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1st International Conference on Sensing Technology November 21-23, 2005 Palmerston North, New Zealand Stabilizing the Operating Frequency of a Resonant Converter for Wireless Power Transfer to Implantable Biomedical Sensors Ping Si 1, Aiguo Partick Hu 1, David Budgett 2, Simon Malpas 2, Joseph Yang 2, Jinfeng Gao 3 The Department of Electrical and Computer Engineering 1 The Bioengineering Institute 2 The University of Auckland, New Zealand School of Electrical Engineering, Zhengzhou University, China3 psi001@ec.auckland.ac.nz Abstract Resonant converters have been applied in wireless power supplies for implantable sensors due to their inherent advantages of low cost, high frequency and high reliability. However, the operating frequency of the resonant converter varies with the load and circuit parameters changes, which can significantly reduce the maximum power that the system can transfer. As a result the implanted sensors may not work properly because of insufficient power delivery. Uncertainty in frequency associated with system instability can contribute to electromagnetic interference for the implanted sensors, wireless communication networks, and other peripheral electronic devices. This paper proposes a new method to stabilize the system operating frequency using a fixed capacitor whose equivalent capacitance is controlled by semiconductor switches. Two control strategies based on Zero Voltage Switching techniques are analysed in details and practically implemented. The simulation and experimental results have demonstrated that the proposed method performs well in stabilizing the operating frequency of a wireless power supply system while maintaining the complete soft switching operation of the resonant converter. Keywords: wireless power, implantable sensor, frequency stabilization, resonant converter. magnetic field is generated by the resonant circuit 1 Introduction formed by capacitor C and inductor L in figure 1. This magnetic field induces electrical power from an A novel wireless power (WP) supply system has been implanted pick-up to power the implanted sensors. developed by the Department of Electrical and Computer Engineering, the Bioengineering Institute Skin of the University of Auckland, to supply contactless power over a highly variable air gap to implanted sensors. The aim of this research is to develop a Sensors C L power supply system suitable for powering Pick-up implantable physiological sensors for use in humans Resonant Implanted Device and animals. The WP supply system offers continuous Circuit operation with complete freedom of movement Push-pull Converter mitigating the need for any percutaneous link [1, 2]. In addition, where power needs are high, a WP system Figure 1: Basic configuration of a WP supply system. can provide continuous operation with reduced size One problem with the basic circuit configuration is compared to systems relying on implanted batteries. that the operating frequency of this type of current-fed Figure 1 shows the basic topology of a WP supply resonant converter varies with the load and circuit system. A current-fed push-pull type of converter is parameter changes. The frequency variation can selected to drive a resonant circuit because it is low significantly reduce the maximum power that can be cost, small in physical size, very reliable and has high transferred due to the resultant detuning of the power efficiency [3]. This type of current-fed resonant pick-up. The implanted sensors may not work converter can easily be designed to operate at high properly due to insufficient power delivery. This frequencies at hundreds of kHz level, which is a problem can be overcome by implementing a constant major factor contributing to minimizing the physical frequency resonant converter [4-7]. Constant size of the implanted power pick-up circuit. frequency operation is straight forward for hard Meanwhile, the resonant circuit enables soft- switched pulse width modulation (PWM) converters switching operation of semiconductor switches, which but it has been a challenging task for resonant help to reduce circuit losses and system EMI (Electro- converters due to the difficulties involved in the soft magnetic interference) [4]. A high frequency switched operation. This paper proposes a new 477 1st International Conference on Sensing Technology November 21-23, 2005 Palmerston North, New Zealand approach to stabilizing the operating frequency of a can be adjusted by controlling the duty-cycles of the wireless power system for implantable sensors, while switches, but for a larger range than figure 3 (a). In maintaining full ZVS (Zero Voltage Switching) both the situations shown in figure 3, f0 is the operation of a push-pull current-fed resonant reference frequency which is set to the constant value converter. required. The measured real-time operating frequency f is compared with f0 to generate a gate control signal 2 Proposed Method for Stabilizing g(t) for switch S in figure 3 (a), or g1(t) and g2(t) for Operating Frequency switches S1 and S2 in figure 3(b), to control the semiconductor switches for frequency stabilisation. If Figure 2 shows the proposed circuit configuration for for some reason (e.g. magnetic field saturation) stabilizing frequency of a WP supply system based on inductance L decreases, frequency f will increase a current-fed resonant converter. In addition to the according to equation (1). Due to the increased power source and the inverting network, there is a difference between f and f0, the on duty-cycle of the resonant circuit including an inductor L, a fixed gate control signal will also increase. Thus, the capacitor C and a variable capacitor Cs [8, 9]. Under equivalent capacitance of Cs will increase, leading to steady state conditions, if harmonics are ignored, the a decrease in frequency. If the controller is designed resonant voltage vr is approximately a sinusoidal properly the system frequency should move back waveform [4]. The circuit oscillation depends on the towards its original setting, thus the frequency is inductance L and the total parallel capacitance stabilised. consisting of C and Cs in the resonant circuit. As a result, the operating frequency can be approximated iCS D2 using equation (1). Here Ceq is the equivalent variable S2 vCS iCS capacitance of the capacitor Cs. L vr Cs L vr vCS C C Cs S D1 S1 f f + + g1(t) Switch g(t) Switch g2(t) f0 Control f0 Control - - (a) Single side switch (b) Dual side switch Figure 3: Switched capacitors in a resonant tank. Figure 2: Proposed strategies for stabilizing 3 Theoretical Analysis of Frequency frequency. Variation 1 f= The equivalent capacitance of the switched capacitor 2 L(C + Ceq ) is analysed to evaluate its effect on the operating (1) frequency of a resonant circuit. The two switching The true operating frequency of the converter is more strategies shown in figure 3 are analysed individually. complicated than that given by equation (1). The resonant frequency is also influenced by factors 3.1 Equivalent Capacitance of a Single including the load, switching harmonics, component tolerances and temperature. However, equation (1) Side Switched Capacitor shows that by varying the equivalent capacitance Ceq, For the resonant circuit using a single side switched the final operating frequency of the converter can be capacitor as shown in figure 3 (a), if voltage vr is compensated for multiple causes of frequency assumed to be pure sinusoidal, the waveforms of the changes. voltages across capacitor C and Cs can be illustrated as vC and vCS shown in figure 4. is defined as the Dynamically varying the capacitance can be achieved switching angle, its value has to be between 0 and /2. in a number of ways. Figure 3 illustrates two The switch S is switched off only during the interval strategies for implementing a variable capacitor of [ , - ], and in this interval the voltage across controlled by a frequency feedback loop. In figure 3 capacitor Cs is a constant Vdc. (a), the capacitor Cs is switched by a single semiconductor switch S, the equivalent capacitance of The relationship between switching angle and Cs can be varied by changing the on duty-cycle of this voltages can be expressed below: switch. In figure 3 (b) the capacitor Cs is switched using two identical switches S1 and S2 [8]. Similarly, Vdc = arcsin( ) the equivalent capacitance of Cs of the dual switches Vac (2) 478 1st International Conference on Sensing Technology November 21-23, 2005 Palmerston North, New Zealand vC (vr) Vac switched capacitor can be analyzed based on the following integral equation: Vdc π- = arcsin( Vac ) C eq Vac sin( ω t)d( ω t) = C S v CS d( ω t) 0 0 (6) t Equation (6) can be further extended as: vCS Vdc 2C eq Vac = C S v CS d(ω t) 0 − = C S Vac sin(ω t) d(ω t) + C S Vdc d(ωt) + C S Vac sin(ω t)d(ωt) 0 − t (7) By solving equation (7), the equivalent capacitance g(t) Ceq can be obtained as shown below: off on off on t 2C S [1 − cos ( )] + C S sin ( )[ −2 ] C eq = Figure 4: Voltages and control signal in single side 2 (8) switching. Similar to the result of analyzing the single side Considering that the absolute value of electric charge switching, equation (8) shows that Ceq equals to zero Q of a switched capacitor Cs during one period should when both switches always keep off ( =0 and Vdc=0), be the same as that of using an equivalent capacitor and equals to Cs when both switches always keep on with capacitance Ceq, an integral equation can be ( = /2 and Vdc=Vac). obtained as: vC (vr) V ac 2 2 C eq V ac sin( ω t) d( ω t) = C S v CS d( ω t) = arcsin( Vdc ) 0 0 (3) Vac where is angular frequency =2 f. Equation (3) − + 2 − t can be further extended to be: − 4C eq Vac = C S Vac sin(ωt)d(ωt) + CS Vdc d(ω t) vCS Vdc 0 2 + C S Vac sin(ωt)d(ωt) + C S Vac sin(ωt) d(ωt) − t (4) g1(t) By solving equation (4), the equivalent capacitance off on off on Ceq of a single side switched capacitor can be obtained t as shown below: g2(t) on off on off 2C S [2 − cos ( )] + C S sin ( )[ −2 ] t C eq = 4 (5) Figure 5: Voltages and control signal in dual side It can be obtained from equation (5) that the switching. equivalent capacitance Ceq in the single side switching method is equal to Cs/2 when the switch always keeps 3.3 Effects of Switched Capacitor on off ( =0 and Vdc=0), and Cs when switch always keep Operating Frequency on ( = /2 and Vdc=Vac). If the maximum frequency variation is a result of the variation of the inductance L, then the equivalent 3.2 Equivalent Capacitance of a Dual capacitance required to compensate can be determined Side Switched Capacitor according to the following equation: In the resonant circuit using the dual side switched 1 capacitor Cs as shown in figure 3 (b), switch S1 and S2 Ceq = 2 −C are separately switched off during [ , - ] and [ + , 0 (L + L) (9) 2 - ] periods. Figure 5 shows the waveforms of the voltages across capacitor C and Cs. It should be noted Where 0 is the pre-designed angular frequency, 0 that the voltage across Cs is Vdc during [ , - ] and - =2 f0, L is a disturbance of inductance L. Vdc during [ + , 2 - ]. If the dual side switching method is used and the Similar to analyzing the single side switched maximum increase in L is L+, then the capacitor Cs capacitor, the equivalent capacitance of a dual side should be fully switched off ( =0), corresponding to an equivalent capacitance of zero. Under such a condition, the resonant tank inductance should be 479 1st International Conference on Sensing Technology November 21-23, 2005 Palmerston North, New Zealand fully tuned with the fixed capacitor to keep the voltage across switch S1 is zero when it is switched operating frequency constant: on. The situation with the single side switched capacitor (shown in figure 3 (a)) is similar, although 1 only half a cycle is controlled. 2 −C = 0 0 (L + L + ) (10) vCS Vdc Therefore, C can be determined by: - 1 t C= 2 0 (L + L + ) (11) iCS After determining the value of fixed capacitor C, the maximum equivalent capacitance of the switched t capacitor can then be calculated using equation (12). g1(t) In this equation, L- is the maximum decrease in the off on off on value of L. Under these circumstances, the capacitor vsyn t Cs should be fully switched on ( = /2) for stabilizing vref the operation frequency. 1 t C eq = 2 −C 0 (L − L − ) (12) Figure 7: Voltage and current waveforms of Cs. As discussed before, Ceq in equation (12) is the maximum equivalent capacitance of a switched 5 Simulation Results capacitor, which is also the value of Cs. Figure 8 shows the PSPICE simulation results of the proposed method as shown in figure 2. The variable 4 Complete ZVS Operation capacitor is switched using the dual side switching Considering the power losses and power ratings of the strategy as shown in figure 3 (b). The capacitances of semiconductor switches, as well as the current-fed capacitor C and Cs are 150nF and 85nF respectively. push-pull switching network topology used, it would The inductance of L is 25uH. It can be seen that the be ideal to achieve ZVS (Zero Voltage Switching) in voltage and current waveforms are consistent with the the whole WP supply system. This eliminates the analyzed results shown in figure 7. surge currents which can be potentially destructive in 60V switching a capacitor. To ensure a ZVS operation, a 0V phase shift control method is employed. Its basic -60V vCS structure is illustrated in figure 6. A f-v block 2.0A converts frequency signal to a DC reference voltage 0A vref. Then, this reference is compared with an ac signal -2.0A iCS vsyn to generate switch control signal(s). Because vsyn 5V is designed to synchronize with the resonant voltage 2.5V vr (shown in figure 3) while vref varies with f, the 0V g1(t) switching angle will also vary with the measured 10V frequency. 5V 0V 1.15ms 1.16ms 1.17ms 1.18ms 1.19ms 1.20ms 1.21ms 1.22ms 1.23ms vsyn vref vref f f-v + Voltage Figure 8: Simulation results of dual side switching. Switches vr vsyn Comparator - Figure 9 illustrates that although resonant inductance Voltage Divider L is changed from 25uH to 30uH, the frequency of the current iL flowing through L is stabilized at a predetermined constant frequency (65kHz). That is Figure 6: Basic structure of phase shift control. achieved by decreasing switching angle to reduce Figure 7 shows the voltage vCS and current iCS of a the equivalent capacitance of the switched capacitor dual side switched capacitor Cs as shown in figure 3 Cs, so that the increased inductance is compensated. (b). It should be noted that when switch S1 is switched Based on the structure shown in figure 2, the single on at phase angle - , the current flow through the Cs side switched capacitor method (shown in figure 3 is negative (iCS 0 as shown in figure 7), which means (a)) is also simulated using PSPICE. Table 1 shows the current is flowing through the body diode D1 the calculated results fcal of the operating frequency (shown in figure 3 (b)). If the voltage drop of the using equation (1) and (5), which is compared with body diode is ignored, ZVS is achieved because 480 1st International Conference on Sensing Technology November 21-23, 2005 Palmerston North, New Zealand simulated results fsim by replacing switch and 6 Experimental Results and switched capacitor Cs with only a fixed capacitor, Discussion whose capacitance equals to the equivalent capacitance of switched Cs determined by equation A prototype resonant converter has been built and (5). It can be seen that the calculated results are in tested in laboratory. This converter is actually a good agreement with the simulation results. Also, it current-fed push-pull converter combined with dual should be noted that the equivalent capacitance of CS side switched capacitor in a resonant tank. The main equals to the maximum value 100nF when the parameters of the resonant tank used include switching angle is about 1.57 rad (90o), which is also inductance L=12.3uH, tuning capacitor C=237nF and consistent with the analytical results. These results switched capacitor Cs=147nF. The constant operating show the validity of the derived equations for frequency of the converter is set at 87kHz. The dual analyzing the equivalent capacitance of a switched side switching strategy as shown in figure 3 (b) is capacitor. used to adjust the total capacitance of the resonant 10A tank. Figure 10 shows the measured waveforms of the switched capacitor voltage and inductor current. In this diagram only the positive voltage is shown for 0A easy measurements. Besides, it should be noted from figure 10 that the voltage of the switched capacitor is -10A iL slightly distorted due to the effects of the switching 100V harmonics. Nevertheless, the experiments show the conduction of the capacitor is fully controllable so that its equivalent capacitance can be varied to 0V stabilize the frequency. Figure 10 clearly shows the system operates at the predetermined frequency of -100V 900us 910us 920us 930us 940us 950us 960us 970us 980us 990us 1000us 87kHz. It has been found that under normal load and vCS operating conditions, the maximum frequency drift is (a) L=25uH less than 300Hz. 10A 0A -10A iL 100V 0V -100V 880us 890us 900us 910us 920us 930us 940us 950us 960us 970us 980us vCS (b) L=30uH Figure 10: Experimental results of switched capacitor Figure 9: Operations with constant frequency 65kHz. voltage and inductor current. Table 1: Calculated equivalent capacitance compared 7 Conclusions with simulation results (C=110nF, CS=100nF). This paper has proposed a new method to stabilize the (rad) Ceq (nF) fcal (kHz) fsim (kHz) frequency of a wireless power supply system for 0.08 56.14 78.09 77.50 implantable sensor applications. The equivalent 0.16 61.89 76.78 75.83 capacitance of a resonant capacitor of a current-fed 0.24 67.35 75.58 74.17 resonant converter is analysed in details. Two control 0.33 72.53 74.51 73.33 strategies, being single side and dual side switching 0.42 77.63 73.49 72.50 configurations, are proposed and practically 0.52 82.56 72.54 71.67 implemented. Simulation and practical results have 0.63 87.37 71.65 70.83 demonstrated that the proposed method is very 0.77 92.05 70.82 70.00 effective in stabilizing the operating frequency while 0.96 96.30 70.08 69.17 maintaining the full ZVS operation of current-fed 1.29 99.63 69.52 68.33 resonant converters. 1.57 100 69.46 68.33 These methods provide a mechanism to maintain effective power transfer levels by providing a stable 481 1st International Conference on Sensing Technology November 21-23, 2005 Palmerston North, New Zealand resonant frequency by varying the resonant [4] Hu, A. P.: "Selected resonant converters for IPT capacitance to compensate for a wide variety of power supplies", PhD thesis, Department of disturbances to the resonant circuit. Electrical and Computer Engineering, University of Auckland, Oct 2001. 8 Acknowledgements [5] Schuylenbergh, K. 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