Performance of a high-voltage dc amplifier for ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 50, NO. 6, DECEMBER 2003

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Performance of a High-Voltage DC Amplifier for Electrostatic Levitation Applications Feng-Tian Han, Zhong-Yu Gao, and Yong-Liang Wang

Abstract—High-voltage amplifiers as a means of amplifying the low-output voltage signals of the feedback controllers to the suspension voltages typically in the kilovolts range are often required for electrostatic force generation in electrostatic levitation. This paper proposes a high-voltage dc amplifier including an amplitude modulator, a power amplifier, a step-up transformer, a pair of peak detectors, and a voltage feedback channel to stabilize the amplifier outputs in an effort to provide high suspension voltage and fast dynamic response. Since the various carrier frequencies have virtually no effect on the power consumption of the dc amplifier by filtering out the high-frequency carrier components with peak detectors while keeping the input signal unaffected, satisfactory dynamic performance can be achieved by choosing a sufficiently high carrier frequency. The operating principle of the dc amplifier is analyzed, followed by an experimental performance evaluation and discussion for electrostatic levitation applications. The experimental results demonstrate the superiority of the high-voltage dc amplifier over classical ac amplifiers in terms of dynamic response, force–voltage coefficient, voltage ripple, power consumption, and long-time stability using a carrier frequency of 30 kHz and the closed-loop control scheme. Index Terms—Electrostatic forces, electrostatic levitation, highvoltage amplifier, high-voltage transformer, peak detector.

I. INTRODUCTION

E

LECTROSTATIC levitation offers the advantage of directly suspending a wide variety of materials without any direct mechanical contact. It has been already utilized to implement a contactless suspension of an aluminum rotor in a vacuum gyro [1]. In addition, a 3.5-in aluminum disk [2] and a thin glass plate [3] have been levitated by electrostatic forces as well. The suspended object is usually supported by strong electric fields between one or more pairs of stator electrodes and the suspended object. As a result, high voltage levels, typically in the kilovolts range, are required to achieve electrostatic levitation. Generally, each pair of electrodes is energized by controllable voltages from high voltage amplifiers, supplying the electrodes with electric charge [4]. High-voltage ac amplifiers which commonly consist of an amplitude modulator, a power amplifier, and a step-up transformer are widely used for generation of electrostatic forces [4], [5], as shown in Fig. 1(a). Generally, the carrier frequencies are limited by power specifications and typically less than 2 kHz because application of high carrier frequency decreases the impedance between the electrodes and the suspended object, Manuscript received January 15, 2002; revised December 11, 2002. Abstract published on the Internet September 17, 2003. The authors are with the Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China. (e-mail: hanft99@ mails.tsinghua.edu.cn). Digital Object Identifier 10.1109/TIE.2003.819664

(a)

(b) Fig. 1. Schematic diagram of (a) ac amplifier and (b) transistor dc amplifier.

as a result, increases the current to be supplied to the electrodes. Thus, high-voltage amplifiers with open-loop configuration and low carrier frequency have inevitably poor robustness, limited bandwidth, and high distortion of output voltages, which somewhat restricts their application in high-performance electrostatic levitation systems. An alternative to the ac amplifier is the dc amplifier [6], [7]. High-voltage power-transistors-based dc amplifiers, as shown in Fig. 1(b) [6], have been introduced in recent years as the simplest solution for the application of electrostatic levitation technology. However, the electrostatic force is often weaker than that of ac amplifiers for some levitation applications, since the maximum output voltage of the transistor amplifier is somewhat limited by available power devices. In addition, since a set of high-voltage power supplies is also required for these transistor amplifiers, the resulting power consumption, weight, and dimensions of electrostatic suspension devices increase correspondingly. Another high-voltage generation method by combination of a less expensive high-voltage dc power supply and dc/ac amplifier is investigated for levitation of an aluminum disk [8]. However, its dynamic response is too slow to be adopted in most highperformance levitation systems. In this paper, a high-voltage dc amplifier based on AM and peak detection which does not show the limitations mentioned above is presented and evaluated. A noticeable feature of the dc amplifier lies mainly in the application of peak detectors for filtering out the high-frequency carrier components while keeping the input signal unaffected. Thus, the various carrier frequencies have virtually no effect on the power consumption of the dc amplifier when a capacitive load is driven for electrostatic

0278-0046/03$17.00 © 2003 IEEE

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Fig. 2.


Schematic diagram of high-voltage dc amplifier.

Fig. 3. Equivalent circuit for high-voltage transformer.

levitation. Additionally, the output voltage of the dc amplifier is virtually unlimited by a proper selection of the turns ratio of the step-up transformer. As a result, satisfactory performance can be achieved by choosing a sufficiently high carrier frequency, together with a closed-loop scheme in the amplifier circuit. II. CIRCUIT DESCRIPTION A schematic diagram of the high-voltage dc amplifier is shown in Fig. 2. Note that the outputs of the amplifier, which are of the same magnitude and opposite polarity, are applied on and . a pair of load capacitors A. Amplitude Modulator and Power Amplifier A linear AM modulator is realized via a wide bandwidth, high accuracy, four-quadrant analog multiplier (MPY634). Let the modulating voltage be given by the expression (1) is the angular frequency of the where is the bias voltage, is the amplitude of the signal. input signal, and Also, let the carrier voltage be given by the expression (2) is the angular frequency of the carrier and is the where amplitude of the carrier. After modulation the instantaneous value of the modulated carrier voltage is represented by (3) is the modulation factor and is the where gain of the analog multiplier. A pair of high-voltage high-current operational amplifiers (OPA548) with a differential output configuration and a voltage is followed to drive the subsequent high-voltage gain of transformer. The peak current through the transformer windings is many times larger than the average current applied to the load. Thus, the devices for power amplifiers must be capable of supplying this repetitive surge current. B. High-Voltage Transformer Instead of using a transformer core typically laminated with silicon steel in high-voltage ac amplifiers, a pair of ferrite cores characterized with an operating frequency ranging from 1 to 500 kHz and a relative permeability of about 2000 is employed in the high-voltage transformer. The number of turns of the primary and the secondary windings of the transformer are 16 and 2880, respectively. The analysis of the high-voltage transformer is most easily achieved by the use of an electrical equivalent circuit [5], [9].

Fig. 4. Frequency response of high-voltage transformer.

A lumped-element equivalent circuit, which is valid around resonance, is shown in Fig. 3, where the transformer includes an internal LC resonance circuit. The indicated values of elements were extracted experimentally by means of paralleling various capacitors in the secondary of the transformer and testing the resulting shunt-resonance frequencies. value The transformer resonance is characterized by the and the magnitude of the transfer function at the resonance frequency [10]. The simplest transfer function representing the resonance is (4) is the resonance frequency which is defined as , and is the value at resonance satisfying . The resonance condition is due to the equivalent inductance and capacitance of the transformer and will set a limit on the carrier frequency of the high-voltage dc amplifier. From the parameter values shown in Fig. 3, it can be calculated that the transformer is operated at a resonance frequency rad/s and a value . There is a excellent agree0.3 dB between the theoretically predicted curve and ment the experimentally measured frequency response, as shown in Fig. 4. It is readily seen that the bandwidth of the transformer is very wide due to a sufficiently low value of its bandpass filter model. Therefore, the transformer can be treated approximately as a constant gain block with a voltage ratio around its resonant frequency in the subsequent analysis.

where

C. Peak Detector The equivalent circuit for the peak detector is shown in Fig. 5, and the resulting output waveform under steady-state conditions is shown in Fig. 6. Note that only the detection circuit for the positive polarity output is shown in Fig. 5 for brevity. A resistor is added into the detection circuit to reject the interference

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TABLE I PARAMETERS FOR DETECTION CIRCUIT

Fig. 5. Peak detection circuit.

TABLE II MEASURED AND CALCULATED DATA FOR DETECTION CIRCUIT

where Fig. 6.

is the discharge time constant which is defined as . , then substituting (6) into (11) yields If we let

Output voltage versus time.

of high suspension voltage levels acting on the position sensors of electric suspension devices [11]. The resistor offers a diswhen both diodes in charge channel for the load capacitor . Fig. 5 are reverse biased and satisfies from the transformer as an ac Considering the output voltage source, we obtain a Thevenin equivalent voltage source at the secondary of the transformer. The resulting equivalent voltage and resistance are given by (5) It can be seen in Fig. 6 that the following equations hold: (6) (7) (8)

(12) Solving the nonlinear equations determined by (7), (8), (10), , and (12), we can obtain the numerical solutions of , , under certain conditions. The parameters and the reand sults for the detection circuit are given in Tables I and II, respectively. D. Voltage Feedback By comparison with the open-loop control scheme typically used in ac amplifiers, a closed-loop control is realized by means of an additional feedback channel and an analog regulator. In particular, the high-voltage transformer offers an extra secondary winding for voltage feedback. Let the output from the feedback winding be given by (13)

represents the peak voltage at the secondary of the where transformer when the capacitor is removed. The voltage-diand the carrier period viding factor . The load capacitor is charged when either of the diodes is on at . During this time, the voltage across the capacitor satisfies (9) is the charge time constant satisfying . Solving (9) associated with (7) the output at is given by

where

is the feedback factor, and is the turns ratio from where the feedback to the primary windings of the transformer. is detected by passing through a The feedback signal precision full-wave rectifier and then a fourth-order Butterworth to suppress the carrier components in the low-pass filter of the filter should demodulated signal. The cutoff frequency and higher are supbe chosen so that the input frequency is pressed sufficiently and the input signal with frequency transferred without being affected. Subsequently, the error signal between the input and the feedback is fed back to a phase-lag compensation network which generates control voltage for the AM modulator and closes a voltage control loop. The transfer function for the lag network is (14)

(10) When both diodes are off , the voltage across the capacitor is now given by (11)

is the regulator gain, and and are the corwhere responding break frequencies, respectively. Finally, the overall loop gain transfer function of the dc amplifier is obtained as follows: (15)

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TABLE III PARAMETERS FOR CLOSED-LOOP CONTROL

III. EXPERIMENTAL RESULTS AND DISCUSSION For all of the experimental results reported in this paper, parameter settings for the detectors are given in Table I and control parameters are shown in Table III. (a)

A. Closed-Loop System Performance The closed-loop frequency response of the dc amplifier was measured using an HP dynamic signal analyzer and is shown in Fig. 7. It was found that the amplifier had a resonant peak of 1.58 dB at resonant frequency of 3.30 kHz, and a closed-loop bandwidth of 4.72 kHz. It is clear that the dc amplifier offers a satisfactory frequency response for electrostatically levitated systems typically with a closed-loop bandwidth of less than 800 Hz. For comparison, the experimental frequency response of the dc amplifier in the open-loop scheme is also shown in Fig. 7. It is clear that the closed-loop configuration provides desired dynamic response and noise rejection. Moreover, the closed-loop amplifier offers strong robustness in the presence of modeling uncertainties and disturbances compared with its open-loop counterpart. The time-domain response of the dc amplifier excited by a square-wave signal of 500 Hz is shown in Fig. 8. The experimental results showed that the response produced a rise time of 0.15 ms, a setting time of 0.43 ms, and a percentage overshoot of 16%. The simulated results confirmed well the experimental data presented above. The measured data further indicated that the dc amplifier provided a maximum attainable output voltage of about 1650 V at a load of 66 pF and a voltage gain of 182.2 with a nonlinearity of less than 0.8%. In addition, the output voltage can be further increased by selecting a lager turns ratio of the high-voltage transformer for electrostatic levitation applications of higher electrode voltages. B. Power Consumption The power consumption of a high-voltage amplifier is a highly important index for inertial instruments using electrostatic suspension technology. The total power consists of the quiescent power , which keeps constant for a designed amplifier, and the dynamic power varying with the output voltage. The resulting total power can be expressed approximately as

(b) Fig. 7. Experimental frequency response. (a) voltage gain. (b) Phase of dc amplifier.

Fig. 8.

Output voltage with square-wave excitation.

1650 V on the capacitor . On the other hand, the maximum power consumption of an ac amplifier with a carrier frequency of 15 kHz was greater than 30.8 W under the same load as the dc amplifier [5]. Therefore, the power consumption of an electrostatically levitated system using the dc amplifier can be reduced significantly by compared with ac amplifiers based systems. Additionally, the variation of load capacitances due to the motion of the suspended object results in the variation of power consumption and electrode voltages for ac amplifiers while the dc amplifier is virtually unaffected by the load.

(16) C. Force–Voltage Coefficient is the where is the efficiency of the transformer, and power supply voltage with a typical value of 24 V in the amplifier reported in this paper. W, while The experimental results indicated that the maximum power was about 5.72 W with a positive output and a negative output of of 1650 V across the capacitor

In order to evaluate the relationship between an electrostatic force and the corresponding peak voltage by which generates the force, we define the force–voltage coefficient as (17)

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TABLE IV FORCE-VOLTAGE COEFFICIENT AND RIPPLE FACTOR

where is the time period of the charge and discharge of the load capacitor. As for the circuit shown in Fig. 6, there exists . for a dc amplifier with the paramWe can obtain eter settings in Table I, while the values of ac amplifiers are typically 0.50 with a carrier signal in sine wave and 0.83 in square wave [5]. The electrostatic attractive force is proportional to the applied on the electrodes square of the suspension voltage and is inversely proportional to the square of the air gap between the suspended object and the electrodes [2]–[5], as given in the following equation: (18) F/m and denote the vacuum perwhere mittivity and the projection area of each electrode, respectively. It is clear that the maximum of electric-field intensity using a dc amplifier is smaller than that of ac amplifiers under the same settings. Thus, the arcing between the electrodes and the suspended member can be significantly reduced [7], and the reliability of levitated systems is improved accordingly. D. Ripple Factor It can be seen in Fig. 6 that the ripple component superposed on is approximately a triangle wave. Here, we calculate the ripple factor of the dc amplifier output by a percent ripple from (19) The calculated and experimental results of the ripple factor with the parameters given in Table I are 3.69% and 3.5%, respectively. A small means less interference acting on sensing and servo electronics of electrostatic levitation systems [11]. The force–voltage coefficients and the ripple factors for various carrier frequencies ranging from 20 to 40 kHz are shown in Table IV. It is clear that a carrier frequency of about 30 kHz is a proper selection for the dc amplifier by considering the resonance characteristics of the high voltage transformer, together with the ripple factor and the force–voltage coefficient. E. Frequency Distortion Generally, the load capacitor is determined by an electrostatic levitation configuration, and similarly, the value of the resistance is limited by the power dissipation specification. The capacitor driven by a dc amplifier charges quickly to the peak value of the output voltage, while its discharge rate determined is relatively low. by the discharge time constant Hence, the intelligence signal may be lost during the discharge interval. The maximum of the modulating frequency without

(a)

(b) Fig. 9. Output voltages with sinusoidal excitation. (a) (b) f = 2:8 kHz.

f

= 1:2 kHz.

frequency distortion is limited not only by the time constant, and is given by [12] but also by the modulation factor (20) , M , With parameters settings pF, we obtain kHz according to (20). and Fig. 9 shows the output waveforms of the amplifier at for various modulating frequencies. The frequency distortion is kHz, while no frequency clearly shown in Fig. 9(b) at kHz. distortion occurs in Fig. 9(a) at If it is assumed that no frequency distortion will occur in electrode voltages, by substituting (20) into (18), the maximum of can be electrostatic force varying with the signal frequency expressed as (21) is typically introduced into all the where a constant voltage suspended electrodes and equal to half of the maximum voltage in order to obtain a linear model for electrostatic levitation. If cm , m, and V, the we set and various suspension forces varying with the frequency are shown in Fig. 10. It can be seen from Fig. 10 that the M are slightly calculated curve utilizing (21) and higher than the measured forces due to the effect of parasitic capacitances in the load loop of the dc amplifier. The conclusion can be drawn from above analytical and experimental results that the dynamic performance of the dc amplifier is limited both by frequency distortion, especially variation of the output voltage in high-frequency and large dynamic range, and by closed-loop bandwidth when the input signal varies in small amplitude. It can be seen from Fig. 10

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Fig. 10.


Influence of signal frequency on suspension force.

that a smaller value of the resister can weaken the frequency distortion at the cost of extra power consumption supplied by the dc amplifier. Consequently, given the fact that the improvement of dynamic performance and the reduction of power consumption are contradictory design criterions, care must be taken when making a decision in levitation applications driven by the dc amplifiers. IV. CONCLUSION A high-voltage dc amplifier based on AM and peak detection has been designed and tested for electrostatically levitated applications. The dc output of the proposed amplifier permits us to select a sufficiently high operating carrier frequency compared with those ac amplifiers. The experimental results demonstrate the superiority of the dc amplifier over classical ac amplifiers in terms of dynamic response, force–voltage coefficient, voltage ripple, and power consumption. At the same time, system performance, such as insensitivity to parameter variation, enhanced steady-state response, and desired dynamic properties, have been improved by the closed-loop control scheme. This technique constitutes a novelty in the field of high-performance electrostatic levitation systems and is likely to offer great perspectives. Efforts are currently in progress at Tsinghua University to extend this work to an electrostatically levitated system supporting a spherical rotor of beryllium. The experimental results on a prototype levitation device have demonstrated the excellent performance of the dc amplifiers. We believe that it will find many industrial and scientific applications in the future.

[6] S. J. Zhao, Y. L. Wang, and F. T. Han, “Experimental research of DC suspension system” (in Chinese), J. Chinese Inertial Technol., vol. 9, no. 3, pp. 39–43, Sept. 2001. [7] C. H. Wu, “DC electrostatic gyro suspension system for the gravity probe B experiment,” Ph.D. dissertation, Dept. Aeronaut. Astronaut., Stanford Univ., Stanford, CA, 1994. [8] T. Niino, K. Eto, and T. Highuchi, “Basic study for electrostatic levitation system in high-vacuum conditions,” in Conf. Rec. IEEE-IAS Annu. Meeting, Oct. 2000, pp. 682–686. [9] S. Y. Hui, S. H. Chung, and S. C. Tang, “Coreless printed circuit board (PCB) transformers for power mosfet/igbt gate drive circuits,” IEEE Trans. Power Electron., vol. 14, pp. 422–430, May 1999. [10] M. Imori, T. Taniguchi, and H. Matsumoto, “Performance of a photomultiplier high voltage power supply incorporating a piezoelectric ceramic transformer,” IEEE Trans. Nucl. Sci., vol. 47, pp. 2045–2049, Dec. 2000. [11] F. T. Han, Z. Y. Gao, and Y. L. Wang, “A differential capacitance to voltage converter for electrostatic levitation applications,” Sens. Actuators A Phys., vol. 99, no. 3, pp. 249–255, June 2002. [12] N. D. Deshpande, D. A. Deshpande, and P. K. Rangole, Communication Electronics. New Delhi, India: Tata McGraw-Hill, 1989.

Feng-Tian Han received the B.S. degree in industrial instrumentation and automation from Nanjing University of Science and Technology, Nanjing, China, in 1990, the M.S. degree in industrial automation from Beijing University of Aeronautics and Astronautics, Beijing, China, in 1996, and the Ph.D. degree in precision instrumentation from Tsinghua University, Beijing, China, in 2002. From 1996 to 1999, he was a Lecturer in the Department of Mechanical and Electrical Engineering, Zhengzhou University, China. He is currently a Research Associate in the Department of Precision Instruments and Mechanology, Tsinghua University. His current research interests are in the fields of active electrostatic levitation and electromechanical control systems. Dr. Han is a Member of the Chinese Society of Inertial Technology.

Zhong-Yu Gao graduated in automatic control from Tsinghua University, Beijing, China, in 1959. From 1984 to 1985, he was a Visiting Scholar in the Department of Electrical Engineering, University of Ottawa, Ottawa, ON, Canada. In 1988, he was a Senior Visiting Scholar in the Department of Mechanics, University of Stuttgart, Germany. Since 1989, he has been a Professor in the Department of Precision Instruments and Mechanology, Tsinghua University. His research interests include mechatronical control engieering, gyro instruments, and navigation systems. Prof. Gao is a Director of the Chinese Society of Inertial Technology and Vice President of the Chinese Society of Mechanical Control Engineering.

REFERENCES [1] H. W. Knoebel, “The electric vacuum gyro,” Control Eng., vol. 11, pp. 70–73, Feb. 1964. [2] J. Jin, H. T. Higuchi, and M. Kanemoto, “Electrostatic levitator for hard disk media,” IEEE Trans. Ind. Electron., vol. 42, pp. 467–473, Oct. 1995. [3] J. U. Jeon and T. Higuchi, “Electrostatic suspension of dielectics,” IEEE Trans. Ind. Electron., vol. 45, pp. 938–946, Dec. 1998. [4] R. C. Staas, “Automatic adaptive centering apparatus for electrically supported inertial instruments,” U. S. Patent 3 954 024, May 4, 1976. [5] M. Yan, “Experimental research on electrostatic gyro suspension circuits with 15 kHz carrier frequency and integrated chips,” Master’s thesis (in Chinese), Dept. Precision Instrum. Mechanol., Tsinghua Univ., Beijing, China, 1991.

Yong-Liang Wang received the B.S. degree in engineering mechanics and the M.S. degree in precision instrumentation from Tsinghua University, Beijing, China, in 1970 and 1982, respectively. Since 1970, he has been with Tsinghua University, where he is currently a Professor in the Department of Precision Instruments and Mechanology. His research interests include inertial sensors and inertial navigation systems. Mr. Wang is a Senior Member of the Chinese Society of Inertial Technology.