, simulation, and proof-of-concept prototype measurement setup of the multi-cycle Q-modulation method are summarized in the Table I. The carrier frequency was chosen at 13.56 MHz in the industrial-scientific and medical (ISM) band. The Tx planar spiral coil (PSC) and Rx wire-wound coil are designed for a nominal distance of 3 cm and have a measured k₂₃ = 0.044. The class-E PA used in the measurement setup had an output impedance of 3.1 Ω, and the switching resistance of the MOSFET pair (DMN5L06K) used for Q-modulation in the prototype Rx was 2 × 2 Ω.

TABLE I.

Prototype Multi-Cycle Q-Modulation Inductive Link Specifications

Parameters	Value
PSC primary coil (L2)	Inductance = 5.8 μH Outer diameter = 4 cm Line width = 0.4 mm Line spacing = 0.2 mm Number of turns = 9 Quality factor = 187
Wire-wound secondary coil (L3)	Inductance = 3.85 μH Outer diameter = 2.2 cm Wire diameter = 0.2 mm Number of turns = 10 Quality factor = 93.7
Resonance Capacitance	C2 = 23.8 pF, C3 = 36.0 pF
L2-L3 nominal distance (d23)	3 cm
Coupling coefficient (k23)	0.044
Switch Resistance (RSW)	4 Ω
PA output resistance (RS)	3.1 Ω
Carrier frequency (fp)	13.56 MHz
Loading (RL)	500 Ω

Using Table I parameters in (21)–(25), and sweeping T_on and T_np from 1 to 10 power carrier cycles, result in Fig. 4a, which shows how the inductive link PTE changes with multi-cycle Q-modulation. Fig. 4a also shows the optimal values for T_on and T_np that would maximize the PA + link efficiency, η_Qmod.

Fig. 4.

Calculated optimal T_on and T_np to maximize the PA + link efficiency in 2-coil inductive link using parameters in Table I. (a) T_on = 3T_P, T_np = 4T_P at R_L = 500 Ω and d₂₃ = 3 cm. (b) Optimal T_on and T_np vs. load variations at d₂₃ = 3cm. (c) Optimal T_on and T_np vs. coil distance variations at R_L = 1 kΩ.

According to Fig. 4a, with R_L = 500 Ω and d₂₃ = 3 cm, the 2-coil inductive link in Table I provides η_{w/o Qmod} = 10.5% at d₂₃ = 3 cm. Using multi-cycle Q-modulation with T_on = 3T_p, T_np = 4T_p, the peak efficiency increases to 32.5%, which represents 182% improvement. Moreover, using the same theoretical analysis in section II, we can find how T_on and T_np should be changed in response to changes in R_L and d₂₃, which are the two parameters that often change during operation of the system. These results, which are shown in Figs. 4b and 4c, respectively, indicate that more load modulation is necessary to achieve the maximum η_Qmod when R_L increases or k₂₃ decreases.

To compare the theoretical model in section II with circuit simulation, we used the Simulink (Mathworks, Natick, MA) environment and parameters in Table I. The calculated and simulated transient waveforms, with T_on = 3T_p, T_np = 4T_p, R_L = 500 Ω, and d₂₃ = 3 cm, using (12) for closed switch, (13) for open switch, and Simulink are presented in Fig. 5a, and show a very good agreement. Fig. 5b shows the calculated, simulated, and measured PA + link efficiency over a wide range of R_L, from 100 Ω to 3.4 kΩ. Since the inductive link is designed by the series LC-tank, the measurement result shows higher PA + link efficiency for the smaller R_L without the Q-modulation while the efficiency dramatically decreases as R_L increases. The external SC pulse (external Q-modulation) generated by the signal generator opens or closes the MOSFET pair in order to verify the effect of the proposed multi-cycle Q-modulation. Because of the approximations in calculating the transient voltage between E_close(t) and E_open(t) in (19) and (20) followed by (22) and (23), the calculated and simulated PA + link efficiencies are not perfectly matched in a wide range of R_L. Parasitic components in the actual circuit further affect the PA + link efficiency by degrading it in the measurement results with externally applied Q-modulation switching pulse. Nonetheless, the calculated, simulated, and measured efficiencies show similar trends, and the multi-cycle Q-modulation in each case significantly increases η_Qmod over a wide range of R_L and k₂₃ variations thanks to the dynamic impedance matching capability of the Rx.

Fig. 5.

(a) Calculated vs. Simulated transient waveform for l₃(t) at R_L = 500 Ω and d₂₃ = 3 cm, and other parameters in Table I. (b) PA + link efficiency vs. loading variations from 100 Ω to 3.4 kΩ with and without multi-cycle Q-modulation.

A key advantage of the multi-cycle Q-modulation is that it does not need delicate synchronization between the current in the Rx L₃C₃-tank and the SC pulse, which might be difficult to achieve when the carrier frequency is high. Although we constructed the lumped circuit model and its waveforms in section II based on the synchronized condition between the switching pulse and the power carrier, adding delay to the SC signal does not affect the circuit performance because in the steady state the energy stored in the L₃C₃-tank is independent of the delay of the SC signal, but dependent on T_on that spans over multiple periods of T_P. Fig. 6 shows the measured η_Qmod with fixed T_on and variable delays between the power carrier and SC pulse. The optimal SC pulse periods for several R_L and d₃₄ combinations are found from Fig. 4 and the SC signal was generated externally with 0 to 80 ns delay with respect to the power carrier (T_P = 73.74 ns). It can be seen that η_Qmod is almost independent of the delay of the SC pulse.

Fig. 6.

Measured η_Qmod for variable delay between the power carrier at 13.56 MHz and the optimal SC pulses for three cases of (d₂₃ = 2 cm, R_L = 2 kΩ), (d₂₃ = 3 cm and R_L = 500 Ω), and (d₂₃ = 3.5 cm, R_L = 100 Ω).

IV. Automatic Resonance Tuning in Multi-Cycle Q-Modulation

It is important to ensure that the Tx and Rx LC-tanks are tuned at the carrier frequency, f_p, to achieve the best PTE against changes in the parasitic capacitance of the surrounding environment or various objects around the inductive link. The inductive link in the IMD is often adversely affected by the parasitic capacitance of the surrounding tissue environment, which can significantly degrade the PTE, particularly when the Q-factor is high [34]. Proper tuning of the Rx LC-tank becomes even more important when Q-modulation is employed because of the impact of this technique on boosting the Q of Rx to improve the overall PTE. Moreover, small deviation in C₃ due to Q-modulation results in reduction of the stored energy in L₃C₃-tank, leading to degradation in the PTE more severely than a conventional 2-coil inductive link. Fig. 7 shows the simulated η_Qmod vs. variations in C₃′ for conventional and Q-modulated 2-coil inductive links at R_L = 200 Ω and d₂₃ = 3 cm. A 11.4% variation in C₃′ results in 7.5% degradation in the η_Qmod of the Q-modulated inductive link, while the same change results in only 2% degradation in the η_{w/o Qmod} of the conventional 2-coil.

Fig. 7.

Simulated η_Qmod vs. C₃′ variations with and without multi-cycle Q-modulation when R_L = 200 Ω and d₂₃ = 3 cm. With 11.4% change in C₃′, η_Qmod decreases by 7.5% in the Q-modulated 2-coil link, while it only decreases by 2% in the conventional 2-coil link.

To resonate the L₃C₃-tank at f_p, a mechanism similar to the ART used in the power management integrated circuit (PMIC) in [37] was adopted, but implemented with COTS components only. Details of the ART design and operation, and its impact on the inductive link are discussed in [37]. The ART constantly tries to find the maximum η_Qmod in a closed loop to oppose any capacitance or inductance changes imposed by the surrounding environment, parasitic components, process, or duty-cycle variations. In the current prototype, C_ART is implemented as a 5-bit binary capacitor bank, swept from 0.15 pF to 11.7 pF by the MCU on the Rx side. Considering the parasitic capacitance of the NMOS switches (~5.9 pF), the implemented ART can compensate the L₃C₃-tank variations to resonate at f_p = 13.56 MHz.

The implemented algorithm in the MCU, shown in Fig. 8, seeks maximum PDL by sweeping T_on and T_np for the multi-cycle Q-modulation and C_ART for the ART, while monitoring V_REC. Since k₁₂ between the coils in this prototype is small, as shown in Table I, the optimal R_L for PTE and PDL is almost the same [25], and the proposed algorithm to monitor V_REC in the multi-cycle Q-modulation optimizes the PTE as well. In Fig. 9, the measured PA + link efficiency (PTE) and PDL are shown in the 2-coil inductive link at d₂₃ = 3 cm vs. loading variations from 100 Ω to 3.4 kΩ without multi-cycle Q-modulation. These curves show that the PDL and PTE follow the same trend and their optimization within PTE < 40% lead to the same result. V_REC is sampled and digitized before and after stepping T_on to decide the optimal pulse width of the SC signal, during which resonating power builds up in the Rx LC-tank. Then, the optimal T_np−T_on is decided for transferring the stored energy to R_L through the same procedure, while T_on is fixed. In the last step, the optimal C_ART is decided based on the optimal T_on and T_np values (see Fig. 8). The optimization order of T_on, T_np−T_on, and C_ART is not very important because they are repeatedly optimized during the operation. Since these parameters effects on the PTE independently, they can be optimized individually unless the Rx can’t receive the enough power from the inductive link. This simple iterative process, which has been implemented in an ultra low power MCU (MSP430), can dynamically search for and reach/track the highest available PDL and PTE for any given inductive link combination, unless the PTE distribution in Fig. 4a, which is decided by T_on and T_np−T_on, has more than one peak.

Fig. 8.

Flowchart of the control algorithm for multi-cycle Q-modulation with ART, which is implemented in the MCU of the current proof-of-concept prototype Rx module.

Fig. 9.

Measured PA + link efficiency and PDL in the 2-coil inductive link at d₂₃ = 3 cm vs. loading variations from 100 Ω to 3.4 kΩ without multi-cycle Q-modulation.

V. Measurement Results

The proposed multi-cycle Q-modulation + ART techniques were verified by a small (1.5 × 1.8 cm²) proof-of-concept prototype Rx module made of COTS components for the experimental setup show in Fig. 10. The 5-bit capacitor bank, controlled by 5 NMOSs and an MSP430 MCU running the algorithm in Fig. 8, provides fine-tuning in parallel with the Rx series LC-tank, which can be considered as part of the resonance capacitor, C₃ [40]. For instance, when SC is closed, the parallel capacitor bank and C₃ are connected to the DC ground, and resonate at f_p. The SC is controlled by the MCU to reduce the current from the L₃C₃-tank to the rectifier down to zero. This has the same effect as directly shorting the load in the theoretical model of Fig. 2 because the loading, R_L, is defined as the resistive equivalent of all the power consumption following the rectifier.

Fig. 10.

Experimental setup and block diagram of a simple proof-of-concept multi-cycle Q-modulation Rx prototype with ART (enclosed in the blue box).

Rectification following the LC-tank is provided by a full-wave low dropout Schottky diode bridge (BAS4002A). V_REC is sampled and digitized by the MSP430 built in ADC through a resistive attenuator. To demonstrate the PA + link efficiency dependence on the load with and without multi-cycle Q-modulation, the 7.4 mW power consumption of in the MCU is excluded from this measurement. As shown in Fig. 10 schematic, R_L in these measurements is the equivalent resistance following the rectifier, calculated from V_REC / I_REC, where I_REC is the average current out of the full-wave rectifier. In order to set R_L at a desired value, besides the MCU and regulator internal power consumption, which are relatively constant, an additional variable resistance, R_L′, was added to the Rx board and its value was swept from 110 Ω to 27 kΩ.

Fig. 11 shows the measured transient waveforms of V_REC, V_IN+, V_IN−, and SC in Fig. 10 with and without the proposed multi-cycle Q-modulation algorithm in Fig. 8, when R_L = 500 Ω and d₂₃ = 3 cm. It can be seen that the rectifier input voltages, V_IN+ and V_IN−, are boosted by Q-modulation, and V_REC has increased significantly from an average of 2.61 V to 4.15 V with the same RF input source, V_S, coil separation, and R_L.

Fig. 11.

Measured transient waveforms of V_REC, V_IN+, V_IN−, and SC in Fig. 8 without and with automatic multi-cycle Q-modulation at P_Vs,rms = 151 mW, f_p = 13.56 MHz, R_L = 500 Ω, and d₂₃ = 3 cm.

To evaluate the performance of the multi-cycle Q-modulation and ART in terms of PA + link efficiency, η_Qmod, six conditions were tested in Fig. 10 setup: 1) manual tuning without Q-modulation, 2) deliberate 4 pF detuning of C₃′ without Q-modulation, 3) ART without Q-modulation, 4) manual tuning with Q-modulation, 5) automatic Q-modulation, and 6) ART + automatic Q-modulation, using the algorithm in Fig. 8. Figs. 12a and 12b show the results of these measurements vs. R_L at d₂₃ = 3 cm and vs. d₂₃ at R_L = 500 Ω, respectively. The PA + link efficiency was calculated by measuring the input power from the source and input power before the rectifier, considering the rectifier efficiency from the datasheet. The results show that the proposed multi-cycle Q-modulation has significantly increased η_Qmod over a wide range of R_L and d₂₃, which are two parameters that often change during WPT in operation. For instance, in Fig. 12a, the multi-cycle Q-modulation with manual tuning has increased η_Qmod from 7.2% to 18.1% at R_L = 1 kΩ and d₂₃ = 3 cm. Similarly, in Fig. 12b, the multi-cycle Q-modulation has improved η_Qmod from 20.4% to 34.0% at d₂₃ = 2.5 cm and R_L = 500 Ω.

Fig. 12.

Measured results of PA + link efficiency in 6 different conditions: with and without Q-modulation and manual tuning, with and without Q-modulation and 4 pF detuning of the Rx LC-tank, without Q modulation but with ART, and with both automatic Q-modulation and ART. (a) η_Qmod vs. load at d₂₃ = 3 cm, and (b) η_Qmod vs. distance at R_L = 500 Ω.

The fully automated multi-cycle Q-modulation and ART show a slightly lower efficiency than the externally controlled Q-modulation, because T_on, T_np−T_on, and C_ART fluctuate due to their continuous up/down search around their optimal values, according to the algorithm in Fig. 8. The 4 pF detuning degrades η_Qmod with Q-modulation more than a conventional 2-coil link, as discussed in Fig. 7, because of the higher Q-factor in the former link. However, the ART can successfully compensate for detuning of C₃′ to achieve the highest η_Qmod close to manual tuning. Figs. 12a and 12b also show that the ART operation with and without the multi-cycle Q-modulation at R_L = 500 Ω and d₂₃ = 3 cm improves the efficiency by 1.9 % and 7.1 % for a 4 pF detuning of C₃′, respectively. The measurement results demonstrate that the effect of the ART operation with the multi-cycle Q-modulation in the 2-coil inductive link is advantageous compared to the same condition without multi-cycle Q-modulation, which can also be seen in Fig. 7. In this experiment, the maximum PDL was 168.1 mW at R_L = 100 Ω when V_REC = 4.1 V.

Fig. 13 shows the measured transient waveforms of V_REC, V_IN+, V_IN−, and SC with automatic multi-cycle Q-modulation and ART when the load suddenly changes from R_L = 500 Ω to R_L = 250 Ω at d₂₃ = 3 cm. V_REC suddenly drop from 4.22 V to 3.33 V due to higher current demand. Fig. 8 algorithm in the MSP430 tries to find a new optimal T_on and T_np combination that would be a batter match for the new loading, and as a result, recovers part of V_REC drop to stabilize at 3.78 V. The zoomed-in segments at the bottom of Fig. 13 shows that at steady state, T_on and T_np have changed from 258 ns and 437 ns for R_L = 500 Ω to 191 ns and 371 ns for R_L = 250 Ω, respectively.

Fig. 13.

Measured transient waveforms of V_REC, V_IN+, V_IN−, and SC with automatic multi-cycle Q-modulation and ART for sudden load variation from R_L = 500 Ω to 250 Ω at d₂₃ = 3 cm. The algorithm in Fig. 8 finds new optimal T_on and T_np to maximize η_Qmod for the new load condition, and as a result T_on and T_np change from 258 ns and 437 ns to 191 ns and 371 ns, respectively.

VI. Conclusions

We have presented a new multi-cycle Q-modulation method, which can maintain the high PTE in wirelessly powered applications that operate in dynamic environments with motion and variable loading, such as implantable medical devices. The proposed multi-cycle Q-modulation circuit can be easily implemented on the Rx side of conventional 2-coil links either in the form of an ASIC or using COTS components, without any complex circuity or fast switching operation, needed in the conventional Q-modulation technique. Moreover, the proposed technique does not need sophisticated synchronization between the power carrier and Q-modulation switching signals, which facilitate its applicability to wireless links with higher power carrier frequencies. We have also demonstrated usage of the ART along with the new multi-cycle Q-modulation to dynamically maintain the PTE of the inductive link at its peak in the presence of disturbance in the surrounding environment or manufacturing process variations, which can otherwise significantly degrade the PTE by detuning the Rx LC-tank. Thanks to their simplicity, these methods can be extended to a wide variety of applications, utilizing the 2-coil inductive links in wide ranges of loading, separation, misalignment, and environmental variations.

Biographies

Byunghun Lee (S’11) received the B.S. degree from Korea University, Seoul, South Korea, and the M.S. degree from Korea Advanced Institute of Technology (KAIST), Daejeon, South Korea, in 2008 and 2010, respectively.

From 2010 to 2011, he worked on wireless power transfer systems at KAIST as a design engineer. He is currently pursuing his Ph.D. degree in Electrical and Computer Engineering at Georgia Institute of Technology. His research interests include analog/mixed-signal IC design and wireless power/data transfer systems for biomedical applications.

Pyungwoo Yeon (S’14) received the B.Sc. degree in electrical and computer engineering from Seoul National University, Seoul, Korea, in 2010, and the M.S. degree in electrical engineering and information systems from the University of Tokyo, Tokyo, Japan, in 2012.

From February 2012 to May 2014, he worked as an analog IC designer at Samsung Electronics, Yongin, Korea, designing wireless power receiver IC for mobile devices. He is now pursuing his doctoral degree in the electrical and computer engineering at Georgia Institute of Technology and working on developing wirelessly powered implantable biomedical system at the GT-Bionics Lab. His research interests include analog/mixed-signal integrated circuit design, wireless power/data transfer, energy harvesting, and biomedical/implantable system design.

Maysam Ghovanloo (S’00–M’04–SM’10) received the B.S. degree in electrical engineering from the University of Tehran in 1994, the M.S. degree in biomedical engineering from the Amirkabir University of Technology in 1997, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan in 2003 and 2004, respectively. From 2004 to 2007, he was an Assistant Professor at NC-State University, Raleigh, NC. He joined Georgia Institute of Technology, Atlanta, GA in 2007, where he is an Associate Professor and the Founding Director of the GT-Bionics Lab. He has authored or coauthored more than 200 peer-reviewed publications.

Dr. Ghovanloo is an Associate Editor of the IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING and IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS. He was the chair of the 2015 IEEE Biomedical Circuits and Systems Conference in Atlanta, GA, and a member of the IEEE CAS Distinguished Lecture Program in 2015–16.