CN112114608A - Piezoelectric transducer controller with model-based sideband balancing - Google Patents

Abstract

The present disclosure relates to piezoelectric transducer controllers with model-based sideband balancing. Various sensors, sensor controllers, and sensor control methods with model-based sideband balancing are provided. In an exemplary embodiment, a controller for a piezoelectric transducer includes a transmitter, a receiver, and processing circuitry coupled to the transmitter and the receiver. The processing circuitry performs calibration and echo detection, the calibration comprising: sensing a phase response of the piezoelectric transducer as a function of frequency; deriving equivalent circuit parameters of the piezoelectric transducer from the phase response; and determining a sideband imbalance based on one or more of the equivalent circuit parameters. Once a sideband imbalance is identified, the processing circuitry may perform echo detection processing that accounts for the sideband imbalance.

Description

Piezoelectric transducer controller with model-based sideband balancing

Technical Field

The present application relates generally to automotive sensors and, more particularly, to controllers for piezoelectric transducers.

Background

Modern vehicles are equipped with a large variety of sensors. For example, automobiles are now commonly equipped with an array of piezoelectric sensors to monitor the distance between the automobile and any nearby people, pets, vehicles, or other obstacles. Due to environmental "noise" and safety issues, each of the sensors may be required to provide tens of measurements per second while the vehicle is in motion. Reliable performance is important for such sensor arrays.

As the number of sensors increases, multiple sensors are also required to operate simultaneously, increasing the risk of interference between the sensors. Because acoustic bursts from multiple sensors may be "in-flight" at the same time, echoes from bursts of a first sensor may be detected by other sensors and become erroneously associated with other bursts, resulting in incorrect time-of-flight determinations and erroneous distance measurements. Related application 15/888, 471 ("Composite Acoustic Bursts for Multi-channel Sensing") addresses this problem by associating an Acoustic burst with its original sensor using signal sideband energy. However, sideband attenuation depends on various factors including temperature, sensor aging, and external loading of the transducer. If the sidebands become unbalanced (subject to unequal attenuation), the accuracy of the time-of-flight determination of the sensor may be adversely affected.

Disclosure of Invention

According to one aspect of the present application, there is provided a controller for a piezoelectric transducer, characterized in that the controller comprises: a transmitter driving the piezoelectric transducer; a receiver that senses a response of the piezoelectric transducer; and processing circuitry coupled to the transmitter and the receiver to perform calibration and echo detection, the calibration comprising: sensing a phase response of the piezoelectric transducer as a function of frequency; deriving equivalent circuit parameters of the piezoelectric transducer from the phase response; and determining a sideband imbalance based on one or more of the equivalent circuit parameters.

In one embodiment, the controller is further characterized in that the equivalent circuit parameter comprises a capacitance C of the series branch_SInductor L_SAnd a resistance R_SAnd the capacitance C of the capacitor connected in parallel with the series branch_P。

In one embodiment, the controller is further characterized in that the equivalent parameter is for an equivalent circuit further comprising an inductance L of an inductor in parallel with the series branch_PAnd the resistance R of the inductor_LP。

In one embodiment, the controller is further characterized in that deriving the equivalent circuit parameter of the piezoelectric transducer from the phase response comprises: a linear phase correction for the sensed phase response is determined based on a comparison of a point on the sensed phase response to a point on the equivalent circuit phase response.

In one embodiment, the controller is further characterized in that deriving the equivalent circuit parameter of the piezoelectric transducer from the phase response comprises: finding a peak in the sensed phase response; determining an average phase of the peak; and adjusting the capacitance C based on a comparison of the average phase of the peak of the sensed phase response and the average phase of the peak of the equivalent circuit phase response_P。

In one embodiment, the controller is further characterized in that determining the average phase comprises finding a valley in the sensed phase response, and further characterized in that deriving the equivalent circuit parameter of the piezoelectric transducer from the phase response comprises: determining an average frequency between the valley and the peak; and adjusting the inductance L based on a comparison of the average frequency with an average frequency of the equivalent circuit phase response_SAnd a capacitor C_SThe product of (a).

In one embodiment, the controller is further characterized in that deriving equivalent circuit parameters of the piezoelectric transducer from the phase response comprises: determining between the valley and the peakThe frequency difference of (a); and adjusting the inductance L based on a comparison of the frequency difference with a frequency difference of the equivalent circuit phase response_SAnd a capacitor C_SThe ratio of (a) to (b).

In one embodiment, the controller is further characterized in that deriving equivalent circuit parameters of the piezoelectric transducer from the phase response comprises: determining a phase difference between the valley and the peak; and adjusting the resistance R based on a comparison of the phase difference to a phase difference of the equivalent circuit phase response_S。

In one embodiment, the controller is further characterized in that the echo detection comprises taking into account a sideband imbalance.

According to one aspect of the present application, there is provided a method of operating a piezoelectric-based sensor, characterized in that the method comprises: sensing a phase response of the piezoelectric transducer as a function of frequency; deriving equivalent circuit parameters of the piezoelectric transducer from the phase response; determining a sideband imbalance based on one or more of the equivalent circuit parameters; and performing an echo detection process that takes into account the sideband imbalance.

Drawings

FIG. 1 is a top view of an exemplary vehicle equipped with a piezoelectric-based sensor.

FIG. 2 is a block diagram of an exemplary parking assist system.

Fig. 3 is a circuit schematic of an exemplary piezoelectric-based sensor.

FIG. 4 is a block diagram of a sensor having an equivalent circuit for a piezoelectric transducer.

FIG. 5 is a graph of an exemplary magnitude response.

Fig. 6 is a graph of an exemplary phase response.

FIG. 7A is a graph of corrected phase response and model phase response.

Fig. 7B is a graph showing four measurements from the phase response.

FIG. 8 is a flow chart of an exemplary sensing method.

Cross Reference to Related Applications

The present application relates to U.S. application 15/888, 471 entitled "Composite Acoustic Bursts for Multi-channel Sensing" filed by inventors t.suchy, m.kassa and m.hustava at 2018-02-05. This related patent application is hereby incorporated by reference in its entirety.

Detailed Description

The drawings and the corresponding detailed description do not limit the disclosure, but on the contrary, the intention is to provide a basis for understanding all modifications, equivalents, and alternatives falling within the scope of the appended claims.

As an illustrative use context, fig. 1 shows a vehicle 102 equipped with a set of piezo-based sensors 104. There are variations in the number and configuration of sensors in the sensor arrangement, and it is not uncommon to have six sensors on each bumper, with two additional sensors on each side serving as blind spot detectors on each side. Vehicles may employ the sensor arrangement to detect and measure distances to objects within various detection regions, possibly using the sensors for individual measurements as well as for cooperative measurement (e.g., triangulation, multi-receiver) measurements.

The piezo-based sensors are transceivers, meaning that each sensor can transmit and receive bursts of acoustic energy. The transmitted pulse train propagates outward from the vehicle until it encounters and is reflected by an object or some other form of acoustic impedance mismatch. The reflected pulse train is returned to the vehicle as an "echo" of the transmitted pulse train. The time between the transmit burst and the received echo is indicative of the distance to the reflection point. In many systems, only one sensor transmits at a time, but all sensors can be configured to measure the resulting echoes. However, multiple simultaneous transmissions may be supported, for example, as described in co-pending application 15/888, 471 ("Composite Acoustic Bursts for Multi-channel Sensing"), or by using orthogonal waveforms or transmissions to non-overlapping detection regions.

Fig. 2 shows an Electronic Control Unit (ECU)202 coupled to various piezo-based sensors 204 as the center of a star topology. Of course, other communication bus topologies, including serial, parallel, and hierarchical (tree) topologies, are suitable and contemplated for use in accordance with the principles disclosed herein. To provide automatic parking assistance, the ECU202 may be further connected to a set of actuators, such as a turn signal actuator 206, a steering actuator 208, a brake actuator 210, and a throttle actuator 212. The ECU202 may also be coupled to a user interactive interface 214 to accept user input and provide displays of various measurements and system status. Using the interfaces, sensors, and actuators, the ECU202 may provide automatic parking, assisted parking, lane change assistance, obstacle and blind spot detection, and other desirable features.

One possible sensor configuration is now described with reference to fig. 3 and 4. In practice, the sensors may employ any of a number of suitable communication and power technologies, such as those provided in the DSI3, LIN, and CAN standards. Some of these standards support data communication over a power conductor or over multiple bus conductors. However, in the embodiment shown in fig. 3, the sensor controller 302 is connected to only two power terminals (Vbat and GND) and a single input/output ("I/O" or "IO") line for bi-directional communication with the ECU 202.

The sensor controller 302 includes an I/O interface 303 that monitors communication from the ECU202 over the I/O lines when placed in the recessive mode, and drives the I/O lines to send measurements or other information to the ECU202 when placed in the dominant mode.

The sensor controller 302 includes core logic 304 that operates in accordance with firmware and parameters stored in non-volatile memory 305 to interpret commands from the ECU and perform appropriate operations, including the transmission and reception of acoustic bursts (typically in the ultrasonic range). To transmit the acoustic pulse train, the core logic 304 is coupled to a transmitter 306 that drives a set of transmit terminals on the sensor controller 302. The transmitter terminal is coupled to the piezoelectric element PZ via a transformer M1. The transformer M1 steps up the voltage from the sensor controller (e.g., 12 volts) to a suitable level for driving the piezoelectric element (e.g.,tens of volts). Parallel resistor R_PThe residual vibration of the piezoelectric element is suppressed.

As used herein, the term "piezoelectric transducer" includes not only piezoelectric elements, but also supporting circuit elements for driving, tuning, and receiving from the piezoelectric elements. In an exemplary embodiment, these support elements are transformer M1, a shunt resistor, and any tuning or DC blocking capacitors. Optionally, the output and input capacitances of the transmitter 306 and amplifier 308, respectively, may also be included as parasitic characteristics of supporting circuit elements that are considered part of the transducer. However, the use of the term "piezoelectric transducer" does not necessarily require the presence of any supporting circuit elements, as piezoelectric elements may be employed alone without such supporting elements.

The terminals of the piezoelectric element PZ are coupled to a pair of receiving terminals of the sensor controller. Because the received echo signal is typically in the millivolt or microvolt range, low noise amplifier 308 amplifies the signal from the receive terminal. When the piezoelectric element is actively driven by the transmitter, the input of the amplifier may be clamped and/or the output may be allowed to saturate at the internal supply voltage. The amplified received signal is digitized and processed by a Digital Signal Processor (DSP)310 with an integrated analog-to-digital converter (ADC).

DSP 310 applies programmable methods to process the signals from the piezoelectric elements to, for example, measure the actuation period of the piezoelectric transducer during the transmission of the pulse train (including the subsequent reverberation or "ringing" period), and detect and measure the timing of any received pulse train or "echo". Such methods may employ filtering, correlation, threshold comparisons, minimum separation, peak detection, zero crossing detection and counting, noise level determination, and other customizable techniques tailored for improved reliability and accuracy. The DSP 310 may further process the amplified received signal to analyze a characteristic of the transducer, such as a phase response of the transducer.

FIG. 4 is a block diagram in which a piezoelectric element PZ is represented by the element as a parallel capacitor C_PThe equivalent circuit 402 of (1) instead, the parallel capacitor and the series inductor L_SSeries capacitorC_SAnd a series resistor R_SAre coupled in parallel. The series combination represents the mechanical action of the piezoelectric element, where RS represents the energy loss of the element (during normal operation, this is mainly due to radiated acoustic energy). Fig. 4 also shows the parasitic inductance L of the secondary winding of the transformer_PAnd parasitic resistance R_LP. The receiver 404 receives and amplifies the voltage signal from the equivalent circuit 402. The magnitude and phase (or alternatively, in-phase and quadrature-phase components) of the amplified signal are measured by detector 406 using the signal from oscillator 408 as a phase reference. The measured phase is the difference between the transmit (tx current) signal and the receive (rx voltage) signal. The DSP 410 operates on the detector measurements to, for example, perform equivalent circuit estimation ("ECE"), system level selectivity ("SLS") determination, side band balancing ("SBB"), and obstacle detection and tracking ("ODT").

Fig. 5 shows an exemplary magnitude response as a function of frequency. The response shown is represented by a negative peak or trough (corresponding to C)_SAnd L_SSeries resonance frequency) of the partial decrease of the positive peak (corresponding to C)_PAnd L_PThe parallel resonance frequency). In at least some embodiments, the Acoustic burst is at least approximately centered at the series resonance frequency, although some signal energy may be transmitted on either side of the center frequency band to enable parallel burst transmissions to be distinguished by source, for example, as described in related applications 15/888, 471 ("Composite Acoustic burst for Multi-channel Sensing").

It should be noted that the response of the transducer will typically vary depending on, for example, temperature, age, and/or accumulation of material on the transducer housing. Such variations may cause the sideband response of the transducer to become unbalanced, which may reduce time-of-flight measurement accuracy if not compensated for or otherwise accounted for. In at least some embodiments, the controller performs calibration of the piezoelectric transducer by measuring the response of the transducer as a function of frequency, or the like. In practice, the controller may not be able to measure the magnitude response in the field due to input clamping and/or output saturation of the receiving amplifier. Even with such effects, the controller is able to determine the phase response as a function of frequency by comparing the timing of transitions or zero crossings.

Fig. 6 shows an exemplary phase response curve D that may be measured by the controller during a calibration operation. The measured phase response curve reflects primarily the response of the piezoelectric transducer, but may also include linear phase error 602 caused by group delay of the transmitter and receiver. Preferably, the linear phase error 602 is estimated and subtracted from the measured phase response 602 to obtain a corrected phase response curve, as described further below. (more generally, some components may introduce non-linear phase errors, and it is expected that at least some implementations will estimate and remove non-linear phase errors.)

Fig. 7A shows an exemplary corrected phase response curve C in solid lines, and fig. 7A also shows an exemplary phase response curve M derived from an equivalent circuit model of the piezoelectric transducer in dashed lines. Five points are shown on each curve: low frequency end point C₀，M₀(ii) a Local minimum (valley) point C₁，M₁(ii) a Local maximum (peak) point C₂，M₂(ii) a Offset point C₃，M₃(ii) a And a high frequency end C₄、M₄。

The low frequency end value measurement is at a predetermined frequency at the low end of the operating range of the transmitter at a point that is comfortably below the expected resonant frequency of the transducer, and thus the phase response is expected to be primarily inductive, e.g., 30 kHz. Conversely, the high frequency end value measurement is at a predetermined frequency at the high end of the operating range of the transmitter at a point that is comfortably above the expected resonant frequency, and thus the phase response is expected to be primarily capacitive, e.g., 90 kHz. The endpoint may be measured using a single frequency transmit pulse.

Local minima and local maxima can be identified using a frequency sweep (e.g., chirp) and will be found on either side of the series resonance frequency. (in this example, the series resonant frequency of the transducer is about 52kHz, and a frequency sweep is performed from 10kHz below the manufacturer specified resonant frequency to 10kHz above the manufacturer specified resonant frequency.) the offset point is at a predetermined frequency offset from the manufacturer specified resonant frequency, in this example 62kHz (the upper end of the frequency sweep).

Although they have been shown with respect to the corrected phase response curve C and the equivalent circuit model response M, the end points, valleys, peaks and offset points are first determined in the measured phase response curve D, resulting in a phase measurement D₀To D₄And D₁And D₂Frequency determination (i.e., f)_D1And f_D2). Equivalent circuit model (M)₀To M₄、f_M1And f_M2) Can be determined analytically or numerically.

The corrected phase response curve measurement (C) may then be determined as follows₀To C₄). Define the linear phase error as (f)₀，D₀-M₀) And (f)₄，D₄-M₄) The line in between. From D₀To D₄Subtracting the linear phase error to obtain C₀To C₄. (since the correction is relative to D₀And D₄Defined, then C₀＝M₀And C₄＝M₄. ) For the remaining points, the ratio k is used (f)_i-f₀)/(f₄-f₀)：

C_i＝[M₀+k*(M₄-M₀)]+[D_i-D₀-k*(D₄-D₀)]

FIG. 7B shows phase response curve measurement C that can be corrected₁、C₂And C₃Four measurements were derived. The corresponding measurement result will be from the equivalent circuit model phase response value M₁、M₂And M₃And (6) exporting. The first is average phase

Wherein a is_iIs a weighted sum coefficient added to 1. For example, each a_iMay be equal to 1/3. Alternatively, a₂May be 0.5, and a₁And a₃Each equal to 0.25. This averaging of the corrected phase responseThe difference between the phase and the corresponding average phase of the model phase response can be used as the parallel capacitance C in the equivalent circuit model_PIs determined by the error in the estimated value of (a).

The second measurement being the average frequency

The difference between this average frequency and the corresponding average frequency (f _ M) — (f _ M1+ f _ M2)/2 can be used as the error in estimating the series resonance frequency (and thus the product L) in the equivalent circuit model_SC_SError in) is detected.

The third measurement result is the frequency difference Δ f_C＝f_C2-f_C1. The difference Δ f _ M between the frequency difference amount and the corresponding frequency difference amount f _ M2-f _ M1 can be used as the error (and thus the ratio L) in the estimated series resonance quality factor Q in the equivalent circuit model_S/C_SError in) is detected.

The fourth measurement is the phase difference delta phi_c＝C₂-C₁. The difference between the phase difference and the corresponding phase difference_M＝M₂-M₁Can be used as series resistance R in equivalent circuit model_SIs determined by the error in the estimated value of (a).

Fig. 8 is a flowchart of a sensor control method using the foregoing measurement results. The method begins at block 802 with initialization of equivalent circuit model parameters. The parameters may be set based on initial values stored in firmware for a "typical" transducer response. Alternatively, the sensor transducer may be characterized at the factory to determine initial parameter values. The parameter may be R_S、L_S、C_SAnd C_POr various combinations thereof. In some variations, the parameter is R_S、C_P、Q_S(depending on the ratio L_S/C_SResonance quality factor of) and f_S(depending on the product L_SC_SThe resonant frequency of). Determining the model phase response value M analytically or by numerical solution using known parameter values₀To M₄. The four measurements (average phase, b) were also determined,Average frequency, dispersion of frequencies, and dispersion of phases).

In block 804, the controller measures the phase responses D0, D4 at the upper and lower ends of the transmitter frequency range. In block 806, the controller measures the phase of the transducer's response to the chirp signal, e.g., sweeping from a frequency of about 10kHz below the expected series resonance frequency to about 10kHz above the expected series resonance frequency. In block 808, the controller identifies a valley frequency f from the chirp response_C1(＝f_D1) Peak frequency f_C2(＝f_D2) And (if not predetermined) an offset frequency f_C3. In block 810, the controller extracts the phase response at the relevant frequency (D1-D3). In block 812, the controller applies linear phase correction to D1-D3 to obtain C1-C3, and finds four measurements (average phase, average frequency, dispersion of frequencies, and dispersion of phases).

In block 814, the controller compares the corrected phase response to the average phase of the equivalent circuit model phase response. If they do not match, the controller adjusts the shunt capacitance C in block 815_P. (for example, if the average phase of the model is too low, then the shunt capacitance C_PAnd decreases. ) This adjustment and other parameter adjustments may be performed in accordance with well-known adaptive techniques.

In block 816, the controller compares the corrected phase response to the average frequency of the equivalent circuit model phase response. If they do not match, the controller adjusts the product L in block 817_SC_S. (e.g., if the average frequency of the model is too high, the product increases.)

In block 818, the controller compares the corrected phase response to the frequency delta of the equivalent circuit model phase response. If they do not match, the controller adjusts the ratio L in block 819_S/C_S. (e.g., if the difference in frequency of the model is too low, the ratio increases.)

In block 820, the controller compares the corrected phase response to the phase delta of the equivalent circuit model phase response. If they do not match, the controller adjusts the resistance R in block 821_S. (for example, if the amount of phase difference of the model is too low, the resistance decreases.)

In block 822, the controller determines whether any parameter adjustments have been made and, if so, repeats block 812-822 with the updated model parameters. In earlier experiments, it was determined that convergence was generally achieved within five iterations.

Once sufficient matching is achieved, the controller estimates a System Level Selectivity (SLS) curve using the equivalent circuit model in block 824 because of the series resistance R_SWith current I through a series resistance_SThe product of (c) is varied in dependence on the frequency. More specifically, a magnitude response at sideband frequencies is determined.

In block 826, the sideband responses are compared. If an imbalance is detected, the controller adjusts the transmit frequency, adjusts the transmit current magnitude, and/or adjusts the filter response in the receive chain to rebalance the sideband response. Then, in block 828, the controller performs measurements using the echo detection process and optional monitoring of detected obstacles. One suitable measurement technique can be found in related applications 15/888, 471 ("Composite Acoustic Bursts for Multi-channel Sensing").

Periodically, the controller repeats blocks 802-827 to identify and accommodate changes in the transducer response.

Although the operations shown and described in fig. 8 are considered to occur sequentially for purposes of explanation, in practice the method may be implemented by multiple integrated circuit components operating concurrently, and possibly even operating speculatively to implement out-of-order operations. The sequential discussion is not intended to be limiting. Furthermore, the above description may omit complications such as parasitic impedances, current limiting resistors, level shifters, wire clamps, etc., which may be present but do not meaningfully affect the operation of the disclosed circuit.

Examples of the present disclosure also include the following enumerated embodiments:

1. a method of operating a piezoelectric-based sensor, the method comprising: sensing a phase response of the piezoelectric transducer as a function of frequency; deriving equivalent circuit parameters of the piezoelectric transducer from the phase response; determining a sideband imbalance based on one or more of the equivalent circuit parameters; and performing echo detection processing that takes into account the sideband imbalance.

2. The method of embodiment 1, wherein the equivalent circuit parameters include a capacitance CS, an inductance LS and a resistance RS of the series branch and a capacitance CP of a capacitor in parallel with the series branch.

3. The method of embodiment 1, wherein the deriving comprises: a linear phase correction for the sensed phase response is determined based on a comparison of a point on the sensed phase response to a point on the equivalent circuit phase response.

4. The method of embodiment 1, wherein the deriving comprises: finding a peak in the sensed phase response; determining an average phase of the peak; and adjusting the capacitance CP based on a comparison of the average phase of the peak of the sensed phase response and an average phase of the peak of an equivalent circuit phase response.

5. The method of embodiment 4, wherein the determining an average phase comprises finding a valley in the sensed phase response, and wherein the deriving further comprises: determining an average frequency between the valley and the peak; and adjusting the product of inductance LS and capacitance CS based on a comparison of the average frequency and the average frequency of the equivalent circuit phase response.

6. The method of embodiment 5, wherein the deriving further comprises: determining a frequency difference between the valley and the peak; and adjusting a ratio of inductance LS to capacitance CS based on a comparison of the frequency difference to a frequency difference of the equivalent circuit phase response.

7. The method of embodiment 6, wherein the deriving further comprises: determining a phase difference between the valley and the peak; and adjusting the resistance RS based on a comparison of the phase difference to a phase difference of the equivalent circuit phase response.

8. A sensor, comprising: a piezoelectric transducer; and a controller driving the piezoelectric transducer and sensing a phase response of the piezoelectric transducer as a function of frequency, the controller including a processing circuit that takes into account an estimated sideband imbalance when performing echo detection processing, the sideband imbalance estimated based on equivalent circuit parameters derived from the phase response.

9. The sensor of embodiment 8, wherein the phase response comprises a phase correction based on a comparison of the sensed phase response to an equivalent circuit phase response.

10. The sensor of embodiment 9, wherein the equivalent circuit parameters include a capacitance CS, an inductance LS, and a resistance RS of the series branch and a capacitance CP of a capacitor in parallel with the series branch.

11. The sensor of embodiment 10, wherein the equivalent circuit parameters are derived in part by: finding a peak in the sensed phase response; finding a valley in the sensed phase response; determining a phase difference between the valley and the peak; and adjusting the resistance RS based on a comparison of the phase difference to a phase difference of the equivalent circuit phase response.

The focus of the foregoing discussion is on ultrasonic sensors, but the principles apply to any acoustic sensor or other pulsed back wave transducer that may benefit from identifying and accommodating changes in transducer response. These and many other modifications, equivalents, and alternatives will become apparent to those skilled in the art once the above disclosure is fully appreciated. It is intended that the following claims be interpreted to embrace all such modifications, equivalents, and alternatives as are appropriate.

Claims (10)

1. A controller for a piezoelectric transducer, the controller comprising:

a transmitter that drives the piezoelectric transducer;

a receiver that senses a response of the piezoelectric transducer; and

processing circuitry coupled to the transmitter and the receiver to perform calibration and echo detection, the calibration comprising:

sensing a phase response of the piezoelectric transducer as a function of frequency;

deriving equivalent circuit parameters of the piezoelectric transducer from the phase response; and

determining a sideband imbalance based on one or more of the equivalent circuit parameters.

2. Controller for a piezoelectric transducer according to claim 1, characterized in that the equivalent circuit parameter comprises the capacitance C of the series branch_SInductor L_SAnd a resistance R_SAnd the capacitance C of a capacitor connected in parallel with the series branch_P。

3. Controller for a piezoelectric transducer according to claim 2, characterized in that the equivalent parameter is for an equivalent circuit further comprising an inductance L of an inductor connected in parallel with the series branch_PAnd the resistance R of the inductor_LP。

4. Controller for a piezoelectric transducer according to any of the preceding claims, characterized in that deriving equivalent circuit parameters of the piezoelectric transducer from the phase response comprises:

a linear phase correction for the sensed phase response is determined based on a comparison of a point on the sensed phase response to a point on the equivalent circuit phase response.

5. Controller for a piezoelectric transducer according to any one of claims 1 to 3, characterized in that deriving equivalent circuit parameters of the piezoelectric transducer from the phase response comprises:

finding a peak in the sensed phase response;

determining an average phase of the peak; and

the average phase and equivalent circuit phase response of the peak based on the sensed phase responseAdjusting the capacitance C in response to a comparison of the average phase of the peaks_P。

6. The controller for a piezoelectric transducer as claimed in claim 5, wherein determining the average phase comprises finding a valley in the sensed phase response, and further wherein deriving equivalent circuit parameters of the piezoelectric transducer from the phase response comprises:

determining an average frequency between the valley and the peak; and

adjusting inductance L based on a comparison of the average frequency to an average frequency of the equivalent circuit phase response_SAnd a capacitor C_SThe product of (a).

7. The controller for a piezoelectric transducer as claimed in claim 6, wherein deriving equivalent circuit parameters of the piezoelectric transducer from the phase response comprises:

determining a frequency difference between the valley and the peak; and

adjusting inductance L based on a comparison of the frequency difference and a frequency difference of the equivalent circuit phase response_SAnd a capacitor C_SThe ratio of (a) to (b).

8. The controller for a piezoelectric transducer as claimed in claim 7, wherein deriving equivalent circuit parameters for the piezoelectric transducer from the phase response comprises:

determining a phase difference between the valley and the peak; and

adjusting the resistance R based on a comparison of the phase difference to a phase difference of the equivalent circuit phase response_S。

9. Controller for a piezoelectric transducer according to claim 5, characterized in that echo detection comprises taking into account the sideband imbalance.

10. A method of operating a piezoelectric-based sensor, the method comprising:

sensing a phase response of the piezoelectric transducer as a function of frequency;

deriving equivalent circuit parameters of the piezoelectric transducer from the phase response;

determining a sideband imbalance based on one or more of the equivalent circuit parameters; and

an echo detection process is performed that takes into account the sideband imbalance.

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