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ABSTRACT

A power supply system using a transcutaneous transformer to power an artificial heart through intact skin has been designed. In order to realize both high-voltage gain and minimum circulating current, compensation of leakage inductances on both sides of a transcutaneous transformer is proposed. A frequency region which realizes the robustness against coupling coefficient and load variation is identified. In this region, the converter has inherent advantages such as zerovoltage switching (ZVS) or zero-current switching (ZCS) of the switches, high-voltage gain, minimum circulating current, and high efficiency.

Artificial heart, energy transmission system, high efficiency, high-frequency converter, high-power density, high-voltage gain, inductance compensation, soft-switched converter, transcutaneous transformer, zero-current switching (ZCS), zero-voltage switching (ZVS).

INTRODUCTION

The artificial heart now in use, like the natural heart it is designed to replace , is a four â€œchambered device for pumping blood. such electrical circulatory assist devices such as total artificial heart or ventricular assist devices generally use a brushless dc motor as their pump They require 12â€œ35 W to operate and can be powered by a portable battery pack and a dcâ€œdc converter.

It would be desirable to transfer electrical energy to these circulatory assist devices transcutaneously without breaking the skin. This technique would need a power supply which uses a transcutaneous transformer to drive use,the motor for the circulatory assist devices. The secondary of this transformer would be implanted under the skin, and the primary would be placed on top of the secondary, external to the body. The distance between the transformer windings would be approximately equal to the thickness of the patientâ„¢s skin, nominally between 1â€œ2 cm. This spacing cannot be assumed constant; the alignment of the cores and the distance between them would certainly vary during the operation.

A transformer with a large (1â€œ2 cm) air gap between the primary and the secondary has large leakage inductances. In this application, the coupling coefficient k ranges approximately from 0.1 to 0.4. This makes the leakage inductances of the same order of magnitude and usually larger than the magnetizing inductance. Therefore, the transfer gain of voltage is very low, and a significant portion of the primary current will flow through the magnetizing inductance. The large circulating current through the magnetizing inductance results in poor efficiency.

A dcâ€œdc converter employing secondary-side resonance has been reported to alleviate the problems by lowering the impedance of the secondary side using a resonant circuit .Although the circulating current is lowered, the transfer gain of the voltage varies widely as the coupling coefficient varies .So, advantages characteristics are reduced as the coupling coefficient deviates at a designated value.

In this paper, compensation of the leakage inductances on both sides of the transcutaneous transformer is presented. This converter offers significant improvements over the converter presented in the following aspects.

Â¢ High-voltage gain with relative small variation with respect to load change as well as the variation of the coupling coefficient of the transformerâ€this reduces the operating frequency range and the size of the transcutaneous transformer is minimized.

Â¢ Higher efficiencyâ€minimize circulating current of magnetizing inductance and zero-voltage switching (ZVS) of the primary switches, and zero-current switching (ZCS) of the secondary rectifier diodes improves the efficiency significantly, especially at the secondary side (inside the body).

A design procedure allowing for a variable output power as well as a variable air gap and misalignment is presented. The theoretical analysis is verified by an experimental converter which transfers 12â€œ48 W through an air gap of 1â€œ2 cm. In addition, the feedback control scheme which processes the secondary sensed signal to the primary switches transcutaneously is presented.

PROPOSED ENERGY TRANSFERENCE SCHEME

To effectively transfer electric energy through the transcutaneous transformer, a high-voltage gain with small variation and small circulating current through the magnetizing inductance is important. To achieve these requirements, a method of the compensation of the leakage inductances on the primary side as well as the secondary side is proposed, as shown in Fig.1. In this scheme, two capacitors C1 and C2 are added in series

Fig. 1. Simplified circuit of proposed scheme.

In Fig. 1, the square-wave voltage source Vs , the magnetizing inductance LM , and the leakage inductances L11 and L12 are the equivalent values reflected to the secondary side of the transformer.

The higher turn ratio requires more windings of the secondary side for a given operating frequency, and the lower turn ratio requires high voltage of the input side. Therefore, the turn ratio of the transformer is considered to unity in this paper.

A. Analysis of the Proposed Scheme

Fig. 2. Equivalent circuit of Fig. 1.

Fig. 2 shows a simplified equivalent circuit model of Fig. 1. The voltage gain characteristics for the frequency variation can be calculated by applying an approximation method .t he load, rectified diodes, and filter in Fig. 1 are modeled by a simple equivalent resister Req , where

Where is an operating frequency of the converter Z, Z, Z. and represent the impedances at various points as shown in Fig. 2. From Fig. 2, the transfer gain of the voltage is

From (5) and (9), the resulting equation of the Gv is as follows:

Equation (10) implies that Gv is always unity at compensated frequency(X1=X2=0), although the leakage inductances of the transformer are very large. In order to analyze Gv for frequency variations, in (10) can be expressed as a function of frequency. From (2) and (3), the compensated frequency o is defined by the conditions of as follows:

Finally, from (10), (12), and (13), the voltage gain [see (15), given at the bottom of the page]. Since the coupling coefficient, varies in wide range, it is necessary to express the voltage gain Gv in terms of k. If we assume that the configurations of the primary and secondary cores are the same, the selfinductances of the primary and secondary have the same value of Ls. Then, the coupling coefficient k becomes

From (15) and (17), the resultant equation of the dc transfer gain for varying frequency is

B. Determination of the Control Region

Fig. 3 compares the analytical results with the simulation results for the varying frequency R, various Q, and three different cases of the coupling coefficient. The solid lines show the analytical values of the gain in (18), and the symbolic marks represent the simulation results of the gain. Fig. 3. . Transfer d .c. gain comparison of approximation analysis and simulation results k=0.1.

Results show that the curves Gv of for the three cases are almost identical except for a small deviation in lowQ. Thus, the analytic curves can be used for design and control for the system. From these curves, the points at unity of the normalized frequency keep a gain unity because the impedance of the leakage inductances is canceled by the additional capacitors at this frequency. As long as the converter operates at this frequency, the Gv keeps unity gain, and circulating current through the magnetizing inductance is largely suppressed. Furthermore, these characteristics do not depend on load as well as coupling coefficient. This frequency, however, varies as the coupling coefficient varies.

For the output-voltage regulation, the feedback control of output voltage should be applied by selecting the desirable region from among three different regions of the Gv in Fig. 3. Region I is the lowest frequency region. The unity gain frequency of R is varied for k. Region II is the middle frequency region. The gain largely depends on variations of load and k because the resonant characteristics change for varying frequency in this region. Region III is the highest frequency region. The Gvâ„¢s linearly decrease from the unity as the operating frequency of the converter increases.

Fig. 3(b) k=0.2

Region II, also called the double-turned circuit, provides the maximum transfer gain of the voltage. However, Gv the in Region II is very sensitive to change in load as well as coupling coefficient k. Furthermore, it has nonlinear characteristics as the frequency varies. Thus, it is difficult to control the output voltage.

Fig. 3 © k=0.4

Regions I or III are able to control the output voltage because the gain is a monatomic function as the frequency varies. Region III is more desirable because the unity gain frequencies for each is much less sensitive than for Region I. In this paper, Region III is suggested as a reliable region to control the output voltage for varying the air gap and the load.

DESIGN OF THE SYSTEM

The design specifications are given by the requirements of the output load of the system. Because the power input to the biological heart is approximately 15 W at resting conditions, and 35 W under heavy exercise, the required output power is set from 12 to 48W. The specification used in this paper are

Vo = 24V

Iomax = 2.0 A

Iomin = 0.5 A

Where Vo is the output voltage, Iomax is the maximum output current, Iomin is the minimum out put current.

A. Transformer and Compensating Capacitance

Many researchers have studied the methods to optimize the geometry of the transformer windings to obtain the maximum coupling coefficient. To simplify the task, it is assumed that the size, geometry, and core material of the transformer and the range of air gap and misalignment between them have already been defined. For the transformer windings, the same cores used in series resonant converter. were selected to compare the overall performance with proposed scheme.

Cores: Ferroxcube Pot Core 6656

3C8 Ferrite

OD 2.6 in, thickness 1.1 in

Air gap: 10â€œ20 mm

Misalignment: 0â€œ10 mm.

Based on the gain characteristics for the predicted kmin and kmaxi in Fig. 3, a design value Q can be selected. In Region III, higher Q provides a high-gain system with respect to the frequency variation. However, due to the deviation of the leakage inductances and, thus, the normalized frequency for the variation of k, it is desirable to select a lower Q to reduce the sensitivity for the variation. The selection of Q in this design is from two at light load to eight at full load. For minimum size and weight and high-efficiency requirement of the system, the compensating resonant frequency is chosen at 120 kHz. From (19), the required leakage inductance can be determined for a designed Qmin and o

Leakage inductances L11and L12 are assumed to be the same when the turn ratio of the transformer is one to one. Therefore, the number of turns of the cores is 20 to get the nearest 63.5 H of L11 for k = 0.265.

Air gap Misalignment LM(H) L11(H) L12(H) K

20mm 13 13.8 70.7 71.2 0.16

13mm 6.5 23.3 63.2 65.8 0.265

10mm 0 36.6 58.3 60.1 .39

Table 1 Inductance of experimental transcutaneous transformer under minimum, intermediate and maximum coupling conditions

The compensating capacitors C1and C2 are calculated by the measured L11 and L12. and the resonant frequency for k=0.265

The resultant values of C1 and C2 are 27 nF.

The measured transformer parameters for the varying coupling coefficient k are summarized in Table I. The coupling coefficient ranges from 0.16 to 0.39, and the leakage inductance varies within 20% from kmin to kmax. Therefore, resonant frequencies for varying k change. That is, frequency of Vs, which is the converter operating frequency, has to be varied to control the output voltage.

B. Input Voltage and Converter Type

Fig. 4. Curves of GV for designed transformer.

To determine input voltage Vs of the converter, the curves of Gv are simulated for the designed transformer as shown in Fig. 4. Although Q slightly varies as the coupling coefficient varies, Q is about eight at full load (48 W) and about two at light load (12 W). Region III is extended for the smaller k and shrunk for the larger k because the frequencies of the unity gain vary as k varies. The output voltage can be controlled to higher gain than 0.45 for full range of load and k when the controller range of R is set from one to two. The gain 0.45 may be considered a relative high gain which can regulate the output voltage.

To get 24 V of the output voltage, the minimized gain of the input voltage to the output voltage is set at 0.4 with about a 10% margin. The input voltage is 60 V for a full-bridge converter. The input voltage can be from 54 to 72 V because of the low margin of the 10% and the high margin which is determined by the limitation of the maximum operating frequency(2R) .

A full-bridge configuration was selected to supply a rectangular voltage source. The basic power circuit is shown in Fig. 5. In this circuit, a pair of the switches, S1 and S4, operates 180 out of phase with respect to the pair of switches S2 and S3.

It is necessary to have a dead time between the turn off of one pair of switches and turn on of the other pair to get ZVS conditions. When S1 and S4 and S2and S3 are still turned off, the energy of the primary leakage inductor causes the capacitor discharge completely, and the current will flow through the body diodes of S2 and S3. Therefore, the ZVS condition of their switches is satisfied. The converter operates at this condition when the control region is the Region III of Fig 3. This condition always exists because the primary current can always be large enough to discharge the capacitors before the end of the dead time.

Fig. 5 Proposed power converter

C. Control of the System

A feedback controller needs to regulate the output voltage of the transcutaneous power supply. A wireless transmission of a control signal is necessary as in the power transfer.

Fig. 6 is a block diagram of the controller. The circuits in a human thorax are only a voltage-controlled oscillator (VCO) and a buffer. The VCO changes the sensed output voltage to a respected ac frequency. The buffer transfers this control by the main transformer with extracorporeal cores. Therefore, the transformer can transfer the ac control signal as well as the main energy. The ac control signal received outside of the human body, however, can have high-frequency noise caused by the main power circuit. To separate this noise, the frequency of the control signal is selected from 9 to 11 kHz, about ten times lower than the operating frequency of the main converter. Then, the transferred signal is filtered to reduce the noise. A voltage-to-frequency converter (VFC) converts the filtered ac signal to respected output voltage in order to compare the reference voltage. The internal controller is used to regulate the output voltage.

Fig. 6 Block diagram of controller

EXPERIMENTAL RESULTS

Fig. 7 shows comparisons in the gain Gv between the analytical results and experimental data for varying frequency, several Qâ„¢s, and k = 0.2. The solid lines show the values of the gain in (18). The symbolic marks represent the experimented results of the gain. The curves of Gv between experiments and analyses are almost matched. A small deviation of Gv is caused by additional resistors such as the series resistors of the power MOSFETâ„¢s, compensating capacitors, transformer, and filter in the system.

Fig. 7 (a)Transfer d.c. gain comparisons in the system k=0.1

Fig. 7 (b) Transfer dc gain comparison k = 0.2

Fig. 7 © Transfer dc gain comparison k = 0.4

Fig. 8 (a) k = 0.39 and Io=0.5A

For the highest coupling and the minimum load and the lowest coupling and full load conditions, the switching waveform of the power MOSFET S1 and the rectified diode are shown in Figs. 8 and 9, respectively. These osillograms show that all switches are softly switched. When a pair of switches (S1,S4)is turned off, the voltage Vs1is nearly increased with a slip from the zero voltage to input voltage (ZVS); the current flows through the parallel capacitors of the power MOSFETâ„¢s ((S1,S4).

Fig. 8 (a) k = 0.39 and Io=0.5A

Fig. 9 (a) k = 0.39 and Io=0.5A

When the voltage of S1 and S4 approaches the input voltage, the voltage of the other pair of switches (S2, S3) discharges to zero. Therefore, switches S2 and S3 are naturally turned on by the internal diodes of their MOSFETâ„¢s. Fig. 9 represents that a rectified diode is always switched at ZCS conditions. This ZVS and ZCS of the switches largely reduces switching losses and voltage spikes of the switches in spite of the lack of snubbers.

Fig. 9 (b) k = 0.16 and Io=2A

Fig. 10

Fig. 10 shows efficiency curves at the minimum, medium, and maximum coupling coefficients for a varying load. As the coupling coefficient lowers, the efficiency is also lowered at the same load condition because the circulating current of the primary circuit is higher. As the output power decreases, the efficiency goes even lower because the circulating current through the magnetizing inductance does not decrease as fast as the output current does.

Although the leakage inductance on the secondary side of the transformer is compensated and circulating current is minimizing, the impedance of magnetizing inductance can be much lower than the equivalent resistor of the output load. Therefore, the circulating current is still large at a low coupling coefficient. The voltage of a switch Vs1and the primary current i11show that much of i11is circulating from the source to the transformer. This tendency increases as the coupling coefficient lowers. The maximum value of the primary current is about 6 A at full load. Because the voltage of the compensating capacitor C1 proportionally increases as the primary current increases, it reaches 300 V at the worst conditions. The secondary current of the transformer and the secondary voltage of the compensating capacitor almost depend on load conditions. The average value of the rectified current is equal to the load current. The maximum value of the capacitor C2 voltage is 130 V at the worst conditions.

The maximum operating frequency of the converter at full load and maximum coupling coefficient. The minimum frequency is at light load and minimum coupling coefficient. The operating frequencies of these conditions are about 173.5 and 122.5 kHz, respectively. The variation ratio of the operating frequency is about 1.45.

CONCLUSION

To realize both the high-voltage gain and the minimum circulating current, a method of the compensating leakage inductances on both sides of the transformer is proposed. The properties of the proposed scheme are summarized as follows.

Â¢ High-voltage gain and the reduced circulating current.

Â¢ A control region of an operating frequency is determined, which realizes the robustness the coupling coefficient as well as the load.

Â¢ The minimized configuration of the devices in the thorax is experimented.

Â¢ The converter guarantees many advantages because of ZVS of all active switches and ZCS of the rectified diodes, low devices switching loss and stress, and high efficiency.

A design procedure to reduce the effects of the given variations of load and coupling coefficient is established, and the above advantages are experimentally verified.

REFERENCES

[1] G.B. Joung and B.H. Cho, An energy transmission system for an artificial heart using leakage inductance compensation of transcutaneous transformer, IEEE power electronics, vol.4, No.: 9, pp1013-1023, Nov 1998.

[2] J. C. Schuder and H. E. Stephenson, Energy transport to a coil which circumscribes a ferrite core and is implanted within the body, IEEE Trans. Bio-Med. Eng., vol. BME-12, nos. 3 and 4, pp. 154â€œ163, 1965.

[3] J. C. Schuder, J. H. Gold, and H. E. Stephenson, Ultra high power electromagnetic energy transport into the body, IEEE Amer. Soc. Artif. Int. Organs, vol. 17, pp. 406â€œ410, 1971.

[4] A. Thumin, G. Reed, F. Lupo, G. Myers, and L. Cortes, A power transformer for mechanical heart, in Artificial Heart Program Conf. Proc., 1966.

[5] C. Sherman, W. Clay, K. Dasse, and B. Daly, Energy transmission across intact skin for powering internal artificial organs, IEEE Amer. Soc. Artif. Int. Organs, vol. 27, pp. 137â€œ141, 1981.

ACKNOWLEDGEMENT

I express my sincere gratitude to Dr.Nambissan, Prof. & Head, Department of Electrical and Electronics Engineering, MES College of Engineering, Kuttippuram, for his cooperation and encouragement.

I would also like to thank my seminar guide Miss. Nisha B Kumar (Lecturer, Department of EEE), Asst. Prof. Gylson Thomas. (Staff in-charge, Department of EEE) for their invaluable advice and wholehearted cooperation without which this seminar would not have seen the light of day.

Gracious gratitude to all the faculty of the department of EEE & friends for their valuable advice and encouragement.

CONTENTS

Â¢ INTRODUCTION 01

Â¢ PROPOSED ENERGY TRANSFERENCE SCHEME 04

Â¢ DESIGN OF THE SYSTEM 13

Â¢ EXPERIMENTAL RESULTS 19

Â¢ CONCLUSION 25

Â¢ REFERENCES 26