Stabilizing the Operating Frequency of a Resonant Converter for

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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



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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)


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      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


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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


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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



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1st International Conference on Sensing Technology
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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. V. and Puers, R.: "Self tuning
                                                            inductive powering for implantable telemetric
The authors would like to thank the Department of
                                                            monitoring systems", The 8th International
Electrical and Computer Engineering and the
                                                            Conference on Solid-State Sensors and Actuators,
Telemetry Research Group of the Bioengineering
                                                            and Eurosensors IX, Stockholm, Sweden, 1995.
Institute, the University of Auckland for their
technical and financial support.                        [6] Boys, J. T., Covic, G. A. and Xu, Y.: "DC
                                                            analysis technique for inductive power transfer
                                                            pick-up", IEEE Power Electronics Letters, Vol.
9    References
                                                            1, No. 2, 2003.
[1] Chen, J. H. and Carr, W. N.: "Induction power
                                                        [7] Si, P. and Hu, A. P.: "Designing the dc
    supply designs for implanted biomedical
                                                            inductance for ICPT power pick-ups", The 5th
    integrated circuits", Annual International
                                                            IASTED International Conference on Power and
    Conference of the IEEE Engineering in Medicine
                                                            Energy Systems, Benalmadena, Spain, 2005.
    and Biology Society, Vol. 12, 1990.
                                                        [8] Hu, A. P. and Hussmann, S.: "Improved power
[2] Salim, A. Baldi, A. and Ziaie, B.:"Inductive link
                                                            flow control for contactless moving sensor
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                                                            applications" IEEE power Electronics Letters,
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                                                            pp:1 - 4, Issue: 99 , 2004.
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    Cancun, Mexico, 2003.                                   A. and Boys, J. T.: "A dynamically on-off
                                                            controlled resonant converter designed for
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    Aug 2004.




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