Resonant tracking of an electromagnetic load

Abstract

A resonant frequency tracker for driving an electromagnetic load with a driving signal may include a signal generator configured to generate a waveform signal at a driving frequency for driving an electromagnetic load and control circuitry. The control circuitry may be configured to, during driving of the electromagnetic load by the waveform signal or a signal derived therefrom, receive a current signal representative of a current associated with the electromagnetic load and a second signal representative of a second quantity associated with the electromagnetic load, the second quantity comprising one of a voltage associated with the electromagnetic load or a back electromotive force of the electromagnetic load. The control circuitry may be further configured to calculate a phase difference between the current signal and the second signal, determine a frequency error of the waveform signal based on the phase difference, and control the driving frequency based on the frequency error.

Description

FIELD OF DISCLOSURE

The present disclosure relates in general to tracking a resonant frequency of a transducer, for example a haptic transducer, and driving such transducer at or near its resonant frequency.

BACKGROUND

Vibro-haptic transducers, for example linear resonant actuators (LRAs), are widely used in portable devices such as mobile phones to generate vibrational feedback to a user. Vibro-haptic feedback in various forms creates different feelings of touch to a user's skin, and may play increasing roles in human-machine interactions for modern devices.

An LRA may be modelled as a mass-spring electro-mechanical vibration system. When driven with appropriately designed or controlled driving signals, an LRA may generate certain desired forms of vibrations. For example, a sharp and clear-cut vibration pattern on a user's finger may be used to create a sensation that mimics a mechanical button click. This clear-cut vibration may then be used as a virtual switch to replace mechanical buttons.

FIG. 1 illustrates an example of a vibro-haptic system in a device 100. Device 100 may comprise a controller 101 configured to control a signal applied to an amplifier 102. Amplifier 102 may then drive a haptic transducer 103 based on the signal. Controller 101 may be triggered by a trigger to output to the signal. The trigger may for example comprise a pressure or force sensor on a screen or virtual button of device 100.

Among the various forms of vibro-haptic feedback, tonal vibrations of sustained duration may play an important role to notify the user of the device of certain predefined events, such as incoming calls or messages, emergency alerts, and timer warnings, etc. In order to generate tonal vibration notifications efficiently, it may be desirable to operate the haptic actuator at its resonance frequency.

The resonance frequency f₀ of a haptic transducer may be approximately estimated as:

$\begin{array}{cc}{f}_0=\frac{1}{2\pi \sqrt{CM}}& \left(1\right)\end{array}$ where C is the compliance of the spring system, and M is the equivalent moving mass, which may be determined based on both the actual moving part in the haptic transducer and the mass of the portable device holding the haptic transducer.

Due to sample-to-sample variations in individual haptic transducers, mobile device assembly variations, temporal component changes caused by aging, and use conditions such as various different strengths of a user gripping of the device, the vibration resonance of the haptic transducer may vary from time to time.

FIG. 2 illustrates an example of a linear resonant actuator (LRA) modelled as a linear system. LRAs are non-linear components that may behave differently depending on, for example, the voltage levels applied, the operating temperature, and the frequency of operation. However, these components may be modelled as linear components within certain conditions. In this example, the LRA is modelled as a third order system having electrical and mechanical elements. In particular, Re and Le are the DC resistance and coil inductance of the coil-magnet system, respectively; and Bl is the magnetic force factor of the coil. The driving amplifier outputs the voltage waveform V (t) with the output impedance Ro. The terminal voltage V_T(t) may be sensed across the terminals of the haptic transducer. The mass-spring system 201 moves with velocity u(t).

Traditional approaches for driving an LRA at resonance rely on detecting a time difference between zero crossings of the LRA's back electromotive force (back-EMF) and the load current or voltage. Such difference may then be used to adjust a period of a signal driven to the LRA. One disadvantage of this approach is its sensitivity to noise because all of the noise power is essentially aliased by an effective sampling rate at approximately two times the resonance frequency. Such approach may also suffer from slow convergence if a loop filter is used to reduce sensitivity to noise, because as a rule of thumb, bandwidth of the loop filter should be one-tenth of the effective sampling rate (or less). Further, using such approaches and LRA may be tri-stated at zero crossing events in order to allow a reading of back-EMF, which may result in a loss of drive duty cycle (e.g., maximum power from a driving amplifier may not be delivered to the LRA).

SUMMARY

In accordance with the teachings of the present disclosure, the disadvantages and problems associated with existing approaches for resonant tracking of an electromagnetic load may be reduced or eliminated.

In accordance with embodiments of the present disclosure, a resonant frequency tracker for driving an electromagnetic load with a driving signal may include a signal generator configured to generate a waveform signal at a driving frequency for driving an electromagnetic load and control circuitry. The control circuitry may be configured to, during driving of the electromagnetic load by the waveform signal or a signal derived therefrom, receive a current signal representative of a current associated with the electromagnetic load and a second signal representative of a second quantity associated with the electromagnetic load, the second quantity comprising one of a voltage associated with the electromagnetic load or a back electromotive force of the electromagnetic load. The control circuitry may be further configured to calculate a phase difference between the current signal and the second signal, determine a frequency error of the waveform signal based on the phase difference, and control the driving frequency based on the frequency error.

In accordance with these and other embodiments of the present disclosure, a method may include generating a waveform signal at a driving frequency for driving an electromagnetic load, and during driving of the electromagnetic load by the waveform signal or a signal derived therefrom, receiving a current signal representative of a current associated with the electromagnetic load and a second signal representative of a second quantity associated with the electromagnetic load, the second quantity comprising one of a voltage associated with the electromagnetic load or a back electromotive force of the electromagnetic load. The method may also include calculating a phase difference between the current signal and the second signal, determining a frequency error of the waveform signal based on the phase difference, and controlling the driving frequency based on the frequency error.

In accordance with these and other embodiments of the present disclosure, a host device may include an electromagnetic load and a resonant frequency tracker for driving the electromagnetic load with a driving signal. The resonant frequency tracker may include a signal generator configured to generate a waveform signal at a driving frequency for driving an electromagnetic load and control circuitry. The control circuitry may be configured to, during driving of the electromagnetic load by the waveform signal or a signal derived therefrom, receive a current signal representative of a current associated with the electromagnetic load and a second signal representative of a second quantity associated with the electromagnetic load, the second quantity comprising one of a voltage associated with the electromagnetic load or a back electromotive force of the electromagnetic load. The control circuitry may be further configured to calculate a phase difference between the current signal and the second signal, determine a frequency error of the waveform signal based on the phase difference, and control the driving frequency based on the frequency error.

Technical advantages of the present disclosure may be readily apparent to one having ordinary skill in the art from the figures, description and claims included herein. The objects and advantages of the embodiments will be realized and achieved at least by the elements, features, and combinations particularly pointed out in the claims.

It is to be understood that both the foregoing general description and the following detailed description are examples and explanatory and are not restrictive of the claims set forth in this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present embodiments and advantages thereof may be acquired by referring to the following description taken in conjunction with the accompanying drawings, in which like reference numbers indicate like features, and wherein:

FIG. 1 illustrates an example of a vibro-haptic system in a device, as is known in the art;

FIG. 2 illustrates an example of a Linear Resonant Actuator (LRA) modelled as a linear system, as is known in the art;

FIG. 3 illustrates an example resonant frequency tracker for driving a haptic transducer with a driving signal, in accordance with embodiments of the present disclosure; and

FIG. 4 illustrates an example demodulator, in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

The description below sets forth example embodiments according to this disclosure. Further example embodiments and implementations will be apparent to those having ordinary skill in the art. Further, those having ordinary skill in the art will recognize that various equivalent techniques may be applied in lieu of, or in conjunction with, the embodiment discussed below, and all such equivalents should be deemed as being encompassed by the present disclosure.

Various electronic devices or smart devices may have transducers, speakers, and acoustic output transducers, for example any transducer for converting a suitable electrical driving signal into an acoustic output such as a sonic pressure wave or mechanical vibration. For example, many electronic devices may include one or more speakers or loudspeakers for sound generation, for example, for playback of audio content, voice communications and/or for providing audible notifications.

Such speakers or loudspeakers may comprise an electromagnetic actuator, for example a voice coil motor, which is mechanically coupled to a flexible diaphragm, for example a conventional loudspeaker cone, or which is mechanically coupled to a surface of a device, for example the glass screen of a mobile device. Some electronic devices may also include acoustic output transducers capable of generating ultrasonic waves, for example for use in proximity detection type applications and/or machine-to-machine communication.

Many electronic devices may additionally or alternatively include more specialized acoustic output transducers, for example, haptic transducers, tailored for generating vibrations for haptic control feedback or notifications to a user. Additionally or alternatively an electronic device may have a connector, e.g., a socket, for making a removable mating connection with a corresponding connector of an accessory apparatus and may be arranged to provide a driving signal to the connector so as to drive a transducer, of one or more of the types mentioned above, of the accessory apparatus when connected. Such an electronic device will thus comprise driving circuitry for driving the transducer of the host device or connected accessory with a suitable driving signal. For acoustic or haptic transducers, the driving signal will generally be an analog time varying voltage signal, for example, a time varying waveform.

As previously mentioned, driving a haptic transducer at resonance frequency may be useful for some types of haptic application.

Referring to FIG. 2, the back electromotive force (EMF) voltage, V_B(t) of the haptic transducer is related to the velocity u(t) of the moving mass inside the haptic transducer by:V_B(t)=Bl·u(t)  (2)

Whether or not the driving signal V(t) is at the resonance frequency of the haptic transducer may be determined from a comparison between the back-EMF, V_B(t) in the haptic transducer, and the terminal voltage, V_T(t). For example, if the phase of V_B(t) is lagging or leading the terminal voltage V_T(t), the driving signal V(t) may be adjusted such that the phase of V_B(t) is in line with the phase of V_T(t).

In general, the back EMF voltage V_B(t) may not be directly measured from outside of the haptic transducer. However, the terminal voltage V_T(t) measured at the terminals of the haptic transducer, may be related to V_B(t) by:

$\begin{array}{cc}{V}_T\left(t\right)=V_B\left(t\right)+\mathrm{Re}·I\left(t\right)+\mathrm{Le}·\frac{\mathrm{dI}\left(t\right)}{\mathrm{dt}}& \left(3\right)\end{array}$ where the parameters are defined as described with reference to FIG. 2.

The haptic transducer terminal voltage itself may only therefore approximate the back-EMF voltage V_B(t) at times when the current I(t) has levels that are very close to zero, and when the driving voltage V(t) is also close to zero. In other words:V_T(t)≈V_B(t)  (4)whenV(t)→0, and  (5)I(t)→0.  (6)

From FIG. 2, it may also be seen that:V_T(t)=V(t)−Ro·I(t)  (7)which further implies that, even at zero-crossings of the driving voltage V(t), the usually very small playback output impedance Ro of the amplifier may be short-circuiting the terminal and making the level of measurable terminal voltage V_T(t) too low to be sensed accurately, as shown by:V_B(t)≈V_T(t)=V(t)−Ro·I(t)→0, if Ro«1  (8)

This difficulty in sensing the terminal voltage V_T(t) close to zero-crossings means that the amplifier may need to be switched into a high impedance mode Ro→0 quickly during zero-crossings of the driving signal (e.g., tri-stating its output); otherwise, the level of terminal voltage V_T(t)≈V_B(t) may be too low to be sensed with acceptable accuracy.

Measuring the back-EMF voltage V_B(t) across the terminals of the haptic transducer may therefore only allow for sensing of the back-EMF voltage V_B(t) during zero-crossings of the terminal voltage. Furthermore, it may require extra amplifier hardware designs that switch the driving amplifier into a high-impedance mode during the zero-crossings, in order for the back-EMF voltage to be sensed with appropriate accuracy, because the voltage level across the terminals of the haptic transducer may be reduced if the impedance of the amplifier is not high enough.

FIG. 3 illustrates an example resonant frequency tracker 300 for driving a haptic transducer 301 with a driving signal V(t), in accordance with embodiments of the present disclosure. In some embodiments, resonant frequency tracker 300 may be integral to a host device comprising resonant frequency tracker 300 and haptic transducer 301. Such device may include, without limitation, a mobile device, home application, a vehicle, and/or any other system, device, or apparatus that includes a human-machine interface.

An electromagnetic load such as an LRA may be characterized by its impedance Z_Lra as seen as the sum of a coil impedance Z_coil and a mechanical impedance Z_mech:Z_Lra=Z_coil+Z_mech  (9)

Coil impedance Z_coil may in turn comprise a direct current (DC) resistance Re in series with an inductance Le:Z_coil=Re+sLe  (10)

Mechanical impedance Z_mech may be defined by three parameters including a resistance at resonance R_ES, an angular resonant frequency ω₀ (e.g., ω₀=2πf₀), and a quality factor q. Or equivalently, mechanical impedance Z_mech may be defined by three parameters including the resistance at resonance R_ES, a capacitance C_MES representing an electrical capacitance representative of an equivalent moving mass M of the spring system of haptic transducer 301, and inductance L_CES representative of a compliance C of the spring system. The relationship among these quantities may be given by the following equations, in which s is the Laplace transform variable:

$\begin{array}{cc}{Z}_{mech}=R_{\mathrm{ES}}\frac{\frac{1}{q{\omega }_0}s}{1+\frac{1}{q{\omega }_0}s+\frac{1}{q{\omega }_0}{s}^2}& \left(11\right)\\ q=\frac{R_{ES}}{{\left(Bl\right)}^2}{\left(\frac{M}{C}\right)}^{\frac{1}{2}}={R_{ES}\left(\frac{C_{\mathrm{MES}}}{L_{\mathrm{CES}}}\right)}^{\frac{1}{2}}& \left(12\right)\\ {\omega }_0=\frac{1}{\sqrt{C_{MES}{L}_{CES}}}& \left(13\right)\end{array}$

At resonance, mechanical impedance Z_mech may be reduced to resistance at resonance R_ES and the total impedance Z_Lra may equal the sum of resistance Re and resistance at resonance R_ES. Thus, at resonance, a back-EMF V_B(t) and current I(t) through haptic transducer 301 may be in phase, and if inductance Le is small, the current I(t) and terminal voltage V_T(t) across the haptic transducer 301 may also be approximately in phase. If haptic transducer 301 is driven with a driving voltage v(t) near resonance (but not at resonance), the phase difference between terminal voltage V_T(t) and current I(t) (or back-EMF V_B(t) and current I(t)), may vary linearly with the frequency offset from resonance.

Such frequency offset or frequency error f_err from resonance frequency error f₀ may be related to a phase error ϕ_err between back-EMF V_B(t) and current I(t) by one of the following relationships:

$\begin{array}{cc}{\varphi }_{\mathrm{err}}=-\frac{\pi }{2}C{R}_{ES}{f}_{\mathrm{err}}& \left(12\right)\\ {\varphi }_{\mathrm{err}}=-\frac{\pi }{2}\frac{q{R}_{ES}}{{\omega }_0}{f}_{\mathrm{err}}& \left(13\right)\end{array}$

In some instances, compliance C and resistance at resonance R_ES may be estimated using offline testing and characterization. In addition, back-EMF voltage V_B(t) may be estimated according to equation (3) which may be rearranged as:

$\begin{array}{cc}{V}_B\left(t\right)=V_T\left(t\right)-\mathrm{Re}·I\left(t\right)-\mathrm{Le}\frac{\mathrm{dI}\left(t\right)}{\mathrm{dt}}& \left(14\right)\end{array}$

The phases of current I(t), terminal voltage V_T(t), or the estimate of back-EMF V_B(t) may be estimated by demodulating these various signals, and a phase error ϕ_err may be given as a difference between back-EMF V_B(t) and current I(t). Using either of equations (12) or (13), phase error ϕ_err may be converted into frequency error f_err.

Thus, turning to the components shown in FIG. 3, in operation, resonance frequency tracker 300 may, as described in more detail below, generate a haptic waveform signal x(t), which may in turn be amplified by amplifier 306 to generate the driving signal V(t) for driving haptic transducer 301.

Responsive to driving signal V(t), a sensed terminal voltage V_T(t) of haptic transducer 301 may be converted to a digital representation by a first analog-to-digital converter (ADC) 303. Similarly, sensed current I(t) may be converted to a digital representation by a second ADC 304. Current I(t) may be sensed across a shunt resistor 302 having resistance Rs coupled to a terminal of haptic transducer 301. The terminal voltage V_T(t) may be sensed by a terminal voltage sensing block 307, for example a volt meter.

As shown in FIG. 3, resonance frequency tracker 300 may include a back-EMF estimate block 308 that may estimate back-EMF voltage V_B(t) in accordance with equation (14) above. In some embodiments, a back-EMF estimate block may be implemented as a digital filter with a proportional and parallel difference path. The estimates of DC resistance Re and inductance Le may not need to be accurate (e.g., within an approximate 10% error may be acceptable), and thus, fixed values from an offline calibration or from a data sheet specification may be sufficient.

A first demodulator 310a may demodulate estimated back-EMF voltage V_B(t) using a carrier with known frequency (e.g., a driving frequency f of driving signal V(t)) to obtain its phase ϕ_VB relative to the carrier. Similarly, a second demodulator 310b may demodulate the digital equivalent of sensed current I(t) using a carrier with known frequency (e.g., a driving frequency f of driving signal V(t)) to obtain its phase ϕ_I relative to the carrier. Turning briefly to FIG. 4, FIG. 4 illustrates an example demodulator 310 that may be used to implement either or both of first demodulator 310a and second demodulator 310b, in accordance with embodiments of the present disclosure.

As shown in FIG. 4, demodulator 310 may be implemented by multiplying an input tone IN (IN=a sin(ωt+ϕ)), where a is the amplitude, ω is the angular frequency, and ϕ is the phase of the signal relative to the carrier with a sinusoid (block 402) having the same frequency. Low-pass filters 404 may be necessary to eliminate alternating current (AC) products of the demodulation.

Turning again to FIG. 3, resonance frequency tracker 300 may include a combiner 312 configured to generate phase error ϕ_err as a difference between phase ϕ_VB and phase ϕ_I. A phase-to-frequency converter 314 may receive phase error ϕ_err and generate frequency error f_err, for example by applying either of equations (12) or (13), above. In some embodiments, phase-to-frequency converter 314 may comprise or may otherwise have access to a lookup table that maps a received phase error ϕ_err to a corresponding frequency error f_err.

A combiner 316 may subtract a frequency offset f_OFFSET (described in greater detail below) from frequency error f_err to generate modified frequency error f′_err. Loop filter 318 may in turn perform loop filtering to generate a drive frequency f for haptic waveform signal x(t) towards resonance frequency f₀ in order to minimize modified frequency error f′_err. An integrator 320 may integrate drive frequency f to produce a phase ϕ for haptic waveform signal x(t).

As also shown in FIG. 3, a waveform controller 322 may generate an initial frequency signal f_i and communicate such signal to loop filter 318, which may pre-initialize loop filter 318 at startup to generate drive frequency f close to resonance frequency f₀ (e.g., within the approximate linear range of frequency error f_err). Waveform controller 322 may also generate an amplitude signal a to modulate the amplitude of haptic waveform signal x(t) in order to generate arbitrary haptic effects while tracking resonance frequency f₀. In some embodiments, waveform controller 322 may also generate frequency offset f_OFFSET in order that haptic waveform signal x(t) is driven at an offset from resonance to generate haptic effects by slowly modulating the offset from resonance.

A signal generator 324 may generate haptic waveform signal x(t) based on drive frequency f, phase ϕ, and amplitude signal a (e.g., x(t)=a sin(2πf+ϕ)).

When loop filter 318 has settled, drive frequency f generated by loop filter 318 may be used to derive an estimate of resonance frequency f₀ which may be used for haptic generation and/or for diagnostic purposes. For example, as shown in FIG. 3, combiner 316 may subtract frequency offset f_OFFSET (if present) from drive frequency f to generate an estimate f_{0_EST} of resonance frequency f₀.

Accordingly, the systems and methods described above may provide for tracking of resonance frequency f₀ using continuous phase estimation. Such continuous phase estimation enables continuous estimation of the difference between drive frequency and resonance frequency, and such frequency error may be used in a feedback loop to steer the drive frequency towards the resonance frequency. Advantageously, unlike traditional approaches, the systems and methods described herein do not constrain the drive duty-cycle of a haptic transducer. Furthermore, the systems and methods described herein may be less sensitive to noise and may achieve resonance tracking more efficiently than existing approaches that rely on zero crossing event detection.

As used herein, when two or more elements are referred to as “coupled” to one another, such term indicates that such two or more elements are in electronic communication or mechanical communication, as applicable, whether connected indirectly or directly, with or without intervening elements.

This disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. Similarly, where appropriate, the appended claims encompass all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. Moreover, reference in the appended claims to an apparatus or system or a component of an apparatus or system being adapted to, arranged to, capable of, configured to, enabled to, operable to, or operative to perform a particular function encompasses that apparatus, system, or component, whether or not it or that particular function is activated, turned on, or unlocked, as long as that apparatus, system, or component is so adapted, arranged, capable, configured, enabled, operable, or operative. Accordingly, modifications, additions, or omissions may be made to the systems, apparatuses, and methods described herein without departing from the scope of the disclosure. For example, the components of the systems and apparatuses may be integrated or separated. Moreover, the operations of the systems and apparatuses disclosed herein may be performed by more, fewer, or other components and the methods described may include more, fewer, or other steps. Additionally, steps may be performed in any suitable order. As used in this document, “each” refers to each member of a set or each member of a subset of a set.

Although exemplary embodiments are illustrated in the figures and described below, the principles of the present disclosure may be implemented using any number of techniques, whether currently known or not. The present disclosure should in no way be limited to the exemplary implementations and techniques illustrated in the drawings and described above.

Unless otherwise specifically noted, articles depicted in the drawings are not necessarily drawn to scale.

All examples and conditional language recited herein are intended for pedagogical objects to aid the reader in understanding the disclosure and the concepts contributed by the inventor to furthering the art, and are construed as being without limitation to such specifically recited examples and conditions. Although embodiments of the present disclosure have been described in detail, it should be understood that various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the disclosure.

Although specific advantages have been enumerated above, various embodiments may include some, none, or all of the enumerated advantages. Additionally, other technical advantages may become readily apparent to one of ordinary skill in the art after review of the foregoing figures and description.

To aid the Patent Office and any readers of any patent issued on this application in interpreting the claims appended hereto, applicants wish to note that they do not intend any of the appended claims or claim elements to invoke 35 U.S.C. § 112(f) unless the words “means for” or “step for” are explicitly used in the particular claim.

Claims

1. A resonant frequency tracker for driving an electromagnetic load with a driving signal, the resonance-frequency tracker comprising: a signal generator configured to generate a waveform signal at a driving frequency for driving the electromagnetic load; andcontrol circuitry configured to: during driving of the electromagnetic load by the waveform signal or a signal derived therefrom: monitor a current signal responsive to the waveform signal or the signal derived therefrom and representative of a current associated with the electromagnetic load; andmonitor a second signal responsive to the waveform signal or the signal derived therefrom and representative of a second quantity associated with the electromagnetic load, the second quantity comprising one of a voltage associated with a back electromotive force of the electromagnetic load;calculate a phase difference between the current signal and the second signal;determine a frequency error of the waveform signal indicative of a difference between the driving frequency and a resonance frequency of the electromagnetic load based on the phase difference; andcontrol the driving frequency based on the frequency error.

2. The resonant frequency tracker of claim 1, wherein the electromagnetic load comprises a haptic transducer.

3. The resonant frequency tracker of claim 1, wherein the electromagnetic load comprises a linear resonant actuator.

4. The resonant frequency tracker of claim 1, wherein the control circuitry is configured to calculate the phase difference by: demodulating the current signal based on the drive frequency to determine a relative phase of the current signal;demodulating the second signal based on the drive frequency to determine a relative phase of the second signal; andcalculating the phase difference to be a difference between the relative phase of the second signal and the relative phase of the current signal.

5. The resonant frequency tracker of claim 1, wherein: the second quantity is the back electromotive force of the electromagnetic load; andthe control circuitry is further configured to estimate the back electromotive force based on the voltage associated with the electromagnetic load, the current associated with the electromagnetic load, and a coil impedance associated with the electromagnetic load.

6. The resonant frequency tracker of claim 1, wherein the control circuitry is configured to control the driving frequency in order to minimize the frequency error.

7. The resonant frequency tracker of claim 1, wherein the control circuitry is configured to control the driving frequency in order to minimize a difference between the frequency error and a predetermined frequency offset.

8. The resonant frequency tracker of claim 1, wherein the control circuitry is further configured to determine the frequency error of the waveform signal based on estimates of an equivalent mass of the electromagnetic load and an impedance at resonance of the electromagnetic load.

9. The resonant frequency tracker of claim 1, wherein the control circuitry is further configured to implement a closed loop control system having a loop filter in order to determine the frequency error.

10. The resonant frequency tracker of claim 9, wherein the control circuitry is further configured to provide an initial drive frequency as a first input to the loop filter to cause the loop filter at its initiation to generate the waveform signal having the drive frequency equal to the initial drive frequency.

11. The resonant frequency tracker of claim 1, wherein: the control circuitry is further configured to integrate the drive frequency to generate a driving phase for the waveform signal; andthe signal generator is further configured to generate the waveform signal having the driving phase.

12. The resonant frequency tracker of claim 1, wherein: the control circuitry is further configured to modulate an amplitude of the driving signal independently of tracking of the resonance frequency of the electromagnetic load; andthe signal generator is further configured to generate the waveform signal having the amplitude of the driving signal as modulated by the control circuitry.

13. A method comprising: generating a waveform signal at a driving frequency for driving an electromagnetic load;during driving of the electromagnetic load by the waveform signal or a signal derived therefrom: monitoring a current signal responsive to the waveform signal or the signal derived therefrom and representative of a current associated with the electromagnetic load; andmonitoring a second signal responsive to the waveform signal or the signal derived therefrom and representative of a second quantity associated with the electromagnetic load, the second quantity comprising one of a voltage associated with a back electromotive force of the electromagnetic load;calculating a phase difference between the current signal and the second signal;determining a frequency error of the waveform signal indicative of a difference between the driving frequency and a resonance frequency of the electromagnetic load based on the phase difference; andcontrolling the driving frequency based on the frequency error.

14. The method of claim 13, wherein the electromagnetic load comprises a haptic transducer.

15. The method of claim 13, wherein the electromagnetic load comprises a linear resonant actuator.

16. The method of claim 13, further comprising calculating the phase difference by: demodulating the current signal based on the drive frequency to determine a relative phase of the current signal;demodulating the second signal based on the drive frequency to determine a relative phase of the second signal; andcalculating the phase difference to be a difference between the relative phase of the second signal and the relative phase of the current signal.

17. The method of claim 13, wherein: the second quantity is the back electromotive force of the electromagnetic load; andthe method further comprises estimating the back electromotive force based on the voltage associated with the electromagnetic load, the current associated with the electromagnetic load, and a coil impedance associated with the electromagnetic load.

18. The method of claim 13, further comprising controlling the driving frequency in order to minimize the frequency error.

19. The method of claim 13, further comprising controlling the driving frequency in order to minimize a difference between the frequency error and a predetermined frequency offset.

20. The method of claim 13, further comprising determining the frequency error of the waveform signal based on estimates of an equivalent mass of the electromagnetic load and an impedance at resonance of the electromagnetic load.

21. The method of claim 13, further comprising implementing a closed loop control system having a loop filter in order to determine the frequency error.

22. The method of claim 21, further comprising providing an initial drive frequency as a first input to the loop filter to cause the loop filter at its initiation to generate the waveform signal having the drive frequency equal to the initial drive frequency.

23. The method of claim 13, further comprising: integrating the drive frequency to generate a driving phase for the waveform signal; andgenerating the waveform signal having the driving phase.

24. The method of claim 13, wherein: further comprising modulating an amplitude of the driving signal independently of tracking of the resonance frequency of the electromagnetic load; andgenerating the waveform signal having the amplitude of the driving signal as modulated by the control circuitry.

25. A host device comprising: an electromagnetic load; anda resonant frequency tracker for driving the electromagnetic load with a driving signal, the resonance-frequency tracker comprising: a signal generator configured to generate a waveform signal at a driving frequency for driving the electromagnetic load; andcontrol circuitry configured to: during driving of the electromagnetic load by the waveform signal or a signal derived therefrom: monitor a current signal responsive to the waveform signal or the signal derived therefrom and representative of a current associated with the electromagnetic load; andmonitor a second signal responsive to the waveform signal or the signal derived therefrom and representative of a second quantity associated with the electromagnetic load, the second quantity comprising one of a voltage associated with a back electromotive force of the electromagnetic load;calculate a phase difference between the current signal and the second signal;determine a frequency error of the waveform signal based indicative of a difference between the driving frequency and a resonance frequency of the electromagnetic load on the phase difference; andcontrol the driving frequency based on the frequency error.