Patent Publication Number: US-9425700-B2

Title: System and method for series resonant converter protection

Description:
BACKGROUND OF THE INVENTION 
     Embodiments of the present invention relate to systems and methods for power supply control. 
     Series resonant converters are one of the switching type power converters that have been widely used in a variety of industrial applications such as communication, medical, welding and so on. Typically, the series resonant converter can be operated to convert unregulated power received from a power source to regulated power which is applied to a load. The series resonant converter utilizes a number of switching devices arranged with half-bridge or full-bridge configurations that can be gated on or off to perform the power regulation. Conventionally, a frequency control is employed to control operation of the series resonant converter. That is, the frequency of the switching signals is varied with respect to the resonant frequency of a resonant tank circuit of the series resonant converter to achieve the desired output voltage from the series resonant converter. However, varying the frequency of the switching signals may cause difficulties in design of magnetic components and filters in association with the series resonant converter. Further, when input power or output load varies, desired output voltage cannot be achieved through the use of conventional control techniques. 
     BRIEF DESCRIPTION OF THE INVENTION 
     According to an embodiment of the present invention, a resonant power supply is provided. The resonant power supply comprises a series resonant converter configured to convert an input direct current (DC) voltage to generate an output DC voltage and a converter controller coupled to the series resonant converter. The converter controller is configured to receive a DC voltage feedback signal measured at the output of the series resonant converter, or a resonant current feedback signal representing a resonant current flowing through the series resonant converter, and to generate control signals to be applied to the series resonant converter to limit the output DC voltage of the series resonant converter according to the DC voltage feedback signal and a predetermined voltage threshold signal, or to limit the resonant current of the series resonant converter according to the resonant current feedback signal and a predetermined current threshold signal. 
     According to another embodiment of the present invention, a method of operating a series resonant converter is provided. The method comprises receiving a DC voltage feedback signal representing an output DC voltage of the series resonant converter, or a resonant current feedback signal representing a resonant current flowing through the series resonant converter, and generating control signals to be applied to the series resonant converter to limit the output DC voltage of the series resonant converter according to the DC voltage feedback signal and a predetermined voltage threshold signal, or to limit the resonant current of the series resonant converter according to the resonant current feedback signal and a predetermined current threshold signal. 
     According to another embodiment of the present invention, a magnetic resonance system is provided. The system comprises a main magnet for generating a main magnetic field, a gradient coil for applying gradient magnetic field to the main magnetic field along selected gradient axes, a gradient amplifier coupled to the gradient coil for driving the gradient coil, a series resonant converter coupled to the gradient amplifier for supplying power to the gradient amplifier, wherein the series resonant converter is configured to convert an input direct current (DC) voltage to generate an output DC voltage, and a converter controller coupled to the series resonant converter. The converter controller is configured to receive a DC voltage feedback signal measured at the output of the series resonant converter, or a resonant current feedback signal representing a resonant current flowing through the series resonant converter, and to generate control signals to be applied to the series resonant converter to limit the output DC voltage of the series resonant converter according to the DC voltage feedback signal and a predetermined voltage threshold signal, or to limit the resonant current of the series resonant converter according to the resonant current feedback signal and a predetermined current threshold signal. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features and aspects of embodiments of the present disclosure will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
         FIG. 1  is a block diagram of a magnetic resonance system in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 2  is a schematic block diagram of a resonant power supply shown in  FIG. 1  in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 3  is a schematic block diagram of a resonant power supply shown in  FIG. 1  in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 4  is a timing diagram of various waveforms that are present in the resonant power supply shown in  FIG. 2  and  FIG. 3  in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 5  is a detailed control diagram implemented in a converter controller shown in  FIG. 2  in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 6  is a detailed control diagram implemented in the converter controller shown in  FIG. 3  in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 7  is a detailed control diagram implemented in the converter controller shown in  FIG. 2  or  FIG. 3  in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 8  is a detailed control diagram implemented in the converter controller shown in  FIG. 2  or  FIG. 3  in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 9  is a schematic block diagram of a gradient amplifier shown in  FIG. 1  in accordance with an exemplary embodiment of the present disclosure; 
         FIG. 10  is a detailed control diagram implemented by an inverter controller shown in  FIG. 9  in accordance with an exemplary embodiment of the present disclosure; and 
         FIG. 11  is a schematic block diagram of an exemplary magnetic resonance system in accordance with an exemplary embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS OF THE INVENTION 
     Exemplary embodiments disclosed herein relate to power supplies for supplying regulated power to a load. More specifically, a series resonant converter type power supply may be incorporated in a magnetic resonance imaging (MRI) system for supplying power to a gradient amplifier so as to enable the gradient amplifier to drive a gradient coil to generate gradient field to facilitate image acquisition. In particular, the power converted from the series resonant converter is regulated using a fixed frequency control algorithm. As used herein, “fixed frequency control algorithm” refers to the switching frequency of the switching devices used in the series resonant converter that is maintained at a constant value even when the input voltage to be regulated has fluctuations and the regulated voltage is experiencing transient conditions. In one implementation, the control is achieved by adjusting a phase delay between the switching signals for driving the switching devices in the series resonant converter. To make the series resonant converter respond quickly to load transient conditions, the “fixed frequency control algorithm” is designed to have two control loops. The first control loop is an average trajectory radius loop and the second control loop is a voltage loop. The average trajectory radius loop which is also an inner loop can be designed to have high bandwidth to make the series resonant converter respond quickly to load transient conditions and eliminate the impact of voltage fluctuations on a regulated output voltage. The second voltage loop which is an outer loop serves to regulate the output voltage according to commanded voltage signals. In some embodiments, an over-voltage protection mechanism and an over-current protection mechanism may be additionally or optionally included in the series resonant converter for protecting the series resonant converter from over-voltage and over-current problems. As can be understood, the over-voltage protection and over-current protection mechanisms can provide soft protection to the power supply without shutting down the power supply, which makes the power supply more stable. Another exemplary embodiment disclosed herein relates to compensating the voltage fluctuations of the input voltage applied to the gradient amplifier for driving the gradient coil. 
     One or more specific embodiments of the present disclosure will be described below. In an effort to provide a concise description of these embodiments, not all features of an actual implementation are described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
     Unless defined otherwise, technical and scientific terms used herein have the same meaning as is commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terms “first”, “second”, and the like, as used herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. Also, the terms “a” and “an” do not denote a limitation of quantity, but rather denote the presence of at least one of the referenced items. The term “or” is meant to be inclusive and mean either or all of the listed items. The use of “including,” “comprising,” or “having,” and variations thereof herein are meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The terms “connected” and “coupled” are not restricted to physical or mechanical connections or couplings, and can include electrical connections or couplings, whether direct or indirect. Furthermore, the terms “circuit”, “circuitry”, and “controller” may include either a single component or a plurality of components, which are either active and/or passive and are connected or otherwise coupled together (e.g., as one or more integrated circuit chips) to provide the described function. 
       FIG. 1  illustrates a block diagram of a sub-system  20  of a magnetic resonance system in accordance with an exemplary embodiment of the present disclosure. The sub-system  20  includes a resonant power supply  100  for receiving input power  102  from a power source (not shown) and regulating the input power  102  to provide output power  104 . The output power  104  is supplied to a gradient amplifier  400  which drives one or more gradient coils  600  (e.g., three gradients coils) to generate a gradient field  602  to facilitate image acquisition of the magnetic resonance system. In an embodiment, the resonant power supply  100  includes a series resonant converter that is operated to convert the input power  102  in the form of unregulated DC voltage to the output power  104  in the form of regulated DC voltage. As will be appreciated by those skilled in the art,  FIG. 1  generally illustrates one of the applications that the resonant power supply  100  can be used to supply power to one or more components of the system. It is not intended to limit the application to magnetic resonance system, and the resonant power supply  100  can be used to supply power in other applications such as communication, medical, welding and so on. 
       FIG. 2  is a schematic block diagram of the resonant power supply  100  shown in  FIG. 1  in accordance with one exemplary embodiment of the present disclosure. In general, the resonant power supply  100  shown in  FIG. 2  includes a switching stage  110 , a resonant tank circuit  120 , an isolation transformer  136 , an output stage  130 , and a converter controller  140 . The switching stage  110  receives input DC voltage  102  at two input terminals  105 ,  106  and selectively supplies the DC voltage  102  to the resonant tank circuit  120  according to the control signals sent from the converter controller  140 . The isolation transformer  136  serves to separate the resonant tank circuit  120  from the output stage  130 . The isolation transformer  136  includes a primary winding  138  and a secondary winding  142 . The primary winding  138  is coupled to the resonant tank circuit  120 , and the secondary winding  142  is coupled to the output stage  130 . The output stage  130  outputs a regulated DC voltage  157  at two output terminals  152 ,  154  and the regulated DC voltage  157  is applied to a load  156 . In an embodiment, the load  156  is the gradient amplifier  400  as shown in  FIG. 1 . 
     In an embodiment, the switching stage  110  is arranged with a full-bridge configuration and includes four switching elements  108 ,  112 ,  114 ,  116  and four diodes  118 ,  122 ,  124 ,  126 . The switching elements  108 ,  112 ,  114 ,  116  may be any suitable type of solid state switching devices, such as insulated gate bipolar transistors (IGBTs) and metal oxide semi-conductor field effect transistors (MOSFETs). Each of the diodes  118 ,  122 ,  124 ,  126  is respectively coupled with each of the switching elements  108 ,  112 ,  114 ,  116  in an anti-parallel configuration. The first switching element  108  and the second switching element  112  are coupled in series in a first converter leg  111  which may be referred to as a lag leg. The third switching element  114  and the fourth switching element  116  are coupled in series in a second converter leg  121  which may be referred to as a lead leg. As used herein, “lead” refers to the switching elements in the corresponding phase leg that initially change their switching state during a switching cycle, and “lag” refers to the switching elements in the corresponding leg that change their switching state with a phase delay with respect to the lead leg. In an embodiment, as will described below in reference to  FIG. 2 , the two switching elements  108 ,  112  in the lag leg  111  are operated in a complementary manner, that is, when the first switching element  108  is gated on, the second switching element  112  is gated off. Similarly, the two switching elements  114 ,  116  in the lead leg  121  are also operated in a complementary manner. In other embodiments, the switching stage  110  may be implemented to have a half-bridge configuration and any other suitable topologies as is known in the art. 
     With continued reference to  FIG. 2 , in one implementation, the resonant tank circuit  120  is coupled between a first node  109  (A) and a second node  115  (B), where the first node  109  is a joint connection between the first switching element  108  and the second switching element  112 , and the second node  115  is a joint connection between the third switching element  114  and the fourth switching element  116 . The resonant tank circuit  120  includes a resonant inductor  132  and a resonant capacitor  134 . The resonant inductor  132 , the resonant capacitor  134  and the primary winding  138  of the isolation transformer  136  are in series connected between the first node  109  and the second node  115 . 
     In an implementation, the output stage  130  includes a full-bridge rectifier  144  coupled to the secondary winding  142  of the isolation transformer  136 . The full-bridge rectifier  144  is configured to rectify the voltage generated across the second winding  142  of the isolation transformer  136 . The output stage  130  may further include an output capacitor  146  coupled in parallel with the full-bridge rectifier  144 . The output capacitor  146  functions as a low pass filter for removing ripple signals in the DC voltage rectified by the full-bridge rectifier  144 . In other embodiments, the output stage  130  may be implemented without using the output capacitor  146 . 
     The converter controller  140  is coupled to a plurality of sensors for monitoring various state variables in association with the series resonant converter  100 . The converter controller  140  is further coupled to the switching stage  110  for supplying switching signals  182 ,  184 ,  186 ,  188  to control operation of the switching devices  108 ,  112 ,  114 ,  116  in the switching stage  110 . In an implementation, the switching signals  182 ,  184 ,  186 ,  188  are generated by implementing a trajectory control according to the monitored state variables and command signals. As used herein, “trajectory control” refers to determining an instantaneous state of the series resonant converter according to various state variables. In an embodiment, the state variables may include a resonant inductor current flowing through the resonant inductor  132 , a resonant capacitor voltage at the resonant capacitor  134 , and a primary winding voltage at the primary winding  138 . The resonant inductor current can be sensed by a current sensor  192  which provides a resonant inductor current signal  168  to the converter controller  140 . The resonant capacitor voltage can be sensed by a first voltage sensor  194  which provides a resonant capacitor voltage signal  172  to the converter controller  140 . The primary voltage can be sensed by a second voltage sensor  196  which provides a primary voltage signal  174  to the converter controller  140 . The converter controller  140  further receives an output voltage feedback signal  162  sensed by a voltage sensor  158  and a voltage command signal  164  which indicates a desired voltage to be achieved at the output of the series resonant converter  100  for control operation of the series resonant converter  100 . 
     In an alternative embodiment, as shown in  FIG. 3 , the state variables may include a resonant inductor current flowing through the resonant inductor  132 , a resonant capacitor voltage at the resonant capacitor  134 , and an output voltage at the output of the series resonant converter  100 . The schematic block diagram shown in  FIG. 3  is similar to the schematic control diagram shown in  FIG. 2 . One of the differences is that the voltage sensor  196  for monitoring the primary voltage at the primary winding of the isolation transformer  136  is omitted in  FIG. 3 . In this embodiment, the converter controller  140  generates the switching signals  182 ,  184 ,  186 ,  188  according to the sensed resonant inductor current signal  168 , resonant capacitor voltage signal  172 , the output voltage feedback signal  162 , and the voltage command signal  164 . In one embodiment, the output voltage feedback signal is detected from the voltage applied to the load  156 . In other embodiments, the output voltage feedback signal  162  can be the voltage appearing at the secondary winding  142  of the isolation transformer  136 . 
       FIG. 4  is a timing diagram of various waveforms that are present in the resonant power supply  100  shown in  FIG. 2  and  FIG. 3  in accordance with an exemplary embodiment of the present disclosure. As shown in  FIG. 4 , a first waveform  182  and a second waveform  184  show the switching signals for driving the first switching device  108  and the second switching device  112  in the first converter leg  111  respectively. In an implementation, the first waveform  182  and the second waveform  184  are synchronized in a complementary manner, that is, when the first waveform  182  is on, the second waveform  184  is off and when the first waveform  182  is off, the second waveform  184  is on. Similarly, a third waveform  186  and a fourth waveform  188  show the switching signals for driving the third switching device  114  and fourth switching device  116  in the second converter leg  121  respectively. The third waveform  186  and the fourth waveform  188  have an adjustable phase delay  193  (Alpha) with respect to the first waveform  182  and the second waveform  184 . Further, a voltage waveform  189  shows the voltage across the first node  109  and the second node  115 , and a current waveform  191  shows the resonant current flowing through the resonant inductor  132  or the resonant tank circuit  120 . In one implementation, as shown in  FIG. 4 , the voltage waveform  189  shows that the voltage between the first node  109  and the second node  115  has three values, positive input DC voltage  102 , zero voltage, and negative input DC voltage  102 . In one implementation, as shown in  FIG. 4 , the current waveform  191  indicates that the resonant current flowing through the resonant inductor  132  or the resonant tank circuit  120  changes in a nearly sinusoidal and discontinuous manner. 
     In an implementation, there are six modes of operation for the series resonant converter  100  using a phase shifted control. Further referring to  FIG. 2  and  FIG. 3 , in the first mode, the first switching device  108  and the fourth switching device  116  are on, the voltage between the first node  109  and the second node  115  is equal to the positive input DC voltage  102 , and the resonant current flowing through the resonant inductor  132  rises continuously in a nearly sinusoidal waveform. In the second mode, the first switching device  108  is turned off, the fourth switching device  116  is kept on, and the diode  112  (D 2 ) is conducting for keeping the current flowing in a closed loop. During this period, the voltage between the first node  109  and the second node  115  is reduced to zero, and the current flowing through the resonant inductor  132  decreases gradually in a nearly sinusoidal waveform. After the resonant current reduces to zero, the states of four switching devices are kept unchanged to make the resonant current remain at zero for a certain time, which is the third mode. That is, the series resonant converter  100  is working in a current discontinuous mode. In the fourth mode, the second switching device  112  and the third switching device  114  are on, the voltage between the first node  109  and the second node  115  is equal to the negative input DC voltage  102 , and the resonant current flows through the resonant inductor  132  in an opposite direction in a nearly sinusoidal waveform. In the fifth mode, the second switching device  112  is turned off, the third switching device  114  is kept on, and the diode  124  (D 3 ) is conducting for keeping the current flowing in a closed loop. During this period, the voltage between the first node  109  and the second node  115  is reduced to zero, and the current also flows through the resonant inductor  132  in a nearly sinusoidal waveform. After the resonant current reaches zero, the states of four switching devices are kept unchanged to make the resonant current remain at zero for certain time which is the sixth mode. 
       FIG. 5  is a detailed control diagram implemented in a converter controller  140  shown in  FIG. 2  in accordance with one exemplary embodiment of the present disclosure. The various blocks illustrated in  FIG. 5  can be implemented in hardware or software or a combination thereof. In practical applications, the converter controller  140  may be implemented by a micro-controller or a digital signal processor (DSP). The converter controller  140  may be a proportional-integral (PI) controller, a proportional controller, a state space controller, a non-linear controller, or any other suitable controllers. In general, the control diagram shown in  FIG. 5  includes two control loops, that is, an outer loop  210  and an inner loop  220 . The outer loop  210  is a voltage loop which is designed to regulate the output voltage or load voltage according to commanded voltage signals. More specifically, the converter controller  140  includes a summation element  202  that is configured to receive an output voltage feedback signal  162  from the output stage  130  of the series resonant converter  100 . The summation element  202  also receives a voltage command signal  204  representative of the voltage to be achieved at the output of the output stage  130  of the series resonant converter  100 . The summation element  202  subtracts the output voltage signal  162  from the voltage command signal  204  and derives a voltage error signal  206 . The derived voltage error signal  206  is supplied to a voltage regulator  208  for generating a trajectory radius command signal  212  designed to drive the voltage error signal  206  to zero. The inner loop  220  is an average trajectory radius loop that is designed to regulate an actual trajectory radius signal according to the trajectory radius command signal  212 . The trajectory radius command signal  212  represents the desired energy to be transmitted from the series resonant converter  100  to the load. More specifically, the converter controller  140  includes a processing module  252  that is used to calculate an actual trajectory radius according to the sensed resonant inductor current signal  168 , the resonant capacitor voltage signal  232 , and the primary winding voltage signal  233 . 
     In an implementation, the processing module  252  includes an average unit  234  and a radius calculator  242  coupled to the average unit  234 . The average unit  234  is configured to receive the resonant inductor current signal  168 , the resonant capacitor voltage signal  232 , and the primary winding voltage signal  233 , and calculates an average resonant inductor current signal  236 , an average resonant capacitor voltage signal  237 , and an average primary winding voltage signal  238  accordingly. The resonant capacitor voltage  233  can be expressed according to the following equation: 
                         V   cr     ⁡     (   t   )       =       (       V   dc     -     V   pri       )     ⁢     {     1   -     cos   (     t         L   r     ⁢     c   r           )       }         ,           Eqn   .           ⁢   1               
where in Eqn. 1, V cr (t) is the resonant capacitor voltage  172 , V dc  is the input DC voltage  102 , V pri  is the primary voltage  174 , L r  is the inductance of the resonant inductor  132 , c r  is the capacitance of the resonant capacitor  134 . The resonant inductor current  168  can be expressed according to the following equation:
 
                         I   Lr     ⁡     (   t   )       =         (       V   dc     -     V   pri       )           L   r     ⁢     c   r           ⁢     sin   (     t         L   r     ⁢     c   r           )         ,           Eqn   .           ⁢   2               
where in Eqn. 2, I Lr (t) is the resonant inductor current  168 , V dc  is the input DC voltage  102 , V pri  is the primary voltage  174 , L r  is the inductance of the resonant inductor  132 , C r  is the capacitance of the resonant capacitor  134 . The solutions to the equations (1) and (2) are circles when drawn in a V cr −Z 0 I Lr  state plane, where Z 0  is the characteristic impedance of the resonant tank circuit  120  and can be expressed according to the following equation:
 
                       Z   0     =         L   r       C   r           ,           Eqn   .           ⁢   3               
Where in Eqn. 3, L r  is the inductance of the resonant inductor  132 , C r  is the capacitance of the resonant capacitor  134 .
 
     In an implementation, the average unit  234  employs a low pass filter for generating root mean square values of the received resonant inductor current signal  168 , resonant capacitor voltage signal  232 , and primary winding voltage signal  233 . The radius calculator  242  is configured to calculate the actual trajectory radius signal  246  according to the average resonant current signal  236 , the average resonant capacitor voltage signal  237 , and the average primary winding voltage  238 . More particularly, the radius calculator  242  employs a control law for calculating a radius distance squared from the point (−V pri , 0) in the V cr −Z 0 I lr  state plane. In an implementation, the actual trajectory radius signal  246  is calculated by the radius calculator  242  according to the following equation:
 
RADIUS 2 =( Z   0   *I   Lr ) 2 +( V   Cr   +V   pri ) 2   Eqn. 4
 
Where in Eqn. 4, Z 0  is the characteristic impedance of the resonant inductor  132  and the resonant capacitor  134 , I Lr  is the resonant inductor current  236 , V cr  is the resonant capacitor voltage  237 , V pri  is the primary winding voltage  238 , and RADIUS is the average radius of the state trajectory.
 
     The converter controller  140  further includes a second summation element  214  for receiving the trajectory radius command signal  212  as a positive input and the actual trajectory radius signal  236  as a negative input. The second summation element  214  subtracts the actual trajectory radius signal  236  and the trajectory radius command signal  212 , and derives a radius error signal  216 , which is supplied to the radius regulator  218 . The radius regulator  218  generates a modulation index signal  222  according to the radius error signal  216 . In an implementation, the modulation index signal  222  includes a phase delay between the lead leg  121  and the lag leg  111  as shown in  FIG. 2 . The modulation index signal  222  is supplied to the signal generator  224  for generation of the driving signals that are used to drive the switching devices in the switching stage  110  shown in  FIG. 2 . 
       FIG. 6  is a detailed control diagram implemented in the converter controller  140  shown in  FIG. 3  in accordance with one exemplary embodiment of the present disclosure. The control diagram shown in  FIG. 6  is similar to the control diagram shown in  FIG. 5 . One of the differences is that the output voltage or the load voltage generated from the output stage  130  of the series resonant converter  100  is used in calculation of the actual trajectory radius signal  246  instead of using a primary voltage  233 . Correspondingly, the average unit  234  processes the output voltage feedback signal  162  to generate an average output voltage signal  239 . In an implementation, the actual trajectory radius signal  246  is calculated by the radius calculator  242  according to the following equation: 
                       RADIUS   2     =         (       Z   0     *     I   Lr       )     2     +       (       V   Cr     +       V   load     N       )     2         ,     
     ⁢       for   ⁢     :     ⁢           ⁢     I   Lr       &gt;   0     ,           Eqn   .           ⁢   5                   RADIUS   2     =         (       Z   0     *     I   Lr       )     2     +       (       V   Cr     -       V   load     N       )     2         ,     
     ⁢       for   ⁢     :     ⁢           ⁢     I   Lr       &lt;   0     ,           Eqn   .           ⁢   6               
where in the Eqns. 5 and 6, Z 0  is the characteristic impedance of the resonant inductor  132  and the resonant capacitor  134 , I Lr  is the resonant inductor current  236 , V Cr  is the resonant capacitor voltage  239 , V load  is the output voltage  162 , N is the turn ratio of the isolation transformer  136 , and RADIUS is the average radius of the state trajectory.
 
       FIG. 7  is a detailed control diagram implemented in the converter controller  140  shown in  FIG. 2  or  FIG. 3  in accordance with another exemplary embodiment of the present disclosure. The control diagram shown in  FIG. 7  is similar to the control diagrams shown in  FIG. 5  and  FIG. 6 . One of the differences is that the converter controller  140  shown in  FIG. 7  further includes a voltage limit module  262 . In general, the voltage limit module  262  is provided for limiting transient voltage conditions such as over voltage conditions related to the output voltage of the series resonant converter  100 . More specifically, the voltage limit module  262  is configured to modify the voltage error signal  206  when the output voltage signal  162  exceeds a threshold voltage. 
     In an implementation, as shown in  FIG. 7 , the voltage limit module  262  includes a voltage reference unit  264 , a third summation element  268 , a limiter  274 , and a fourth summation element  278 . The voltage reference unit  264  is configured to provide a voltage threshold signal  266  as a negative input to the third summation element  268 , which also receives the output voltage signal  162  as a positive input. The resulted voltage error signal  272  representing a difference between the output voltage signal  162  and the voltage threshold signal  266  is supplied to the limiter  274 , which may be set with an upper limit and a lower limit for limiting the voltage error signal  272 . The limited voltage signal  276  is supplied as a negative input to the fourth summation element  278  which also receives the voltage error signal  206  as the positive input. The fourth summation element  278  subtracts the limited voltage signal  276  from the voltage error signal  206  and provides another voltage error signal  282  to the voltage regulator  208 . In an implementation, the limiter  274  is configured to allow positive voltage error signal to pass through while block negative voltage error signal. In operation, when the output voltage exceeds the preset threshold voltage, that is, the output voltage signal  162  is greater than the threshold voltage signal  266 , and the voltage error signal  272  is positive. The positive voltage error signal  272  passes through the limiter  274  and is supplied to the fourth summation element  278 . When the output voltage falls below the preset threshold voltage, the output voltage signal  162  is smaller than the threshold voltage signal  266 , and the voltage error signal  272  is negative. In this case, the limiter  274  blocks the negative voltage error signal  272 . 
       FIG. 8  is a detailed control diagram implemented in the converter controller  140  shown in  FIG. 2  or  FIG. 3  in accordance with yet another exemplary embodiment of the present disclosure. The control diagram shown in  FIG. 8  is similar to the control diagrams shown in  FIG. 5  and  FIG. 6 . One of the differences is that the converter controller  140  shown in  FIG. 8  further includes a current limit module  290 . In general, the current limit module  290  is provided for limiting over current conditions related to the resonant tank circuit  120 . 
     In an implementation, as shown in  FIG. 8 , the current limit module  290  includes a fifth summation element  286 , a current reference unit  288 , a current regulator  296 , and a limiter  298 . The fifth summation element  286  is configured to receive the resonant inductor current signal  168  and a current threshold signal  292  provided from the current reference unit  288 . The current threshold signal  292  indicates a maximum allowable current to be flowing through the resonant tank circuit  120 . The resulted current error signal  294  representing a difference between the resonant inductor current signal  168  and the threshold current signal  292  is supplied to the current regulator  296 . In an embodiment, the current regulator  196  is a PI controller. The current regulator  296  generates a modulation index correction signal  295  according to the current error signal  294 . The modulation index correction signal  295  is limited by the limiter  298  which supplies a limited modulation index correction signal  299  to the sixth summation element  221 . When the resonant inductor current exceeds the preset threshold value, that is, the resonant inductor current signal  168  is greater than the current threshold signal  292 , the current error signal  294  will be positive. In such case, the modulation index signal  222  is reduced, and the signal generator  224  uses the reduced modulation index signal  222  to adjust the control signals  226  sent to the series resonant converter  228  so as to reduce the resonant inductor current flowing through the resonant tank circuit  120 . When the resonant inductor current signal  168  is smaller than the current threshold signal  292 , the current error signal  294  will be negative, and the limiter  298  will block the modulation index correction signal  295  provided from the current regulator  296 , such that the modulation index signal  222  remains unchanged in this condition. 
       FIG. 9  is a schematic block diagram of a gradient amplifier  400  shown in  FIG. 1  in accordance with one exemplary embodiment of the present disclosure. The gradient amplifier  400  is configured to accept power from a power supply and provide output signals for driving a load  438 , such as a gradient coil for example. In an embodiment, the gradient amplifier  400  is a switching type amplifier. The switching type gradient amplifier  400  receives input DC voltage  406  at input terminals  402 ,  404 . The input DC voltage  406  may be generated from the series resonant converter  100  using the various control algorithms described above with reference to  FIGS. 2-8 . The gradient amplifier  400  includes an input filter  408 , which is shown as a smoothing capacitor for removing ripple signals contained in the input DC voltage  406 . The gradient amplifier  400  further includes an inverter  410  and an inverter controller  420  electrically coupled to the inverter  410 . The filtered DC voltage  409  is applied to the inverter  410  which is controlled under the control signals provided from the inverter controller  420  to generate output voltage  434  at two nodes  415 ,  417 . The gradient amplifier  400  further includes an output stage  436  for supplying the output voltage  434  to the load  438 . 
     Further referring to  FIG. 9 , the inverter  410  includes four switching devices  414 ,  416 ,  418 ,  422  and four free-wheeling diodes  424 ,  426 ,  428 ,  432 . The switching devices  414 ,  416 ,  418 ,  422  may be any suitable switching devices, such as insulated gate bipolar transistors (IGBTs) and metal oxide semi-conductor field effect transistors (MOSFETs). The switching devices  414 ,  416 ,  418 ,  422  can be gated on or off according to switching signals provided from the inverter controller  420 . 
     With continued reference to  FIG. 9 , the inverter controller  420  includes a compensation circuit  456 , a regulation circuit  446 , and a modulation circuit  452 . The compensation circuit  456  is configured to receive an input DC voltage feedback signal  299  at a DC bus  407  obtained by means of a voltage sensor  412  placed across the capacitor  408 . The compensation circuit  456  provides a compensation factor signal  458  indicating a voltage fluctuation of the input DC voltage  406 . The compensation factor signal  458  is supplied to the modulation circuit  452  in generation of switching signals  462 ,  464 ,  466 ,  468 . The regulation circuit  446  is configured to receive a reference voltage signal  444  indicating a desired voltage to be achieved at the output of the gradient amplifier  400 . The regulation circuit  446  also receives a feedback output voltage signal  442  representing an actual output voltage produced by the gradient amplifier  400 . The regulation circuit  446  further provides a regulator signal  448  according to the feedback output voltage signal  442  and the reference voltage signal  444 . The regulator signal  448  is used for generating the switching signals  462 ,  464 ,  466 ,  468  for controlling operation of the switching devices  414 ,  416 ,  418 ,  422 . 
       FIG. 10  is a detailed control diagram implemented by an inverter controller  420  shown in  FIG. 9  in accordance with an exemplary embodiment of the present disclosure. More specifically, the regulation circuit  446  includes a difference element  472 , an integration element  476 , a proportional element  478 , a differentiation element  482 , and a summation element  486 . The difference element  472  is configured to receive the reference voltage signal  444  and the feedback output voltage signal  442  and generates a voltage error signal  474  representing a difference between the reference voltage signal  444  and the feedback output voltage signal  442 . The voltage error signal  474  is supplied to the integration element  476 , the proportional element  478 , and the differentiation element  482 . The resulting signals processed by the integration element  476 , the proportional element  478 , and the differentiation element  482  are combined in the summation element  486  to generate the regulation signal  448 . 
     With continued reference to  FIG. 10 , the inverter controller  420  further includes a multiplication element  492  which is configured to multiply a carrier signal  488  by a compensation factor signal  458  and generate a compensated carrier signal  494 . In one embodiment, the compensation factor signal  458  can be provided from the compensation circuit shown in  FIG. 9  according to the following equation: 
                     CF   =       U   in       U   N         ,           Eqn   .           ⁢   7               
where in Eqn. 7, U in  is the feedback DC voltage measured at the input of the inverter  410 , U N  is a nominal voltage desired to be supplied at the input of the inverter  410 , and CF is the compensation factor signal  458 .
 
     With continued reference to  FIG. 10 , the inverter controller  420  further includes a comparator  496  which is configured to receive the regulation signal  448  provided from the regulation circuit  492  and the compensated carrier signal  494 . The comparator  496  is further configured to generate the switching signals  462 ,  464 ,  466 ,  468  by comparing the regulation signal  448  and the compensated carrier signal  494 . 
     In an implementation, the switching devices  414 ,  422  are turned on synchronously, and the switching devices  418 ,  416  are also turned on synchronously. Further, the switching devices  414 ,  418  are operated in a complementary manner, and the switching devices  416 ,  422  are operated in a complementary manner, thus, the following equations apply:
 
 MS   1   +MS   2 =1  Eqn. 8
 
 MS   3   +MS   4 =1  Eqn. 9
 
where in Eqn. 8 and Eqn. 9, MS 1  is the duty cycle of the switching signal  462 , MS 2  is the duty cycle of the switching signal  464 , MS 3  is the duty cycle of the switching signal  466 , and MS 4  is the duty cycle of the switching signal  468 . In one implementation, the carrier signal  494  is voltage signal having a triangular waveform and is defined with a positive maximum magnitude CS 0  and a negative maximum magnitude −CS 0 . In an implementation, the duty cycles for example, the duty cycle MS 1  of the switching signal  462  can be generated according to the following equation:
 
                       MS   1     =     0.5   +     0.5   *     RS     CS   0             ,           Eqn   .           ⁢   10               
where RS is the regulation signal  448  generated by the regulation circuit  446 , CS 0  is the positive maximum magnitude of the carrier signal  494 . The relationship between the duty cycle MS 1  and the output voltage  434  can be expressed by the following equation:
 
                       U   out     =           U   in     0.5     *     MS   1       -     U   in         ,           Eqn   .           ⁢   11               
where U out  is the output voltage  434 , U in  is the input DC voltage  406 . Combining the equations 10 and 11, it can yield:
 
                       U   out     =       U   in     *     RS     CS   0           ,           Eqn   .           ⁢   12               
From equation 12, it can be known that the output voltage  434  is not only linearly dependent on the regulation signal RS, but also dependent on the input DC voltage  406 . For compensating the fluctuations in the input DC voltage  406 , the output voltage  434  can be modified as the following equation:
 
                       U   out     =         U   in     *     RS       CS   0     *   CF         =       U   N     *     RS     CS   0             ,           Eqn   .           ⁢   13               
From equation 13, it can be seen that the modified output voltage  434  is only dependent on the regulation signal  448  after compensation. Thus, the fluctuations in the input DC voltage are substantially eliminated.
 
       FIG. 11  is a schematic block diagram of an exemplary magnetic resonance (MR) system  10  in accordance with one embodiment of the present disclosure. The MR system  10  is capable of incorporating the various embodiments described above for supplying power to gradient amplifiers of the MR system  10 . The operation of MR system  10  is controlled from an operator console  12  that includes an input device  13 , a control panel  14 , and a display  16 . The operator console  12  communicates through a link  18  with a computer system  20  and provides an interface for an operator to prescribe MR scans, display resultant images, perform image processing on the images, and archive data and images. The input device  13  may include a mouse, joystick, keyboard, track ball, touch activated screen, light wand, voice control, or any similar or equivalent input device, and may be used for interactive geometry prescription. 
     The computer system  20  includes a number of modules that communicate with each other through electrical and/or data connections, for example, such as are provided by using a backplane  20 A. Data connections may be wired links or wireless communication links or the like. The modules of the computer system  20  may include an image processor module  22 , a CPU module  24 , and a memory module  26 . The memory module  26  may include a frame buffer for storing image data arrays. The memory module  26  includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the image data arrays. In an alternative embodiment, the image processor module  22  may be replaced by image processing functionality on the CPU module  24 . The computer system  20  may be linked to archival media devices, permanent or back-up memory storage or a network. The computer system  20  may also communicate with a separate system control computer  32  through a link  34 . 
     The system control computer  32  in one aspect includes a set of modules in communication with each other via electrical and/or data connections  32 A. Data connections  32   a  may be wired links or wireless communication links or the like. In alternative embodiments, the modules of computer system  20  and system control computer  32  may be implemented on the same computer system or a plurality of computer systems. The modules of system control computer  32  may include a CPU module  36  and a pulse generator module  38  that connects to the operator console  12  through a communications link  40 . 
     The pulse generator module  38  in one example is integrated into the scanner equipment (e.g., resonance assembly  52 ). It is through link  40  that the system control computer  32  receives commands from the operator to indicate the scan sequence that is to be performed. The pulse generator module  38  operates the system components that perform the desired pulse sequence by sending instructions, commands and/or requests describing the timing, strength and shape of the RF pulses and pulse sequences to be produced and the timing and length of the data acquisition window. The pulse generator module  38  connects to a gradient amplifier system  42  and produces data called gradient waveforms that control the timing and shape of the gradient pulses that are used during the scan. The pulse generator module  38  may also receive patient data from a physiological acquisition controller  44  that receives signals from a number of different sensors connected to the patient, such as ECG signals from electrodes attached to the patient. The pulse generator module  38  connects to a scan room interface circuit  46  that receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit  46  that a patient positioning system  48  receives commands to move the patient table to the desired position for the scan. 
     The gradient waveforms produced by the pulse generator module  38  are applied to the gradient amplifier system  42  that is comprised of Gx, Gy, and Gz amplifiers. Each gradient amplifier excites a corresponding physical gradient coil in a gradient coil assembly generally designated  50  to produce the magnetic field gradient pulses used for spatially encoding acquired signals. The gradient coil assembly  50  forms part of a resonance assembly  52  that includes a polarizing superconducting magnet with superconducting main coils  54 . In one implementation, the MR system  10  includes a power supply  43  for supplying power to the gradient amplifier system  42 . The power supply  43  may be constructed from embodiments described above with reference to  FIGS. 1-10 . 
     Resonance assembly  52  may include a whole-body RF coil  56 , surface or parallel imaging coils  76  or both. The coils  56 ,  76  of the RF coil assembly may be configured for both transmitting and receiving or for transmit-only or receive-only. A patient or imaging subject  70  may be positioned within a cylindrical patient imaging volume  72  of the resonance assembly  52 . A transceiver module  58  in the system control computer  32  produces pulses that are amplified by an RF amplifier  60  and coupled to the RF coils  56 ,  76  by a transmit/receive switch  62 . The resulting signals emitted by the excited nuclei in the patient may be sensed by the same RF coil  56  and coupled through the transmit/receive switch  62  to a preamplifier  64 . Alternatively, the signals emitted by the excited nuclei may be sensed by separate receive coils such as parallel coils or surface coils  76 . The amplified MR signals are demodulated, filtered and digitized in the receiver section of the transceiver  58 . The transmit/receive switch  62  is controlled by a signal from the pulse generator module  38  to electrically connect the RF amplifier  60  to the RF coil  56  during the transmit mode and to connect the preamplifier  64  to the RF coil  56  during the receive mode. The transmit/receive switch  62  can also enable a separate RF coil (for example, a parallel or surface coil  76 ) to be used in either the transmit mode or receive mode. 
     The MR signals sensed by the RF coil  56  are digitized by the transceiver module  58  and transferred to a memory module  66  in the system control computer  32 . Typically, frames of data corresponding to MR signals are stored temporarily in the memory module  66  until they are subsequently transformed to create images. An array processor  68  uses a known transformation method, most commonly a Fourier transform, to create images from the MR signals. These images are communicated through the link  34  to the computer system  20  where it is stored in memory. In response to commands received from the operator console  12 , this image data may be archived in long-term storage or it may be further processed by the image processor  22  and conveyed to the operator console  12  and presented on the display  16 . The system control computer  32  further includes a hyperthermia source for generating hyperthermia RF signals. 
     While the disclosure has been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the disclosure. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the disclosure without departing from the essential scope thereof. Therefore, it is intended that the disclosure not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this disclosure, but that the disclosure will include all embodiments falling within the scope of the appended claims.