Design of Wireless Power and Information Transfer Systems Considering Figure of Merit for Information

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Abstract

I. Introduction

Wireless power transfer (WPT) based on inductively coupled resonance was first introduced in [1], where an efficiency of about 40% was achieved with a separation of approximately 2 m between Tx and Rx of spiral shapes. Since then, the inductively coupled resonant WPT technology has been developed in theory and also applied to many applications including WPTs to multiple receivers, electric mobile phones, home appliances, motor vehicles, biomedical devices, and so on [2–6]. In most practical WPT devices, the information of power-receiving units needs to be transferred to power-transmitting units. There may be a variety of information but the identification numbers, stored power levels, etc., are essentially required in the basic operation of WPT devices. To cope with this necessity, the simultaneous wireless and information power transfer (SWIPT) has been studied in various forms of geometry and for the possible merging of information and power in the near future [7–10]. However, most of the research papers in this area focus on the numerous architectures in the high level of the hierarchy. However, some papers focusing on actual structures enabling information transfer in the current WPT frame are at times available, under the name of wireless power and information transfer (WPIT).

In [11], theory of high-order modulation for near-field RF identification (RFID) and WPT was presented. A system that transmits power using a triangular current waveform and transmits information to its third-order harmonic was reported in [12]. In [13], a WPIT technology based on binary frequency shift keying modulation using the dual bands of a series-parallel combined resonant circuit was proposed. Its experimental prototype exhibited a communication rate up to 20 kbps, while maintaining a power transfer efficiency greater than 85% at a distance of 50 mm. However, these systems are complex in configuration. In [14], a frequency-agile load modulation scheme was proposed for a reliable near-field magnetic resonance WPT system. A wireless power and bidirectional data transmission scheme through mutual coupling between two isolated LC resonators was proposed in [15]. The near-field communication (NFC) [16] used for RFID technology may also be promising for delivery of this information by means of load modulation techniques. The existing NFC and other WPIT demonstrations are practically limited within a distance of several centimeters.

In this paper, we use simple mathematical expressions to analyze a WPIT system in terms of power and information transfer capabilities. Then, we provide design equations for a specifically required efficiency and transfer capability of Rx status information. Especially, to assess the information (including Rx status) transfer capability from Rx to Tx in a systematic manner, we propose a new metric using the input impedances at the Tx terminal depending on Rx loads. Its effectiveness and usefulness is validated by several design examples.

In Section II, the WPT performance of a single-input multiple-output (SIMO) system in terms of input impedances, efficiencies, and optimum loads for maximum efficiency are briefly discussed. Then, we newly define the figure of merit for information delivery using Tx input impedance variations depending on Rx load variations and demonstrate its usefulness. In Section III, we present some practical examples to validate the proposed WPIT methodology with electromagnetic (EM)-simulated results. The conclusions and closing comments are in Section IV.

II. Design Theory

Fig. 1 shows the equivalent circuit of a WPIT system. The system is composed of Tx0 (or Tx) and Rx1 (or Rx) coils (or loops), which may be a single turn loop or a multi-turn loop or a spiral coil, separated by a certain distance d. The loops, having inductances, are loaded with capacitors for LC resonance. The power is transferred from Tx to Rx via magnetically coupled resonant loops. R_i and L_i are the resistance and inductance of the Tx (i = 0) and Rx (i = 1) loops, respectively. C_i is the capacitance of the lumped capacitor for Tx (i = 0) and Rx (i = 1), respectively. r_i is the radius of the i^th loop and r_in,i is the inner radius of the i^th loop wire. V₀ is the voltage at the input. The single-pole single-through (SPST) switch is operated between off (for an optimum load) and on (for a shorted load). The usual function of the Rx matching circuit is to transform the usually small Rx optimum load to the large device load (say, 50 Ω). Conventional WPT has been made with the switch off to achieve maximum efficiency. The Rx status information (such as a device identity, energy charged levels, etc.) can be transferred from Rx to Tx by switching between the on and off states of the SPST. Based on this equivalent circuit, the system is usually formulated by a Z-matrix given by

Fig. 1

Configuration of a magnetically coupled wireless power and information transfer (WPIT) system.

where k is the coupling coefficient between Tx and Rx loops [17]. It is well known that k approaches 1 as the distance between Tx and Rx becomes 0 and it approaches 0 as the distance between Tx and Rx becomes very large. V₀ is the source voltage, R_L is the Rx load resistance, and ω is the angular frequency. I₀ and I₁ are the currents on loop 1 and 2, respectively. The ratio of currents on Tx and Rx loops is given by [18]:

It is observed that as R_L increases, (2) becomes small and approaches 0 as R_L goes to infinity (open). The phase of the current flowing on Rx (I₁) is 90° ahead of that flowing on Tx (I₀) following Faraday’s law. The input impedance is defined as the ratio of V₀ and I₀ on a Tx terminal and expressed as

At the resonant frequency, the input impedance (3) reduces to

If we define the figure of merit for the power transfer (F) as

the input impedance (4) at the resonant frequency depending on the Rx load R_L can be re-written as

which is a purely real number. At this point, the essential part of power transfer efficiency for a resonant WPT system needs to be summarized [17]. The efficiency can be stated in a simple manner by

where b is the deviation factor against the Rx optimum load R_L,opt defined by

A short observation of (7) tells that it is a function of the figure of merit for power transfer (F) and b, and a large F is merely a necessary condition for a high efficiency. The maximum efficiency is guaranteed with the additional condition of b=1 (RL=RL,opt=R11+F2).

Now, we examine the ways of transferring Rx status information (or others) to Tx. Monitoring (6) at the Tx terminal depending on R_L is just like monitoring the current on Tx (I₀) depending on R_L since I₀ = V₀/Z_in. When R_L = 0 (short), the system is at the over-coupled limit, no power is transferred to Rx, and the efficiency (7) is 0. However, the largest current is induced on Rx and the magnetic flux back to Tx affects the Tx input impedance most significantly, and the input impedance becomes the largest: R₀(1 + F₂). With this, the Tx current I₀ becomes the smallest. When R_L = ∞ (open), no current is induced on the Rx loop, the system is at the under-coupled limit, no power is transferred to Rx, the efficiency (7) is also 0, the Tx is as if being isolated from Rx, and the Tx input impedance becomes that of its own: R₀. When RL=RL,opt=R11+F2 (b=1) (optimum for maximum efficiency), (6) becomes

The current variations on Tx (or the input impedance variations) depending on R_L (open, short, optimum) can be used for the information transfer from Rx to Tx. These input impedances (6) and the power transfer efficiencies (7) are summarized in Table 1.

Table 1

Input impedances and transfer efficiencies depending on Rx loads at resonant frequency

NFC [16] more or less utilizes these variations of Z_in at the Tx terminal occurring between the two load states of Rx, but mostly at a close proximity of Tx to Rx. Using the results in Table 1, we can assess the transfer capability of Rx information for the usual resonant WPT systems.

The best choice of the Rx load set for information transfer from Rx to Tx may be the short (over-coupled limit) and open (under-coupled limit) states, since this results in the largest current variation at the Tx with the effect of a lowest bit error rate. However, it is noted that with this choice, power is not transferred to Rx. The best Rx load choice for WPIT may be the short (for the greatest magnetic flux effect to Tx) and optimum (for the highest power transfer efficiency) loads. The real resistance of the SPST switch (Fig. 1) for the short state is not exactly 0. The practical resistance is about 10 mΩ but does not much affect the results in Table 1.

For the purpose of quantitative assessment by a new metric, we define the figure of merit for Rx information transfer to Tx (F_I) as a ratio of the Tx Z_in when R_L = 0 and the same when R_L = R_L,opt in Table 1, given by

The figure of merit for Rx information transfer to Tx (F_I) as defined in (10) also corresponds to the current (I₀) variation at the Tx terminal depending on Rx loads of “short” and “optimum” R_L since I₀ = V₀/Z_in. The metric (10) is plotted in Fig. 2 together with the maximum efficiencies as a function of the figure of merit for power transfer (F). We can see that as the figure of merit for power (F) increases, the figure of merit for information transfer (F_I) also increases and the power transfer efficiency also increases. Notice that when F is roughly larger than 3, the efficiency is greater than 50% and F_I almost ap proaches F. Taking an example, the transfer efficiency of about 80% is achieved with F = 9, where F_I is also about 9.

Fig. 2

Figure of merit for Rx information transfer to Tx (F_I) and maximum efficiency (η_max) at the resonant frequency as a function of figure of merit for power (F) for a WPIT system.

III. Design Examples Validated with Electromagnetic Simulations

The real resonant WPT systems realized for an F given by (5) are numerous. Several realizations for a system consisting of a Tx loop with r₀ = 10 cm and a Rx loop with r₀ = 5 cm are shown in Table 2, where the quality factor Q is the geometrical mean of Q₀ and Q₁ (5). The coupling coefficients k were obtained using [16].

Table 2

Examples of design system configurations (r₀ = 10 cm, r₁ = 5 cm, r_in0 = r_in1 = 0.1 cm, Q₁ = 388.81, and Q₂ = 334.23)

In Table 3, we summarize the same as in Table 2 but for a different system with larger Tx and Rx loops with r₀ = r₁ = 20 cm, enabling power and information transfer in longer ranges. It is seen in Table 3 that an efficiency of 56% is achieved for the case of d = 80 cm with F_I ≈ F = 7.3. The figure of merit for power (F), one important parameter in the resonant WPT efficiency, can now be understood as the Tx current variations used for Rx information transfer.

Table 3

Examples of design system configurations (r₀ = r₁ = 20 cm, r_in0 = r_in1 = 0.2 cm, Q₀ = Q₁ = 776.2)

We take the two system configurations with d = 15 cm and 25 cm in Table 2 and plot the real part (a) and imaginary part (b) of the input impedance (3) for different loads of R_L = 0 and RL=RL,opt=R11+F2 as a function of frequency in Fig. 3. The radii of Tx and Rx loops are 10 cm (Q₀ = 388.8) and 5 cm (Q₁ = 334.2), respectively. The Tx and Rx loop wire radii are 0.1 cm. The imaginary parts (b) of the input impedances for both cases of d = 15 cm and d = 25 cm are observed to be zero at the resonant frequency since the system is at resonance. The real parts (a) of the input impedances at the resonant frequency, given by (6) and in Table 1, have the maximums when R_L = 0. The circuit-simulated figures of merit for information transfer (F_I) are 3.7/0.5 (= 7.38) for the case of d = 15 cm and 0.42/0.17 (= 2.48) for the case of d = 25 cm. The EM-simulated figures of merit for information transfer (F_I) are 3.26/0.45 (= 7.2) for the case of d = 15 cm and 0.33/0.16 (= 2.1) for the case of d = 25 cm. The results are in agreement with the theoretical ones of 7.4 and 2.5 in Table 2. These F_Is should be understood as the Tx current variations due to the Rx load changes. The overall EM-simulated input impedances are shown to be in good agreement with the theoretical ones.

Fig. 3

Input impedances of SISO system for different loads (r₀ = 10 cm, r₁ = 5 cm, r_in0 = r_in1 = 0.1 cm, Q₁ = 388.81, and Q₂ = 334.23): (a) real parts and (b) imaginary parts.

Fig. 4 shows the transient responses of the Tx currents when the Rx load switches between with R_L = 0 and RL=RL,opt=R11+F2 with 10 kbps (a) and 20 kbps (b) for the case of d = 15 cm and Q=Q0Q1=360.5 in Table 2. Based on the AC steady state analysis, the Tx current variation (characterized by F_I) with each Rx load has been found to be almost identical to the theoretical value of 7.4. Based on the transient analysis with increasing switching rates, Fig. 4(a) and 4(b) show that it takes about 0.5 ms for the Tx current to reach a steady state. The source voltage V₀ in Fig. 1 is assumed to be 1 V. For the shorted Rx load with R_L = 0 Ω and optimum load with R_L = 0.25 Ω, the average Tx current envelopes are 0.33 A and 1.97 A, respectively, for the case of the 10 kbps switching rate (Fig. 4(a)). Thus, the ratio of the Tx currents is 6.0 (= 1.97/0.33). For the case of 20 kbps (Fig. 4(b)), the ratio of the Tx current envelopes is 5.0 (= 1.96/0.39). Even though the ratio of Tx currents somewhat deviates from the expected F_I due to the effects of the transients from switching operations.

Fig. 4

Circuit-simulated transient Tx current (I₀) for different Rx loads with 0 (short) and 0.25 Ω (optimum) (V₀ = 1 V, frequency = 6.78 MHz, r₀ = 10 cm, r₁ = 5 cm, r_in0 = r_in1 = 0.1 cm, Q₁ = 388.8, Q₂ = 334.2, d = 15 cm, k = 0.0203, and F = 7.3): (a) data rate = 10 kbps and (b) data rate = 20 kbps.

Fig. 5 shows the same as plotted in Fig. 4 for the different configuration of d = 80 cm and Q=Q0Q1=776.2 (F=3.4,FI=3.6) in Table 3. The Tx current variation with the mentioned two Rx loads when reached in steady state is about 3.5 (close to the theoretical F_I of 3.6). The source voltage V₀ in Fig. 1 is assumed to be 1 V. The short and optimum loads (R_Ls) are 0 Ω and 0.24 Ω. The ratio of Tx current envelopes is 3.3 for the case of 10 kbps and 3.1 for the case of 20 kbps, again close to the theoretical value (F_I) of 3.6.

Fig. 5

Circuit-simulated transient Tx current (I₀) for different Rx loads with 0 (short) and 0.24 Ω (optimum) (V₀ = 1 V, frequency = 6.78 MHz, r₀ = r₁ = 20 cm, r_in0 = r_in1 = 0.2 cm, Q₁ = Q₂ = 776.2, d = 80 cm, k = 0.0044, and F = 3.4): (a) data rate = 10 kbps and (b) data rate = 20 kbps.

The figure of merit for information transfer (F_I) as defined in (10), expressed as a function of the figure of merit for power transfer (F), has been shown to be very useful in characterizing and estimating the resonant WPIT systems, especially in their capability of transferring Rx information to Tx.

IV. Conclusion

A new metric named “a figure of merit for information transfer” has been defined to assess WPIT systems in their capability to transfer information from Rx to Tx. Its usefulness has been verified for several WPIT system configurations with wide ranges of Tx to Rx distances. It has been found to be close to the figure of merit for power and shown to be the ratio of the Tx currents when the Rx load is shorted and optimum. Introduction of the new metric is expected to put a basic foundation in the evaluation of WPIT systems which started being developed recently.

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