Patent Publication Number: US-9837712-B2

Title: Antenna array calibration for wireless charging

Description:
PRIORITY APPLICATIONS 
     This application claims the benefit of U.S. provisional patent application Nos. 62/024,621, filed Jul. 15, 2014; 62/024,628, filed Jul. 15, 2014; 62/051,023, filed Sep. 16, 2014; 62/052,517, filed Sep. 19, 2014; 62/053,845, filed Sep. 23, 2014; and 62/052,822, filed Sep. 19, 2014, which are incorporated herein by reference in their entireties. 
    
    
     FIELD OF THE DISCLOSURE 
     The technology of the disclosure relates generally to wireless charging of a battery. 
     BACKGROUND 
     Mobile communication devices have become increasingly common in current society. The prevalence of these mobile communication devices is driven in part by the many functions that are now enabled on such devices. Demand for such functions increases processing capability requirements for the mobile communication devices. As a result, increasingly complex integrated circuits (ICs) have been designed and manufactured to provide increasingly greater functionality in the mobile communication devices. However, the increasingly complex ICs also tend to consume more battery power during operation. 
     It has become more challenging to prolong battery life of the mobile communication devices in the face of continuing demand for higher processing speed, richer multimedia experience, and constant connectivity. As a result, the mobile communication devices are increasingly equipped with high-capacity batteries that are both expensive and space consuming. Even with the high-capacity batteries, the mobile communication devices often need to be plugged into the wall for recharging before the day is over. 
     SUMMARY 
     Aspects disclosed in the detailed description include antenna array calibration for wireless charging. In this regard, a wireless charging station is provided and configured to calibrate a plurality of antenna elements in the wireless charging station. In one aspect, an initial calibration sequence is performed each time the wireless charging station is powered on. The initial calibration sequence utilizes a reference antenna element, which is an antenna element randomly selected from the plurality of antenna elements, to determine relative receiver phase errors between the reference antenna element and each of the other antenna elements in the antenna array. In another aspect, a training sequence is performed after completing the initial calibration sequence. The training sequence utilizes a wireless training signal and the relative receiver phase errors obtained in the initial calibration sequence to determine total relative phase errors between the reference antenna element and each of the other antenna elements in the antenna array. Adjustments can then be made to match respective total relative phase errors among the plurality of antenna elements to achieve phase coherency among the plurality of antenna elements for improved wireless charging power efficiency. 
     In this regard, in one aspect, a wireless charging station is provided. The wireless charging station comprises a plurality of antenna elements. Each of the plurality of antenna elements comprises a receiver and a transmitter coupled to an antenna. Each of the plurality of antenna elements also comprises a phase shift circuitry coupled to the transmitter and configured to adjust transmitter phase of the transmitter. The wireless charging station also comprises a controller coupled to the plurality of antenna elements. The controller is configured to select a reference antenna element from the plurality of antenna elements wherein unselected ones of the plurality of antenna elements are non-reference antenna elements. For each of the non-reference antenna elements, the controller is configured to transmit a first calibration signal from a transmitter of the reference antenna element. For each of the non-reference antenna elements, the controller is also configured to measure phase a x  of the first calibration signal at a receiver of the reference antenna element. For each of the non-reference antenna elements, the controller is also configured to measure phase b x  of the first calibration signal at a receiver of a non-reference antenna element. For each of the non-reference antenna elements, the controller is also configured to transmit a second calibration signal from a transmitter of the non-reference antenna element. For each of the non-reference antenna elements, the controller is also configured to measure phase a y  of the second calibration signal at the receiver of the non-reference antenna element. For each of the non-reference antenna elements, the controller is also configured to measure phase b y  of the second calibration signal at the receiver of the reference antenna element (phase b y ). For each of the non-reference antenna elements, the controller is also configured to determine relative receiver phase error and relative transmitter phase error between the non-reference antenna element and the reference antenna element based on the phase a x , the phase a y , the phase b x , and the phase b y . 
     Those skilled in the art will appreciate the scope of the disclosure and realize additional aspects thereof after reading the following detailed description in association with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings incorporated in and forming a part of this specification illustrate several aspects of the disclosure and, together with the description, serve to explain the principles of the disclosure. 
         FIG. 1A  is an exemplary illustration of a lithium-ion (Li-ion) battery charging profile; 
         FIG. 1B  is a capacity-voltage curve providing an exemplary illustration of Li-ion battery capacity as a function of a charging voltage and a charging current; 
         FIG. 2  is a schematic diagram of an exemplary wireless charging system, in which a wireless charging station is configured to charge one or more wireless stations via one or more respective wireless radio frequency (RF) charging signals; 
         FIG. 3  is a schematic diagram of an exemplary wireless charging station including a plurality of antenna elements that may be calibrated to achieve phase coherency when transmitting the one or more wireless RF charging signals of  FIG. 2 ; 
         FIG. 4  is a schematic diagram of an exemplary first configuration for performing an initial calibration sequence among the plurality of antenna elements of  FIG. 3 ; 
         FIG. 5  is a schematic diagram of an exemplary second configuration for performing an initial calibration sequence among the plurality of antenna elements of  FIG. 3 ; 
         FIG. 6  is a schematic diagram of an exemplary third configuration for performing an initial calibration sequence among the plurality of antenna elements of  FIG. 3 ; 
         FIG. 7  is a schematic diagram of an exemplary configuration for performing a training sequence among the plurality of antenna elements of  FIG. 3 ; and 
         FIG. 8  is a schematic diagram of an exemplary configuration for verifying phase coherency among the plurality of antenna elements of  FIG. 3 . 
     
    
    
     DETAILED DESCRIPTION 
     The embodiments set forth below represent the necessary information to enable those skilled in the art to practice the disclosure and illustrate the best mode of practicing the disclosure. Upon reading the following description in light of the accompanying drawings, those skilled in the art will understand the concepts of the disclosure and will recognize applications of these concepts not particularly addressed herein. It should be understood that these concepts and applications fall within the scope of the disclosure and the accompanying claims. 
     Aspects disclosed in the detailed description include antenna array calibration for wireless charging. In this regard, a method for calibrating a plurality of antenna elements of an antenna array in a wireless charging station is provided. In one aspect, an initial calibration sequence is performed each time the wireless charging station is powered on. The initial calibration sequence utilizes a reference antenna element, which is an antenna element randomly selected from the plurality of antenna elements, to determine relative receiver phase errors between the reference antenna element and each of the other antenna elements in the antenna array. In another aspect, a training sequence is performed after completing the initial calibration sequence. The training sequence utilizes a wireless training signal and the relative receiver phase errors obtained in the initial calibration sequence to determine total relative phase errors between the reference antenna element and each of the other antenna elements in the antenna array. Adjustments can then be made to match respective total relative phase errors among the plurality of antenna elements to achieve phase coherency among the plurality of antenna elements for improved wireless charging power efficiency. 
     Before discussing the wireless charging concepts of the present disclosure, a brief overview of a lithium-ion (Li-ion) battery charging profile is provided with reference to  FIGS. 1A and 1B . The discussion of specific exemplary aspects of wireless charging starts below with reference to  FIG. 2 . 
     In this regard,  FIG. 1A  is an exemplary illustration of a Li-ion battery charging profile  10 . As is well known in the industry, a Li-ion battery (not shown) has strict requirements on charging voltage and charging current because Li-ion cells (not shown) in the Li-ion battery cannot accept overcharge. In this regard, the Li-ion battery can only take what it can absorb. Anything extra can cause stress and even permanent damage to the Li-ion battery. 
     When the Li-ion battery is connected to a charging source (not shown) at time T 0 , the Li-ion battery is in a constant current stage  12 , in which charging voltage (referenced in drawings as V) rises while charging current (referenced in drawings as I) remains constant. As such, an effective charging power (referenced in drawings as P EFF ) (P EFF =V×I) increases as a result of the charging voltage increase, thus enabling fast charging of the Li-ion battery. At time T 1 , the Li-ion battery is in a saturation charge stage  14 , in which the charging voltage peaks and levels off while the charging current starts to decline. As such, the effective charging power decreases as a result of the charging current decline. At time T 2 , the Li-ion battery is in a ready stage  16 , wherein the Li-ion battery is charged to a desired voltage level and the charging current drops to zero (0). In this regard, the effective charging power also drops to zero (0) to prevent overcharging damage to the Li-ion battery. At time T 3 , the Li-ion battery is in a standby stage  18 , in which the charging current may be applied occasionally to top the Li-ion battery up to the desired voltage level. 
       FIG. 1B  is a capacity-voltage curve  20  providing an exemplary illustration of a Li-ion battery capacity as a function of the charging voltage and the charging current of  FIG. 1A . The capacity-voltage curve  20  comprises a capacity curve  22 , a charging voltage curve  24 , and a charging current curve  26 . When the Li-ion battery is connected to the charging source, the charging voltage curve  24  shoots up quickly. In this regard, the Li-ion battery is in the constant current stage  12  according to the Li-ion battery charging profile  10  of  FIG. 1A . As the capacity curve  22  gradually peaks, the charging current curve  26  declines quickly and the charging voltage curve  24  levels off. In this regard, the Li-ion battery is in the saturation charge stage  14  according to the Li-ion battery charging profile  10 . Since the Li-ion battery cannot accept overcharge, the charging current must be cut off. A continuous trickle charge (maintenance charge) would cause plating of metallic lithium, thus compromising safety of the Li-ion battery. Hence, according to the Li-ion battery charging profile  10  and the capacity-voltage curve  20 , the effective charging power increases when the Li-ion battery is in the constant current stage  12  and decreases when the Li-ion battery is in the saturation charge stage  14  to ensure fast charging and protect the Li-ion battery from overcharging damage. 
     The Li-ion battery has become increasingly popular in battery-operated electronic devices, such as smartphones, tablets, and portable computers, due to many advantages over traditional batteries (e.g., nickel-cadmium batteries). For example, the Li-ion battery has higher power density, produces less self-discharge, and requires lower maintenance to prolong battery life than the traditional batteries. Concurrent to the prevalence of Li-ion battery technology, wireless charging is also gaining traction in the wireless communication industry and may one day replace charging plugs and wires, similar to how Bluetooth™ and wireless-fidelity (Wi-Fi) have eliminated communication cables (e.g., Ethernet cables) in peer-to-peer and peer-to-multi-peer communications. 
     In this regard,  FIG. 2  is a schematic diagram of an exemplary wireless charging system  28 , wherein a wireless charging station  30  is configured to charge one or more wireless stations  32 ( 1 )- 32 (N) via one or more respective wireless RF charging signals  34 ( 1 )- 34 (N). The one or more wireless stations  32 ( 1 )- 32 (N) include one or more respective batteries  36 ( 1 )- 36 (N). In a non-limiting example, the one or more batteries  36 ( 1 )- 36 (N) are Li-ion batteries. In this regard, the Li-ion battery charging profile  10  of  FIG. 1A  and the capacity-voltage curve  20  of  FIG. 1B  are applicable when charging the one or more batteries  36 ( 1 )- 36 (N) in the wireless charging system  28 . In another non-limiting example, the one or more wireless RF charging signals  34 ( 1 )- 34 (N) are provided on an industrial, scientific, and medical (ISM) band that may operate in nine hundred fifteen megahertz (915 MHz), twenty-four hundred megahertz (2400 MHz), fifty-eight hundred megahertz (5800 MHz), or twenty-four gigahertz (24 GHz) RF spectrums. 
     The wireless charging station  30  has a total available power (referenced in drawings as P TOTAL ), which must be set below a maximum power (not shown) that is set by regulatory authorities such as the Federal Communications Commission (FCC) in the United States. The total available power is shared among the one or more wireless stations  32 ( 1 )- 32 (N). The wireless charging station  30  dynamically determines how the total available power is distributed among the one or more wireless stations  32 ( 1 )- 32 (N). In this regard, the more wireless stations that are in the wireless charging system  28 , the smaller share of the total available power each wireless station will receive. 
     With continuing reference to  FIG. 2 , the wireless charging station  30  includes a plurality of antenna elements (not shown). In a non-limiting example, the wireless charging station  30  can have in excess of ten thousand ( 10 , 000 ) antenna elements. The plurality of antenna elements in the wireless charging station  30  may be further configured to form one or more antenna arrays  38 ( 1 )- 38 (N), in which each of the one or more antenna arrays  38 ( 1 )- 38 (N) includes at least two antenna elements among the plurality of antenna elements of the wireless charging station  30 . The one or more antenna arrays  38 ( 1 )- 38 (N) are configured to transmit the one more wireless RF charging signals  34 ( 1 )- 34 (N) to the one or more wireless stations  32 ( 1 )- 32 (N), respectively. To illustrate the configuration and operation of the wireless charging system  28 , wireless station  32 ( 1 ), wireless RF charging signal  34 ( 1 ), and antenna array  38 ( 1 ) are discussed as a non-limiting example. It should be understood that the configuration and operation discussed herein are applicable to the one or more antenna arrays  38 ( 1 )- 38 (N), the one or more wireless RF charging signals  34 ( 1 )- 34 (N), and the one or more wireless stations  32 ( 1 )- 32 (N) as well. 
     If, for example, the antenna array  38 ( 1 ) includes four antenna elements  40 ( 1 )- 40 ( 4 ), the wireless RF charging signal  34 ( 1 ) will include four RF signals  42 ( 1 )- 42 ( 4 ) transmitted from the four antenna elements  40 ( 1 )- 40 ( 4 ), respectively. In this regard, the wireless RF charging signal  34 ( 1 ) is a beamformed wireless RF charging signal. Beamforming is a modern wireless signal transmission scheme, in which multiple wireless signals, such as the four RF signals  42 ( 1 )- 42 ( 4 ), are transmitted simultaneously toward a single wireless receiver. If phases of the multiple wireless signals are coherent, the wireless receiver will be able to linearly combine the multiple wireless signals for improved signal strength and power gain. 
     Since the four RF signals  42 ( 1 )- 42 ( 4 ) may arrive at the wireless station  32 ( 1 ) through different paths, the four antenna elements  40 ( 1 )- 40 ( 4 ) in the antenna array  38 ( 1 ) are calibrated to ensure phase coherence when the four RF signals  42 ( 1 )- 42 ( 4 ) arrive at the wireless station  32 ( 1 ). By having the phase coherence among the four RF signals  42 ( 1 )- 42 ( 4 ), a total RF power (referenced in drawings as P RF ) of the wireless RF charging signal  34 ( 1 ) can be linearly controlled by adjusting individual RF power of the four RF signals  42 ( 1 )- 42 (N). Hence, the total RF power of the wireless RF charging signal  34 ( 1 ) can be maximized. 
     If the antenna array  38 ( 1 ) and the wireless station  32 ( 1 ) are disposed in a line-of-sight (LOS) arrangement, transmitter phases and amplitudes of the four RF signals  42 ( 1 )- 42 ( 4 ) can be estimated based on a training signal (not shown) provided by the wireless station  32 ( 1 ) under the assumption that the training signal would have a high degree of phase correlation with the wireless RF charging signal  34 ( 1 ). However, this may not always be the case in the wireless charging system  28  because the antenna array  38 ( 1 ) and the wireless station  32 ( 1 ) may not always be disposed in the LOS arrangement. When the antenna array  38 ( 1 ) and the wireless station  32 ( 1 ) are not disposed in the LOS arrangement, the estimated transmitter phases and amplitudes based on the training signal may be inaccurate. As a result, it may be more difficult to preserve phase coherence among the four RF signals  42 ( 1 )- 42 ( 4 ) and control the total RF power in the wireless RF charging signal  34 ( 1 ). Consequently, it is also difficult for the wireless charging station  30  to control the effective charging power according to the Li-ion battery charging profile  10  of  FIG. 1A  since the effective charging power is proportionally related to the total RF power. In this regard, one or more battery charging signal indications (BCSIs)  44 ( 1 )- 44 (N) are provided by one or more wireless charging circuits  46 ( 1 )- 46 (N) in the one or more wireless stations  32 ( 1 )- 32 (N), respectively, to help control the effective charging power according to the Li-ion battery charging profile  10 . 
     For example, BCSI  44 ( 1 ) provided by the wireless station  32 ( 1 ) indicates a difference between the effective charging power being provided to battery  36 ( 1 ) and a target charging power determined based on the Li-ion battery charging profile  10  of  FIG. 1A . In a non-limiting example, the BCSI  44 ( 1 ) is set to zero (0) when the effective charging power is greater than the target charging power to request a decrease of the total RF power in the wireless RF charging signal  34 ( 1 ). In another non-limiting example, the BCSI  44 ( 1 ) is set to one (1) when the effective charging power is less than the target charging power to request an increase of the total RF power in the wireless RF charging signal  34 ( 1 ). Upon receiving the BCSI  44 ( 1 ), the wireless charging station  30  adjusts the individual RF power of the four RF signals  42 ( 1 )- 42 ( 4 ) accordingly. For example, the wireless charging station  30  can decrease the individual RF power of the four RF signals  42 ( 1 )- 42 ( 4 ) if the BCSI  44 ( 1 ) is set to zero (0), or increase the individual RF power of the four RF signals  42 ( 1 )- 42 ( 4 ) when the BCSI  44 ( 1 ) is set to one (1). Hence, by providing the BCSI  44 ( 1 ) to the wireless charging station  30  continuously, or according to a predefined feedback schedule, the effective charging power provided to the battery  36 ( 1 ) can be gradually adjusted to eventually match the target charging power. 
     In addition to providing the one or more BCSIs  44 ( 1 )- 44 (N), the one or more wireless stations  32 ( 1 )- 32 (N) may be configured to provide one or more BCSI resolution (BCSIr) signals  44 ′( 1 )- 44 ′(N). The one or more BCSIr signals  44 ′( 1 )- 44 ′(N) indicate one or more power differentials between one or more effective charging powers provided to the one or more batteries  36 ( 1 )- 36 (N) and one or more target charging powers required by the one or more batteries  36 ( 1 )- 36 (N), respectively. 
     As mentioned earlier, if phases of the multiple wireless signals, such as the four RF signals  42 ( 1 )- 42 ( 4 ) transmitted by the antenna array  38 ( 1 ), are coherent, the wireless receiver at the wireless station  32 ( 1 ) will be able to linearly combine the multiple wireless signals for improved signal strength and power gain. To further illustrate how the wireless charging station  30  may be configured to transmit coherently the one more wireless RF charging signals  34 ( 1 )- 34 (N),  FIG. 3  is a schematic diagram of an exemplary wireless charging station  48  including a plurality of antenna elements  50 ( 1 )- 50 (M) that may be calibrated to achieve phase coherency when transmitting the one or more wireless RF charging signals  34 ( 1 )- 34 (N) of  FIG. 2 . 
     With reference to  FIG. 3 , the plurality of antenna elements  50 ( 1 )- 50 (M) respectively include a plurality of receivers  52 ( 1 )- 52 (M) and a plurality of transmitters  54 ( 1 )- 54 (M). The plurality of receivers  52 ( 1 )- 52 (M) and the plurality of transmitters  54 ( 1 )- 54 (M) are respectively coupled to a plurality of antennas  56 ( 1 )- 56 (M) via a plurality of signal paths  58 ( 1 )- 58 (M). In a non-limiting example, the plurality of signal paths  58 ( 1 )- 58 (M) may be provided as coaxial cables. The plurality of transmitters  54 ( 1 )- 54 (M) may be powered by a power source  60 . The plurality of receivers  52 ( 1 )- 52 (M) is coupled to a plurality of receiver oscillators  62 ( 1 )- 62 (M) that determines operation frequency of the plurality of receivers  52 ( 1 )- 52 (M), respectively. The plurality of transmitters  54 ( 1 )- 54 (M) is coupled to a plurality of transmitter oscillators  64 ( 1 )- 64 (M) that determines operation frequency of the plurality of transmitters  54 ( 1 )- 54 (M), respectively. 
     The plurality of antenna elements  50 ( 1 )- 50 (M) comprises a plurality of phase shift circuitries  66 ( 1 )- 66 (M), respectively. The plurality of phase shift circuitries  66 ( 1 )- 66 (M) is coupled to the plurality of transmitters  54 ( 1 )- 54 (M) and configured to adjust transmitter phases of the plurality of transmitters  54 ( 1 )- 54 (M), respectively. The plurality of antenna elements  50 ( 1 )- 50 (M) also comprises a plurality of registers  68 ( 1 )- 68 (M), respectively. The plurality of registers  68 ( 1 )- 68 (M) is coupled to the plurality of phase shift circuitries  66 ( 1 )- 66 (M) and configured to store the transmitter phases of the plurality of transmitters  54 ( 1 )- 54 (M), respectively, after being adjusted by the plurality of phase shift circuitries  66 ( 1 )- 66 (M). 
     The wireless charging station  48  comprises a controller  70  coupled to the plurality of receivers  52 ( 1 )- 52 (M) and the plurality of transmitters  54 ( 1 )- 54 (M). As is further discussed later with reference to  FIGS. 4-9 , the controller  70  is configured to collect a plurality of feedback information  72 ( 1 )- 72 (M) from the plurality of receivers  52 ( 1 )- 52 (M), respectively. The controller  70  then controls the plurality of phase shift circuitries  66 ( 1 )- 66 (M) to adjust the transmitter phases of the plurality of transmitters  54 ( 1 )- 54 (M) based on the plurality of feedback information  72 ( 1 )- 72 (M), respectively. 
     The wireless charging station  48  also comprises a wireless communication interface  74 , which may be configured to receive the one or more BCSIs  44 ( 1 )- 44 (N) and the one or more BCSIr signals  44 ′( 1 )- 44 ′(N) of  FIG. 2 . In a non-limiting example, the wireless communication interface  74  may be configured to operate based on Wi-Fi, Bluetooth, Bluetooth Low Energy (BLE), and ZigBee communication protocols. 
     When the wireless charging station  48  is powered on, the transmitter phases of the plurality of antenna elements  50 ( 1 )- 50 (M) may be out of alignment and become incoherent because relative phases of the plurality of transmitter oscillators  64 ( 1 )- 64 (M) may be randomized at the power on event. Furthermore, impedance variations among the plurality of signal paths  58 ( 1 )- 58 (M) may also cause the plurality of antenna elements  50 ( 1 )- 50 (M) to lose phase coherency during transmission. As such, it is necessary to calibrate the plurality of antenna elements  50 ( 1 )- 50 (M) to ensure phase coherency after power-up of the wireless charging station  48 . 
     Calibrations for the plurality of antenna elements  50 ( 1 )- 50 (M) may be conducted in several steps. In a first step (hereinafter referred to as “initial calibration sequence”), relative transmitter phase error and relative receiver phase error is determined between each pair of antenna elements among the plurality of antenna elements  50 ( 1 )- 50 (M). The initial calibration sequence may be conducted with three different configurations, which will be discussed with reference to  FIGS. 4-6 . After completing the initial calibration sequence, a second step (hereinafter referred to as “training sequence”) may be conducted to further determine total relative phase error between each pair of antenna elements among the plurality of antenna elements  50 ( 1 )- 50 (M). The training sequence is illustrated and discussed with reference to  FIG. 7 . Subsequently, a third step (hereinafter referred to as “validation sequence”) may be performed to validate phase coherency among the plurality of antenna elements  50 ( 1 )- 50 (M). In a non-limiting example, the validation sequence may be performed after the initial calibration sequence and/or after the training sequence. The validation sequence is illustrated and discussed with reference to  FIG. 8 . 
     In this regard,  FIG. 4  is a schematic diagram of an exemplary first configuration  76  for performing the initial calibration sequence among the plurality of antenna elements  50 ( 1 )- 50 (M) of  FIG. 3 . Common elements between  FIGS. 3 and 4  are shown therein with common element numbers and will not be re-described herein. 
     With reference to  FIG. 4 , to determine the relative transmitter phase error and the relative receiver phase error between each pair of antenna elements among the plurality of antenna elements  50 ( 1 )- 50 (M), the controller  70  designates an antenna element selected randomly from the plurality of antenna elements  50 ( 1 )- 50 (M) as a reference antenna element. The controller  70  then determines the relative transmitter phase error and the relative receiver phase error between the reference antenna element and each of the antenna elements among the plurality of antenna elements  50 ( 1 )- 50 (M) not designated as the reference antenna element (non-reference antenna element). For the convenience of discussion, antenna element  50 (X) and antenna element  50 (Y), which may be any of the plurality of antenna elements  50 ( 1 )- 50 (M), are discussed hereinafter in  FIGS. 4-7  as the reference antenna element and the non-reference antenna element, respectively. It should be understood that the configuration and operation discussed in connection to the antenna element  50 (X) and the antenna element  50 (Y) are applicable to all of the plurality of antenna elements  50 ( 1 )- 50 (M). 
     In a non-limiting example, the controller  70  may be configured to perform the initial calibration sequence according to the first configuration  76 . The controller  70  instructs the reference antenna element  50 (X) to transmit a first calibration signal  78  from respective transmitter  54 (X) of the reference antenna element  50 (X). The reference antenna element  50 (X) and the non-reference antenna element  50 (Y) receive the first calibration signal  78  at respective receiver  52 (X) and respective receiver  52 (Y). The controller  70  measures a respective phase of the first calibration signal  78  at the receiver  52 (X) (phase a x ) and at the receiver  52 (Y) (phase b x ). The phase a x  and the phase b x  are both compounded by multiple factors that can be respectively expressed by equations Eq. 1 and Eq. 2 below.
 
phase  a   x   =T   x   +λ+R   X   (Eq. 1)
 
phase  b   x   =T   X   +P   XY   +R   Y   (Eq. 2)
 
     With reference to the equations Eq. 1 and Eq. 2, T X  represents a phase shift associated with the transmitter  54 (X) of the reference antenna element  50 (X). R X  represents a phase shift associated with the receiver  52 (X) of the reference antenna element  50 (X). λ represents a phase shift associated with coupling the receiver  52 (X) of the reference antenna element  50 (X) to the transmitter  54 (X) of the reference antenna element  50 (X). R Y  represents a phase shift associated with the receiver  52 (Y) of the non-reference antenna element  50 (Y). P XY  represents a phase shift associated with signal path  58 (X) and signal path  58 (Y) that convey the first calibration signal  78  from the transmitter  54 (X) of the reference antenna element  50 (X) to the receiver  52 (Y) of the non-reference antenna element  50 (Y). 
     Subsequently, the controller  70  instructs the non-reference antenna element  50 (Y) to transmit a second calibration signal  80  from respective transmitter  54 (Y) of the non-reference antenna element  50 (Y). In a non-limiting example, the non-reference antenna element  50 (Y) may be instructed to transmit the second calibration signal  80  at a same frequency as the first calibration signal  78  or at a different frequency from the first calibration signal  78 . The reference antenna element  50 (X) and the non-reference antenna element  50 (Y) receive the second calibration signal  80  at the respective receiver  52 (X) and the respective receiver  52 (Y). The controller  70  then measures a respective phase of the second calibration signal  80  at the receiver  52 (X) (phase b y ) and at the receiver  52 (Y) (phase a y ). The phase a y  and the phase b y  are both compounded by multiple factors that can be respectively expressed by equations Eq. 3 and Eq. 4 below.
 
phase  a   y   =T   Y   +λ+R   Y   (Eq. 3)
 
phase  b   y   =T   Y   +P   YX   +R   X   (Eq. 4)
 
     With reference to the equations Eq. 3 and Eq. 4, T Y  represents a phase shift associated with the transmitter  54 (Y) of the non-reference antenna element  50 (Y). R Y  represents a phase shift associated with the receiver  52 (Y) of the non-reference antenna element  50 (Y). Δ represents a phase shift associated with coupling the receiver  52 (Y) of the non-reference antenna element  50 (Y) to the transmitter  54 (Y) of the non-reference antenna element  50 (Y). R X  represents a phase shift associated with the receiver  52 (X) of the reference antenna element  50 (X). P YX  represents a phase shift associated with the signal path  58 (Y) and the signal path  58 (X) that convey the second calibration signal  80  from the transmitter  54 (Y) of the non-reference antenna element  50 (Y) to the receiver  52 (X) of the reference antenna element  50 (X). 
     As previously mentioned, the purpose of the initial calibration sequence is to determine the relative transmitter phase error and the relative receiver phase error among the plurality of antenna elements  50 ( 1 )- 50 (M). In this regard, the relative transmitter phase error and the relative receiver phase error between the non-reference antenna element  50 (Y) and the reference antenna element  50 (X) can be determined by equations Eq. 5 and Eq. 6 below.
 
relative transmitter phase error= T   Y   −T   X   (Eq. 5)
 
relative receiver phase error= R   Y   −R   X   (Eq. 6)
 
     Assuming that P XY  and P YX  are equal, the equations Eq. 5 and Eq. 6 can be transformed to the following equations Eq. 7 and Eq. 8, respectively, based on the equations Eq. 1, Eq. 2, Eq. 3, and Eq. 4.
 
 T   Y   −T   X =[( a   y   −a   x )+( b   y   −b   x )]/2  (Eq. 7)
 
 R   Y   −R   X =[( a   y   −a   x )−( b   y   −b   x )]/2  (Eq. 8)
 
     Hence, the relative transmitter phase error (T Y −T x ) and the relative receiver phase error (R Y −R X ) can be determined based on the phase a x , the phase a y , the phase b x , and the phase b y  that are measured by the controller  70  during the initial calibration sequence. 
       FIG. 5  is a schematic diagram of an exemplary second configuration  82  for performing the initial calibration sequence among the plurality of antenna elements  50 ( 1 )- 50 (M) of  FIG. 3 . Common elements between  FIGS. 3, 4, and 5  are shown therein with common element numbers and will not be re-described herein. 
     To perform the initial calibration sequence based on the second configuration  82 , a calibration antenna element  84 , which is identical to the plurality of antenna elements  50 ( 1 )- 50 (M), is provided in the wireless charging station  48 . The controller  70  instructs the reference antenna element  50 (X) to transmit a first calibration signal  86  from the transmitter  54 (X) of the reference antenna element  50 (X). The reference antenna element  50 (X) and the calibration antenna element  84  receive the first calibration signal  86  at the respective receiver  52 (X) and a calibration receiver  88 . The controller  70  then measures a respective phase of the first calibration signal  86  at the respective receiver  52 (X) (phase a x ) and at the calibration receiver  88  (phase b y ). The phase a x  and the phase b x  are both compounded by multiple factors that can be respectively expressed by equations Eq. 9 and Eq. 10 below.
 
phase  a   x   =T   X   +λ+R   X   (Eq. 9)
 
phase  b   x   =T   X   +P   X   (Eq. 10)
 
     With reference to the equations Eq. 9 and Eq. 10, T X  represents a phase shift associated with the transmitter  54 (X) of the reference antenna element  50 (X). R X  represents a phase shift associated with the receiver  52 (X) of the reference antenna element  50 (X). λ represents a phase shift associated with coupling respective receiver  52 (X) of the reference antenna element  50 (X) to the transmitter  54 (X) of the reference antenna element  50 (X). P X  represents a phase shift associated with the signal path  58 (X) and a signal path  90  in the calibration antenna element  84  that convey the first calibration signal  86  from the transmitter  54 (X) of the reference antenna element  50 (X) to the calibration receiver  88  of the calibration antenna element  84 . 
     Next, the controller  70  instructs the non-reference antenna element  50 (Y) to transmit a second calibration signal  92  from the respective transmitter  54 (Y) of the non-reference antenna element  50 (Y). The non-reference antenna element  50 (Y) and the calibration antenna element  84  receive the second calibration signal  92  at the respective receiver  52 (Y) and the calibration receiver  88 . The controller  70  then measures a respective phase of the second calibration signal  92  at the respective receiver  52 (Y) (phase a y ) and at the calibration receiver  88  (phase b y ). The phase a y  and the phase b y  are both compounded by multiple factors that can be respectively expressed by equations Eq. 11 and Eq. 12 below.
 
phase  a   y   =T   Y   +λ+R   Y   (Eq. 11)
 
phase  b   y   =T   Y   +P   Y   (Eq. 12)
 
     With reference to the equations Eq. 11 and Eq. 12, T Y  represents a phase shift associated with the transmitter  54 (Y) of the non-reference antenna element  50 (Y). R Y  represents a phase shift associated with the receiver  52 (Y) of the non-reference antenna element  50 (Y). λ represents a phase shift associated with coupling the receiver  52 (Y) of the non-reference antenna element  50 (Y) to the transmitter  54 (Y) of the non-reference antenna element  50 (Y). P Y  represents a phase shift associated with the signal path  58 (Y) and the signal path  90  in the calibration antenna element  84  that convey the second calibration signal  92  from the transmitter  54 (Y) of the non-reference antenna element  50 (Y) to the calibration receiver  88  of the calibration antenna element  84 . 
     Subsequently, the controller  70  instructs the calibration antenna element  84  to transmit a third calibration signal  94  from a calibration transmitter  96  of the calibration antenna element  84 . The receiver  52 (X) of the reference antenna element  50 (X) and the receiver  52 (Y) of the non-reference antenna element  50 (Y) receive the third calibration signal  94 . The controller  70  then measures a respective phase of the third calibration signal  94  at the receiver  52 (X) (phase c x ) and at the receiver  52 (Y) (phase c y ). The phase c x  and the phase c y  are compounded by multiple factors that can be respectively expressed by equations Eq. 13 and Eq. 14 below.
 
phase  c   x   =R   X   +Δ+P   X   (Eq. 13)
 
phase  c   y   =R   Y   +Δ+P   Y   (Eq. 14)
 
     With reference to the equations Eq. 13 and Eq. 14, Δ represents a phase differential between the calibration transmitter  96  and the calibration receiver  88  of the calibration antenna element  84 . 
     Accordingly, the relative receiver phase error (R Y −R X ) between the non-reference antenna element  50 (Y) and the reference antenna element  50 (X) can be determined based on the equations Eq. 9-14 and expressed by the equation (Eq. 15) below.
 
 R   Y   −R   X =[( c   y   −b   y   +a   y )−( c   x   −b   x   +a   x )]/2  (Eq. 15)
 
     Hence, the relative receiver phase error (R Y −R X ) can be determined based on the phase a x , the phase a y , the phase b x , the phase b y , the phase c x , and the phase c y  that are measured by the controller  70  during the initial calibration sequence. 
       FIG. 6  is a schematic diagram of an exemplary third configuration  98  for performing the initial calibration sequence among the plurality of antenna elements  50 ( 1 )- 50 (M) of  FIG. 3 . Common elements between  FIGS. 3, 4, 5 , and  6  are shown therein with common element numbers and will not be re-described herein. 
     To perform the initial calibration sequence based on the third configuration  98 , a calibration device  100  is provided outside the wireless charging station  48 . The controller  70  instructs the reference antenna element  50 (X) to transmit a first calibration signal  102  from the transmitter  54 (X) of the reference antenna element  50 (X). The receiver  52 (X) of the reference antenna element  50 (X) and a receiver (not shown) of the calibration device  100  receive the first calibration signal  102 . The controller  70  then measures a respective phase of the first calibration signal  102  at the receiver  52 (X) (phase a x ) and at the receiver of the calibration device  100  (phase b x ). The phase a x  and the phase b x  are both compounded by multiple factors that can be respectively expressed by equations Eq. 16 and Eq. 17 below.
 
phase  a   x   =T   X   +λ+R   X   (Eq. 16)
 
phase  b   x   =T   X   +P   X   (Eq. 17)
 
     With reference to the equations Eq. 16 and Eq. 17, P X  represents a multipath phase shift associated with the signal path  58 (X) and a wireless path  104  to the calibration device  100  that convey the first calibration signal  102  from the transmitter  54 (X) of the reference antenna element  50 (X) to the receiver of the calibration device  100 . 
     Next, the controller  70  instructs the non-reference antenna element  50 (Y) to transmit a second calibration signal  106  from the transmitter  54 (Y) of the non-reference antenna element  50 (Y). The receiver  52 (Y) of the non-reference antenna element  50 (Y) and the receiver of the calibration device  100  receive the second calibration signal  106 . The controller  70  then measures a respective phase of the second calibration signal  106  at the receiver  52 (Y) (phase a y ) and at the receiver of the calibration device  100  (phase b y ). The phase a y  and the phase b y  are both compounded by multiple factors that can be respectively expressed by equations Eq. 18 and Eq. 19 below.
 
phase  a   y   =T   Y   +λ+R   Y   (Eq. 18)
 
phase  b   y   =T   Y   +P   Y   (Eq. 19)
 
     With reference to the equations Eq. 18 and Eq. 19, P Y  represents a multipath phase shift associated with the signal path  58 (Y) and a wireless path  108  to the calibration device  100  that convey the second calibration signal  106  from the transmitter  54 (Y) of the non-reference antenna element  50 (Y) to the receiver of the calibration device  100 . 
     Subsequently, a third calibration signal  110  is transmitted from a transmitter (not shown) of the calibration device  100 . The receiver  52 (X) of the reference antenna element  50 (X) and the receiver  52 (Y) of the non-reference antenna element  50 (Y) receive the third calibration signal  110 . The controller  70  measures a respective phase of the third calibration signal  110  at the receiver  52 (X) (phase c x ) and at the receiver  52 (Y) (phase c y ). The phase c x  and the phase c y  are compounded by multiple factors that can be expressed by equations Eq. 20 and Eq. 21 below.
 
phase  c   x   =R   X   +Δ+P   X   (Eq. 20)
 
phase  c   y   =R   Y   +Δ+P   Y   (Eq. 21)
 
     With reference to the equations Eq. 20 and Eq. 21, Δ represents a phase differential between the transmitter and the receiver of the calibration device  100 . 
     The calibration device  100  may communicate the phase b x  and the phase b y  to the controller  70  via a wireless link  112 . In a non-limiting example, the wireless link  112  operates in one of the ISM bands. In another non-limiting example, the wireless link  112  may operate based on Wi-Fi, Bluetooth, BLE, and ZigBee communication protocols. In another non-limiting example, the wireless link  112  may be established between the calibration device  100  and the wireless communication interface  74  in the wireless charging station  48 . 
     Accordingly, the relative receiver phase error (R Y −R X ) between the non-reference antenna element  50 (Y) and the reference antenna element  50 (X) can be determined based on the equations Eq. 16-21 and expressed by equation Eq. 22 below.
 
 R   Y   −R   X =[( c   y   −b   y   +a   y )−( c   x   −b   x   +a   x )]/2  (Eq. 22)
 
     Hence, the relative receiver phase error (R Y −R X ) can be determined based on the phase a x , the phase a y , the phase b x , the phase b y , the phase c x , and the phase c y , which can be measured and recorded by the controller  70  during the initial calibration sequence. 
     As previously mentioned, after completing the initial calibration sequence, the training sequence may be conducted to further determine the total relative phase error between each pair of antenna elements among the plurality of antenna elements  50 ( 1 )- 50 (M). In this regard,  FIG. 7  is a schematic diagram of an exemplary configuration  114  for performing the training sequence among the plurality of antenna elements  50 ( 1 )- 50 (M) of  FIG. 3 . Common elements between  FIGS. 3, 4, 5, 6, and 7  are shown therein with common element numbers and will not be re-described herein. 
     To perform the training sequence, a training device  116  transmits a wireless training signal  118  to the plurality of antenna elements  50 ( 1 )- 50 (M) in the wireless charging station  48 . The receiver  52 (X) of the reference antenna element  50 (X) and the receiver  52 (Y) of the non-reference antenna element  50 (Y) receive the wireless training signal  118  simultaneously. The controller  70  measures a respective phase of the wireless training signal  118  at the receiver  52 (X) (phase t x ) and at the receiver  52 (Y) (phase t y ). The phase t x  and the phase t y  are both compounded by multiple factors that can be expressed respectively by equations Eq. 23 and Eq. 24 below.
 
phase  t   x   =R   X   +P   X +Δ  (Eq. 23)
 
phase  t   y   =R   Y   +P   Y +Δ  (Eq. 24)
 
     With reference to the equations Eq. 23 and Eq. 24, P X  represents a multipath phase shift experienced by the wireless training signal  118  when traveling from a transmitter of the training device  116  to the receiver  52 (X) of the reference antenna element  50 (X). P Y  represents a multipath phase shift experienced by the wireless training signal  118  when traveling from the transmitter (not shown) of the training device  116  to the receiver  52 (Y) of the non-reference antenna element  50 (Y). Δ represents a phase differential between the transmitter and a receiver (not shown) in the training device  116 . 
     Using the phase t x  and the phase t y  in connection with the phase a x  and the phase a y , which have been respectively determined during the initial calibration sequence according to the equations Eq. 1, 9, and 16 and the equations Eq. 2, 10, and 17, it is possible for the controller  70  to estimate a respective transmitter phase of the reference antenna element (φ X ) and a respective transmitter phase of the non-reference antenna element (φ Y ) based on the following equations Eq. 25 and Eq. 26, respectively.
 
φ X   =T   X   +P   X   =a   x   +t   x −2 R   X −λ−Δ  (Eq. 25)
 
φ Y   =T   Y   +P   Y   =a   y   +t   y −2 R   Y −λ−Δ  (Eq. 26)
 
     Based on the equations Eq. 25 and Eq. 26, the controller  70  can determine a total relative phase error (φ Y −φ X ) between the non-reference antenna element  50 (Y) and the reference antenna element  50 (X) based on equation Eq. 27 below.
 
φ Y −φ X =( a   y   +t   y )−( a   x   +t   x )−2( R   Y   −R   X )  (Eq. 27)
 
     With reference to the equation Eq. 27, R Y −R X  represents the relative receiver phase error between the non-reference antenna element  50 (Y) and the reference antenna element  50 (X), which has been determined during the initial calibration sequence. In this regard, if the initial calibration sequence is conducted based on the first configuration  76  of  FIG. 4 , the controller  70  can determine the relative receiver phase error (R Y −R X ) based on the equation Eq. 8. Thus, by substituting the R Y −R X  in the equation Eq. 27 with the R Y −R X  in the equation Eq. 8, the total relative phase error (φ Y −φ X ) can be expressed as equation Eq. 28 below.
 
φ Y −φ X =( b   y   +t   y )−( b   x   +t   x )  (Eq. 28)
 
     If the initial calibration sequence is conducted based on the second configuration  82  of  FIG. 5  or the third configuration  98  of  FIG. 6 , the relative receiver phase error (R Y −R X ) is determined by either the equation Eq. 15 or the equation Eq. 22. Thus, by substituting the R Y −R X  in the equation Eq. 27 with the R Y −R X  in the equation Eq. 15 or the equation Eq. 22, the total relative phase error (φ Y −φ X ) can be expressed as equation Eq. 29 below.
 
φ Y −φ X =( t   y   +b   y   −c   y )−( t   x   +b   x   −c   x )  (Eq. 29)
 
     The training sequence described above is based on an assumption that some kind of reciprocity exists between the training device  116  and the plurality of antenna elements  50 ( 1 )- 50 (M). That is, the multipath amplitude and phase changes experienced by the wireless training signal  118  are the same as the amplitude and phase changes the plurality of antenna elements  50 ( 1 )- 50 (M) would experience when transmitting wireless RF charging signals. Because of this reciprocity assumption, it is possible for the controller  70  to estimate the total relative phase error (φ Y −φ X ) between the non-reference antenna element  50 (Y) and the reference antenna element  50 (X) based on the multipath phase shifts P X  and P Y  of the wireless training signal  118  in the equations Eq. 25-27. However, the reciprocity assumption may not always be true. Hence, it may be necessary to validate phase coherence among the plurality of antenna elements  50 ( 1 )- 50 (X) after conducting the initial calibration sequence and the training sequence. 
     In this regard,  FIG. 8  is a schematic diagram of an exemplary configuration  120  for verifying phase coherency among the plurality of antenna elements  50 ( 1 )- 50 (M). Common elements between  FIGS. 3, 4, and 8  are shown therein with common element numbers and will not be re-described herein. 
     With reference to  FIG. 8 , the controller  70  instructs the plurality of antenna elements  50 ( 1 )- 50 (M) to transmit a plurality of wireless signals  122 ( 1 )- 122 (M) to a receiving device  124 . The receiving device  124  provides a first power measurement  126 , which indicates a first total power received from the plurality of wireless signals  122 ( 1 )- 122 (M), to the controller  70  via a wireless link  128 . In a non-limiting example, the wireless link  128  operates in one of the ISM bands. In another non-limiting example, the wireless link  128  may operate based on Wi-Fi, Bluetooth, BLE, and ZigBee communication protocols. In another non-limiting example, the wireless link  128  may be established between the receiving device  124  and the wireless communication interface  74  in the wireless charging station  48 . 
     The controller  70  then instructs at least one antenna element among the plurality of antenna elements  50 ( 1 )- 50 (M) to increase power level of at least one wireless signal among the plurality of wireless signals  122 ( 1 )- 122 (M) by a predetermined amount P UP . The receiving device  124  subsequently provides a second power measurement  130 , which indicates a second total power received from the plurality of wireless signals  122 ( 1 )- 122 (M), to the controller  70  via the wireless link  128 . If phase coherency exists among the plurality of antenna elements  50 ( 1 )- 50 (M), the second power measurement  130  shall increase from the first power measurement  126  by the predetermined amount P UP . If the second power measurement  130  does not increase from the first power measurement  126  by the predetermined amount P UP , it can be concluded that the plurality of antenna elements  50 ( 1 )- 50 (M) are phase incoherent. 
     Those skilled in the art will recognize improvements and modifications to the embodiments of the present disclosure. All such improvements and modifications are considered within the scope of the concepts disclosed herein and the claims that follow.