Patent Publication Number: US-2021167637-A1

Title: Wireless Power Systems With Foreign Object Detection

Description:
This application claims the benefit of provisional patent application No. 62/943,043, filed Dec. 3, 2019 and provisional patent application No. 63/012,813, filed Apr. 20, 2020, which are hereby incorporated by reference herein in their entireties. 
    
    
     FIELD 
     This relates generally to power systems, and, more particularly, to wireless power systems for charging electronic devices. 
     BACKGROUND 
     In a wireless charging system, a wireless power transmitting device such as a charging mat wirelessly transmits power to a wireless power receiving device such as a portable electronic device. The wireless power transmitting device uses a wireless power transmitting coil to transmit wireless power signals to the wireless power receiving device. The wireless power receiving device has a coil and rectifier circuitry. The coil of the wireless power receiving device receives alternating-current wireless power signals from the wireless power transmitting device. The rectifier circuitry converts the received signals into direct-current power. 
     SUMMARY 
     It is desirable to understand how much power that is transmitted by a wireless power transmitting device is, or is not, received by the wireless power receiving device. 
     In some embodiments, the wireless power transmitting device determines whether an external object is present in the vicinity of the wireless power transmitting coil. The external object may be a foreign object such as a coin or paperclip or may be a wireless power receiving device. If a foreign object is detected, suitable action may be taken such as forgoing wireless power transmission. 
     In some embodiments, external objects can be detected using quality-factor measurements. Current quality-factor measurements are compared to a baseline quality measurement to determine whether an external object is present. Wireless communications can be used to discriminate between foreign objects and wireless power receiving devices. 
     Quality-factor measurements may be made by applying an impulse to the wireless power transmitting coil and measuring a decay envelope associated with an impulse response in the coil or by measuring the impedance of the wireless power transmitting coil directly and determining the current quality factor from the measured impedance. Quality factor measurements can be compensated for aging and temperature effects using temperature measurements and compensation factors based on frequency and coil resistance measurements. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic diagram of an illustrative wireless power system in accordance with an embodiment. 
         FIG. 2  is a circuit diagram of an illustrative wireless power system in accordance with an embodiment. 
         FIG. 3  is a graph showing the impulse response of a wireless power transmitting coil can be analyzed to measure a quality-factor value for the coil in accordance with an embodiment. 
         FIG. 4  is a circuit diagram of an illustrative wireless power transmitter showing circuitry that may be used to make quality-factor measurements in accordance with an embodiment. 
         FIG. 5  shows equations that may be used in determining parameters such as a coil quality-factor based on impedance measurements in accordance with an embodiment. 
         FIG. 6  is an equation showing compensation factors that may be applied to a current quality factor measurement to determine a compensated quality-factor value in accordance with an embodiment. 
         FIGS. 7 and 8  are diagrams showing illustrative operations involved in using a wireless power system in accordance with embodiments. 
         FIG. 9  is a graph showing the impulse response of a wireless power transmitting circuit in accordance with an embodiment. 
         FIG. 10  is a graph in which change in quality factor has been plotted as a function of coil resistance in accordance with an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     A wireless power system includes a wireless power transmitting device such as a wireless charging mat. The wireless power transmitting device wirelessly transmits power to a wireless power receiving device. The wireless power receiving device may be a device such as a wrist watch, cellular telephone, tablet computer, laptop computer, or other electronic equipment. The wireless power receiving device uses power from the wireless power transmitting device for powering the device and for charging an internal battery. 
     Wireless power is transmitted from the wireless power transmitting device to the wireless power receiving device using one or more wireless power transmitting coils. The wireless power receiving device has one or more wireless power receiving coils coupled to rectifier circuitry that converts received wireless power signals into direct-current power. 
     If a foreign object such as a paperclip, coin, or other metallic object is present near the wireless power transmitting coil of the wireless power transmitting device, there may be a risk of eddy current generation in the foreign object that could elevate the temperature of the foreign object. To determine whether a foreign object such as a paperclip or coin is present in the vicinity of the wireless power transmitting device, the wireless power transmitting device measures the quality factor of the wireless power transmitting coil and determines whether the quality factor has been affected by the presence of a foreign object. By detecting whether foreign objects are present, suitable action can be taken (e.g., the wireless power transmitting device may forgo wireless power transfer operations whenever a foreign object is detected). 
     An illustrative wireless power system (wireless charging system) is shown in  FIG. 1 . As shown in  FIG. 1 , wireless power system  8  includes a wireless power transmitting device such as wireless power transmitting device  12  and includes a wireless power receiving device such as wireless power receiving device  24 . Wireless power transmitting device  12  includes control circuitry  16 . Wireless power receiving device  24  includes control circuitry  30 . Control circuitry in system  8  such as control circuitry  16  and control circuitry  30  is used in controlling the operation of system  8 . This control circuitry may include processing circuitry associated with microprocessors, power management units, baseband processors, digital signal processors, microcontrollers, and/or application-specific integrated circuits with processing circuits. The processing circuitry implements desired control and communications features in devices  12  and  24 . For example, the processing circuitry may be used in selecting coils, determining power transmission levels, processing sensor data and other data to detect foreign objects and perform other tasks, processing user input, handling negotiations between devices  12  and  24 , sending and receiving in-band and out-of-band data, making measurements, and otherwise controlling the operation of system  8 . 
     Control circuitry in system  8  may be configured to perform operations in system  8  using hardware (e.g., dedicated hardware or circuitry), firmware and/or software. Software code for performing operations in system  8  is stored on non-transitory computer readable storage media (e.g., tangible computer readable storage media) in control circuitry  8 . The software code may sometimes be referred to as software, data, program instructions, instructions, or code. The non-transitory computer readable storage media may include non-volatile memory such as non-volatile random-access memory (NVRAM), one or more hard drives (e.g., magnetic drives or solid state drives), one or more removable flash drives or other removable media, or the like. Software stored on the non-transitory computer readable storage media may be executed on the processing circuitry of control circuitry  16  and/or  30 . The processing circuitry may include application-specific integrated circuits with processing circuitry, one or more microprocessors, a central processing unit (CPU) or other processing circuitry. 
     Power transmitting device  12  may be a stand-alone power adapter (e.g., a wireless charging mat or charging puck that includes power adapter circuitry), may be a wireless charging mat or puck that is coupled to a power adapter or other equipment by a cable, may be a portable device, may be equipment that has been incorporated into furniture, a vehicle, or other system, may be a removable battery case, or may be other wireless power transfer equipment. Illustrative configurations in which wireless power transmitting device  12  is a wireless charging mat are sometimes described herein as an example. 
     Power receiving device  24  may be a portable electronic device such as a wrist watch, a cellular telephone, a laptop computer, a tablet computer, an accessory such as an earbud, or other electronic equipment. Power transmitting device  12  may be coupled to a wall outlet (e.g., an alternating current power source), may have a battery for supplying power, and/or may have another source of power. Power transmitting device  12  may have an alternating-current (AC) to direct-current (DC) power converter such as AC-DC power converter  14  for converting AC power from a wall outlet or other power source into DC power. DC power may be used to power control circuitry  16 . During operation, a controller in control circuitry  16  uses power transmitting circuitry  52  to transmit wireless power to power receiving circuitry  54  of device  24 . Power transmitting circuitry  52  may have switching circuitry (e.g., inverter circuitry  61  formed from transistors) that is turned on and off based on control signals provided by control circuitry  16  to create AC current signals through one or more wireless power transmitting coils such as wireless power transmitting coil(s)  36 . These coil drive signals cause coil(s)  36  to transmit wireless power. Multiple coils  36  may be arranged in a planar coil array (e.g., in configurations in which device  12  is a wireless charging mat) or may be arranged to form a cluster of coils (e.g., in configurations in which device  12  is a wireless charging puck). In some arrangements, device  12  (e.g., a charging mat, puck, etc.) may have only a single coil. In other arrangements, a wireless charging device may have multiple coils (e.g., two or more coils, 5-10 coils, at least 10 coils, 10-30 coils, fewer than 35 coils, fewer than 25 coils, or other suitable number of coils). 
     As the AC currents pass through one or more coils  36 , alternating-current electromagnetic (e.g., magnetic) fields (wireless power signals  44 ) are produced that are received by one or more corresponding receiver coils such as coil(s)  48  in power receiving device  24 . Device  24  may have a single coil  48 , at least two coils  48 , at least three coils  48 , at least four coils  48 , or other suitable number of coils  48 . When the alternating-current electromagnetic fields are received by coil(s)  48 , corresponding alternating-current currents are induced in coil(s)  48 . The AC signals that are used in transmitting wireless power may have any suitable frequency (e.g., 100-250 kHz, etc.). Rectifier circuitry such as rectifier circuitry  50 , which contains rectifying components such as synchronous rectification metal-oxide-semiconductor transistors arranged in a bridge network, converts received AC signals (received alternating-current signals associated with electromagnetic signals  44 ) from one or more coils  48  into DC voltage signals for powering device  24 . 
     The DC voltage produced by rectifier circuitry  50  (sometime referred to as rectifier output voltage Vrect) can be used in charging a battery such as battery  58  and can be used in powering other components in device  24 . For example, device  24  may include input-output devices  56 . Input-output devices  56  may include input devices for gathering user input and/or making environmental measurements and may include output devices for providing a user with output. As an example, input-output devices  56  may include a display for creating visual output, a speaker for presenting output as audio signals, light-emitting diode status indicator lights and other light-emitting components for emitting light that provides a user with status information and/or other information, haptic devices for generating vibrations and other haptic output, and/or other output devices. Input-output devices  56  may also include sensors for gathering input from a user and/or for making measurements of the surroundings of system  8 . Illustrative sensors that may be included in input-output devices  56  include three-dimensional sensors (e.g., three-dimensional image sensors such as structured light sensors that emit beams of light and that use two-dimensional digital image sensors to gather image data for three-dimensional images from light spots that are produced when a target is illuminated by the beams of light, binocular three-dimensional image sensors that gather three-dimensional images using two or more cameras in a binocular imaging arrangement, three-dimensional lidar (light detection and ranging) sensors, three-dimensional radio-frequency sensors, or other sensors that gather three-dimensional image data), cameras (e.g., infrared and/or visible cameras with respective infrared and/or visible digital image sensors and/or ultraviolet light cameras), gaze tracking sensors (e.g., a gaze tracking system based on an image sensor and, if desired, a light source that emits one or more beams of light that are tracked using the image sensor after reflecting from a user&#39;s eyes), touch sensors, buttons, capacitive proximity sensors, light-based (optical) proximity sensors such as infrared proximity sensors, other proximity sensors, force sensors, sensors such as contact sensors based on switches, gas sensors, pressure sensors, moisture sensors, magnetic sensors, audio sensors (microphones), ambient light sensors, optical sensors for making spectral measurements and other measurements on target objects (e.g., by emitting light and measuring reflected light), microphones for gathering voice commands and other audio input, distance sensors, motion, position, and/or orientation sensors that are configured to gather information on motion, position, and/or orientation (e.g., accelerometers, gyroscopes, compasses, and/or inertial measurement units that include all of these sensors or a subset of one or two of these sensors), sensors such as buttons that detect button press input, joysticks with sensors that detect joystick movement, keyboards, and/or other sensors. Device  12  may have one or more input-output devices  70  (e.g., input devices and/or output devices of the type described in connection with input-output devices  56 ). 
     Device  12  and/or device  24  may communicate wirelessly using in-band or out-of-band communications. Device  12  may, for example, have wireless transceiver circuitry  40  that wirelessly transmits out-of-band signals to device  24  using an antenna. Wireless transceiver circuitry  40  may be used to wirelessly receive out-of-band signals from device  24  using the antenna. Device  24  may have wireless transceiver circuitry  46  that transmits out-of-band signals to device  12 . Receiver circuitry in wireless transceiver  46  may use an antenna to receive out-of-band signals from device  12 . In-band transmissions between devices  12  and  24  may be performed using coils  36  and  48 . With one illustrative configuration, frequency-shift keying (FSK) is used to convey in-band data from device  12  to device  24  and amplitude-shift keying (ASK) is used to convey in-band data from device  24  to device  12 . Power may be conveyed wirelessly from device  12  to device  24  during these FSK and ASK transmissions. 
     It is desirable for power transmitting device  12  and power receiving device  24  to be able to communicate information such as received power, battery states of charge, and so forth, to control wireless power transfer. However, the above-described technology need not involve the transmission of personally identifiable information in order to function. Out of an abundance of caution, it is noted that to the extent that any implementation of this charging technology involves the use of personally identifiable information, implementers should follow privacy policies and practices that are generally recognized as meeting or exceeding industry or governmental requirements for maintaining the privacy of users. In particular, personally identifiable information data should be managed and handled so as to minimize risks of unintentional or unauthorized access or use, and the nature of authorized use should be clearly indicated to users. 
     Control circuitry  16  has external object measurement circuitry  41  that may be used to detect whether external objects are present on the charging surface of the housing of device  12  (e.g., to detect objects on the top of a charging mat or, if desired, to detect objects adjacent to the coupling surface of a charging puck). The housing of device  12  may have polymer walls, walls of other dielectric, metal structures, fabric, and/or other housing wall structures that enclose coils  36  and other circuitry of device  12 . The charging surface may be a planer outer surface of the upper housing wall of device  12  or an outer surface having other shapes (e.g., concave, convex, etc.). Circuitry  41  can detect foreign objects such as coils, paper clips, and other metallic objects and can detect the presence of wireless power receiving devices  24  (e.g., circuitry  41  can detect the presence of one or more coils  48 ). During object detection and characterization operations, external object measurement circuitry  41  can be used to make measurements on coils  36  and/or on other coils such as optional foreign object detection coils in device  12  to determine whether any devices  24  are present on device  12 . 
     In an illustrative arrangement, measurement circuitry  41  of control circuitry  16  contains signal generator circuitry such as a pulse generator that supplies control signals to inverter  61 . These control signals cause inverter  61  to create impulses so that impulse responses can be measured by circuitry  41  (e.g., by using a voltage sensor, an analog-to-digital converter configured to convert analog voltage measurements to digital voltage measurements, and/or other sensing circuitry). Measurement circuitry may also have alternating-current sources and other circuitry for making measurements on coil  36 . 
     In some embodiments, quality-factor measurements are made on coil  36  to determine whether a foreign object is present. For example, direct impedance measurements and/or impulse responses can be analyzed to make quality-factor (Q-factor) measurements on coil  36 . Measurements of the Q-factor of coil  36  (including measurements of changes in the Q-factor value from a baseline value) may be performed at any suitable time such as prior to transmitting wireless power from device  12  to device  24 . If the Q-factor value deviates by more than a threshold amount and the object causing the Q-factor deflection does not respond to a subsequent digital ping, device  12  can conclude that a foreign object is present on coil  36  and can forgo wireless power transmission and/or take other suitable action (e.g., by transmitting power at a restricted level that is lower than the level permitted in absence of detecting the foreign object, by halting power transmission, etc.). 
       FIG. 2  shows illustrative circuitry in system  8  that allows measurements to be made of the Q-factor (Q) of coil  36 . The wireless power circuitry of  FIG. 2  includes wireless power transmitting circuitry  52  in wireless power transmitting device  12  and wireless power receiving circuitry  54  in wireless power receiving device  24 . During operation, wireless power signals  44  are transmitted by wireless power transmitting circuitry  52  and are received by wireless power receiving circuitry  54 . As shown in  FIG. 2 , wireless power transmitting circuitry  52  includes inverter circuitry  61 . 
     Inverter circuitry (inverter)  61  may be used to provide signals to coil  36 . During wireless power transmission, the control circuitry of device  12  supplies signals to control input  82  of inverter circuitry  61  that cause inverter  61  to supply alternating-current drive signals to coil  36 . Circuit components such as capacitor  70  may be coupled in series with coil  36  as shown in  FIG. 2 . When alternating-current current signals are supplied to coil  36 , corresponding alternating-current electromagnetic signals (wireless power signals  44 ) are transmitted to nearby coils such as illustrative coil  48  in wireless power receiving circuitry  54 . This induces a corresponding alternating-current (AC) current signal in coil  48 . Capacitors such as capacitors  72  may be coupled in series with coil  48 . Rectifier  50  receives the AC current from coil  48  and produces corresponding direct-current power (e.g., direct-current voltage Vrect) at output terminals  76 . This power may be used to power a load. 
     Device  12  may have measurement circuitry for monitoring signals on coil  36 . This circuitry may include, for example, voltage sensor  90  (e.g., a voltage sensing circuit coupled to and/or formed as part of an analog-to-digital converter, etc.). Current-source  92  and/or inverter  61  may be also be used to supply signals to coil  36  during foreign object detection operations (e.g., so that Q may be measured for coil  36 ). In some embodiments, Q-factor measurements are made using direct measurement of impedance of coil  36  with an AC current source. Measurements of Q may be made in the presence of wireless power receiving device  24  and in the absence of any wireless power receiving devices (e.g., periodic free-air Q measurements may be made when device  24  is not present). By monitoring changes in Q from its free-air value, the presence of a foreign object can be detected and appropriate action taken. 
     With a first illustrative Q-factor measurement arrangement, the control circuitry of device  12  cause inverter  61  to provide signal pulses to coil  36  and measurement circuitry such as voltage sensor  90  is used to measure corresponding impulse responses. Due to resonance in the circuit of  FIG. 2 , application of a signal pulse to coil  36  creates a ringing signal with a decay envelope such a decay envelope  94  of  FIG. 3 . The decay envelope has a characteristic given by e −tπfr/Q , where fr is the frequency of the ringing signal. By measuring fr and decay envelope  94 , the value of Q can be determined. 
     If desired, capacitor  70  of  FIG. 2  may be implemented using an adjustable capacitor arrangements (e.g., a capacitor circuit with switching circuitry and multiple capacitors that can be selectively switched into use under control of control circuitry  16  to adjust the capacitance value in the resonant circuit and thereby adjust the resonant frequency). In arrangements in which capacitor  70  has a selectable value, a first value (e.g., C 1 ) can be used when the impulse response of the wireless power transmitting circuitry is being measured to determine Q (as described in connection with  FIG. 3 ) and a second value (e.g., C 2 ) can be used when the wireless power transmitting circuitry is transmitting wireless power signals  44 . 
     With a second illustrative Q-factor measurement arrangement, the value of Q is obtained from a direct measurement of the impedance of coil  36 .  FIG. 4  is a circuit diagram of wireless power transmitting circuitry and measurement circuitry of  FIG. 2 , showing how a parasitic resistance R may be associated with the resonant circuit. With the direct impedance measurement approach, a small current is injected into coil  36  from current source  92  while voltage measurements are made using voltage sensor  90 . The magnitude of the injected current may be sufficiently low to allow the current to be injected without using large power field-effect transistors. The current may be, for example, an alternating-current (AC) current at a frequency such as 125 kHz, more than 125 kHz, or less than 125 kHz, or other suitable frequency (e.g., a frequency that can be selected independent of the resonant frequency associated with the wireless power transmitting circuit). The complex impedance of coil  36  is then determined at this frequency and the value of Q inverted from the angle θ of the measured impedance.  FIG. 5  shows equations associated with the determination of Q (coil Q-factor) from the angle of the complex impedance and optional values of inductance L and resistance R (the real part of the AC impedance) that may be computed from the direct impedance measurement. In the equations of  FIG. 5 , I is the injected AC current and V is the resulting voltage that is measured by voltage sensor  90 . 
     Measurement circuitry  41  of device  12  can be calibrated during manufacturing. For example, the value of Q-factor (Q 0 ) that is measured at an initial time when device  12  is being manufactured (using the first illustrative Q-factor measurement arrangement, the second illustrative Q-factor measurement arrangement, and/or additional Q-factor measurement techniques) can be stored in device  12  as a baseline value for later use. If desired, device-specific calibration operations may be performed so that each device  12  is individually calibrated with a corresponding individual baseline value of Q. When device  12  is operated in the field, device  12  can measure the present value of Q and can compare this measured value of Q to the stored baseline value of Q 0  from the factory. In this way, the amount of change in Q can be determined, which is indicative of whether a foreign object or other external object is present on the charging surface of device  12 . 
     If desired, compensation techniques may be used to compensate for the effects of temperature, aging, and other effects that can induce drift in Q. Temperature variations can affect the parasitic resistance of components such as coil  36 . Coil inductance L can also depend on temperature. Frequency changes and aging effects (e.g., mechanical wear) can affect component values and therefore the measured value of Q as well. Compensating for these effects when comparing Q to Q 0  can help enhance the accuracy of foreign object detection measurements. 
     The value of baseline Q-factor Q 0  and the value of resonant frequency ω (2πfr) that are measured during calibration (e.g., at an initial time during manufacturing) are given by equations 1 and 2. 
         Q   0 =ω 0   L   0   /R   0 (ω 0 )  (1)
 
       ω 0 =1/( L   0   C ) 1/2   (2)
 
     The values of Q and ω (and of L and R) that are measured at runtime (sometimes referred to as current Q, current ω, current L and current R) are given, respectively, by Q FO , ω FO , L FO , and R FO  of equations 3, 4, 5, and 6. 
         Q   FO =ω FO   L   FO   /R   FO (ω FO )  (3)
 
       ω FO =1/( L   FO   C ) 1/2   (4)
 
         L   FO   =L   0   +ΔL   FO   (5)
 
         R   FO   =R   0   +ΔR   FO   (6)
 
     During compensation operations, the current temperature T of device  12  is measured using temperature sensor  60  of device  12  (see, e.g.,  FIG. 1 ). The change in temperature ΔT from the temperature T0 measured during calibration measurements during manufacturing is given by equation 7. 
       Δ T=T−T 0  (7)
 
     The equation of  FIG. 6  shows how a compensated value of Q (e.g., the value of Qcomp) can be determined as a function of the currently measured Q-factor (Q′ in the equation of  FIG. 6 ) based on one or more compensation factors. 
     A first illustrative compensation factor involves frequency compensation. As shown in the equation of  FIG. 6 , Q′ can be multiplied by compensation factor (ω0/ω) to compensate for changes in resonant frequency during measurement of Q′ relative to the resonant frequency during measurement of Q0 during manufacturing. 
     A second illustrative compensation factor relates to the temperature dependence of inductance and resistance. As shown in the equation of  FIG. 6 , Q′ can be multiplied by the compensation factor (1+κRΔT)/(1+κLΔT), where κR is the resistive temperature change coefficient and κL is the inductive temperature change coefficient. The values of these temperature coefficients are influenced by the design of device  12  and may, if desired, be determined empirically by performing measurements on one or more representative units of wireless power transmitting device  12  during manufacturing. 
     A third illustrative compensation factor involves compensating for shifts in the AC resistance RAC of coil  36  and DC resistance RDC of coil  36  from baseline values. With this resistance-compensation technique, the current value of the quality factor is compensated based on a compensated value of the entire (total) inductive coil resistance associated with wireless power transmitting coil  36 . Coil  36  is characterized by an entire inductive coil resistance value having direct-current and alternating-current portions. During compensating operations, control circuitry  16  compensates for changes in the entire inductive coil resistance by computing a compensated value of the entire inductive coil resistance from a sum of a baseline direct-current portion of the entire inductive coil resistance that was measured at an initial time and the current alternating-current portion of the entire coil resistance. This compensated entire inductive coil resistance value is then used in compensating the current quality factor using the compensated entire inductive coil resistance. 
     As shown in the equation of  FIG. 6 , the resistance-based compensation factor is based on the measured baseline DC resistance (R DC,0 ) that was obtained during calibration measurements during manufacturing, the baseline AC resistance (R AC ) that was obtained during calibration measurements during manufacturing, and the value of η, which is the coefficient of change in AC resistance R AC  as a function of changes in resonant frequency ω (e.g., 50 m-Ω per 100 kHz or other suitable value) that was obtained during calibration measurements during manufacturing. The parameter R meas  is equal to the sum of the measured AC resistance R AC  and measured DC resistance R DC . 
     In the example of  FIG. 6 , all three of these illustrative compensation factors have been applied to the measured Q′ value (e.g., Qcomp has been determined by compensating Q′ based on changes in frequency and frequency-change-induced effects and for temperature-change-induced effects). In general, one or two of these compensation techniques may be used and/or other compensation techniques may be used to calibrate Q-factor measurements based on measured temperature, resonant frequency, and/or other variables. 
     As set forth in the foregoing example, a compensated Q-factor value Qcomp may be produced based on measurements of temperature and frequency. This value can then be compared to a baseline value of Q that was measured during manufacturing and stored in device  12  for use during later comparisons. If desired, compensation operations may be performed on the baseline Q-factor value to produce a compensated baseline Q rather than performing compensation operations on the in-field measured value of Q. Approaches in which compensation operations are performed on an in-field measured Q value rather than on baseline Q value are described herein as an example. 
     A flow chart of illustrative operations for detecting foreign objects using system  8  is shown in  FIG. 7 . In this embodiment, power delivery is inhibited if a foreign object is detected. It is also possible to simply flag the detection of the foreign object for use as additional information in determining appropriate power delivery levels during the power delivery phase. As an example, the maximum power level that is used during power delivery operations may be lowered to a predetermined level that is below the maximum power level in response to detection of the presence of the foreign object. 
     During the operations of block  100 , device  12  measures a current value of Q using the first illustrative Q-factor measurement arrangement (e.g., using inverter  61  to apply an impulse and measuring Q from envelope  94  of the impulse response) or the second illustrative Q-factor measurement arrangement (e.g., deriving Q from a direct impedance measurement of coil  36  performed by injecting current into coil  36  using AC current source  92 ). The measurement of Q using techniques such as these or other suitable Q-factor measurement techniques may sometimes be referred to as a low-power ping (LPP) or analog ping operation. 
     During the operations of block  102 , the value of the change in Q (e.g., Q-factor deflection value Qdefl) can be determined. During the operations of block  102 , compensation techniques such as the compensation techniques described in connection with  FIG. 6  can be applied to compensate the measured value of Q or the baseline value of Q (Q 0 ) that was stored in device  12  during manufacturing may be compensated. The value of Qdefl may, as an example, be computed using equation 8. 
         Q defl=( Q   0   −Q comp)/ Q   0 =1−( Q comp/ Q   0 )  (8)
 
     In the example of equation 8, Qdefl is computed based at least partly on a difference between compensated measured Q (Qcomp) and baseline Q (Q 0 ) and on a ratio between Qcomp and Q 0 . With equation 8, if the current value of Q drops by 5% relative to baseline Q 0 , Qdefl will be 5%. In general, Qdefl may be based only on a difference between measured Q and baseline Q, may be based only on a ratio between measured Q and baseline Q, may be based on both a difference between measured and baseline Q and a ratio between measured Q and baseline Q, and/or may be based on other functions of measured Q and baseline Q. The measured value of Q that is used in computing Qdefl may be compensated for temperature, frequency, and aging effects and/or the baseline value of Q may be compensated for temperature, frequency, and aging effects as described in connection with the compensation techniques of  FIG. 6 . 
     During the operations of block  103 , the control circuitry of device  12  determines whether Q has settled. If Q is changing rapidly (e.g., due to movement of an external object across the charging surface of device  12  as measurements are being made), the value of Qdefl has not settled sufficiently and operations may return to block  100 . A new measurement of Q may then be obtained during the operations of block  100 . So long as Q hasn&#39;t settled, a new Q measurement may be obtained in this way each 0.1 s (or at another suitable sampling rate). Once successive values of Qdefl have changed by less than a predetermined threshold amount (e.g., 1%), Q can be deemed to have settled sufficiently to permit analysis of the value of Qdefl to determine whether a foreign object is present and operations may proceed to block  104 . 
     During the operations of block  104 , device  12  compares the value of Qdefl to a predetermined threshold value TH (e.g., 3% or other suitable value). If Qdefl does not exceed the threshold (e.g., if the measured value of Q has not been reduced by more than 3% relative to baseline Q), device  12  can conclude that no external object is present (e.g., wireless power receiving device  24  is not present and no coins or other foreign objects are present). Measurement operations may then continue at block  100 . If, however, it is determined during the operations of block  104  that Qdefl exceeds the threshold, device  12  can conclude that measured Q has been reduced by more than the threshold amount relative to baseline Q 0  (e.g., Q is at least 3% lower than Q 0 ) and that therefore an external object of some type is present (either a foreign object such as a coin or wireless power receiving device  24 ). Operations may then proceed to block  106  to distinguish between these two possibilities. 
     During the operations of block  106 , device  12  can attempt to wirelessly communicate with wireless power receiving device  24 . As an example, device  12  may use in-band communications to transmit a wireless digital request. The wireless digital request is used to request that device  24  acknowledge its presence by using in-band communications to wirelessly transmit a corresponding digital response device  12 . This digital communications request process may sometimes be referred to as a digital ping. During the operations of block  108 , device  12  determines whether a response to the digital ping has been received from device  24  to indicate that device  24  is present. 
     If device  24  is present on the charging surface of device  12 , device  24  will respond to the digital ping with a wireless digital response. This response may include information such as a digital identifier corresponding to the type of device  24  that is present, etc. In response to determining, during the operations of block  108 , that a cellular telephone, wristwatch, or other wireless power receiving device  24  is present, device  12  will transmit wireless power signals  44  to device  24  (e.g., during the operations of block  110 ). 
     If, device  24  is not present on the charging surface of device  12 , device  12  will not receive any acknowledgement from device  24 . In response to determining, during the operations of block  108 , that device  24  is not present, device  12  can conclude that a foreign object is present at the charging surface of device  12  and operations can proceed to blocks  112 . 
     During blocks  112 , device  12  monitors Q to determine when the foreign object that is present has been removed. In particular, Q is measured during the operations of block  114 , as described in connection with the Q measurements of block  100 . The value of Qdefl is computed at block  116 . The operations of block  118  involve comparing Qdefl to threshold TH or another threshold. If the foreign object remains present, Qdefl will remain at a value that exceeds the threshold and additional measurements may be performed at block  114 . If, however, the foreign object is removed, processing will return to block  100 , so that device  12  can determine whether device  24  is present and, if so, can begin delivering wireless power to device  24 . 
     In determining Qdefl, device  12  performs comparisons of measured Q to the baseline value of Q that was obtained during manufacturing and stored in device  12  for future use. Temperature changes, frequency changes, coil resistance changes, and other changes can affect Qbaseline, so, if desired, Qbaseline can be continually updated. With an illustrative arrangement, a filter is used in updating Q baseline based on a newly measured Q reading each time it is determined that there are no external objects present at the charging surface of device  12 . For example, each time device  12  determines, during the operations of block  104 , that Qdefl is not greater than the threshold, device  12  can conclude that there are no foreign objects and no wireless power transmitting devices present on the charging surface. Accordingly, device  12  can conclude that the most recent measurement of Q from block  100  is, in effect, an updated value that can be at least partly used in updating Qbaseline (e.g., a current Q value that can be used as a filter input). 
     With this embodiment, an updated value of Qbaseline can therefore be stored in device  12  at point P 1  of the flow chart of  FIG. 7  each time it is determined that Qdefl is not greater than threshold TH. In updating Qbaseline, the current value of Q (measured during the most recent visit to block  100 ) can be incorporated into Qbaseline using a suitable filtering scheme (e.g., using a weighted historical average, using an averaging scheme that deemphasizes noisy data, or other filtering arrangement). By updating Qbaseline with current measurement data in this way, the effects of aging on the baseline Q value can be reduced. 
     With an illustrative configuration, device  12  updates Qbaseline with the current value of measured Q using a low-pass filter. Let q[n] be a valid Q deflection sample. An example of a low-pass filter for Q is a one-pole filter (see, e.g., equation 9) in which α∈[0,1] and close to 1. 
         Q   filt [ n ]=α Q   filt [ n− 1]+(1−α) Q   defl [ n ], Q   filt [0]=0  (9)
 
     Another example is the sliding window average given in equation 10. 
     
       
         
           
             
               
                 
                   
                     
                       Q 
                       filt 
                     
                      
                     
                       [ 
                       n 
                       ] 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               ∑ 
                               
                                 m 
                                 = 
                                 0 
                               
                               n 
                             
                              
                             
                               
                                 Q 
                                 defl 
                               
                                
                               
                                 [ 
                                 m 
                                 ] 
                               
                             
                           
                         
                         
                           
                             
                               for 
                                
                               
                                   
                               
                                
                               n 
                             
                             &lt; 
                             M 
                           
                         
                       
                       
                         
                           
                             
                               ∑ 
                               
                                 m 
                                 = 
                                 
                                   n 
                                   - 
                                   M 
                                 
                               
                               n 
                             
                              
                             
                               
                                 Q 
                                 defl 
                               
                                
                               
                                 [ 
                                 m 
                                 ] 
                               
                             
                           
                         
                         
                           
                             
                               for 
                                
                               
                                   
                               
                                
                               n 
                             
                             ≥ 
                             M 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     As these examples demonstrate, there are multiple possible arrangements for incorporating current Q measurement data from block  100  into the baseline Q value that is retained in device  12  and that is subsequently used in computing Qdefl. In these updating operations, control circuitry  16  periodically updates the baseline quality factor using a filtering operation based on a history of current quality factor measurements, thereby ensuring that the value of the baseline quality factor is adjusted for aging and other effects that could cause quality factor measurements to drift over time. 
     Updating the baseline Q value at point P 1  involves performing a separate filtering operation following each measurement of Q at block  100 . If desired, the number of filtering operations per unit time (and therefore the number of times that an updated value of Q baseline is computed and stored in device  12  per unit time) can be reduced by performing filtering operations at point P 2  instead of P 1 . With this type of arrangement, the values of Q that are measured during the operations of block  100  are stored (cached) by control circuitry  16  each time point P 1  is reached (e.g., each time it is determined that no foreign object is present). If the operations of block  104  determine that the latest Q value exceeds threshold TH, processing proceeds to block  106  where a digital ping is performed. During the operations of block  108 , control circuitry  16  determines whether a) no response has been received corresponding to the digital ping (in which case a foreign object is present and processing proceeds to blocks  112 ) or whether b) a wireless digital response has been received from device  24 . At this point (e.g., at point P 2 ), device  12  knows that device  24  has just been placed on the charging surface of device  12 . Before initiating power delivery at block  110 , device  12  retrieves that last value of Q that was cached at point P 1  (and which represents a Q factor measurement when no foreign object or other external object is present on device  12 ) and uses this retrieved current value of Q to update the value of Q baseline. 
     With this approach, the filtering operation used to update Q baseline is performed only upon determining that a wireless power receiving device is newly present (and no foreign object is present). The filtering operation is performed using the most recently obtained value of Q when no external object was present (e.g., the no-external-object present value of Q that was cached at point P 1 ). There is still a Q value storage operation each time point P 1  is reached, but computation of the updated baseline Q value using the filter is performed less frequently (e.g., only when P 2  is reached). Updating the baseline Q value only when it has been determined that no wireless power receiving device is present and no foreign object is present ensures that value of the baseline quality factor is adjusted for aging and other effects that could cause quality factor measurements to drift over time, but does not involves as many separate filtering operations as when filtering operations are performed at point P 1 . 
     In addition to periodically updating the baseline value of Q (either at point P 1  or at point P 2 , as examples), control circuitry  16  may periodically update the value of threshold TH that is used during the comparison operations of block  104  (e.g., an adjustable threshold value TH may be used rather than a fixed predetermined value). For example, a low-pass filtering operation or other filtering operation may be used to update the value of TH based on a history of Q factor measurements or other measurements (e.g., Q factor measurements made when no external object is present and cached at point P 1 ). This filtering operation to update the value of TH may be performed at point P 2  (e.g., upon determining that no foreign object is present), using measurements such as one or more cached Q factor measurements made when no wireless power receiving device or foreign object was present. 
     If desired, the value of Qdefl may be compared to multiple different thresholds (e.g., to determine whether a small or large foreign object is present). Device  12  can then take different actions depending on whether a small or large foreign object is present. For example, wireless power can be transmitted at a restricted power level if a small foreign object is detected in the presence of a wireless power receiving device but can be forgone entirely in the presence of a large foreign object. 
     Consider, as an example, the diagram of  FIG. 8 , which illustrates the operation of device  12  in a system with multiple foreign object detection thresholds. In the example of  FIG. 8 , system  8  has a lower first threshold THair (e.g., 3% or any other suitable value such as a value less than 3% or a value greater than 3%) and a higher second threshold THfo (e.g., 6%, a value above or below 6%, or any other suitable value higher than the first threshold). Device  12  operates in states  120 ,  122 ,  124 , and  126 . Transitions are made between these states in accordance with transition rules  128 . The values of thresholds THair and THfo can be adjusted appropriately to distinguish a moderate foreign object (e.g., an object with a relatively small amount of metal and/or metal of moderate conductivity) from a strong foreign object (e.g., an object with more metal and/or metal of greater conductivity). Power will be inhibited in the case of a strong foreign object until free air is seen. However, by setting the threshold high enough, implementations can opt to avoid using the “strong foreign object” state. 
     As shown in  FIG. 8 , in block  122 , device  12  has compared Qdefl to the first and second thresholds and has determined that Qdefl is lower than the first threshold. In this scenario, device  12  can conclude that no foreign object is present and can therefore set the power delivery level for wireless power signals  44  at a relatively high power level (power level  2 ). Power can then be wirelessly transmitted from device  12  to device  24  during the power delivery operations of block  126 . 
     In block  120 , it has been determined that a foreign object is present because Qdefl is greater than the first threshold. It has also been determined that Qdefl is less than the second threshold. As a result, device  12  can conclude that although a foreign object is present, it is not a large foreign object. Device  12  can therefore proceed to deliver power wirelessly to device  24  during the operations of block  126 . Because power is being delivered to device  24  in the presence of a small foreign object, the level (e.g., the maximum level) at which power is wirelessly transmitted is reduced to a relatively low power level (e.g., power level  1 , which is less than power level  2 ). This helps prevent excess heating of the small foreign object. 
     In block  124 , it has been determined that a large foreign object is present, because Qdefl is greater than the second threshold. In this situation, no wireless power is transmitted by device  12 . 
     The following section further describes the foregoing embodiments. 
     This section describes an accurate, pre-wireless power transfer foreign object detection (FOD) technique that is useful for detecting foreign objects placed on device  10  (e.g., a PTx mat, sometimes referred to as PTx) prior to the arrival of device  24  (e.g., a portable device or other power receiving device sometimes referred to as PRx). This technique addresses several challenges: 
     1. Mated-Q foreign object detection (FOD) has trouble distinguishing between foreign objects (FOs) and alignment offsets between 
     PRx and PTx. This is due to the fact that the reference Q is computed as the average of the mated-Q at predetermined (e.g., five) different positions rather than being stored as a function of position which cannot easily be determined at run-time. There are other potential challenges with mated-Q:
         a. It relies on a reference measurement for Q that is measured at 100 KHz. The in-system frequency may be different. Since the inductance, L, is a function of frequency, this difference in frequency can lead to a discrepancy in Q measured at run-time compared to the calibrated Qref.   b. It doesn&#39;t account for capacitor ESR when non-COG capacitors are used), PCB trace resistance and FET Rds(on) resistance.   c. It doesn&#39;t account for temperature or frequency drift.   d. The reference Q is measured against the TPR which may have different deflections on Q from other transmitters.       

     A general flow for open-air Q testing which conveys the general concept is shown in  FIG. 7 . During the start-up phase (block  100 ), the PTx uses analog ping to detect objects placed on the mat. The ping is used to measure a deflection to Q defined as: 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     Q 
                   
                   = 
                   
                     1 
                     - 
                     
                       Q 
                       
                         Q 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     where Q 0  is the calibrated value for open-air Q measured at production and Q is measured by analog ping at run-time (see, e.g., Q deflection computation at block  102  and the operations waiting for Q to settle of block  103 ). Note that ΔQ≈0 if there is no FO present, but often it is not exactly zero because of effects such as temperature drift. Component aging will also cause ΔQ≠0. 
     When an object is placed on the mat, the Q will be deflected by some amount. If ΔQ (sometimes referred to as Qdefl) exceeds a threshold, something is detected. In some implementations the absolute value (|ΔQ|) is compared against a threshold (block  104 ) to account for the presence of a very high-Q receiver that is placed on the PTx mat. To determine if that something is an FO or a receiver, a response from digital ping is awaited (block  106 ). In the case digital ping is acknowledged, the system can proceed to negotiation. If it is not, the object is presumed to be an FO and power delivery is blocked until the FO is removed from the mat and ΔQ≈0 again. 
     There are many approaches for measuring Q such as:
         1. Perform a frequency sweep to find the resonance frequency, then compute Q as the ratio of the tank voltage over the inverter voltage at the resonance frequency.   2. Use an LCR meter connected directly to the coil to measure L and Q at a specific frequency.       

     It is possible to perform the Q measurement in other ways as well. 
     As a first example, Q may be estimated from the decay of the ringing response. In this approach, a pulse of energy is injected into the coil and the decay of the ringing response is measured as illustrated in  FIG. 3 . Q is then estimated from the decay envelope. 
     Estimating Q requires accurate sampling of the waveform peaks to obtain its envelope. To eliminate the impact of the DC offset, b, from the decay estimate, it is recommended that the envelope amplitude be measured as the peak-to-valley difference as shown in  FIG. 9 . 
     That is, define 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       i 
                     
                     = 
                     
                       
                         V 
                         i 
                         + 
                       
                       - 
                       
                         V 
                         i 
                         - 
                       
                     
                   
                   , 
                   
                     i 
                     = 
                     1 
                   
                   , 
                   2 
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 then 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Q 
                     est 
                   
                   = 
                   
                     
                       π 
                        
                       
                           
                       
                        
                       N 
                     
                     
                       log 
                        
                       
                         ( 
                         
                           
                             V 
                             1 
                           
                           
                             V 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where N is the separation (in terms of number of peaks) between the second samples and the first samples (N=1 means the peaks are adjacent). 
     This approach is affected by frequency drift caused, primarily, from changes in L due to the presence of an FO. 
     As a second example, Q is computed from a coil impedance measurement. In this approach, illustrated in  FIG. 4 , the coil Q is directly measured at a fixed frequency. This approach has the advantage of eliminating frequency drift from the Q measurement but requires protection from high voltages at the positive coil node. 
     An AC current, I, is injected into to the coil and the complex voltage is measured: 
         V =( jjωL+R ) I   (14)
 
     The angle between V and I is 
     
       
         
           
             
               
                 
                   
                     ∠ 
                      
                     
                       V 
                       I 
                     
                   
                   = 
                   
                     
                       tan 
                       
                         
                           - 
                           1 
                         
                          
                         
                           
                             ω 
                              
                             
                                 
                             
                              
                             L 
                           
                           R 
                         
                       
                     
                     = 
                     
                       
                         tan 
                         
                           - 
                           1 
                         
                       
                        
                       Q 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Therefore, 
     
       
         
           
             
               
                 
                   Q 
                   = 
                   
                     tan 
                      
                     
                       ( 
                       
                         ∠ 
                          
                         
                           V 
                           I 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The phase angle between V and I can be determined by comparing the offsets in their peaks or zero-crossings or by taking the dot-product of the waveforms. 
     The presence of an FO causes a shift ΔL and ΔR of, respectively, L and R: 
     
       
         
           
             
               
                 
                   
                     L 
                     FO 
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     L 
                     + 
                     
                       
                         Δ 
                          
                         L 
                       
                       FO 
                     
                   
                 
               
               
                 
                   ( 
                   
                     17 
                      
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     FO 
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     R 
                     + 
                     
                       
                         Δ 
                          
                         R 
                       
                       FO 
                     
                   
                 
               
               
                 
                   ( 
                   
                     17 
                      
                     b 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     ω 
                     FO 
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     1 
                     
                       
                         
                           L 
                           FO 
                         
                          
                         C 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     17 
                      
                     c 
                   
                   ) 
                 
               
             
           
         
       
     
     This shift causes a change in Q, 
     
       
         
           
             
               
                 
                   
                     Q 
                     FO 
                   
                   = 
                   
                     
                       
                         ω 
                         FO 
                       
                       * 
                       
                         L 
                         FO 
                       
                     
                     
                       R 
                       FO 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     which results in a measurable Q deflection, 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     Q 
                   
                   = 
                   
                     
                       | 
                       
                         1 
                         - 
                         
                           
                             Q 
                             FO 
                           
                           Q 
                         
                       
                     
                     = 
                     
                       1 
                       - 
                       
                         
                           
                             
                               L 
                               FO 
                             
                             
                               L 
                               0 
                             
                           
                         
                         
                           ( 
                           
                             
                               R 
                               FO 
                             
                             
                               R 
                               0 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     There may be an accentuation of Q deflection due to frequency drift caused by FO. In addition to measuring Q, it is possible to accurately measure the frequency of the ringing response. By (17c), the FO also deflects that ringing response. We can use this fact to accentuate the deflection in Q: 
     
       
         
           
             
               
                 
                   
                     Q 
                     comp 
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     Q 
                      
                     
                       ( 
                       
                         
                           ω 
                           0 
                         
                         ω 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     This results in an enhanced Q deflection in the presence, primarily, of a non-ferrous FO which causes a reduction in L, 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     Q 
                   
                   = 
                   
                     
                       1 
                       - 
                       
                         
                           Q 
                           comp 
                         
                         
                           Q 
                           0 
                         
                       
                     
                     = 
                     
                       1 
                       - 
                       
                         
                           ( 
                           
                             
                               L 
                               FO 
                             
                             
                               L 
                               0 
                             
                           
                           ) 
                         
                         
                           ( 
                           
                             
                               R 
                               FO 
                             
                             
                               R 
                               0 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     The result of equation (21) is greater than that of (19) when ΔL FO &lt;0. 
     This enhanced Q deflection does not apply to the approach of the second example of Q measurement which operates at a fixed frequency. 
     The value of Q can be compensated for drift. There are possibilities for improving the Q deflection measurement in some implementations. The Q deflection in equation (11) is intended to compare the run-time measurement of Q against the production calibrated measurement of Q. During run-time, effects besides the presence of an FO such as temperature and frequency drift can result in Q deflection. Compensating for these effects improves the reliability of the open-air Q test. 
     DC and AC resistances can be separated. Various drift effects in the measurement of Q occur to the DC portion of the resistance which, itself, is not affected by the presence of an FO. DC resistances include resistances from the PCB traces, capacitor ESR and inverter FET resistances. If we separate the DC resistance from the overall resistance, we can use the DC resistance calibrated at production and remove the impact of DC resistance drift. Specifically, let 
         R=R   DC ( T ) R   coil,AC ( T ,ω)  (22)
 
     where we&#39;ve indicated that RDC is sensitive to temperature while R coil,AC  is sensitive to temperature and frequency. 
     Using (22), Q can be written as 
     
       
         
           
             
               
                 
                   Q 
                   = 
                   
                     
                       
                         ω 
                          
                         L 
                       
                       R 
                     
                     = 
                     
                       
                         ω 
                          
                         L 
                       
                       
                         
                           R 
                           DC 
                         
                         + 
                         
                           R 
                           
                             coil 
                             , 
                             AC 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     The total resistance, R, can also be determined by the analog ping ringing response (or impedance measurement): 
     
       
         
           
             
               
                 
                   L 
                   = 
                   
                     1 
                     
                       
                         
                           ( 
                           
                             2 
                              
                             
                               
                                 π 
                                  
                                 F 
                               
                               r 
                             
                           
                           ) 
                         
                         2 
                       
                        
                       C 
                     
                   
                 
               
               
                 
                   ( 
                   
                     24 
                      
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   R 
                   = 
                   
                     
                       ( 
                       
                         2 
                          
                         
                           
                             π 
                              
                             F 
                           
                           r 
                         
                          
                         L 
                       
                       ) 
                     
                     Q 
                   
                 
               
               
                 
                   ( 
                   
                     24 
                      
                     b 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     
                       coil 
                       , 
                       AC 
                     
                   
                   = 
                   
                     R 
                     - 
                     
                       R 
                       DC 
                     
                   
                 
               
               
                 
                   ( 
                   
                     24 
                      
                     c 
                   
                   ) 
                 
               
             
           
         
       
     
     If we measure the DC resistance, we can store its value, RDC,0, at production and then compute Q at run-time as, 
     
       
         
           
             
               
                 
                   
                     Q 
                     comp 
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     
                       
                         ω 
                          
                         L 
                       
                       
                         
                           R 
                           DC 
                         
                         + 
                         
                           R 
                           
                             coil 
                             , 
                             AC 
                           
                         
                       
                     
                     = 
                     
                       Q 
                       · 
                       
                         ( 
                         
                           R 
                           
                             
                               R 
                               
                                 DC 
                                 , 
                                 0 
                               
                             
                             + 
                             
                               R 
                               
                                 coil 
                                 , 
                                 AC 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     This effectively eliminates DC drift from the Q measurement at the cost of additional measurement error of the resistances. 
     As indicated in (22), the coil RAC may be a function of frequency, 
         R   coil,AC (ω)≈ R   coil,AC,0 (1+ηΔω)  (26)
 
     where Δω ω−ω0 is the change in frequency compared to the frequency measured at production and η is slope of the drift. Let, 
     
       
         
           
             
               
                 
                   
                     C 
                     
                       F 
                       , 
                       R 
                     
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     1 
                     
                       1 
                       + 
                       ηΔω 
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     Then (25) can be furthered compensated for RAC frequency drift as follows: 
     
       
         
           
             
               
                 
                   
                     Q 
                     comp 
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     Q 
                     · 
                     
                       ( 
                       
                         R 
                         
                           
                             R 
                             
                               DC 
                               , 
                               0 
                             
                           
                           + 
                           
                             
                               R 
                               
                                 coil 
                                 , 
                                 AC 
                               
                             
                             · 
                             
                               C 
                               
                                 F 
                                 , 
                                 R 
                               
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
           
         
       
     
     If the design of the PTx dictates it, a frequency compensation for L can also be applied, 
     
       
         
           
             
               
                 
                   
                     Q 
                     comp 
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     
                       
                         Q 
                         · 
                         
                           C 
                           
                             F 
                             , 
                             L 
                           
                         
                       
                        
                       
                           
                       
                        
                       with 
                        
                       
                           
                       
                        
                       
                         C 
                         
                           F 
                           , 
                           L 
                         
                       
                     
                     = 
                     
                       1 
                       
                         1 
                         + 
                         vΔω 
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     As indicated in (22), the coil RAC may be a function of temperature, 
         R   coil,AC   ≈R   coil,AC,0 (1+κ R   ΔT )  (30)
 
     where ΔT=T−TO is the change in temperature compared to the temperature when the device was calibrated at production and KR is the coil resistance temperature coefficient. Assuming the PTx has a means for measuring the coil temperature, T, then the Q measurement can be further compensated for temperature as follows: 
     
       
         
           
             
               
                 
                   
                     C 
                     T 
                   
                    
                   
                     = 
                     Δ 
                   
                    
                   
                     1 
                     
                       1 
                       + 
                       
                         κΔ 
                          
                         T 
                       
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
             
               
                 
                   
                     Q 
                     comp 
                   
                   = 
                   
                     Q 
                     · 
                     
                       ( 
                       
                         R 
                         
                           
                             R 
                             
                               DC 
                               , 
                               0 
                             
                           
                           + 
                           
                             
                               R 
                               
                                 coil 
                                 , 
                                 AC 
                               
                             
                             · 
                             
                               C 
                               
                                 F 
                                 , 
                                 R 
                               
                             
                             · 
                             
                               C 
                               T 
                             
                           
                         
                       
                       ) 
                     
                     · 
                     
                       C 
                       
                         F 
                         , 
                         L 
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
     Combining (20), (28) and (32), we have the following options for improving Q accuracy. 
     Q Measurement Approach 1 
     
       
         
           
             
               
                 
                   
                     Q 
                     comp 
                     1 
                   
                   = 
                   
                     Q 
                     · 
                     
                       ( 
                       
                         
                           ω 
                           0 
                         
                         ω 
                       
                       ) 
                     
                     · 
                     
                       ( 
                       
                         R 
                         
                           
                             R 
                             
                               DC 
                               , 
                               0 
                             
                           
                           + 
                           
                             
                               R 
                               
                                 coil 
                                 , 
                                 AC 
                               
                             
                             · 
                             
                               C 
                               F 
                             
                             · 
                             
                               C 
                               T 
                             
                           
                         
                       
                       ) 
                     
                     · 
                     
                       C 
                       
                         F 
                         , 
                         L 
                       
                     
                   
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     Q Measurement Approach 2 
     
       
         
           
             
               
                 
                   
                     Q 
                     comp 
                     2 
                   
                   = 
                   
                     Q 
                     · 
                     
                       ( 
                       
                         R 
                         
                           
                             R 
                             
                               DC 
                               , 
                               0 
                             
                           
                           + 
                           
                             
                               R 
                               
                                 coil 
                                 , 
                                 AC 
                               
                             
                             · 
                             
                               C 
                               T 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
     Finally, we replace (11) with 
     
       
         
           
             
               
                 
                   
                     Δ 
                      
                     Q 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         Q 
                         comp 
                       
                       
                         Q 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
     
     The sensitivity of Q deflection to an FO can also be plotted [using, for example, eqn. (21)] for specific PTx implementations. For example, assuming ΔLFO=0, ΔRFO=22mΩ we can see how ΔQ varies versus the coil resistance in  FIG. 10 . 
       FIG. 10  indicates that in order to achieve a Q deflection of 15%, the PTx AC resistance should be no more than 125Ω. If the PTx can measure Q more accurately, it can afford to have a higher AC resistance. 
     The foregoing is merely illustrative and various modifications can be made to the described embodiments. The foregoing embodiments may be implemented individually or in any combination.