- Email: [email protected]
High power resonant tracking amplifier using admittance locking
Ultrasonics 39 (2001) 257±261
www.elsevier.nl/locate/ultras
High power resonant tracking ampli®er using admittance locking B. Mortimer a,*, T. du Bruyn a, J. Davies b, J. Tapson b a
Department of Electrical Engineering, Centre for Instrumentation Research, Cape Technikon, P.O. Box 652, Cape Town 8000, South Africa b Department of Electrical and Electronic Engineering, University of Cape Town, UCT Private Bag, Rondebosch 7701, South Africa Received 30 November 2000; accepted 5 January 2001
Abstract A high power resonance tracking ultrasonic ampli®er is described. The ampli®er is a class D type inverter, con®gured as a halfbridge in which the output MOSFETs are driven into saturation when on. The resonance tracking system makes use of a new method of frequency locking; admittance locking is used to track the optimum power conversion frequency for the transducer. This new arrangement oers some advantages over phase locking and motional feedback methods. The system is capable of delivering up to 3 kW at up to 25 kHz in resonance tracking operation. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 43.35.Z Keywords: High power; Ultrasonic; Transducers; Control; Resonance locking
1. Introduction High power ultrasound has many industrial applications including cleaning, atomization, degassing, homogenization, sterilization, washing and welding. Most of these industrial applications simply require the conversion of electrical power into ultrasonic power. Usually, no modulation is necessary, which means that driving circuits based on conventional linear ampli®ers (classes AB or B) are unnecessarily complex and are often not required. Transducers used in high power applications in liquids are usually either sandwich (tonpilz) or horn concentrators. In air, the stepped plate transducer has shown considerable promise for high power applications [1]. All of these transducers are likely to have very high resonance quality factors (high Q), which implies that the useful bandwidth will be very narrow. In practice, the characteristics of the mechanical components in the transducer will vary under changing operating conditions (especially in power applications); so the resonant frequency will change. Driving high-Q transducers at frequencies other than the transducer resonant frequency results in very poor power conversion ecien-
*
Corresponding author. Fax: +27-21-460-3705. E-mail address: [email protected] (B. Mortimer).
cies. Coupling transducers to liquid and solid media will result in a reduction in Q. For high eciency, an automatic control system is required to keep the ampli®er at the optimum frequency. There are a number of ways of doing this [2]. One method is to use self-resonance, in which the transducer forms the frequency-determining part of a power oscillator circuit. Many dierent types of oscillator circuit, including most of those used for crystal oscillators, can be used. This method can be unstable if the transducer has multiple resonant modes, which is invariably the case when the transducer is a composite structure is coupled to a resonant load. Alternatively, the current and voltage supplied to the transducer can be measured, and their phases compared using a phase locked loop [3,4]. A voltage controlled oscillator (VCO) can then be adjusted by the phase locked loop, and its output used to drive a power ampli®er and the transducer [2]. This technique requires a transducer reactance compensation element in the driving circuit and has been widely used. A further method has been to use motional feedback, in which the motion of the front face of the transducer is measured and used as a tuning variable; however, this method has the weakness that the measurement does not inherently indicate in which direction to alter the frequency, which makes automation dicult. This paper describes the design of a low cost class D type ampli®er, in which the driving frequency is optimized by locking the admittance of the transducer. This
0041-624X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 1 - 6 2 4 X ( 0 1 ) 0 0 0 6 0 - 9
258
B. Mortimer et al. / Ultrasonics 39 (2001) 257±261
novel technique measures only the transducer current. Results are presented for the case of a horn transducer. 2. Dynamic locking: transducer electrical behavior A piezoelectric ultrasonic transmitterÕs electrical behavior can be approximated by the equivalent circuit shown in Fig. 1 [5]. The transducer has in essence three components; the electrical parameters consisting mainly of a capacitance Ce , the mechanical transducer parameters consisting of a mechanical compliance Cm , a mass component Lm , a mechanical loss resistance Rm and ®nally a load component, which can be represented as a transformer-coupled resistance Rl . Normally the load characteristics are referred to the mechanical side and combined with these elements. The transformer represents the acoustic coupling between the transmitter and the transmission medium. The resistive part of the load represents the sink for the real power transferred into the medium. It is instructive to compare this with a real transducer, particularly when the load is varying. The admittance plots for a horn transducer measured in air and measured in water are shown in Fig. 2. From these plots, the mechanical resonant frequency is measured to be 18.896 kHz for air and 18.691 kHz for a water load. Both measurements are dependent on a number of other variables, e.g. the real acoustic impedance of the volumes of water and air (standing waves set up in the water volume will be a particular problem if the transmitter is not radiating into an in®nite space). The behavior of the transducer will not be consistent at dierent power levels either [6]. The diculty with driving a load with this sort of equivalent circuit, particularly from an electrical point of view, is ®rstly that the impedance at resonance is very low (33 X in water), and secondly that the load and mechanical components can change signi®cantly during operation. This is illustrated in
Fig. 1. This shows the typical equivalent circuit of the ultrasonic transmitter. The capacitor Ce represents the electrical capacitance, which is a function of the physical structure of the piezoelectric elements and their electrodes. The components Rm , Cm and Lm represent the mechanical loss, compliance and mass respectively. The acoustic load is represented by the resistance Rl , which is coupled to the transmitter by the transformer A which represents the acoustic coupling between transmitter and transmission or load medium. If the electrical capacitance is to be tuned out (in order to get an approximation to a simple RLC circuit), an inductor Le (see Eq. (1)) must be added in parallel to Ce .
Fig. 2. Admittance plot of the horn transducer used in this study, when transmitting into air and water. This graph shows only the series (mechanical) resonance; the parallel resonance is not shown. It can be seen that if the transmitter were driven at the average of the series resonant frequencies for water and air (say 18.794 kHz), the output power would be considerably below the optimum level.
Fig. 3 where the relative vibrational peak amplitude has been plotted vs. the normalized driving frequency. In this case the transducer was driven at medium power (80 V supply voltage) with an air load. A particular problem in which varying loads may be applied to the transmitter is in the insoni®cation of multi-phase ¯ows. In many atomization and homogenization processes, the transmission medium is inherently multi-phase (for example, a water/air/foam) and there is no likelihood of ®nding a satisfactory ®xed frequency at which to drive the transducer. Since the point of maximum power transfer to the load occurs at the mechanical resonant frequency, the driving current and voltage phases can be used to lock the transducer at an optimum driving frequency. It is clear from Fig. 1, however, that a compensating inductor is required to match the transducer electri-
Fig. 3. This diagram shows the measured amplitude of the front face excursion of the horn transducer used in this study, relative to the resonant frequency measured at low power. The frequency has been normalized relative to the low-power series resonant frequency. The excursion was measured using a capacitive displacement probe [4]. This illustrates how the resonant frequency can vary from a measurement made at low power, when the transducer is driven at higher powers.
B. Mortimer et al. / Ultrasonics 39 (2001) 257±261
cal capacitance Ce . This compensation inductor can be in series or parallel and in the latter case is chosen from: Le
1 2
2pfs Ce
1
where fs is the resonant frequency. This matching is only approximate, as we have shown that fs varies with load and can be dierent under high power driving conditions (Fig. 3). The value of Le will only be correct for one value of fs ; at other values, its usefulness depends on the overall electrical Q which is usually adequately low for liquid applications. It is straightforward to phase lock the transducer driving current and voltage [2,3]. The fundamental problem concerns the relationship between phase and resonance. If we do not make use of a matching inductor (Le , above) to tune out the resonant capacitance, then the phase of the current will not fall as low as zero anywhere near resonance (it may do so at some higher frequency), and we will have to try and lock to a phase minimum of unknown value. If we add the correct matching inductor, then we should have a phase of zero exactly at resonance, which we can lock onto. However, in practice the matching inductor will only be correct at one resonant frequency, and we are pursuing this problem as a consequence of changing resonant frequencies. A second issue is that the equivalent circuit shown in Fig. 1 is only an approximate model of a real transducer, and in real transducers the phase is not usually zero at resonance, even when Ce has been perfectly tuned out by the addition of Le . This problem is relevant when transducers are coupled to high acoustic resistance loads such solid welding, where the overall electrical Q is increased and the compensation element bandwidth reduced. Further, in high power applications, the compensation inductor will draw a relatively large reactive current which will produce heating. The above reservations notwithstanding, phase locking has been used by ourselves and other workers in the past, as it seemed to oer some improvement over openloop driving of the transmitter. In the remainder of this paper, we describe a new system based on admittance locking, which oers the capability to track resonance without the use of a compensation element. In addition, it allows the use of complex non-sinusoidal driving waveforms, which may be more eective in some applications where the multiple resonant modes of certain transducers can be exploited [7]. 3. Admittance locking The admittance locking method is based on the principle that the maximum power transfer from the
259
transmitter to the medium occurs when the transmitter is at maximum admittance (since that is when the maximum input electrical power is achieved). This assumption is reasonable as long as it can be assumed that the acoustic coupling between transmitter and medium is not frequency dependent within the bandwidth of the transmitter. We therefore require a circuit which will track the maximum input admittance of the transmitter. The input admittance is easily calculated as the quotient of current and voltage. In order to track its maximum, we require an automatic hill-climbing system. The combination of these two requirements is met by the system shown in Fig. 4. The system uses an rms-DC converter to extract the average magnitude of the transducer current. A small ``dither'' 50% duty cycle modulation is added to the transducer drive frequency. This dither causes a small modulation on the transducer current due to the fact that the transducer shifts its operating frequency slightly up and down from its average value. The magnitude of the transducer current detected by the rms-DC converter will include a small signal due to the dither modulation. The dither oscillator is used to synchronously detect this small signal (or demodulate it). The output of the demodulator represents the slope of the admittance curve dG=df . A PI controller moves the VCO set point to the local admittance maximum. This circuit establishes the direction in which to move the operating frequency by detecting the current level at the extremities of dither frequency excursion (above and below the operating point frequency). The system moves towards
Fig. 4. Block diagram of the admittance locking system used in this work. The transducer is driven through the (class D) power ampli®er, whose frequency is set by the VCO. The current through the transducer is measured by means of a series resistor. A DC voltage equivalent to the rms value of the current is obtained by means of an rms-DC converter. This voltage is multiplied with a dither signal, which is also used to dither the input to the VCO; the multiplier output is proportional to dG=df , where G is the admittance and f is the frequency. The proportional±integral (PI) loop controller uses the gradient information to adjust the input level of the VCO, thereby tracking the peak admittance of the transducer.
260
B. Mortimer et al. / Ultrasonics 39 (2001) 257±261
the operating frequency where the transducer current is maximum, which could be above or below the local set point, until such time as dG=df is zero. This system has the advantage that only the current measurement is used in the locking process. Further, the locking system will establish the optimum operating point for the case of any frequency dependent load; for example, a combination of parallel transducer loads. This is often a problem in ultrasonic cleaning systems which cannot be optimally solved using phase locking techniques.
4. The class D power ampli®er Transistor ampli®ers are generally de®ned in terms of a class, which describes the arrangement of the output drive transistors. Class D is a type of ampli®er in which there are two output transistors in a bridge con®guration. These transistors are always driven to be completely on or completely o, which results in a square-wave drive to the load. This is clearly not a linear ampli®cation of the drive signal. It should be noted that the loss of linearity is acceptable given that the purpose of the system is usually to deliver the maximum ultrasonic power into the load. In practice a matching or wave shaping circuit is used or it is assumed that the load itself will act as a ®lter to shape the input wave. In the current work, the ultrasonic transmitter is used without reactance compensation and acts as a complex resonant ®lter. A signi®cant aspect of this design is that it is the ®rst resonance tracking system known to us, in which the transmitter can be driven by any periodic signal (rather than a sine wave). The use of an rms-DC converter in the measurement loop means that the circuit eectively tracks the frequency at which the current±voltage product for the transmitter is a maximum, regardless of the shape of either signal. This substantially simpli®es the driving stage, given that it need not be linear but must simply meet the constraints of eciency and practicality that are imposed by a particular implementation. The ampli®er used in this work was based on the SA16 PWM integrated circuit ampli®er supplied by Apex Microtechnology Corp. [8]. This circuit implements a 5 kW half-bridge with overload current limiting and thermal shutdown control, and was designed with the driving of piezoelectronic elements in mind. A block diagram of the system is shown in Fig. 5. In practice, it has been found that electrical layout is critical to keep noise levels low in the system; given the high currents used, it is easy to create spurious signals which interfere with the operation of the admittance locking system. In our system, the low-voltage measurement and control electronics were entirely isolated from the high-voltage
Fig. 5. This block diagram shows the arrangement of the half-bridge class D ampli®er, and the optical isolation used to isolate the highvoltage system from the measurement and control system. In practice, the high-voltage DC bus was 80 V. The system was able to drive a horn transducer at frequencies up to 25 kHz with no appreciable drop in performance.
driving circuitry by means of linear isolation ampli®ers and digital opto-isolators. 5. Experimental results The purpose of this system is to track the resonant frequency of the transmitter while the load condition varies. An example of this in operation is shown in Fig. 6, in which the transmitter (a horn concentrator) is moved from air to water and back to air again. These represent the extreme cases of the load which this transmitter is likely to experience. As can be seen, the
Fig. 6. This shows the real frequency response of the system as the load on the transducer changes. The transducer is a horn concentrator, the end of which is in air at time zero. The horn is dipped into water after about 1.2 s and removed from water at about 3.6 s. It can be seen that the frequency adjusts smoothly to compensate for the change in load impedance and coupling. The eect of the dither signal can be seen as the apparent ``noisiness'' of the frequency. The dither amplitude and loop bandwidth can be adjusted according to the characteristics of the transducer and load.
B. Mortimer et al. / Ultrasonics 39 (2001) 257±261
circuit automatically detects the change in resonant frequency and adjusts the frequency accordingly. There is a complex relationship between the frequency of the dither signal, the bandwidth of the transmitter and the response of the resonance tracking circuit. The purpose of the dither signal is to establish the value of dG=df automatically. To do this, it has to change the frequency and make a measurement of the changed admittance. The speed with which the frequency can be changed is determined by the transducer bandwidth. The measurement bandwidth is determined by the time constant of the rms-DC converter. The loop ®lter, which controls the speed of response of the resonance tracking, must have a response which suciently slow that the frequency changes caused by the dither signal are not themselves eliminated by the tracking loop (this recursive behavior is possible because the loop will generally track even if the control signal is highly degraded). In the implementation described in this paper, the dither signal was approximately 300 Hz and the control ®lter was a simple integrator (type II controller) with a time constant of 100 ms. The time constant for the rms-DC converter was 500 ls. Readers familiar with the use of phase-locked loops in resonance tracking will recognize that these elements are orders of magnitude slower than would be required for phase measurement with minimal phase error; this is a considerable advantage of the current approach. Any real transmitter will have several admittance peaks in its frequency spectrum, any one of which can be locked on by the admittance locking system. Fortunately, we can usually de®ne a frequency range for the VCO which will contain only the peak of interest. It is then trivial to set up the integrator so that it charges up from zero after a reset, gradually increasing the frequency until an admittance lock is obtained.
261
6. Conclusions We have designed and constructed a high power resonance tracking ultrasonic ampli®er, based on an admittance locking control loop and a class D halfbridge driving stage. The system has been successfully used to drive a typical transducer under changing load conditions. This system has the advantage that it will track the maximum power output for the transducer, regardless of the shape of the periodic input waveform. The system is superior to a phase-locked loop resonance tracking system in that it measures the transducer output power rather than the phase between current and voltage, which eliminates the problems of phase measurement error and non-ideal transducer modeling. The system also has the advantage that the most of the measurement elements do not have to slew at the system frequency, so it can be constructed using low slew-rate components, which are generally cheaper and simpler. The overall system is capable of delivering up to 3 kW of electrical power at frequencies up to 25 kHz, into narrow-bandwidth piezoelectric loads. References [1] J.A. Gallego-Juarez, J. Phys. E: Sci. Instrum. 22 (1989) 804±806. [2] A. Ramos-Fernandez, F. Montoya-Vitini, J.A. Gallego-Juarez, Ultrasonics 23 (1985) 151±156. [3] J. Tapson, Ultrasonics 33 (1995) 441±444. [4] J. Tapson, J.R. Greene, Meas. Sci. Technol. 4 (1994) 337±343. [5] W.P. Mason, Electromechanical Transducers and Wave Filters, 2nd ed., D. van Nostrand Co., New York, 1943. [6] B.J.P Mortimer, A. Green, T. du Bruin, J. Tapson, J. Acoust. Soc. Am. 108 (2000) 2638. [7] S Payne, Ultrasonic Generator Drive Circuit, US Patent 3975650, 1976. [8] Apex Microtechnology Corporation, 5980 North Shannon Road, Tuscon, AZ 85741, USA.
www.elsevier.nl/locate/ultras
High power resonant tracking ampli®er using admittance locking B. Mortimer a,*, T. du Bruyn a, J. Davies b, J. Tapson b a
Department of Electrical Engineering, Centre for Instrumentation Research, Cape Technikon, P.O. Box 652, Cape Town 8000, South Africa b Department of Electrical and Electronic Engineering, University of Cape Town, UCT Private Bag, Rondebosch 7701, South Africa Received 30 November 2000; accepted 5 January 2001
Abstract A high power resonance tracking ultrasonic ampli®er is described. The ampli®er is a class D type inverter, con®gured as a halfbridge in which the output MOSFETs are driven into saturation when on. The resonance tracking system makes use of a new method of frequency locking; admittance locking is used to track the optimum power conversion frequency for the transducer. This new arrangement oers some advantages over phase locking and motional feedback methods. The system is capable of delivering up to 3 kW at up to 25 kHz in resonance tracking operation. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 43.35.Z Keywords: High power; Ultrasonic; Transducers; Control; Resonance locking
1. Introduction High power ultrasound has many industrial applications including cleaning, atomization, degassing, homogenization, sterilization, washing and welding. Most of these industrial applications simply require the conversion of electrical power into ultrasonic power. Usually, no modulation is necessary, which means that driving circuits based on conventional linear ampli®ers (classes AB or B) are unnecessarily complex and are often not required. Transducers used in high power applications in liquids are usually either sandwich (tonpilz) or horn concentrators. In air, the stepped plate transducer has shown considerable promise for high power applications [1]. All of these transducers are likely to have very high resonance quality factors (high Q), which implies that the useful bandwidth will be very narrow. In practice, the characteristics of the mechanical components in the transducer will vary under changing operating conditions (especially in power applications); so the resonant frequency will change. Driving high-Q transducers at frequencies other than the transducer resonant frequency results in very poor power conversion ecien-
*
Corresponding author. Fax: +27-21-460-3705. E-mail address: [email protected] (B. Mortimer).
cies. Coupling transducers to liquid and solid media will result in a reduction in Q. For high eciency, an automatic control system is required to keep the ampli®er at the optimum frequency. There are a number of ways of doing this [2]. One method is to use self-resonance, in which the transducer forms the frequency-determining part of a power oscillator circuit. Many dierent types of oscillator circuit, including most of those used for crystal oscillators, can be used. This method can be unstable if the transducer has multiple resonant modes, which is invariably the case when the transducer is a composite structure is coupled to a resonant load. Alternatively, the current and voltage supplied to the transducer can be measured, and their phases compared using a phase locked loop [3,4]. A voltage controlled oscillator (VCO) can then be adjusted by the phase locked loop, and its output used to drive a power ampli®er and the transducer [2]. This technique requires a transducer reactance compensation element in the driving circuit and has been widely used. A further method has been to use motional feedback, in which the motion of the front face of the transducer is measured and used as a tuning variable; however, this method has the weakness that the measurement does not inherently indicate in which direction to alter the frequency, which makes automation dicult. This paper describes the design of a low cost class D type ampli®er, in which the driving frequency is optimized by locking the admittance of the transducer. This
0041-624X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 1 - 6 2 4 X ( 0 1 ) 0 0 0 6 0 - 9
258
B. Mortimer et al. / Ultrasonics 39 (2001) 257±261
novel technique measures only the transducer current. Results are presented for the case of a horn transducer. 2. Dynamic locking: transducer electrical behavior A piezoelectric ultrasonic transmitterÕs electrical behavior can be approximated by the equivalent circuit shown in Fig. 1 [5]. The transducer has in essence three components; the electrical parameters consisting mainly of a capacitance Ce , the mechanical transducer parameters consisting of a mechanical compliance Cm , a mass component Lm , a mechanical loss resistance Rm and ®nally a load component, which can be represented as a transformer-coupled resistance Rl . Normally the load characteristics are referred to the mechanical side and combined with these elements. The transformer represents the acoustic coupling between the transmitter and the transmission medium. The resistive part of the load represents the sink for the real power transferred into the medium. It is instructive to compare this with a real transducer, particularly when the load is varying. The admittance plots for a horn transducer measured in air and measured in water are shown in Fig. 2. From these plots, the mechanical resonant frequency is measured to be 18.896 kHz for air and 18.691 kHz for a water load. Both measurements are dependent on a number of other variables, e.g. the real acoustic impedance of the volumes of water and air (standing waves set up in the water volume will be a particular problem if the transmitter is not radiating into an in®nite space). The behavior of the transducer will not be consistent at dierent power levels either [6]. The diculty with driving a load with this sort of equivalent circuit, particularly from an electrical point of view, is ®rstly that the impedance at resonance is very low (33 X in water), and secondly that the load and mechanical components can change signi®cantly during operation. This is illustrated in
Fig. 1. This shows the typical equivalent circuit of the ultrasonic transmitter. The capacitor Ce represents the electrical capacitance, which is a function of the physical structure of the piezoelectric elements and their electrodes. The components Rm , Cm and Lm represent the mechanical loss, compliance and mass respectively. The acoustic load is represented by the resistance Rl , which is coupled to the transmitter by the transformer A which represents the acoustic coupling between transmitter and transmission or load medium. If the electrical capacitance is to be tuned out (in order to get an approximation to a simple RLC circuit), an inductor Le (see Eq. (1)) must be added in parallel to Ce .
Fig. 2. Admittance plot of the horn transducer used in this study, when transmitting into air and water. This graph shows only the series (mechanical) resonance; the parallel resonance is not shown. It can be seen that if the transmitter were driven at the average of the series resonant frequencies for water and air (say 18.794 kHz), the output power would be considerably below the optimum level.
Fig. 3 where the relative vibrational peak amplitude has been plotted vs. the normalized driving frequency. In this case the transducer was driven at medium power (80 V supply voltage) with an air load. A particular problem in which varying loads may be applied to the transmitter is in the insoni®cation of multi-phase ¯ows. In many atomization and homogenization processes, the transmission medium is inherently multi-phase (for example, a water/air/foam) and there is no likelihood of ®nding a satisfactory ®xed frequency at which to drive the transducer. Since the point of maximum power transfer to the load occurs at the mechanical resonant frequency, the driving current and voltage phases can be used to lock the transducer at an optimum driving frequency. It is clear from Fig. 1, however, that a compensating inductor is required to match the transducer electri-
Fig. 3. This diagram shows the measured amplitude of the front face excursion of the horn transducer used in this study, relative to the resonant frequency measured at low power. The frequency has been normalized relative to the low-power series resonant frequency. The excursion was measured using a capacitive displacement probe [4]. This illustrates how the resonant frequency can vary from a measurement made at low power, when the transducer is driven at higher powers.
B. Mortimer et al. / Ultrasonics 39 (2001) 257±261
cal capacitance Ce . This compensation inductor can be in series or parallel and in the latter case is chosen from: Le
1 2
2pfs Ce
1
where fs is the resonant frequency. This matching is only approximate, as we have shown that fs varies with load and can be dierent under high power driving conditions (Fig. 3). The value of Le will only be correct for one value of fs ; at other values, its usefulness depends on the overall electrical Q which is usually adequately low for liquid applications. It is straightforward to phase lock the transducer driving current and voltage [2,3]. The fundamental problem concerns the relationship between phase and resonance. If we do not make use of a matching inductor (Le , above) to tune out the resonant capacitance, then the phase of the current will not fall as low as zero anywhere near resonance (it may do so at some higher frequency), and we will have to try and lock to a phase minimum of unknown value. If we add the correct matching inductor, then we should have a phase of zero exactly at resonance, which we can lock onto. However, in practice the matching inductor will only be correct at one resonant frequency, and we are pursuing this problem as a consequence of changing resonant frequencies. A second issue is that the equivalent circuit shown in Fig. 1 is only an approximate model of a real transducer, and in real transducers the phase is not usually zero at resonance, even when Ce has been perfectly tuned out by the addition of Le . This problem is relevant when transducers are coupled to high acoustic resistance loads such solid welding, where the overall electrical Q is increased and the compensation element bandwidth reduced. Further, in high power applications, the compensation inductor will draw a relatively large reactive current which will produce heating. The above reservations notwithstanding, phase locking has been used by ourselves and other workers in the past, as it seemed to oer some improvement over openloop driving of the transmitter. In the remainder of this paper, we describe a new system based on admittance locking, which oers the capability to track resonance without the use of a compensation element. In addition, it allows the use of complex non-sinusoidal driving waveforms, which may be more eective in some applications where the multiple resonant modes of certain transducers can be exploited [7]. 3. Admittance locking The admittance locking method is based on the principle that the maximum power transfer from the
259
transmitter to the medium occurs when the transmitter is at maximum admittance (since that is when the maximum input electrical power is achieved). This assumption is reasonable as long as it can be assumed that the acoustic coupling between transmitter and medium is not frequency dependent within the bandwidth of the transmitter. We therefore require a circuit which will track the maximum input admittance of the transmitter. The input admittance is easily calculated as the quotient of current and voltage. In order to track its maximum, we require an automatic hill-climbing system. The combination of these two requirements is met by the system shown in Fig. 4. The system uses an rms-DC converter to extract the average magnitude of the transducer current. A small ``dither'' 50% duty cycle modulation is added to the transducer drive frequency. This dither causes a small modulation on the transducer current due to the fact that the transducer shifts its operating frequency slightly up and down from its average value. The magnitude of the transducer current detected by the rms-DC converter will include a small signal due to the dither modulation. The dither oscillator is used to synchronously detect this small signal (or demodulate it). The output of the demodulator represents the slope of the admittance curve dG=df . A PI controller moves the VCO set point to the local admittance maximum. This circuit establishes the direction in which to move the operating frequency by detecting the current level at the extremities of dither frequency excursion (above and below the operating point frequency). The system moves towards
Fig. 4. Block diagram of the admittance locking system used in this work. The transducer is driven through the (class D) power ampli®er, whose frequency is set by the VCO. The current through the transducer is measured by means of a series resistor. A DC voltage equivalent to the rms value of the current is obtained by means of an rms-DC converter. This voltage is multiplied with a dither signal, which is also used to dither the input to the VCO; the multiplier output is proportional to dG=df , where G is the admittance and f is the frequency. The proportional±integral (PI) loop controller uses the gradient information to adjust the input level of the VCO, thereby tracking the peak admittance of the transducer.
260
B. Mortimer et al. / Ultrasonics 39 (2001) 257±261
the operating frequency where the transducer current is maximum, which could be above or below the local set point, until such time as dG=df is zero. This system has the advantage that only the current measurement is used in the locking process. Further, the locking system will establish the optimum operating point for the case of any frequency dependent load; for example, a combination of parallel transducer loads. This is often a problem in ultrasonic cleaning systems which cannot be optimally solved using phase locking techniques.
4. The class D power ampli®er Transistor ampli®ers are generally de®ned in terms of a class, which describes the arrangement of the output drive transistors. Class D is a type of ampli®er in which there are two output transistors in a bridge con®guration. These transistors are always driven to be completely on or completely o, which results in a square-wave drive to the load. This is clearly not a linear ampli®cation of the drive signal. It should be noted that the loss of linearity is acceptable given that the purpose of the system is usually to deliver the maximum ultrasonic power into the load. In practice a matching or wave shaping circuit is used or it is assumed that the load itself will act as a ®lter to shape the input wave. In the current work, the ultrasonic transmitter is used without reactance compensation and acts as a complex resonant ®lter. A signi®cant aspect of this design is that it is the ®rst resonance tracking system known to us, in which the transmitter can be driven by any periodic signal (rather than a sine wave). The use of an rms-DC converter in the measurement loop means that the circuit eectively tracks the frequency at which the current±voltage product for the transmitter is a maximum, regardless of the shape of either signal. This substantially simpli®es the driving stage, given that it need not be linear but must simply meet the constraints of eciency and practicality that are imposed by a particular implementation. The ampli®er used in this work was based on the SA16 PWM integrated circuit ampli®er supplied by Apex Microtechnology Corp. [8]. This circuit implements a 5 kW half-bridge with overload current limiting and thermal shutdown control, and was designed with the driving of piezoelectronic elements in mind. A block diagram of the system is shown in Fig. 5. In practice, it has been found that electrical layout is critical to keep noise levels low in the system; given the high currents used, it is easy to create spurious signals which interfere with the operation of the admittance locking system. In our system, the low-voltage measurement and control electronics were entirely isolated from the high-voltage
Fig. 5. This block diagram shows the arrangement of the half-bridge class D ampli®er, and the optical isolation used to isolate the highvoltage system from the measurement and control system. In practice, the high-voltage DC bus was 80 V. The system was able to drive a horn transducer at frequencies up to 25 kHz with no appreciable drop in performance.
driving circuitry by means of linear isolation ampli®ers and digital opto-isolators. 5. Experimental results The purpose of this system is to track the resonant frequency of the transmitter while the load condition varies. An example of this in operation is shown in Fig. 6, in which the transmitter (a horn concentrator) is moved from air to water and back to air again. These represent the extreme cases of the load which this transmitter is likely to experience. As can be seen, the
Fig. 6. This shows the real frequency response of the system as the load on the transducer changes. The transducer is a horn concentrator, the end of which is in air at time zero. The horn is dipped into water after about 1.2 s and removed from water at about 3.6 s. It can be seen that the frequency adjusts smoothly to compensate for the change in load impedance and coupling. The eect of the dither signal can be seen as the apparent ``noisiness'' of the frequency. The dither amplitude and loop bandwidth can be adjusted according to the characteristics of the transducer and load.
B. Mortimer et al. / Ultrasonics 39 (2001) 257±261
circuit automatically detects the change in resonant frequency and adjusts the frequency accordingly. There is a complex relationship between the frequency of the dither signal, the bandwidth of the transmitter and the response of the resonance tracking circuit. The purpose of the dither signal is to establish the value of dG=df automatically. To do this, it has to change the frequency and make a measurement of the changed admittance. The speed with which the frequency can be changed is determined by the transducer bandwidth. The measurement bandwidth is determined by the time constant of the rms-DC converter. The loop ®lter, which controls the speed of response of the resonance tracking, must have a response which suciently slow that the frequency changes caused by the dither signal are not themselves eliminated by the tracking loop (this recursive behavior is possible because the loop will generally track even if the control signal is highly degraded). In the implementation described in this paper, the dither signal was approximately 300 Hz and the control ®lter was a simple integrator (type II controller) with a time constant of 100 ms. The time constant for the rms-DC converter was 500 ls. Readers familiar with the use of phase-locked loops in resonance tracking will recognize that these elements are orders of magnitude slower than would be required for phase measurement with minimal phase error; this is a considerable advantage of the current approach. Any real transmitter will have several admittance peaks in its frequency spectrum, any one of which can be locked on by the admittance locking system. Fortunately, we can usually de®ne a frequency range for the VCO which will contain only the peak of interest. It is then trivial to set up the integrator so that it charges up from zero after a reset, gradually increasing the frequency until an admittance lock is obtained.
261
6. Conclusions We have designed and constructed a high power resonance tracking ultrasonic ampli®er, based on an admittance locking control loop and a class D halfbridge driving stage. The system has been successfully used to drive a typical transducer under changing load conditions. This system has the advantage that it will track the maximum power output for the transducer, regardless of the shape of the periodic input waveform. The system is superior to a phase-locked loop resonance tracking system in that it measures the transducer output power rather than the phase between current and voltage, which eliminates the problems of phase measurement error and non-ideal transducer modeling. The system also has the advantage that the most of the measurement elements do not have to slew at the system frequency, so it can be constructed using low slew-rate components, which are generally cheaper and simpler. The overall system is capable of delivering up to 3 kW of electrical power at frequencies up to 25 kHz, into narrow-bandwidth piezoelectric loads. References [1] J.A. Gallego-Juarez, J. Phys. E: Sci. Instrum. 22 (1989) 804±806. [2] A. Ramos-Fernandez, F. Montoya-Vitini, J.A. Gallego-Juarez, Ultrasonics 23 (1985) 151±156. [3] J. Tapson, Ultrasonics 33 (1995) 441±444. [4] J. Tapson, J.R. Greene, Meas. Sci. Technol. 4 (1994) 337±343. [5] W.P. Mason, Electromechanical Transducers and Wave Filters, 2nd ed., D. van Nostrand Co., New York, 1943. [6] B.J.P Mortimer, A. Green, T. du Bruin, J. Tapson, J. Acoust. Soc. Am. 108 (2000) 2638. [7] S Payne, Ultrasonic Generator Drive Circuit, US Patent 3975650, 1976. [8] Apex Microtechnology Corporation, 5980 North Shannon Road, Tuscon, AZ 85741, USA.