IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 1

Class-DE Ultrasound Transducer Driver for HIFUTherapy

Carlos Christoffersen, Senior Member, IEEE, Wai Wong, Member, IEEE, Samuel Pichardo, Member, IEEE,Greg Togtema and Laura Curiel, Member, IEEE

Abstract—This paper presents a practical implementationof an integrated MRI-compatible CMOS amplifier capable ofdirectly driving a piezoelectric ultrasound transducer suitable forhigh-intensity focused ultrasound (HIFU) therapy. The amplifieroperates in Class DE mode without the need for an output match-ing network. The integrated amplifier has been implementedwith the AMS AG H35 CMOS process. A class DE amplifierdesign methodology for driving unmatched piezoelectric loadsis presented along with simulation and experimental results.The proposed design achieves approximately 90% efficiency withover 800 mW of output power at 1010 kHz. The total die areaincluding pads is 2 mm2. Compatibility with MRI was validatedwith B1 imaging of a phantom and the amplifier circuit.

Index Terms—Biomedical electronics, Class DE amplifier, Ul-trasonic transducer, HIFU, Magnetic resonance imaging

I. INTRODUCTION

H IGH intensity focused ultrasound (HIFU), is a non-invasive surgical technique that thermally ablates tissue

in human organs without the need of incision. Tissue ablationis achieved by focusing acoustic energy that translates into heatenergy delivered to the focal zone of the ultrasound transducer[1] . HIFU operation can be guided by Magnetic ResonanceImaging (MRI) since this imaging modality provides highcontrast volumetric information and it is capable of perform-ing real-time monitoring of thermal effects [2], [3]. Thesedevelopments often require the use of multi-element ultrasonictransducers. This allows controlling the location where theenergy is focused by electronically driving each element ata different phase. The advantage of this approach is thatdifferent locations can be treated without physically movingthe array. Using multiple independent elements increase thecomplexity of the connections and driving electronics requiredto pilot HIFU devices. There is considerable interest both atthe research and commercial levels for developing new andimproved electronic systems for HIFU that can drive multi-element devices with 1000 or more elements at an affordablecost. By providing a driving system that can pilot a largenumber of elements with enough power to achieve therapeuticlevels, we could achieve the necessary degree of freedom toconcentrate the HIFU energy where it is needed. Furthermore,this system should allow piloting devices that are under MRIguidance, providing thermal control for the therapy.

C. Christoffersen, S. Pichardo and L. Curiel are with the Depart-ment of Electrical Engineering, Lakehead University, Canada. e-mail:c.christoffersen@ieee.org, spichard@lakeheadu.ca, lcuriel@lakeheadu.ca.

W. Wong and G. Togtema were with Lakehead University. e-mail: wl-wong1@lakeheadu.ca, gtogtema@lakeheadu.ca

This work reports progress towards that goal. We proposea MRI-compatible, integrated CMOS class DE amplifier thatcan directly drive a piezoelectric ultrasound transducer withhigh efficiency. The amplifier is intended to be mounted insidethe transducer enclosure. High efficiency translates in lowheat dissipation at the amplifier and thus simplified thermalmanagement. The removal of the output matching networkresults in a more compact design and helps to overcome oneof the challenges of developing an MRI-compatible device, i.e.to eliminate the use of magnetic components such as inductors.The work presented here expands previous work by the authors[4] in two ways: (1) a methodology to determine optimumexcitation parameters for a given transducer is presented and(2) the amplifier has been fabricated and experimentally tested.

Most high power drivers for piezoelectric ultrasound trans-ducers require external matching networks or external in-ductors that would interfere with the MRI-guidance system.In current designs these matching networks are located sev-eral meters away outside the MRI chamber or are near thetransducer but require bulky air-core inductors. This increasesthe size and installation cost of the system. Hall and Cain[5] proposed a low-cost high-efficiency amplifier for drivingtransducer arrays; however, the proposed design requires anLC circuit with high-Q inductors. Compact high-Q inductorsof suitable values require ferrite cores and are incompatiblewith the MRI environment. If these LC filters are omitted, theamplifier efficiency degrades and the square wave excitationcauses the transducer to produce unwanted sidelobes in theacoustic power field [6]. These sidelobes will eventually distortthe shape of the focal zone and the precision of the focusingpoint. Tang and Clement [6] evaluated the performance ofthe harmonic cancellation technique for a therapeutic ultra-sound transducer in HIFU application. However, the proposedamplifier requires a transformer that cannot be integratedon-chip. Lewis and Olbricht [7] developed a high-efficiencyamplifier for a high intensity ultrasound system applicationwithout using an external matching circuit, but exciting anultrasound transducer with a square wave is not suitable forHIFU application and the design is not small enough for acompact solution. Ang et al. [8] have fabricated an integratedamplifier chip for ultrasound dental tissue healing. Althoughit has a power efficiency of 70% and an output power of0.58W, it requires an external LC matching network. Recently,Bozkurt [9] proposed an 8-channel IC driver for an ultrasoundcatheter ablation system. The driver for each channel consistsin a push-pull switch directly connected to a CMUT with aninput capacitance of 20 pF at 10 MHz. That driver does not use

2 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS

inductors and is likely to be compatible with MRI, but powerefficiency and harmonic content are not discussed in thatwork. Several other integrated ultrasonic transducer drivers forsensing and imaging applications have been proposed in theliterature, [10]–[14] are some examples. However these driversare intended for producing sharp pulses instead of a continuoussine wave and are not suitable for HIFU.

The remainder of this paper is organized as follows: apiezoelectric transducer model for a class DE amplifier designis presented in Section II, followed by a proposed designmethodology to determine the optimum parameters of theclass DE amplifier and circuit design overview in Section III.Simulation and experimental results, including magnetic res-onance imaging compatibility are presented and discussed inSection IV.

II. TRANSDUCER MODEL

The transducer used in this work is a piezo-compositecrystal (DL47, DeL Piezo, West Palm Beach, FL) shaped as asection of sphere with a radius of 50 mm, a diameter of 25 mmand a thickness of 2.8 mm (Fig. 1). The transducer power effi-ciency is approximately 80 %. This transducer was measuredusing a vector network analyzer with a calibration procedureto remove the effect of cables and connectors. The crystal

25 mm50 mm

2.8 mm

Fig. 1. Piezoelectric transducer geometry.

has a natural resonant frequency near 1 MHz. A piezoelectricresonator can be represented by the Butterworth Van Dyke(BVD) equivalent circuit and the detailed characterization forpiezoelectric load for this work is discussed in References [4],[20]. For the purpose of amplifier tuning only the part of the

Ls = 78.6 uH

Cs = 340 pFCo = 1.39 nF

Rs = 31.9 Ω

Fig. 2. Piezoelectric transducer simplified equivalent circuit.

equivalent circuit corresponding to the fundamental resonanceis considered, as shown in Fig. 2. The reflection coefficient ofthe model is compared with the measured reflection coefficientin Fig. 3. The Q factor (Q = ωLs/Rs) of the equivalent circuitnear 1 MHz is approximately 15. It is important to note that thedriver has to be designed to work with that equivalent circuitwith no external inductors. This rules out class E amplifiers. Aregular class D amplifier would be inefficient because switcheswould have to turn on and off with a nonzero voltage appliedto its terminals resulting in a waste of power. However it is

Model

Measured

Fig. 3. Smith Chart with measured reflection coefficient and simplified modelreflection coefficient.

possible to prevent this and achieve high efficiency by drivingthe amplifier in class DE mode.

III. DESIGN METHODOLOGY

Fig. 4 shows a simplified schematic diagram of a class Damplifier operated in class DE mode. The parallel capacitor

Cp = C0 + CSW + Cext ,

includes the transducer parallel capacitor (C0), the parasiticcapacitance of the switches (CSW ) and any additional externalcapacitance (Cext). The duty cycle (D) is defined as follows:

D =tonT

,

where ton is the conduction time and T is the period ofthe excitation. The switches are operated with a duty cyclebetween 0 and 0.5, usually close to 0.25. Fig. 5 shows thewaveforms in class DE operation. The main feature of this

S1

S2

Cp

Is1

Is2

Ic

VoVcc

Vcc

Ls

Rs

Cs

Ir

Fig. 4. Simplified schematic of a class DE amplifier.

operation mode is that losses in switches are minimized sinceat the time one switch closes, the voltage across the switchand its derivative are zero. This condition is often referred aszero voltage switching (ZVS) and zero derivative switching(ZDS). In order for this to happen, Cp must provide the loadcurrent while charging to a peak value equal to ±Vcc duringthe times that both S1 and S2 are open.

CHRISTOFFERSEN et al.: CLASS-DE ULTRASOUND TRANSDUCER DRIVER 3

on

on

S2

S1

Vcc

−Vcc

0

0

Ir

ton

T/2 T0

ton

φ/ω

Fig. 5. Ideal waveforms in class DE amplifier.

A. Optimum frequency and duty cycle

Since the Q factor of the resonant branch is high, the resistorcurrent (Ir) is almost sinusoidal and the following analysis isvalid. The switches are assumed to have zero resistance. Thereactance of the resonant branch at the frequency of operation(ω) is defined as:

XS = ωLS −1

ωCS. (1)

The condition for class DE operation (ZVS and ZDS) is thatthe impedance of the series branch (RS + jXS) satisfies thefollowing equations [17]:

RS =1− cos(2φ)

2πωCp(2)

XS =2φ− sin(2φ)

2πωCp(3)

where φ is an angle that depends on the duty cycle (see Fig 5):

φ = π(1− 2D) .

Equations (2) and (3) would normally be used to find thevalue of the external parallel capacitor and to design animpedance matching network for the load that provides therequired impedance at the frequency of operation [17]. For theproblem considered in this work, however, the load is fixed andthe optimum frequency of operation and duty cycle must bedetermined. The following procedure is proposed here: solvefor ω in Eq. (2):

ωr =1− cos(2φ)

2πCpRS, (4)

substitute Eq. (1) in Eq. (3) and solve for ω:

ωx =

√2φ− sin(2φ)

2πCPLS+

1

CSLS. (5)

Class DE switching occurs when ωr = ωx for a given valueof D. By plotting the corresponding frequencies as a functionof D, the optimum frequencies and duty cycles are found as

shown in Fig. 6. In that figure, f(RS) and f(XS) are thefrequencies corresponding to ωr and ωx, respectively. In thiscalculation CSW was assumed to be 60 pF and Cext was setto zero. From this graph we conclude that the transducer can

1000

1010

1020

1030

1040

1050

1060

1070

1080

0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3

Fre

qu

en

cy (

kH

z)

Duty cycle (D)

f(Rs)f(Xs)

Class DE

frequency

range

Fig. 6. Frequency range and duty cycle for class DE operation.

be driven in optimum class DE mode only at two frequencies:f1 = 1010 kHz and f2 = 1045 kHz with D1 = 0.295 andD2 = 0.215, respectively. If Cext is increased, f1 increasesand f2 decreases until they meet. The maximum Cext thatallows optimum operation with this transducer is 100 pF. Inthat case, there is a single optimum point at f = 1024 kHzwith D = 0.255.

Since the transducer load is not exactly equal to the RLCcircuit used for design, in practice the amplifier will operateslightly outside of the optimum condition. It has been shown[18] that the efficiency is not very sensitive to deviations infrequency and duty cycle. Sensitivity with respect to Cext

is also low [4]: when this transducer is driven at 1 MHzwith Cext up to 1 nF, the efficiency remains greater than79 % with any value of D between 0.25 and 0.35 (theseresults were obtained using a different but conceptually similarchip design). This property is important because the trans-ducer impedance has small variations due to changes in thesurrounding acoustic environment and temperature. In theproposed application acoustic environment and temperaturedo not significantly change and thus a fixed tuning to typicalconditions is acceptable.

For maximum load power given a constant supply voltage,the operating frequency must be closest to the series resonancefrequency:

fs =1

2π√LSCS

= 973kHz .

Since in class DE mode the operating frequency must begreater than the series resonance frequency of the transducer(i,e., XS(fS) > 0) [16] it follows that the operating frequencyshould be set to the lowest optimum value, f1 = 1010 kHz.

B. Integrated driver design

The driver was implemented using the AMS AG H35CMOS process. Fig. 7 shows a simplified schematic dia-gram of the proposed integrated amplifier. The output stageimplements a Class DE amplifier. Only control logic, gate

4 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS

drivers and switches are integrated: the output network hasbeen replaced by a piezoelectric ultrasound transducer. Thechip substrate is connected to the negative supply (−Vcc). A

Driver

Gate

Gate

Driver

10V

−10V

Logic

Combinational

−5V

−5V 10V

−10V

Enable

p_in

n_in

−Vcc

+Vcc

Vlogic

Vout

Integrated Driver

Piezoelectric

M1

M2

Transducer

Yn

Yp

Fig. 7. Simplified diagram of proposed integrated driver.

micrograph of the chip is shown in Fig. 8. Several pads havebeen used for the high-voltage supplies and the output pinto reduce the current density. The switching transistors, M1

M1

M2 −Vcc

+Vcc

Vout

Logic

andgate

drivers

2 mm

1 mm

Fig. 8. Micrograph of the chip.

and M2 are implemented using high voltage MOS transistors.They are sized to provide the same on-resistance and thisrequires a wider PMOS transistor. This resistance should beas low as possible, but there is a trade-off between chiparea, drain capacitance and on-resistance. For an on-resistanceapproximately equal to 2.3 Ω, M1 and M2 are designedaccording to Table I and they use most of the chip area. Thecombined drain capacitance is approximately 35 pF.

TABLE ISWITCH TRANSISTOR PARAMETERS.

M1 M2Transistor finger W/L (µm/µm) 50/1.4 50/1Number of parallel fingers 360 140

Two static level shifters [19] implement the gate drivers.They convert a 5 V logic signal to the ±10 V required forthe amplifier stage. Another functionality of the gate driversis to control the rise and fall time of the gate driving signalsthat feed the M1 and M2 switches. The drivers are designedto produce approximately the same rise and fall times inboth switches. Schematic and design considerations for thelevel shifters are discussed in [4], [20]. The maximum supplyvoltage in this chip is currently limited to 20 V (±10 V) dueto these shifters. With the same fabrication technology, thislimit could be raised to 50 V using a different shifter design.

The combinational logic block provides the functions ofpower stage enabling, input buffering and protection fromfaulty input combinations. It is located prior to the gate driversof the amplifier. It accepts a standard 5 V power supply,consisting of three inputs and two outputs. Table II summarizesthe purpose of each input/output. The Enable pin is responsible

TABLE IICOMBINATIONAL LOGIC INPUTS AND OUTPUTS.

Pin I or O DescriptionEnable I Enables or disables the complete chip.p in I Logic input to drive M1n in I Logic input to drive M2Yp O Signal for M1 gate driverYn O Signal for M2 gate driver

for the on-off function of the power stage. When the Enableinput is low, both power transistors (M1 and M2) are biasedin the cut off mode. When Enable is high, outputs will followthe respective inputs, except when a faulty input (p in , n in)= (0,1) is identified. This input would turn on both powertransistors at the same time and cause a short circuit.

The same driver circuit could be used with different trans-ducers as this chip is capable of operating in a wide frequencyrange up to several MHz with any D < 0.5. Tuning isperformed by adjusting the operating frequency and duty cyclefor optimum efficiency for a given transducer as outlined inSection III-A.

IV. RESULTS AND DISCUSSION

Fig. 9 shows the simulated output voltage of the designedchip driving the equivalent circuit of Fig. 2 as a load under thecalculated optimum conditions with f = 1010 kHz and D =0.295. The waveforms are close to ideal the ZVS and ZDSconditions are (practically) met. Fig. 10 shows the simulated

-10

-5

0

5

10

600 800 1000 1200 1400 1600

Ou

tpu

t vo

lta

ge

(V

)

Time (ns)

-300-200-100

0 100 200 300

600 800 1000 1200 1400 1600

Cu

rre

nt

(mA

)

Time (ns)

Switch currentLoad resistor current

Fig. 9. Simulated output waveforms at 1010 kHz with D = 0.295 usingthe equivalent circuit of Fig. 2 as a load.

waveforms using an accurate transducer model. The transducerwas modelled by fitting a high-order rational transfer functionto the measured frequency domain reflection coefficient. Itcan be observed that the amplifier is now operating outside

CHRISTOFFERSEN et al.: CLASS-DE ULTRASOUND TRANSDUCER DRIVER 5

-10

-5

0

5

10

600 800 1000 1200 1400 1600

Ou

tpu

t vo

lta

ge

(V

)

Time (ns)

-300-200-100

0 100 200 300

600 800 1000 1200 1400 1600Ou

tpu

t cu

rre

nt

(mA

)

Time (ns)

Fig. 10. Simulated waveforms at 1010 kHz with D = 0.295 using anaccurate transducer model.

(but close) to the optimum condition. A duty cycle sweepwas performed to analyze potential for improvement. Thesimulated efficiency and output power as functions of the dutycycle are summarized in Fig. 11. As expected [4], [18], an

80

85

90

95

100

0.25 0.26 0.27 0.28 0.29 0.3 0.31

Eff

icie

ncy (

%)

820

840

860

880

0.25 0.26 0.27 0.28 0.29 0.3 0.31

Ou

tpu

t p

ow

er

(mW

)

Duty cycle

Fig. 11. Simulated efficiency and output power at 1010 kHz versus D.

increase in duty cycle results in a small increase in outputpower. The efficiency is almost constant.

The proposed integrated driver is intended to be attachedat the back of a piezoelectric ultrasound transducer. For thereported measurements, as the transducer must be tested underwater, a short section of coaxial cable was used to keepthe driver outside of the water container and accessible formeasurements as shown in Fig. 12. The output power wasdetermined by averaging the product of the measured loadvoltage and current. A low resistance was connected in serieswith the transducer (R1) to determine the load current.Figures 13 and 14 compare the simulated and experimentaloutput current for D = 0.290. The simulated circuit wasmodified to account for the conditions of the experimentalsetup with the introduction of a series resistor (0.77 Ω),additional capacitances to account for the oscilloscope probes

Water container

Transducer

R1

Absorber

Resistor to

measure

load current

VoutDriver

to driver

to resistor

Coaxial cable

Fig. 12. Experimental setup diagram. R1 = 0.77 Ω is connected to theouter conductor (see inset) of the coaxial cable in series with the load and isused to determine the load current.

-10

-5

0

5

10

-600 -400 -200 0 200 400 600 800

Ou

tpu

t vo

lta

ge

(V

)

Time (ns)

Meas.Sim.

Fig. 13. Comparison of experimental and simulated output voltage at1010 kHz with D = 0.290.

(20 pF in parallel with the driver and in parallel with R1) anda transmission line to model the coaxial cable (Z0 = 50 Ω,length= 190 mm, normalized propagation velocity= 0.674).The voltage waveforms agree almost perfectly but the exper-imental current waveform presents significantly more ringingthan the simulated one. This discrepancy however has a smalleffect in the simulated prediction for efficiency and outputpower. As shown in Fig. 15, the simulated and experimentalefficiency and output power versus duty cycle agree quitewell. The output power level is somewhat lower comparedto Fig. 11 due to the introduction of R1. For the efficiencycalculation only the power delivered by the ±10 V sourceswas considered. Both simulated and experimental results agreeand the efficiency always remains high. These results suggestthat a fine adjustment of the duty cycle of the gate-drivingpulses may not be required for efficient operation.

The effect of the operation frequency is investigated inFig. 16. The measured efficiency and output power withconstant D = 0.25 are plotted as a function of frequency. Asthe measurements for this sweep were taken on a different daythat for the duty cycle sweep, differences in water temperature

6 IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS

-300

-200

-100

0

100

200

300

-600 -400 -200 0 200 400 600 800

Ou

tpu

t cu

rre

nt

(mA

)

Time (ns)

Meas.Sim.

Fig. 14. Comparison of experimental and simulated output current at1010 kHz with D = 0.290.

85

90

95

100

0.25 0.26 0.27 0.28 0.29 0.3

Eff

icie

ncy (

%)

Duty cycle

Meas.Sim.

810

820

830

840

850

860

0.25 0.26 0.27 0.28 0.29 0.3

Ou

tpu

t p

ow

er

(mW

)

Duty cycle

Meas.Sim.

Fig. 15. Comparison between simulated and experimental results forefficiency and output power at 1010 kHz versus D.

and transducer position in the water tank produce slightlydifferent values for f = 1010 kHz. Nevertheless the valuesare close and the results agree with the expectations set by thetheory. The output power decreases as the operating frequencyis increased away from fS . These results confirm the lowsensitivity of efficiency with respect to frequency and dutycycle.

Experimental and simulated output voltage third harmoniclevel versus duty cycle and frequency is shown in Fig. 17.If the transducer is operated at 1010 kHz, the expected thirdharmonic level is −16.4 db. The third harmonic will be furtherattenuated approximately 9.6 dB [20] by the transducer fora total attenuation of 26 dB in the acoustic wave. Whetherthis third harmonic level will produce or not unacceptablesidelobes in the acoustic power field generated by a transducerarray has not yet been determined. A small improvement inthird harmonic reduction can be achieved by increasing theoperating frequency at the expense of reduced output power(Fig. 16). Another alternative to reduce the third harmonic isto connect an external capacitor (Cext) and operating at lower

80

85

90

95

100

1000 1010 1020 1030 1040 1050 1060

Eff

icie

ncy (

%)

Frequency (kHz)

Meas.Sim.

200

400

600

800

1000

1200

1000 1010 1020 1030 1040 1050 1060

Ou

tpu

t p

ow

er

(mW

)

Frequency (kHz)

Meas.Sim.

Fig. 16. Experimental and simulated results for efficiency and output powerversus frequency with D = 0.25.

-25

-20

-15

-10

1000 1010 1020 1030 1040 1050

3rd

. H

arm

. (d

B)

Frequency (kHz)

Meas.Sim.

-25

-20

-15

-10

0.25 0.26 0.27 0.28 0.29 0.3

3rd

. H

arm

. (d

B)

Duty cycle

Meas.Sim.

Fig. 17. Experimental and simulated results for the output voltage thirdharmonic level versus duty cycle with f = 1010 kHz and versus frequencywith D = 0.25.

efficiency farther away from optimum conditions as shown in[4]. Another more promising alternative to be investigated isto excite some of the transducers in an array with the thirdharmonic in order to cancel any unwanted sidelobes.

A. Magnetic resonance imaging compatibility

As the driver is just a silicon die without any magneticcomponents, it is not expected to cause any artifacts in theMR image. To verify this, image quality was assessed inthe presence of the chip. A standard small phantom wasimaged using a SENSE Wrist coil 8 elements coil1 in an 3TAchieva scanner. The chip was located immediately on topof the phantom and gradient echo images with and withoutthe chip were subtracted (Gradient Echo, TE/TR= 7.80/17,FOV= 10 cm, Slice= 5 mm, ETL= 1, 1 NEX). A B1 mapwas also obtained with and without the chip to detect potentialchanges in homogeneity caused by the chip (Gradient Echo,

1Philips, The Netherlands

CHRISTOFFERSEN et al.: CLASS-DE ULTRASOUND TRANSDUCER DRIVER 7

TE/TR= 7.80/531, FOV= 10 cm, Slice= 5 mm, ETL= 1,1 NEX, dual flip angle).

The presence of the chip did not significantly alter thequality of the image as observed by an average SNR of49.5± 2.3 dB without the chip and 47± 1 dB with the chip.An MR image of a phantom where the chip was located atthe top is shown in Fig. 18. The image remains similar with(left) and without (right) chip and the subtracted and B1 mapimages show no visible impact of the chip.

With Die Without Die Subtracted B1 map with Die

Fig. 18. Example MR images of the phantom with and without the chip andthe corresponding subtracted and B1 map image with the chip.

B. Discussion

The proposed driver presents some shortcomings comparedto alternative designs using external matching networks. Theseshortcomings and some possible workarounds are discussed inthe next paragraphs.

Limited voltage supply range: this is not an intrinsic prob-lem of class DE operation but just a limitation of this particularimplementation. Even with this limitation the proposed driverwould be adequate for transducer array with several hundredsof elements, as the power contribution of each individualtransducer is small.

Operating frequency range: for efficient operation the fre-quency range is limited to a relatively small interval abovethe transducer’s series resonance frequency. This range isenough to handle small changes in transducer impedance dueto fabrication tolerances and/or relatively small changes inenvironmental conditions. If large environmental changes areexpected, the frequency and duty cycle should be adapted foreach condition.

Transducer compatibility: if C0 in the transducer equivalentcircuit is too high then it is not possible to achieve optimumclass DE operation. Ideally transducers should be designedto admit at least one optimum operation point as describedin Section III-A. The driver may still be usable even if nooptimum operation point exists. In that case a numericaloptimization procedure could be performed to tune frequencyand duty cycle.

Output power control: output power can be controlled byvarying the supply voltage, but this is a disadvantage comparedto a standard class D amplifier with a load filter [21] thatadmits power control by varying the duty cycle.

Harmonic content: it is difficult to further reduce the thirdharmonic level present at the output. Some alternatives havebeen discussed earlier in this section but this is an area forimprovement.

Several steps remain to be performed in order to producea practical compact multi-element HIFU driver. Although itwould be possible to drive a transducer array with this chip,

the number of input signals with specific duty cycles wouldrequire too much external processing. More logic will beadded in a future revision to simplify this. Also, a feedbackcircuit may be required to measure the power being sentto the transducer in real time to adapt the frequency/dutycycle according to changes in transducer impedance with theenvironment conditions.

V. CONCLUSION

This work has demonstrated the feasibility of directly driv-ing a piezoelectric transducer for HIFU applications using aclass DE amplifier. The elimination of the external matchingnetwork between the amplifier and the piezoelectric crystalresults in a more compact design and MRI-compatibility.The proposed driver could be installed inside the transducerenclosure. High efficiency translates in low heat dissipationat the amplifier and thus simplified thermal management.The driver has a measured output power of 830 mW at1010 kHz with an efficiency over 90 %. The output voltagethird harmonic level is −16.4 dB below the fundamental. Thetotal chip area, including pads is 2 mm2.

The driver has been tested with one particular transducer,but it can also be used with other transducers as long as theconditions presented in Section III-A are satisfied. Only theamplifier excitation needs to be modified. Another conclusionfrom the results presented here is that a very fine controlof the duty cycle is not critical for efficiency nor harmonicperformance. Efficiency is always high if duty cycle toleranceis within ±0.025 for the tested case. On the other hand as theduty cycle can not be varied in a wide range, output powercontrol of an individual amplifier would require a variablesupply voltage.

ACKNOWLEDGMENT

The authors would like to thank the National ResearchCouncil of Canada (NSERC) and CMC Microsystems forsupporting this work.

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Carlos Christoffersen received the Electronic En-gineer degree at the National University of Rosario,Argentina in 1993. From 1993 to 1995 he wasresearch fellow of the National Research Council ofArgentina (CONICET). He received an M.S. degreeand a Ph.D. degree in electrical engineering in 1998and 2000, respectively, from North Carolina StateUniversity (NCSU). From 1996 to 2001 he waswith the Department of Electrical and ComputerEngineering at NCSU. He is currently an AssociateProfessor in the Department of Electrical Engineer-

ing and the Department of Software Engineering at Lakehead University,Thunder Bay, Canada.

Dr. Christoffersen’s current research interests include development of HIFUtherapeutic devices and modelling, simulation and design of analog, RF andmicrowave circuits in general.

Wai Wong received the MSc degree in Electricaland Computer Engineering in 2013 specializing inanalog circuit design and CMOS layout, and theBEng degree in Electrical Engineering in 2011 fromLakehead University, Thunder Bay, Ontario. He wasappointed as a Research Assistant in the same insti-tute after graduation.

Mr. Wong’s current interests are in the areas ofanalog circuit design, MEMS and communications.

Samuel Pichardo received the B.E. degree in elec-tronic systems from the Monterrey Institute of Tech-nology and Higher Education, Mexico city, Mex-ico, in 1995, and the M.Sc. and Ph.D. degrees inImaging and Systems from the National AppliedSciences Institute, Lyon, France, in 2001 and 2005,respectively. In 2008, he joined the Thunder BayRegional Research Institute, Thunder Bay, Canada,as Junior Scientist, then as a full scientist in 2014.He joined the department of Electrical Engineeringat Lakehead University, Thunder Bay, Canada, as

Adjunct Professor in 2008. He is also Adjunct Professor in the departmentof Physics of Lakehead Univeristy since 2010. His main areas of researchare Magnetic Resonance Imaging-guided High Intensity Focused Ultrasound(MR-HIFU), characterization of ultrasound properties of bone tissue, bio-effects of ultrasound, software tools for real time control of MR-HIFU, newdevices and driving systems for ultrasound and interventional MRI.

G. Togtema was born in Brampton, ON. Canadain 1985. He received his bachelors degree in theEngineering Sciences program at the University ofToronto in 2008 and his Masters of Science inEngineering at Lakehead University in 2013.

He worked in the medical instrumentation andcomputer hardware industry for three years spe-cializing in radiofrequency circuit design and elec-tromagnetic applications. From 2011 to 2013, heresearched the applications of low temperature thinfilm growth methods on the performance of LEDs

and the manufacturing of device subcomponents. He is now a product designerfor energy harvesting devices.

Laura Curiel was born in Mexico City and receiveda degree in Electronic Systems Engineering fromthe Technologic Institute of Superior Studies ofMonterrey, Mexico in 1995. She holds a PhD inImaging and Systems from the National Instituteof Applied Sciences in Lyon, France and a Mastersdegree from the University of Lyon. She is currentlyan Adjunct Professor at Lakehead University and ascientist at the Thunder Bay Regional Research In-stitute. Her research interests center on developmentof HIFU therapeutic devices and novel guidance and

interactions of high intensity ultrasound with tissues.