Patent Publication Number: US-11387685-B2

Title: Load-induced resonance-shift-keying modulation scheme for simultaneous near-field wireless power and data transmission through a pair of inductive coils

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The current application is a national stage of PCT Patent Application No. PCT/US2018/046779, entitled “Load-Induced Resonance-Shift-Keying Modulation Scheme for Simultaneous Near-Field Wireless Power and Data Transmission through a Pair of Inductive Coils” to Pan et al., filed Aug. 14, 2018, which claims priority under 35 U.S.C. 119(e) to U.S. Provisional Patent Application Ser. No. 62/545,303, entitled “Load-Induced Frequency-Shift-Keying: A new modulation scheme that enables simultaneous near-field wireless power and data transmission through a single set of inductive coils”, filed Aug. 14, 2017 and U.S. Provisional Patent Application Ser. No. 62/558,798, entitled “Load-Induced Frequency-Shift-Keying Modulation Scheme that Enables Simultaneous Near-Field Wireless Power and Data Transmission through a Single Set of Inductive Coils”, filed Sep. 14, 2017, the disclosures of which are hereby incorporated herein by reference in their entirety. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with government support under Grant Number N66001-14-2-4029, awarded by the U.S. Department of Defense, Defense Advanced Research Projects Agency. The Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention generally relates to power and data links and, more specifically, simultaneous near-field wireless power and data transmission. 
     BACKGROUND 
     Implanted devices can include electronic biomedical devices used for patient monitoring, diagnostics, and various other purposes. These devices can be implanted inside a patient&#39;s body, typically by means of a surgical operation. Implanted devices can act as either sensors or stimulators. Sensors can measure biosignals, such as body temperature and blood pressure, from inside the body and transmit this information to an external device. Stimulators can receive information externally, such as from an external unit operated by medical professionals, and can produce signals within the body, such as stimulating specific nerves. Common applications of stimulators include the use of microelectrodes for diagnosing and determining treatment of brain disorders and neurological conditions. Early implanted devices were interfaced with wires through the skin in order to receive energy and transmit data. However, this arrangement can restrict the patient&#39;s movements and require bulky, rack-mounted electronics. Furthermore, because of penetration through the skin, there is a greater risk of infection. As such, a need for wireless telemetry systems exists. 
     SUMMARY OF THE INVENTION 
     One embodiment includes a wireless inductive telemetry link including an external transceiver including a demodulation circuit including a counter and a finite state machine circuit for outputting an output data signal, and an internal transceiver including a modulation circuit including a switch load capacitor for receiving an input data signal, wherein the switch capacitor is capable of receiving a data signal and modulating the data signal under a load-induced resonance-shift-keying modulation scheme, wherein the external transceiver is configured to transfer power to the internal transceiver while receiving data from the internal transceiver contemporaneously. 
     In another embodiment, the external transceiver further includes a first inductive coil, the internal transceiver further includes a second inductive coil, and the external is configured to transfer power to the internal transceiver while receiving data from the internal transceiver contemporaneously using the first and second inductive coils. 
     In a further embodiment, the load-induced resonance-shift-keying modulation scheme is implemented by using a switch capacitor to flip oscillation between two resonant frequencies, ω L  and ω H . 
     In still another embodiment, the demodulation circuit further includes an oscillator shut-down switch. 
     In a still further embodiment, the internal transceiver further includes a large capacitor for supplying charge at oscillator shut-down. 
     In yet another embodiment, the external transceiver is configured to provide self-regulated power to the internal transceiver. 
     In a yet further embodiment, the external transceiver is configured to provide self-regulated power to the internal transceiver within a coil separation d C  range of 4.2 centimeters. 
     In another additional embodiment, the external transceiver is configured to provide self-regulated power to the internal transceiver within a coil separation d C  range of 0.8 centimeters. 
     In a further additional embodiment, the internal transceiver is configured to transmit data to the external transceiver at a data rate of 5 Mbps. 
     In another embodiment again, the power transfer efficiency is above 35%. 
     A further embodiment again includes a method for simultaneous power and data transmission, the method including transmitting data from an internal transceiver to an external transceiver, wherein the external transceiver includes a demodulation circuit including a counter and a finite state machine circuit for outputting an output data signal, and the internal transceiver includes a modulation circuit including a switch load capacitor for receiving an input data signal, wherein the switch capacitor is capable of receiving a data signal and modulating the data signal under a load-induced resonance-shift-keying modulation scheme, and transferring power from the external transceiver to the internal transceiver contemporaneously with the transmittal of data from the internal transceiver. 
     In still yet another embodiment, the external transceiver further includes a first inductive coil, the internal transceiver further includes a second inductive coil, and the transmission of data and transferal of power are performed through the first and second inductive coils. 
     In a still yet further embodiment, the load-induced resonance-shift-keying modulation scheme is implemented by using a switch capacitor to flip oscillation between two resonant frequencies, ω L  and ω H . 
     In still another additional embodiment, the demodulation circuit further includes an oscillator shut-down switch. 
     In a still further additional embodiment, the internal transceiver further includes a large capacitor for supplying charge at oscillator shut-down. 
     In still another embodiment again, the external transceiver is configured to provide self-regulated power to the internal transceiver. 
     In a still further embodiment again, the external transceiver is configured to provide self-regulated power to the internal transceiver within a coil separation d C  range of 4.2 centimeters. 
     In yet another additional embodiment, the external transceiver is configured to provide self-regulated power to the internal transceiver within a coil separation d C  range of 0.8 centimeters. 
     In a yet further additional embodiment, the data is transmitted to the external transceiver at a data rate of 5 Mbps. 
     In yet another embodiment again, the power is transferred with a power transfer efficiency above 35%. 
     Additional embodiments and features are set forth in part in the description that follows, and in part will become apparent to those skilled in the art upon examination of the specification or may be learned by the practice of the invention. A further understanding of the nature and advantages of the present invention may be realized by reference to the remaining portions of the specification and the drawings, which forms a part of this disclosure. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The description will be more fully understood with reference to the following figures, data graphs, and diagrams, which are presented as exemplary embodiments of the invention and should not be construed as a complete recitation of the scope of the invention. 
         FIG. 1  conceptually illustrates a circuit diagram of an external transceiver and an internal transceiver utilizing a load shift keying system for carrier signal modulation. 
         FIG. 2  conceptually illustrates a diagram detailing the architecture of a telemetry link system utilizing load-induced resonance-shift-keying modulation in accordance with an embodiment of the invention. 
         FIG. 3  conceptually illustrates a detailed circuit diagram of a telemetry link system in accordance with an embodiment of the invention. 
         FIG. 4  shows a photograph of a test setup and micrographs of chips in accordance with an embodiment of the invention. 
         FIG. 5  conceptually illustrates the principle operation of a free-running oscillator with automatic amplitude control as the driver of a wireless power system in accordance with an embodiment of the invention. 
         FIG. 6  conceptually illustrates the principle operation of self-regulated power over changes in distance and in load in accordance with an embodiment of the invention. 
         FIG. 7  conceptually illustrates an exemplary circuit with parallel resonators in accordance with an embodiment of the invention. 
         FIG. 8A  conceptually illustrates an oscillator with automatic amplitude control capable of distance and load self-regulation in accordance with an embodiment of the invention. 
         FIG. 8B  shows a graph depicting how a smaller load can reduce the regulation range in accordance with an embodiment of the invention. 
         FIG. 8C  shows a graph depicting load-range expansion by reducing ω 0  when out-range happens in accordance with an embodiment of the invention. 
         FIGS. 9A-9C  show graphs depicting the splitting of ω L,H  for k&gt;k C  for self-regulating power in accordance with various embodiments of the invention. 
         FIG. 10  shows the input admittance Y in (jω) of coupled resonators in the complex plane with frequency as a parameter in accordance with an embodiment of the invention. 
         FIG. 11  conceptually illustrates a series-LCR circuit implementing a power link in accordance with an embodiment of the invention. 
         FIG. 12  conceptually illustrates a series-LCR power link with which a circuit analysis can be performed in accordance with an embodiment of the invention. 
         FIGS. 13A and 13B  conceptually illustrate input impedance in a series-LCR circuit under feedback. 
         FIGS. 14A and 14B  show graphical representations of maximum power transfer conditions of a wireless power transfer system in accordance with various embodiments of the invention. 
         FIGS. 15A-15C  show graphical representations of three power transfer scenarios with respect to the coupling coefficient k in accordance with various embodiments of the invention. 
         FIGS. 16A-16C  show graphical representations of a shift in the optimal operation frequency due to asymmetry in accordance with various embodiments of the invention. 
         FIG. 17  shows an exemplary circuit for implementing a simultaneous data and power transmission system in accordance with an embodiment of the invention. 
         FIGS. 18A and 18B  show measured operating waveforms at two oscillation frequencies in accordance with various embodiments of the invention. 
         FIG. 19  shows the measured range of regulated power delivery over varying coil separation and effective load resistance in accordance with an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Biomedical implants in accordance with various embodiments of the invention can be implemented in many different ways. In many embodiments, the implants are configured to receive power and transmit data wirelessly. In further embodiments, the implants are configured to simultaneously receive power and transmit data. Such devices can be configured to receive power from an external source and transmit data, such as but not limited to recorded neural data and/or other biological data, to outside the body. In many cases, the data is transmitted to the device that delivers power to the implant. For example, the power and data transmission system can be implemented with a pair of transceivers. The implant transceiver can receive power wirelessly though an external transceiver while simultaneously transmitting data to the external transceiver. In several embodiments, both forward (power) and reverse (data) links use the same pair of inductive coils in the transceivers, one coil mounted in the implant and the other in the external unit. The forward power link can be configured to deliver tens of mW to drive multiple stimulator engines. The reverse data link can be configured to support rates as high as a few Mb/s to transmit multiplexed neural waveforms sensed from an array of electrodes. In some embodiments, the system is configured to deliver self-regulated power to the implant. In several embodiments, the devices are configured for simultaneous power and data transmissions at reasonable distances. The delivered voltage at the implant can be regulated over changes in coil distance, misalignment, and/or load current. In a number of embodiments, the voltage remain constant as the distance between the coils changes or if their axes misalign. In further embodiments, the system is designed such that when data is transmitted over the power-carrying waveform, it does not induce a noticeable ripple on the rectified voltage supplying the implant current. Wireless data and power transmission systems are discussed below in further detail. 
     Data Modulation 
     Many different methods of transmitting data through wireless inductive telemetry links can be implemented, such as but not limited to carrier based modulation. Carrier based modulation is a scheme that can be used to transmit data by varying a periodic waveform, called the carrier signal. Modulation schemes can include but are not limited to load modulation, amplitude modulation, frequency modulation, and/or phase modulation. The modulated signal can be demodulated in the receiving device to retrieve the source waveform. Different modulation schemes can have different advantages and utilities. Important considerations in determining which modulation scheme to utilize can include the amount of power consumption and the ability to transmit power and data simultaneously. For example, load shift keying can transmit data at low power, but it can be difficult to transmit power and data simultaneously. A circuit diagram of an external transceiver and an internal transceiver utilizing a load shift keying system for carrier signal modulation is conceptually illustrated in  FIG. 1 . As shown, the system  100  includes an internal transceiver  102  sending data to an external transceiver  104  using a pair of inductor coils  106  and a data switch  108  for modulation. 
     Data transmission systems in accordance with various embodiments of the invention can be implemented using a low-power, high-rate modulation scheme. In some embodiments, a load-induced resonance-shift-keying (“L-RSK”) modulation scheme is used to transmit data between transceivers. L-RSK can be used as a low-powered, high rate data transmission scheme and can be implemented through the switching of a load capacitor to modulate an input signal, or carrier signal. A diagram detailing the architecture of a telemetry link system utilizing L-RSK in accordance with an embodiment of the invention is conceptually illustrated in  FIG. 2 . The telemetry link system  200  can include an implanted transceiver  202  and an external transceiver  204 . The implanted transceiver  202  can be used to transmit data, termed uplink data, to an external transceiver  204  while simultaneously receiving power. As shown in the exemplary embodiment, the implanted transceiver  202  implements a switch capacitor  206  that can be used to induce a load. This load induced modulation scheme typically consumes low power. In various embodiments, the external transceiver  204  can include an oscillator driver component  208 . The oscillator side can be configured to maintain a constant envelope, which can facilitate consistent and uninterrupted power transmission. In several embodiments, the modulated signal can be demodulated by sensing the frequency. 
       FIG. 3  conceptually illustrates a detailed circuit diagram of a telemetry link system in accordance with an embodiment of the invention. As shown, the data transmission circuitry  300  can include a demodulation circuit  302  implemented in an external transceiver  304  and a modulation circuit  306  implemented in an implanted transceiver  308 . The demodulation circuit  302  can include an oscillator shut-down switch  310  and a circuit for outputting data  312 . In various embodiments, the data output circuit  312  can include a counter  314  and a sequential circuit implementing a finite state machine (“FSM”)  316 . The modulation circuit  306  can include a switch capacitor  318  that can implement L-RSK by modulating a source waveform in accordance with a data input. In many embodiments, switching activity can occur within an oscillator shut-down window. In several embodiments utilizing L-RSK, when the oscillator starts up, the received signal can be demodulated by measuring the frequency. In the illustrative embodiment, the implanted transceiver  308  includes a large capacitor  320  at rectifier load, which can supply charge at oscillator shut-down. 
     Although specific modulation schemes are described above, a person having ordinary skill in the art would appreciate that other modulation schemes can be used in accordance with the requirements of a given application. For example, in some embodiments, an amplitude shift keying (“ASK”) scheme is used to modulate a carrier signal. Different modulation schemes can have varying degrees of performance with respect to power consumption, noise performance, data transmission rate, and other performance metrics. For instance, frequency shift keying (“FSK”) can have better noise performance than ASK for some applications. 
     Wireless Power Transfer System 
     Near-field wireless power transfer systems can be implemented in a variety of different ways, such as but not limited to the use of inductive links. An inductive link-based wireless power transfer system generally includes a power transmitter, where power originates, followed by a power transfer link through which power could flow from source to load. A power receiver can harvest power from the link and deliver it to the load. In many embodiments, an inductive link-based wireless power transfer system can be implemented using coupled inductor coils with which power carrying electromagnetic waves are linked. The power transfer distance can be comparable to the physical dimensions of the inductor coils and can achieve a high power transfer efficiency. Power transmitters can be considered as energy sources and can be equivalently treated as voltage sources, current sources, or combinations of both. These energy sources can be implemented in a variety of ways. For example, an LC oscillator, which can be considered as a current source, can be implemented as a cross-coupled field-effect transistor (“FET”) pair followed by an LC-tank circuit. The oscillator driver can be followed by a resonator link, delivering power to a resistive load. 
       FIG. 4  shows a photograph of a test setup and micrographs of chips in accordance with an embodiment of the invention. As shown, coil separation and axial misalignment of the external and internal subsystems can be studied with such a test setup. There is a trade-off between delivered power P L  and maximum regulation distance d C :
 
| V   2 | 2 /(2 R   L )=     ⇒ k   C =1/ Q   2 ≈(ω res   L   2 )/ R   L ↑⇒ .
 
The resonant frequency can be configured to expand the range of regulation distance and load variations.
 
       FIG. 5  conceptually illustrates the principle operation of a free-running oscillator with automatic amplitude control (“AAC”) as the driver of a wireless power system in accordance with an embodiment of the invention. In the illustrative embodiment, the free-running oscillator with AAC can appear in steady-state to the admittance (Y in =Y S +Y T ) as a constant-amplitude voltage source (Y S ) of variable frequency (around ω res ). The oscillator can self-tune to one of a pair of frequencies such that the coupled inductors act as a transformer of fixed turns ratio (√{square root over ((L 1 /L 2 )}) over a range of coupling coefficients k C &lt;k&lt;1. Within this range, a constant V S  maintained by AAC implies that the voltage amplitude V 2  on the secondary is also constant even as the implant load R L  changes. Regulation can be maintained up to a maximum coil separation (d C ) or axial misalignment, where the coupling coefficient drops below the critical value (k C =1/Q 2 ). 
       FIG. 6  conceptually illustrates the principle operation of self-regulated power over changes in distance and in load in accordance with an embodiment of the invention. As shown, coupled inductors are modeled by a T-network of inductors that depend on ±k, with an ideal transformer of turns ratio √{square root over ((L 1 /L 2 )}):1 in between. The “±” accounts for the in-phase (common) and anti-phase (differential) modes of operation. Provided that each resonator, when uncoupled, is tuned to the same ω 0 =1/√{square root over (L 1 /C 1 )}=1√{square root over (L 2 /C 2 )}, then when coupled with coefficient k, inductors in the primary and secondary sides will both resonate with their series capacitors at one of two new natural mode frequencies, ω L,H =ω 0 /√{square root over (1±k)}. If kω 0 L 2 »R L , the driving voltage source is loaded by R 1  and a transformed resistance (L 1 /L 2 )R L  that is independent of k⇒the actual R L  receives a constant power. This can be considered distance self-regulation. As kω 0 L 2 →R L , this will no longer hold, setting a lower limit on k where self-regulation ceases: k C =R L /ω 0 L 2 =1/Q 2 . The higher the loaded Q 2 , the larger the range of distance self-regulation (d C ). Although coupled series resonators are discussed, the same properties can hold for coupled parallel resonators, but now k C =ω 0 L 2 /R L .  FIG. 7  conceptually illustrates an exemplary circuit with parallel resonators in accordance with an embodiment of the invention. 
       FIG. 8A  conceptually illustrates an oscillator with AAC capable of distance and load self-regulation in accordance with an embodiment of the invention. The current-mode oscillator tuned by the coupled resonators can operate at one natural mode, i.e. tracks one of ω L,H  as distance changes for k&gt;k C  so that power delivery remains distance-regulated. When the implant is stimulated with a large current, the effective R L  can drop, causing oscillation amplitude to also drop. An AAC compares it with a DC reference and adjusts the commutated bias current I S  to restore the amplitude. This maintains a constant V 2  at the implant as load varies. This can be considered load self-regulation. However, the smaller R L  can raise k C , which could put the coils at their present separation outside the range of distance self-regulation.  FIG. 8B  shows a graph depicting how a smaller load can reduce the regulation range in accordance with an embodiment of the invention. This condition can be detected by sensing over-range in the digital-to-analog converter of the AAC. The rise in k C  can be counteracted by lowering ω 0  ( FIG. 8C ) with switched capacitor banks. Conversely, when the implant is in sensing mode, R L  ↑. ω 0  can then be tuned higher for better efficiency ( FIG. 7 : ω 0  ↑⇒η↑), supporting a higher data rate. 
     Many embodiments of the invention include methods of modulation for sending data from the implant to the external unit without inducing ripple on the delivered voltage. In some embodiments, the oscillator will choose one of the two modes ω km    FIGS. 9A-9C  show graphs depicting the splitting of ω L,H  for k&gt;k C  for self-regulating power in accordance with various embodiments of the invention.  FIG. 10  shows the input admittance Y in (jω) of coupled resonators in the complex plane with frequency as a parameter in accordance with an embodiment of the invention. Oscillation can occur at a frequency where ∠Y in =0, as set by the Barkhausen stability criterion. When the resonators are weakly coupled (0≤k≤k C ), ∠Y in =0 at resonant frequency ω res . For stronger coupling (k C ≤k≤1), ∠Y in =0 at three frequencies: the resonant frequency and two bifurcated frequencies, ω L ≤ω res ≤ω H , which split apart as k rises. Oscillation is possible, in principle, at any of the three frequencies, but can be be unstable at ω res  as perturbations can drive it away to settle stably into one of the two split frequencies. As shown in  FIG. 10 , if the oscillator&#39;s tuning admittance is smaller at ω H , then at startup the oscillation mode at ω H  sees a higher loop gain and therefore grows faster in amplitude and forces the nonlinearity in the active circuit to suppress the mode at ω L . In this instance, the mode at ω H  can prevail in steady state. This asymmetry in admittance can be deliberately induced by off-tuning the two resonators after adding or removing a small ΔC 2 . Thus, oscillation can be repeatably initiated at either ω L  or ω H . 
     Ideally, while data is being continuously uplinked, downlinked power should be delivered without noticeable ripple. The most common data modulation used in inductive links (LSK) typically fails to meet this criterion. In order to be detected, it must modulate the amplitude of V 2  substantially, thus inducing ripples on the load supply voltage. For smooth delivery of power, a constant envelope modulation such as FSK will be preferred. Switching ΔC 2  in the implant will toggle oscillation frequency. However, for smooth power flow, ΔC 2  should be «C 2 , thus making it difficult to detect the resulting narrowband FSK when the data rate (˜1 Mb/s) is as high as 10% of the carrier frequency (˜13 MHz). However, uniquely to this system (L-RSK), the same ΔC 2  can induce a shift in frequency that is almost ten times larger by forcing the oscillation to jump between the two modes—i.e., ω L  to ω H  or vice-versa. At every non-return-to-zero (“NRZ”) data transition, the oscillation can be quenched (shut down), the switch S DATA  toggled, and the oscillation restarted to acquire the other mode. Unlike LSK where the amplitude of V 2  is modulated over entire bit periods, oscillation quench and restart in L-RSK take place over transition edges. The bit rate can be independent of carrier frequency, and L-RSK needs only a simple non-coherent demodulator. 
     L-RSK modulation schemes can modulate data by switching a tiny ΔC 2  (≈0.05 C 2 ) to flip oscillation between resonant modes ω L  and ω m  two frequencies whose ratio is √{square root over ((1+k)/(1−k))}. For k C &lt;k&lt;1, this ratio is large so that the frequency difference can be easily detected. At either mode frequency, the properties of self-regulation are preserved. The modulator typically consumes only the power to toggle a switch, similar to the commonly used LSK; but now the oscillation maintains an almost constant envelope for stable power flow. L-RSK is in effect a wideband binary FSK that ensures power is being transferred at ω L,H . If the FSK were realized by switching a large ΔC 2  at implant side, then it could strongly mistune the two resonators, sacrificing power self-regulation. L-RSK can maintain self-regulated wireless power delivery while communicating data in the reverse link at a high rate. 
     Different types of circuitry can be implemented to realize an inductive link. In some embodiments, a parallel-LCR power link is used as the inductive link. In other embodiments, a series-LCR power link is used as the inductive link. Choice of power link used can be considered based on various factors, such as but not limited to the type of source transmitter. For example, a parallel-LCR power link can preferably be considered if the power source transmitter is a current source power transmitter. For a voltage source power transmitter, a series-LCR power link can be the preferred implementation. A series-LCR circuit implementing a power link in accordance with an embodiment of the invention is conceptually illustrated in  FIG. 11 . In the illustrated embodiment, the power transmitter is modeled as a voltage source V S  while the power receiver is modeled as a constant resistor R 2 . 
     Although the discussions above describe specific implementations of inductive power link systems, a person having ordinary skill in the art would understand that a variety of circuit designs exists and can be implemented. For example, equivalent circuits can be exchanged as appropriate to produce the same or a similar effect. 
     Circuit analysis can be performed on wireless power links to provide design intuition that can influence performance of the circuit.  FIG. 12  conceptually illustrates a series-LCR power link with which a circuit analysis can be performed in accordance with an embodiment of the invention. As shown, an equivalent circuit can be used to replace the inductor coupling with controlled energy sources. In the illustrated embodiment, feedback analysis shows the transfer function as: 
                 H   ⁡     (   s   )       =           V   L     ⁡     (   s   )           V   S     ⁡     (   s   )         =       -       R   2     sM       ·       T   ⁡     (   s   )         1   +     T   ⁡     (   s   )                 ,       T   ⁡     (   s   )       =       -       (   sM   )     2             Z   1     ⁡     (   s   )       ·       Z   2     ⁡     (   s   )             ,         
where Z 1 (s)=1/sC 1 +R 1 +sL 1  and Z 2 (s)=1/sC 2 +R 2 +sL 2  are the series impedances.
 
     The system&#39;s input impedance under feedback can be calculated as:
 
= Z   in,f/b   =Z   in | T→0 ·(1+ T )
 
⇒ Z   in   =Z   1 ·(1+ T )= Z   1   +Z   r .
 
     Equivalently, the circuit can be drawn as a source V S  driving an impedance Z 1  in series with a transformed impedance Z T  that is dependent on the rest of the circuit. A series-LCR system with input impedance is conceptually illustrated in  FIG. 13A , and the transformed impedance for the series-LCR system is conceptually illustrated in  FIG. 13B . In  FIG. 13B , Z 1  can be considered the original L 1 , C 1 , and R 1  associated with the transmitter-side network. 
               Z   T     =         Z   1     ·   T     =         -     s   2       ⁢     k   2     ⁢     L   1     ⁢     L   2         Z   2               
is effectively the impedance looking at the port over the left controlled source sM·I 2  ( FIG. 12 ). Looking into that port from left to right, the energy-dissipating element can be considered the load R 2 . As a result, it can be concluded that energy dissipated in Z 1  is the energy wasted in source impedance, and energy dissipated in Z T  is the energy delivered to the load.
 
     The following conditions can be used to maximize the power delivered to the load at sinusoidal steady state: 
                   Z   1     ⁡     (     j   ⁢           ⁢   ω     )       =             Z   T     ⁡     (     j   ⁢           ⁢   ω     )       *     ⇒       Z   1     ⁡     (     j   ⁢           ⁢   ω     )         =       [         -       (     j   ⁢           ⁢   ω     )     2       ⁢     k   2     ⁢     L   1     ⁢     L   2           Z   2     ⁡     (     j   ⁢           ⁢   ω     )         ]     *         ,         
which can be equivalent to the following two conditions:
 
     
       
         
           
             
               
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     A graphical representation of the first condition is shown in  FIG. 14A . As illustrated, the condition for maximum power transfer is manifested as two “Q-curves” intersecting on the graph. The second condition is shown in  FIG. 14B . As illustrated, if the two “Q-curves” have different quality factor values, the point where ∠Z 1 (jω) and ∠Z 2 (jω) can be equal is at resonant frequency ω 0 . If Z 1  and Z 2  have the same quality factors, the two curves can completely coincide, meaning that the angles are equal to each other all the time. For instance, under the assumptions: 
                 ω     res   ,   1       =       1         L   1     ⁢     C   1           =       1         L   2     ⁢     C   2           =     ω     res   ,   2             ,         and   ⁢           ⁢     Q   1       =             L   1       C   1         ⁢     1     R   1         =             L   1       C   1         ⁢     1     R   1         =     Q   1           &gt;&gt;   1     ,         
∠Z 1 (jω)=∠Z 2 (jω) is satisfied at all frequencies. To sum up, it can be desirable to set the two parts of the network to have the same resonant frequencies (ω res,1 =ω res,2 ), the same quality factors (Q 1 =Q 2 ), and as large quality factors as possible (Q 1 ,Q 2 »1). A system meeting these requirements can transfer power in the following three different scenarios depending on the value of the coupling coefficient k in comparison to the critical coupling coefficient k c , which can be defined as:
 
     
       
         
           
             
               
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     When the system is under-coupled (k&lt;k c ), the “Q-tips” never touch, and the system will typically not meet the maximum power transfer conditions. When the system is at critical-coupling (k=k c ), the “Q-tips” touch at the tips, and the system can meet the maximum power transfer conditions at resonant frequency. When the system is over-coupled (k&gt;k c ), the “Q-tips” intersect at two points, and the system can meet the maximum power transfer conditions at the frequencies where the “Q-tips” intersect. The three power transfer scenarios are graphically depicted in  FIGS. 15A-15C , respectively. 
     For k&gt;k c  (over-coupled), there are typically two frequencies (ω 1 , ω 2 ) at which power transfer is ideal. A graphical representation of such conditions is shown in  FIG. 16A . In this scenario, the system can eventually fall into one of the frequencies due to asymmetry. The frequency selection can depend on the values of ω res,1  and ω res,2 . The two selection scenarios, ω res,2 &lt;ω res,1  and ω res,2 &gt;ω res,1 , is graphically depicted in  FIGS. 16B and 16C , respectively. 
     Simultaneous Wireless Data and Power Transmission Systems 
     Biomedical implant systems configured for simultaneous data and power transmission in accordance with various embodiments of the invention can be implemented in many different ways.  FIG. 17  shows an exemplary circuit for implementing a simultaneous data and power transmission system in accordance with an embodiment of the invention. As shown, the system  1700  includes an external transceiver  1702  for delivering power and receiving data. The system  1300  further includes an internal transceiver  1704  for receiving power and transmitting data. In the illustrative embodiment, the oscillator  1706  uses wide FETs to reduce the I 2 R loss during conduction. An AAC  1708  compares the rectified oscillator output with a DC reference and adjusts the tail current. The differential voltage across L 1  has a Class D-like waveform that exceeds the supply voltage (amplitude around 4 V). To expand the regulation range, the natural frequency ω res  of both resonators can be programmed with capacitor banks C 1  and C 2  through switches S 1 -S 8 . Therefore, when the implant current rises largely, such as at a transition from sensing to stimulation mode, the effective R L  drops. In response, the switches lower ω res  to maintain the maximum regulation distance d c . 
     Wireless data can be transmitted from the implant to the primary side by toggling on-chip switch S DATA . Before transmitting each bit, S SHUT,TX  and S SHUT,RX  can be closed to critically damp the two resonators and quench the original oscillation within one cycle. If the data bit transitions, S DATA  can be toggled to force the oscillation to the other frequency. When S SHUT,TX  and S SHUT,RX  are released, the oscillation can build up quickly to reach steady-state at the new frequency. Diodes in the rectifier can be turned off during this process, but the large capacitor C L  at the rectifier&#39;s output maintains steady load voltage with a droop less than 1 mV. In some embodiments, frequency switching takes ˜10% of a bit period. In several embodiments, an all-digital FSK demodulator on the primary side over-samples the oscillation waveform at 200 MHz. A frequency estimate can be computed and compared with a threshold value to decide on the transmitted bit.  FIGS. 18A and 18B  show measured operating waveforms at two oscillation frequencies in accordance with an embodiment of the invention. 
     The external and implant subsystems can be integrated on two separate chips in 180 nm CMOS. In many embodiments, most power management blocks employ 350 nm I/O FETs. In some embodiments, L 1  and L 2  can be realized as 3-turn and 2-turn coils of 3 cm diameter wound with AWG18 copper wires. The discrete tuning capacitors can program resonance f res  at one of 1.8, 3.39, 6.78, or 13.56 MHz. In a number of embodiments, oscillation can be tuned up to 30 MHz for highest data rate, but at the cost of more loss in the rectifier. In several embodiments, the drive can supply up to 93 mW to the implant, and the rectified DC output is around 2.1 V. 
       FIG. 19  shows the measured range of regulated power delivery over varying coil separation and effective load resistance in accordance with an embodiment of the invention. Data rate can be limited by the bandwidth of the transfer function across the coupled resonators and also by the clock rate of the FSK demodulator. In many embodiments, the system can transmit 1 Mbps at f res =13 MHz and 4 Mbps at f res =30 MHz across coils as far apart as 2 cm, which is sufficient for a brain-machine interface. In further embodiments, a data rate of 5 Mbps can be achieved, limited to a distance of ˜0.8 cm. Over all operating frequencies and at maximum transmitted power, the system complies with FCC § 15.209 radiation emission limits. FSK demodulation typically consumes about 7 mW of digital power. Modulator power in the implant can be set by the dynamic power to switch the gate capacitance of the FETs involved in modulation. 
     Although specific methods and systems for simultaneous near-field wireless power and data transmission are discussed above, many different systems can be implemented in accordance with many different embodiments of the invention. It is therefore to be understood that the present invention may be practiced in ways other than specifically described, without departing from the scope and spirit of the present invention. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive. Accordingly, the scope of the invention should be determined not by the embodiments illustrated, but by the appended claims and their equivalents.