Abstract:
One heuristic for tuning a wireless power transfer device includes monitoring a circuit parameter while sweeping a power source frequency; identifying two frequencies related to local maxima of the circuit parameter values; estimating self-resonant frequency of an electromagnetically coupled device based on the two frequencies; determining a value for a tuning component of the wireless power transfer device such that the device self-resonant frequency equals the estimated coupled device self-resonant frequency; and adjusting the tuning component to the determined value. 
     Another tuning heuristic includes monitoring a circuit parameter while sweeping the power source frequency; identifying two frequencies related to two local maximum for the values of the circuit parameter; determining a desired resonance frequency for the wireless power transfer device based on stored information; and adjusting the tuning component to a value that causes the wireless power transfer device when uncoupled to operate at or near the desired resonance frequency.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application claims benefit to U.S. provisional application No. 61/428,070 filed Dec. 29, 2010 entitled RESONANCE TUNING, the contents of which is incorporated herein in its entirety. 
    
    
     BACKGROUND 
     In a wireless power transfer system, the amount of power and the efficiency of the power transfer are affected by many factors. As a few of many examples, distance between power transfer coils, orientation of coils, and number and type of objects in the vicinity all affect power transfer. As coupling between the coils decreases, from the above illustrative factors or other factors, power transfer tends to decrease. 
     Power transfer is increased when both the transmitter and receiver in a wireless power transfer system are operating at the same resonance frequency. In some systems, the resonance frequency of one or both of the transmitter and receiver may be tuned by adjusting a circuit parameter. 
     It is desirable to have the capability to tune the transmitter based solely on information measured or retrieved from within the transmitter, or to tune the receiver based solely on information measured or retrieved from within the receiver. 
    
    
     
       FIGURES 
         FIG. 1  illustrates an exemplary wireless power transfer system model. 
         FIG. 2  illustrates another exemplary wireless power transfer system model. 
         FIG. 3  illustrates exemplary simulation results for an exemplary wireless power transfer system model. 
         FIG. 4  illustrates further exemplary simulation results for an exemplary wireless power transfer system model. 
         FIG. 5  illustrates an exemplary heuristic for tuning a device to achieve improved power transfer. 
         FIG. 6  illustrates another exemplary heuristic for tuning a device to achieve improved power transfer. 
         FIG. 7  illustrates a representative set of steps for a single-pass tuning heuristic. 
         FIG. 8  illustrates another exemplary heuristic for tuning a device to achieve improved power transfer. 
     
    
    
     DETAILED DESCRIPTION 
     Described below are exemplary heuristics for tuning of dual series resonance circuits coupled for wireless power transfer and having a low coefficient of coupling. A first heuristic provides fast tuning based on reiteratively tuning the self-resonant frequency of the primary to approach the self-resonant frequency of the secondary. A second heuristic provides single-pass tuning for the self-resonant frequency of the primary to the self-resonant frequency of the secondary. 
       FIG. 1  illustrates an exemplary wireless power transfer system  100 . A transmitter  110  transfers power to a receiver  120  through a power transfer from transmitter coil  130  having inductance L 1  to receiver coil  140  having inductance L 2 . Coils  130  and  140  are coupled with a coefficient of coupling k. 
     Transmitter  110  may be a stationary or a portable device, and may be configured to provide power to multiple receivers  120 . 
     Receiver  120  may be a stationary or a portable device. Receiver  120  may be implemented within a handheld device such as smart phone or personal digital assistant, or within a computing device such as a tablet or laptop computer or a reading device. Further, receiver  120  may be implemented within household use devices or industry use devices. For example, receiver  120  may be included within a hearing aid or a toothbrush, or may be included within rechargeable tools or automated factory transport devices. 
     In some implementations both transmitter  110  and receiver  120  are implemented as stationary devices wherein wireless power transfer provides for powering of receiver  120  while maintaining physical isolation between transmitter  110  and receiver  120 . 
     Coil  130  and coil  140  each may be formed in one or more layers, in one or more of a variety of geometries, and in one or more of a variety of materials. Further, each of coil  130  and coil  140  may be a combination of two or more coils electrically connected. Although coils  130  and  140  are illustrated in  FIG. 1  as being external to transmitter  110  and receiver  120 , respectively, coils  130  and  140  may alternatively be internal or may be a combination of internal and external. The terms internal and external in this context are in relation to the associated housing. 
       FIG. 2  illustrates an exemplary wireless power transfer system  200  including a device A with coil  210  having inductance L_A and a device B with coil  220  having inductance L_B. One of device A and device B is a transmitter and the other of device A and device B is a receiver. Power transfers between coils  210  and  220 . 
     Device A includes a capacitor  230  having capacitance C_A. Coil  210  and capacitor  230  together form or are part of a resonant circuit with self-resonant frequency ωA. Device B includes a capacitor  240  having capacitance C_B. Coil  220  and capacitor  240  together form or are part of a resonant circuit with self-resonant frequency ωB. 
     Device A further includes a power source  250  including a direct current (DC) source  260  with output voltage Vdc that is converted to an alternating current (AC) voltage Vac by a variable DC/AC converter  270 . The frequency of DC/AC converter  270  output Vac is variable and may be controlled. For example, if DC/AC converter  270  is implemented with a set of switches, the frequency or duration of the switch control signals may be adjusted to change the frequency of voltage Vac. 
     Devices A and B may include additional components, not shown. Further, other topologies may be implemented. For example, although devices A and B are illustrated with series resonant circuits wherein a capacitor is in series with the power transfer coil, alternative topologies include parallel-series resonant and series-parallel resonant circuit implementations using multiple capacitors in series with and parallel to the power transfer coil. However, for ease of understanding, the exemplary series resonant circuits are illustrated and used as a basis for the following discussion and equations. 
     Transfer of power between two self-resonant devices such as devices A and B in  FIG. 2  occurs when the self-resonant frequencies of the two devices are nearly equal. For example, for devices A and B in  FIG. 2 , transfer of power occurs when ωA is approximately equal to ωB. For a series-resonant circuit, the self-resonant frequency ω is defined as function of the inductance of the coil and the capacitance of the series capacitor. 
     
       
         
           
             
               
                 
                   ω 
                   = 
                   
                     1 
                     
                       LC 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     When coupling occurs between the coils of two resonant circuits the coils influence each other resulting in a splitting of the resonant frequencies into resonant modes (i.e., mode splitting). The resonant modes, or Eigen-frequencies ωi, may be determined from equation 3 for a system such as the system  200  illustrated in  FIG. 2 . 
     
       
         
           
             
               
                 
                   
                     ω 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ⅈ 
                   
                   = 
                   
                     
                       
                         
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             A 
                             2 
                           
                         
                         + 
                         
                           
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               B 
                               2 
                             
                           
                           ± 
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         A 
                                         2 
                                       
                                     
                                     - 
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         B 
                                         2 
                                       
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               + 
                               
                                 4 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   A 
                                   2 
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   B 
                                   2 
                                 
                                 ⁢ 
                                 
                                   k 
                                   2 
                                 
                               
                             
                           
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               k 
                               2 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Setting ωA=ωB=ω0 in equation 2 results in the relationship shown in equation 3. 
     
       
         
           
             
               
                 
                   ω 
                   = 
                   
                     
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       0 
                     
                     
                       
                         1 
                         ± 
                         k 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     From equation 3 it can be seen that for non-zero coupling coefficient k, mode splitting happens even with perfectly tuned coils. For small k, equation 3 may be approximated as shown in equation 4. 
     
       
         
           
             
               
                 
                   ω 
                   ≈ 
                   
                     ω 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     0 
                     ⁢ 
                     
                       ( 
                       
                         1 
                         ± 
                         
                           k 
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     The distance Δω between the resonant modes is thus approximately as shown in equation 5 for two resonant circuits tuned to the same resonant frequency and with small coupling coefficient k. The resonant modes are centered at ω0.
 
Δω≈ k*ω 0  (5)
 
     Returning to equation 2, it can be seen that for very small values of coupling coefficient k, the resonant modes are approximately equal to the self-resonant frequencies of the two resonant circuits, as shown in equations 6-8. 
     
       
         
           
             
               
                 
                   
                     ω 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ⅈ 
                   
                   ≈ 
                   
                     
                       
                         
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             A 
                             2 
                           
                         
                         + 
                         
                           
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               B 
                               2 
                             
                           
                           ± 
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         A 
                                         2 
                                       
                                     
                                     - 
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         B 
                                         2 
                                       
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                               + 
                               0 
                             
                           
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             0 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     ω 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     ⅈ 
                   
                   ≈ 
                   
                     
                       
                         
                           ω 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             A 
                             2 
                           
                         
                         + 
                         
                           
                             ω 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               B 
                               2 
                             
                           
                           ± 
                           
                             ( 
                             
                               
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   A 
                                   2 
                                 
                               
                               - 
                               
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   B 
                                   2 
                                 
                               
                             
                             ) 
                           
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       ⅈ 
                     
                     ≈ 
                     
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       A 
                     
                   
                   , 
                   
                     ω 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     B 
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     The relationships given by equations 1-8 were confirmed by both simulation and measurement of a coupled system substantially represented by system  200  of  FIG. 2 . For the system and for the simulation the values L_A=100 μH, L_B=100 μH, and C_B=2.903 nF were kept constant while the value C_A was varied. Coupling coefficient k was 0.08. The results are of the simulations and measurements are provided in Table 1, where frequency f relates to ω according to the equation ω=2πf. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
             
             
               
                   
                   
               
               
                   
                 k = 0.08 
                 Simulation 
                   
                 Measurement 
                   
               
             
          
           
               
                   
                   
                 C_A 
                 fA 
                 fB 
                 fA 
                 fB 
               
               
                   
                 Trial 
                 (nF) 
                 (kHz) 
                 (kHz) 
                 (kHz) 
                 (kHz) 
               
               
                   
                   
               
             
          
           
               
                   
                 1 
                 2.50 
                 290.4 
                 324.4 
                 291.2 
                 324.3 
               
               
                   
                 2 
                 2.60 
                 289.4 
                 319.2 
                 288.9 
                 319.2 
               
               
                   
                 3 
                 2.70 
                 288.1 
                 314.7 
                 287.8 
                 314.7 
               
               
                   
                 4 
                 2.80 
                 286.3 
                 310.9 
                 287.0 
                 310.8 
               
               
                   
                 5 
                 2.90 
                 284.1 
                 307.9 
                 284.7 
                 307.6 
               
               
                   
                 6 
                 3.00 
                 281.7 
                 305.7 
                 281.9 
                 305.2 
               
               
                   
                 7 
                 3.10 
                 278.7 
                 303.9 
                 278.9 
                 303.5 
               
               
                   
                 8 
                 3.20 
                 275.5 
                 302.6 
                 275.6 
                 302.2 
               
               
                   
                 9 
                 3.30 
                 272.2 
                 301.6 
                 272.3 
                 301.2 
               
               
                   
                   
               
             
          
         
       
     
     As described above, the relationship Δω≈k*ω0 of equation 5 provides the theoretical distance between the resonant modes when both devices are operating at the same self-resonant frequency. In Table 1, the self-resonant frequency of device B is calculated using equation 1 and the relationship ω=2πf as 295.4 kHz. Multiplying 295.4 kHz by k=0.08 results in a theoretical distance of 23.6 kHz between the resonant modes. Device A self-resonant frequency is substantially equal to device B self-resonant frequency for C_A=2.9 nF, thus the distance between the resonant modes should be approximately 23.6 kHz. Table 1 provides a simulation distance of 23.8 kHz and a measured distance of 22.9 kHz for trial 5. The example calculation provided in this paragraph illustrates that equations 1-8 may be used to approximate a system such as system  200  in  FIG. 2 . 
     In equation 8 it is shown that when the coefficient of coupling is very low, the resonant modes are approximately equal to the self-resonant frequencies of the two circuits. As the self-resonant frequencies of the two circuits are tuned such that the self-resonant frequencies approach the point where they are substantially equally, resonant modes tend to coincide and may not be separable. 
       FIG. 3  provides the results of a simulation of a system similar to the system  200  illustrated in  FIG. 2  with matching self-resonant frequencies of approximately 295 kHz. For the simulation, the coupling coefficient was varied from a relatively small value of k=0.09 to a very small value of k=0.01. As can be seen by the results presented in  FIG. 3 , as k increases the distance between the resonant modes increases, and as k decreases to a very small value, the resonant modes combine to a single resonant mode at the matching self-resonant frequency of the two resonant circuits. 
       FIG. 4  provides the results of a further simulation of a system similar to the system  200  illustrated in  FIG. 2 . The simulation results presented in  FIG. 4  illustrate the relationship described by equation 2 between the resonant modes of the system, the self-resonant frequencies of the circuits, and the coupling coefficient k. When the circuits are not tuned to same self-resonant frequency, the resonant modes will be farther apart. Simulation results are presented for capacitance C_A of device A (referred to in  FIG. 4  as CS 1 ) for capacitance values 2.9 nF to 3.3 nF. For the simulation the values L_A=L_B=100 uH, and C_B=2.9 nF were kept constant. 
     From the above discussions it can be seen that it is desirable to have the capability to tune one of the resonant circuits in a coupled system such that the self-resonant frequency of the one circuit is substantially equal to the self-resonant frequency of the other circuit for improved wireless power transfer. Three exemplary heuristics  500 ,  600 , and  800  are provided below for achieving matched tuning between two resonant circuits. Heuristics  500  and  600  are iterative heuristics, whereas heuristic  800  is a single-pass heuristic. 
       FIG. 5  illustrates a first exemplary heuristic for tuning a device A to achieve improved power transfer between the device A and a device B. 
     Heuristic  500  in  FIG. 5  starts with optional blocks  505 - 520  in which the self-resonant frequency fA of device A is determined. In block  505 , device A is uncoupled from all other devices. Uncoupling in this context refers to physically removing or otherwise isolating device A from the influence of any other device that could electromagnetically couple to the power transfer coil of device A. 
     In block  510 , the source frequency of device A is swept and a circuit parameter monitored, wherein the frequency of the source is stepped from a starting frequency to an ending frequency in discrete steps and at each frequency step the value of a circuit parameter is measured. For example, the input current may be measured at each frequency step. Other circuit parameters that could be monitored include but are not limited to voltage across the coil of device A, or power delivered by the source. 
     In block  515 , the data from the monitored circuit parameter is analyzed to determine a maximum value for the parameter. 
     In block  520 , the frequency corresponding to the maximum value of the monitored circuit parameter is saved as the self-resonant frequency fA of device A. 
     In block  525 , tuning of device A to device B begins by coupling device A and device B. Coupling in this context refers to physically placing device B in the vicinity of device A, or removing an isolation mechanism from device A. Coupling requires both device A and device B to be powered and the corresponding resonant circuits to be active. 
     In block  530 , the source frequency of device A is swept and a circuit parameter monitored, wherein the frequency of the source is stepped from a starting frequency to an ending frequency in discrete steps and at each frequency step the value of a circuit parameter is measured. The frequency steps of block  530  are not necessarily the same frequency steps and do not necessarily have the same frequency delta between the steps as do the steps of block  510 . The monitored circuit parameter may be the same as the parameter monitored in block  515  but may alternatively be a different parameter or set of parameters. Circuit parameters that could be monitored include but are not limited to source current of device A, voltage across the coil of device A, power delivered by the source of device A, efficiency of power delivery, voltage across the coil of device B, coil current of device B, output voltage of device B, and output power of device B. 
     In block  535 , the data from the monitored circuit parameter is analyzed to determine the two local maxima for the monitored parameter corresponding to the two resonant modes of the coupled devices. 
     In block  540 , the two frequencies corresponding to the two local maxima of the circuit parameter are saved as frequencies f 1  and f 2 . 
     In block  545 , the self-resonant frequency fB of device B is estimated from frequencies f 1  and f 2  and saved as fB_est. There are many ways of estimating fB from f 1  and f 2 , including using equation 9.
 
 fB _est= m*f 1 +n*f 2  (9)
 
     In a simple instance of an estimation using equation 9, variables m and n are set to m=n=½. 
     In decision block  550 , the difference between device A self-resonant frequency fA and device B estimated self-resonant frequency fB is calculated and compared to a threshold. In exemplary heuristic  500  the logical comparison is whether the difference is “greater than” a threshold. Other heuristics may use alternative logical comparisons, such as “equal to”, “less than”, “greater than or equal to”, or “less than or equal to”. 
     The first time that the decision of block  550  is made during the execution of heuristic  500 , self-resonant frequency fA may be the frequency saved as fA in optional block  520 . However, fA may alternatively be, for example, the self-resonant frequency of device A as designed. 
     If at decision block  550  the result is “NO”, heuristic  500  ends. If, however, the result is “YES”, heuristic  500  continues at block  555 . 
     In block  555 , capacitance C_A of device A is calculated such that the self-resonant frequency of device A is equal to the estimated self-resonant frequency fB_est of device B. For example, knowing the inductance L_A of the device A coil and setting the self-resonant frequency of device A to fA=fB_est, the value of C_A may be determined from equation 1, as illustrated in equation 10. 
     
       
         
           
             
               
                 
                   
                     2 
                     ⁢ 
                     π 
                     * 
                     fB_est 
                   
                   = 
                   
                     1 
                     
                       
                         L_A 
                         * 
                         C 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     At block  560 , the capacitor of the device A resonant circuit is adjusted to the value of C_A calculated in block  555 . Heuristic  500  continues at block  530  with the adjusted capacitor. 
     Heuristic  500  continues iteratively until the difference calculated at block  550  is within an acceptable limit, for example is less than or equal to a threshold, at which point heuristic  500  ends. 
     A frequency sweep may be performed in digital or analog form. In digital form, the source, as described above with respect to block  510  for example, is stepped from a starting frequency to an ending frequency in discrete steps. In analog form, the frequency may be increased from a starting frequency to an ending frequency continuously. Further, the starting frequency may be greater than or less than the ending frequency, such that there is a sweep down or a sweep up, respectively. 
     Thus, heuristic  500 , and other heuristics described herein, may be implemented in digital circuitry, analog circuitry, or mixed analog and digital circuitry. 
       FIG. 6  illustrates a second exemplary heuristic for tuning a device A to achieve improved power transfer between the device A and a device B. 
     Heuristic  600  in  FIG. 6  starts with optional blocks  605 - 620  in which the self-resonant frequency fA of device A is determined. In block  605 , device A is uncoupled from all other devices. Uncoupling in this context refers to physically removing or otherwise isolating device A from the influence of any other device that could electromagnetically couple to the power transfer coil of device A. 
     In block  610 , the source frequency of device A is swept and a circuit parameter monitored, wherein the frequency of the source is stepped from a starting frequency to an ending frequency in discrete steps and at each frequency step the value of a circuit parameter is measured. For example, the input current may be measured at each frequency step. Other circuit parameters that could be monitored include but are not limited to voltage across the coil of device A, or power delivered by the source. 
     In block  615 , the data from the monitored circuit parameter is analyzed to determine a maximum value for the parameter. 
     In block  620 , the frequency corresponding to the maximum value of the monitored circuit parameter is saved as the self-resonant frequency fA of device A. 
     In block  625 , tuning of device A to device B begins by coupling device A and device B. Coupling in this context refers to physically placing device B in the vicinity of device A, or removing an isolation mechanism from device A. Coupling requires both device A and device B to be powered and the corresponding resonant circuits to be active. 
     In block  630 , the source frequency of device A is swept and a circuit parameter monitored, wherein the frequency of the source is stepped from a starting frequency to an ending frequency in discrete steps and at each frequency step the value of a circuit parameter is measured. The frequency steps of block  630  are not necessarily the same frequency steps and do not necessarily have the same frequency delta between the steps as do the steps of block  610 . The monitored circuit parameter may be the same as the parameter monitored in block  615  but may alternatively be a different parameter or set of parameters. Circuit parameters that could be monitored include but are not limited to source current of device A, voltage across the coil of device A, power delivered by the source of device A, efficiency of power delivery, voltage across the coil of device B, coil current of device B, output voltage of device B, and output power of device B. 
     In block  635 , the data from the monitored circuit parameter is analyzed to determine the two local maxima for the monitored parameter corresponding to the two resonant modes of the coupled devices. 
     In block  640 , the two frequencies corresponding to the two local maxima of the circuit parameter are saved as frequencies f 1  and f 2 . 
     In block  645 , the self-resonant frequency fB of device B is estimated from frequencies f 1  and f 2  and saved as fB_est. There are many ways of estimating fB from f 1  and f 2 , including using equation 9.
 
 fB _est= m*f 1 +n*f 2  (9)
 
     In a simple instance of an estimation using equation 9, variables m and n are set to m=n=½. 
     In decision block  650 , the difference between device A self-resonant frequency fA and device B estimated self-resonant frequency fB is calculated and compared to a threshold. In exemplary heuristic  60  the logical comparison is whether the difference is “greater than” a threshold. Other heuristics may use alternative logical comparisons, such as “equal to”, “less than”, “greater than or equal to”, or “less than or equal to”. 
     The first time that the decision of block  650  is made during the execution of heuristic  600 , self-resonant frequency fA may be the frequency saved as fA in optional block  620 . However, fA may alternatively be, for example, the self-resonant frequency of device A as designed. 
     If at decision block  650  the result is “NO”, heuristic  600  ends. If, however, the result is “YES”, heuristic  600  continues at block  655 . 
     In block  655 , device A is uncoupled from device B. 
     In block  660 , the source frequency of device A is set to the estimated frequency fB_est of block  645 . 
     In block  665 , the capacitance value C_A of the resonant circuit of device A is swept, meaning that the capacitance value C_A is stepped from one value to another value in a sequence, and at each value a circuit parameter value is measured. 
     In block  670 , the maximum value of C_A is determined from the measurements in block  665 . 
     In block  675 , the capacitor of the device A resonant circuit is adjusted to the value of C_A determined in block  670 . 
     In block  680 , device A is coupled to device B, and heuristic  500  continues at block  630  with the adjusted capacitor. 
     Heuristic  600  continues iteratively until the difference calculated at block  650  is within an acceptable limit, for example is less than or equal to a threshold, at which point heuristic  600  ends. 
     The heuristics described in alternative heuristics  500  and  600  have been shown to converge within ten iterations or less. An exemplary test run is shown in Table 2 for a coupling coefficient of k=0.02 in which convergence occurs in just eight iterations through heuristic  500 . 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Trial 
                 fA 
                 fB 
                 k 
                 f1 
                 f2 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 3.30E+05 
                 2.91E+05 
                 0.02 
                 3.30E+05 
                 2.91E+05 
               
               
                 2 
                 3.10E+05 
                 2.91E+05 
                 0.02 
                 3.11E+05 
                 2.90E+05 
               
               
                 3 
                 3.01E+05 
                 2.91E+05 
                 0.02 
                 3.02E+05 
                 2.90E+05 
               
               
                 4 
                 2.96E+05 
                 2.91E+05 
                 0.02 
                 2.97E+05 
                 2.90E+05 
               
               
                 5 
                 2.93E+05 
                 2.91E+05 
                 0.02 
                 2.95E+05 
                 2.89E+05 
               
               
                 6 
                 2.92E+05 
                 2.91E+05 
                 0.02 
                 2.95E+05 
                 2.89E+05 
               
               
                 7 
                 2.92E+05 
                 2.91E+05 
                 0.02 
                 2.94E+05 
                 2.88E+05 
               
               
                 8 
                 2.91E+05 
                 2.91E+05 
                 0.02 
                 2.94E+05 
                 2.88E+05 
               
               
                 9 
                 2.91E+05 
                 2.91E+05 
                 0.02 
                 2.94E+05 
                 2.88E+05 
               
               
                 10 
                 2.91E+05 
                 2.91E+05 
                 0.02 
                 2.94E+05 
                 2.88E+05 
               
               
                   
               
             
          
         
       
     
     Heuristics  500  and  600  illustrated the adjustment of device A capacitor value C_A to tune device A. Additionally or alternatively, other circuit elements may be adjusted for tuning. For example, one or more of the device A coil, device B coil, device B capacitor may be additionally or alternatively adjusted. 
     For a given value of coupling coefficient k, the frequency sweep of block  510  or block  610  should be performed in steps of less than f_step=k*ω0/2. 
     As mentioned, heuristics  500  and  600  are reiterative heuristics. It may instead be desirable to complete tuning in a single pass, for example, to reduce tuning time. 
       FIG. 7  is a copy of the graph of  FIG. 4  with various points on the graph highlighted.  FIG. 7  is used for reference in the discussion of  FIG. 8 . For the purposes of the discussion of  FIG. 8 , the graph may be the result of either simulation or measurement, and may be stored as, for example, as a set of equations or as a look-up table. 
       FIG. 8  illustrates an exemplary single-pass heuristic  800  for tuning a device A to achieve improved power transfer between the device A and a device B. 
     In block  805 , the self-resonant frequency fA of device A is determined, for example, as described above. 
     In block  810 , device A is coupled to device B, as described above. 
     In block  815 , the source frequency of device A is swept and a circuit parameter monitored, as described above. 
     In block  820 , the data from the monitored circuit parameter is analyzed to determine the two local maxima for the monitored parameter corresponding to the two resonant modes of the coupled devices. 
     In block  825 , the two frequencies corresponding to the two local maxima of the circuit parameter are saved as frequencies fmax 1  and fmax 2 . 
     In block  830 , referring to the graph in  FIG. 7 , the f 2  curve related the present value of the device A tuning component is selected. The present value of the tuning component is, for example, retrieved from a register or other memory location. In  FIG. 7 , the tuning component is a capacitor, thus curves are shown for various capacitance values. 
     In block  835 , the point on the selected  12  curve corresponding to frequency fmax 2  is determined. For example, in  FIG. 7 , fmax 2  is identified by the circle labeled A. A line is drawn through circle A perpendicular to the y-axis. The point where the line intersects the selected  12  curve is identified, as indicated by the circle labeled B in  FIG. 7 . 
     In block  840 , the x-axis point corresponding to the frequency fmax 2  for the selected curve is determined. For example, in  FIG. 7 , a line is drawn through the point within circle B perpendicular to the x-axis. The coupling coefficient Xfmax 2  at the intersection of the line and the x-axis is determined, as indicated by the circle labeled C in  FIG. 7 . 
     In block  845 , an f 1  curve, on or near which there is an intersection of Xfmax 2  and fmax 1 , is selected. For example, on  FIG. 7 , fmax 1  is found on the y-axis, as indicated by circle D. A line is drawn through circle D perpendicular to the y-axis. An f 1  curve on or near the intersection of the lines through circles C and D is selected. In  FIG. 7 , the intersection of the lines is on or near the third f 1  curve, as indicated by circle E. 
     In block  850 , the point f 01  where the selected f 1  curve intersects the y-axis is determined. For example, in  FIG. 7 , the selected third f 1  curve is traced back from circle E to where the curve intersects the y-axis, as indicated by circle F. The intersection of the selected curve with the y-axis is frequency f 01 . 
     In block  855 , a value for the device A tuning component is determined such that the device A resonant frequency fA is equal to the frequency f 01  determined in block  850 . For example, the device A tuning component value may be calculated using fA=f 01 . For another example, device A may be uncoupled from device B and the tuning component value may be swept to find the value at which fA=f 01 . 
     In block  860 , the tuning component is adjusted to the value determined in block  855 . 
     Following block  860 , heuristic  800  ends. 
       FIG. 8  illustrates an exemplary single-pass heuristic. However, one or more blocks of the heuristic may be repeated as desired. For example, an additional sweep may be incorporated to minimize the difference between the magnitude of the maxima at f 1  and f 2 . 
     Thus is described three exemplary heuristics that may be used to tune a wireless power transfer device such that, when the device is coupled with another device, the frequency difference between the two resonant modes of a system containing the coupled devices is minimized. 
     The exemplary heuristics described herein may be performed by a processor executing instructions from a memory on the wireless power transfer device. One or more heuristics may be included as instructions in the memory. If more than one heuristic is included as instructions in the memory, a heuristic may be selected for a given set of conditions. As just one example, the heuristic of  FIG. 5  may be used during production of the wireless power transfer device for initializing the device and the heuristic of  FIG. 8  may be used prior to or during power transfer in a user environment. 
     In a production environment, a test setup using a representative coupled device may be used. If the transmitter and receiver of a wireless power transfer system are to be packaged together, a heuristic such as one of the exemplary heuristics described above may be used to tune the system. 
     CONCLUSION 
     With regard to the processes, systems, methods, heuristics, etc. described herein, it should be understood that, although the steps of such processes, etc. have been described as occurring according to a certain ordered sequence, such processes could be practiced with the described steps performed in an order other than the order described herein. It further should be understood that certain steps could be performed simultaneously, that other steps could be added, or that certain steps described herein could be omitted. In other words, the descriptions of processes herein are provided for the purpose of illustrating certain embodiments, and should in no way be construed so as to limit the claimed invention. 
     Accordingly, it is to be understood that the above description is intended to be illustrative and not restrictive. Many embodiments and applications other than the examples provided would be apparent upon reading the above description. The scope of the invention should be determined, not with reference to the above description, but should instead be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. It is anticipated and intended that future developments will occur in the technologies discussed herein, and that the disclosed systems and methods will be incorporated into such future embodiments. In sum, it should be understood that the invention is capable of modification and variation. 
     All terms used in the claims are intended to be given their broadest reasonable constructions and their ordinary meanings as understood by those knowledgeable in the technologies described herein unless an explicit indication to the contrary in made herein. In particular, use of the singular articles such as “a,” “the,” “said,” etc. should be read to recite one or more of the indicated elements unless a claim recites an explicit limitation to the contrary.