Patent Publication Number: US-2022238269-A1

Title: System To Optimize Voltage Distribution Along High Voltage Doubler String

Description:
FIELD 
     Embodiments of this disclosure are directed to systems for uniformly distributing voltage along a high voltage doubler string in the secondary windings of a printed circuit board. 
     BACKGROUND 
     Insulated Core Transformer (ICT) high voltage power supplies are a common method of generating a high voltage DC output from an AC voltage. The input AC voltage is in communication with a primary winding. 
     In certain embodiments, there is a single secondary winding that multiplies the input voltage by a factor equal to the ratio of the number of turns in the secondary winding to the number of turns in the primary winding. Rectification and doubling of the voltage is provided using a voltage doubler circuit, which comprises diodes and capacitors. Typically, the voltage doubler comprises two capacitors to store voltage and two diodes, each of which allows current flow in only one direction. The capacitors are arranged in series, resulting in a doubling of the voltage. Because of cost and high voltage ratings, rather than using two diodes and two capacitors, a larger number of low voltage rated diodes and capacitors may be arranged in series. For example, 20 capacitors, each rated for 100V, may be arranged in series rather than using two capacitors, each rated for 1000V. Diodes may be similarly configured. 
     In other embodiments, there are a plurality of secondary windings, each with a dedicated voltage doubler circuit. The voltage doubler circuits are arranged in series to generate the desired higher DC voltage. 
     In each embodiment, ideally, the same voltage would be stored by each capacitor in the system. In other words, if the desired output voltage was 2000V, and there were 20 capacitors, ideally, there would be a 100V potential across each of these capacitors. However, in reality, stray capacitance affects each capacitor, such that some store less than the ideal voltage, while other capacitors are forced to store more than the ideal voltage. Similarly, the voltage across some diodes may be greater than the voltage across other diodes. 
     This non-uniform distribution of voltage across the capacitors and diodes may lead to voltage stress on these components, which may result in premature component failure. 
     Therefore, it would be advantageous if there were a system and method to improve the voltage uniformity across these components. Further, it would be beneficial if this approach was low cost and easy to implement. 
     SUMMARY 
     A high voltage power supply is disclosed. The high voltage power supply comprises a primary winding and one or more secondary windings. In one embodiment, a single secondary winding is used and the high voltage doubler circuit comprises a capacitor string and a diode string. In another embodiment, a plurality of secondary windings are used and the high voltage doubler circuit comprises a plurality of low voltage doubler circuits arranged in series. To create a more uniform distribution of voltage across the capacitors in the high voltage doubler circuit, one or more shields are disposed on the printed circuit board. In certain embodiments, a high voltage shield is disposed at the high voltage output and a low voltage shield is disposed at the lower voltage end of the high voltage doubler circuit. One or more intermediate shields may be disposed in the high voltage doubler circuit. 
     According to one embodiment, a high voltage power supply is disclosed. The high voltage power supply comprises a primary winding; a secondary winding, having a first end and a second end; and a printed circuit board comprising: a capacitor string, comprising a plurality of capacitors arranged in series, wherein a negative end of a first capacitor in the capacitor string is at a lower voltage and a positive end of a last capacitor in the capacitor string is at a high voltage output; a diode string, comprising a plurality of diode arranged in series, wherein an anode of a first diode in the diode string is connected to the lower voltage and a cathode of a last diode in the diode string is connected to the high voltage output; wherein the first end is electrically connected to a midpoint of the capacitor string and the second end is electrically connected to a midpoint of the diode string; and a high voltage shield disposed at the positive end of the last capacitor and electrically connected to the high voltage output, wherein a shield comprises a wide trace disposed on one or more layers of the printed circuit board. In certain embodiments, the high voltage power supply comprises a low voltage shield disposed at the negative end of the first capacitor and electrically connected to the lower voltage. In certain embodiments, the high voltage shield and the low voltage shield each comprises a signal trace having a length of between 40 mm and 100 mm and a width of between 3 mm and 10 mm. In some embodiments, the high voltage shield and the low voltage shield are disposed on a same side of the printed circuit board as the capacitor string. In some embodiments, the high voltage shield and the low voltage shield are disposed on an opposite side of the printed circuit board as the capacitor string. In certain embodiments, the high voltage power supply comprises an intermediate shield disposed between two adjacent capacitors in the capacitor string and electrically connected to a trace connecting the two adjacent capacitors. In certain embodiments, the intermediate shield is disposed at the midpoint of the capacitor string. In certain embodiments, the high voltage power supply comprises a second intermediate shield disposed between a different two adjacent capacitors in the capacitor string. In some embodiments, a voltage across the first capacitor is within 10% of a voltage across the last capacitor. 
     According to another embodiment, a high voltage power supply is disclosed. The high voltage power supply comprises: a primary winding; a plurality of secondary windings, each having a first end and a second end; and a printed circuit board comprising: a plurality of low voltage doubler circuits, arranged in series, to form a high voltage doubler circuit having a lower voltage at a first end and a high voltage output at a second end, wherein each low voltage doubler circuit comprises a positive end and a negative end and comprises a first capacitor and a second capacitor arranged in series and a first diode and a second diode arranged in series, wherein a positive end of the first capacitor is electrically connected a cathode of the first diode and comprises the positive end of the low voltage doubler circuit, and a negative end of a second capacitor is electrically connected to an anode of the second diode and comprises the negative end of the low voltage doubler circuit, wherein a first end of a respective secondary winding is electrically connected to a trace connecting the first capacitor and the second capacitor, and the second end of the secondary winding is electrically connected to a trace connecting the first diode and the second diode; and a high voltage shield disposed at the second end of the high voltage doubler circuit and electrically connected to the high voltage output, wherein a shield comprises a wide trace disposed on one or more layers of the printed circuit board. In certain embodiments, the high voltage power supply comprises a low voltage shield disposed at the first end of the high voltage doubler circuit and electrically connected to the lower voltage. In some embodiments, the high voltage shield and the low voltage shield each comprises a signal trace having a length of between 40 mm and 100 mm and a width of between 3 mm and 10 mm. In some embodiments, the high voltage shield and the low voltage shield are disposed on a same side of the printed circuit board as the high voltage doubler circuit. In some embodiments, the high voltage shield and the low voltage shield are disposed on an opposite side of the printed circuit board as the high voltage doubler circuit. In certain embodiments, the high voltage power supply comprises an intermediate shield disposed between two adjacent low voltage doubler circuits. In some embodiments, the intermediate shield is disposed at a midpoint of the high voltage doubler circuit. In certain embodiments, the high voltage power supply comprises a second intermediate shield disposed between a different two adjacent low voltage doubler circuits. In some embodiments, a voltage across a first low voltage doubler circuit disposed closest to the first end is within 10% of a voltage across a last low voltage doubler circuit disposed closest to the second end. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       For a better understanding of the present disclosure, reference is made to the accompanying drawings, which are incorporated herein by reference and in which: 
         FIG. 1  shows a representative schematic showing a high voltage power supply in which voltage non-uniformity has been compensated according to one embodiment; 
         FIG. 2  shows the layout of the high voltage power supply of  FIG. 1  according to one embodiment; 
         FIG. 3  shows a representative schematic showing a high voltage power supply in which voltage non-uniformity has been compensated according to one embodiment; 
         FIG. 4  shows the layout of the high voltage power supply of  FIG. 3  according to one embodiment; 
         FIG. 5  shows a process to determine the placement, dimensions and number of shields according to one embodiment; and 
         FIG. 6  shows the voltage distribution of elements in a high voltage power supply as compared to the prior art. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure describes a system and method for creating a more uniform voltage distribution across a plurality of capacitors and diodes in an ICT high voltage DC power supply. 
       FIG. 1  shows a first embodiment of a voltage doubler circuit  1 , wherein there is an external power supply  10 , a primary winding  20  and a single secondary winding  30 . The components of the voltage doubler circuit  1  are disposed on a printed circuit board. The printed circuit board may be a traditional printed circuit board having a plurality of layers, wherein conductive layers are separated from one another by an insulating material, such as FR4. In certain embodiments, the printed circuit may comprise two conductive layers; the top surface and the bottom surface. Electrical traces may be disposed on these layers of the printed circuit board. Via may be used to connect traces on the top surface to traces on the bottom surface. These electrical traces are used to electrically connect various components disposed on the printed circuit board. In other embodiments, there may be more than two conductive layers. 
     The voltage doubler circuit  1  also comprises a capacitor string. The string comprises a plurality of capacitors  100 , such as capacitors  100   a ,  100   b ,  100   c ,  100   d  arranged in series. The capacitor may each have the same capacitance and voltage rating. A first end of the capacitor string is connected to the lower voltage, which may be ground, and the second end of the capacitor string is the high voltage output  150 . The voltage doubler circuit  1  also comprises a string of diodes. The diode string comprises plurality of diodes  110 , such as diodes  110   a ,  110   b ,  110   c ,  110   d , also arranged in series. A first end of the diode string is connected to the lower voltage, and the second end of the diode string is the high voltage output  150 . The cathode of one diode is connected to an anode of an adjacent diode in the diode string. Thus, the anode of the first diode is connected to the lower voltage and the cathode of the last diode in the diode string is connected to the high voltage output  150 . During the positive portion of the AC cycle, diodes  110   a ,  110   b  conduct and charge the capacitors  100   a ,  100   b  disposed between the midpoint and the high voltage output  150 . During the negative portion of the AC cycle, diodes  110   c , 110   d  conduct and charge the capacitors  100   c ,  100   d  disposed between the midpoint and the lower voltage. Thus, the cathode of each diode is at a higher voltage than the anode of that diode. Further, diode  110   a  is at a higher voltage than diode  110   b . Similarly, diode  110   c  is at a higher voltage than diode  110   d.    
     In certain embodiments, the number of diodes  110  and capacitors  100  is equal. In other embodiments, the number of diodes  110  and capacitors  100  may be different. The number of capacitors  100  and diodes  110  may be an even number such that there is an equal number of diodes and capacitors on each side of the midpoint. The first end of the secondary winding  30  is electrically connected to the midpoint of the capacitor string. The second end of the secondary winding  30  is electrically connected to the midpoint of the diode string. The midpoint denotes that the same number of capacitors  100  (and diodes  110 ) are disposed between the first end and the midpoint as are disposed between the midpoint and the second end. 
     While  FIG. 1  shows four capacitors  100   a ,  100   b ,  100   c ,  100   d  and four diodes  110   a ,  110   b ,  110   c ,  110   d , the disclosure is not limited to this embodiment. Rather, the number of capacitors  100  and diodes  110  is not limited by this disclosure. Further, the number of capacitors  100  and diodes  110  do not need to be the same. 
     Because the voltage doubler circuit  1  is disposed on a printed circuit board, there may an inherent capacitance between each trace in the voltage doubler circuit  1  and other traces that are at a different voltage. These stray capacitances are illustrated in  FIG. 1  as stray capacitor  120   a ,  120   b ,  120   c . Note that these stray capacitors  120   a ,  120   b ,  120   c  are not physical components. Rather,  FIG. 1  represents the stray capacitance as actual components to better illustrate the subject matter. Although not shown, there is stray capacitance associated with each diode  110 . 
     In reality, the stray capacitors  120   a ,  120   b ,  120   c  affect the voltage that is stored in each capacitor  100   a ,  100   b ,  100   c ,  100   d . In practice, as current flows down the capacitor string, a small amount of current is diverted from each trace and passes through the corresponding stray capacitor. Therefore, slightly more current may flow through capacitor  100   a  than flows through capacitor  100   b . This may cause more voltage to be stored by capacitor  100   a  than by capacitor  100   b . Similarly, more current may flow through capacitor  100   b  than flows through capacitor  100   c.    
     To compensate for this stray capacitance, the present system utilizes one or more shields  130 . A shield  130  is a wide trace disposed on one or more layers of the printed circuit board. A shield may have a width and/or length that is larger than a typical trace. For example, a shield may be a rectangular trace that is connected to a voltage. For example, in certain embodiments, the shield  130  may be disposed on the top surface or the bottom surface of the printed circuit board. In certain embodiments, the shield  130  may be disposed on both the top surface and the bottom surface. The shield  130  is electrically connected to a voltage. For example, in  FIG. 1 , there are three shields  130 . The high voltage shield  130   a  is disposed at the top of the capacitor string and electrically connected to the high voltage output  150 . 
     Due to the size of the high voltage shield  130   a , it creates capacitive coupling with other traces in the voltage doubler circuit  1 . For example, there is a capacitive coupling between the high voltage shield  130   a  and the lower voltage end of capacitor  100   a . This capacitance is represented as shield capacitor  140   a . Similar capacitive coupling exists between the high voltage shield  130   a  and some of the other traces in the capacitor string. One such coupling is represented as shield capacitor  140   b . Note that these shield capacitors  140   a ,  140   b ,  140   c  are not physical components. Rather,  FIG. 1  represents the shield capacitance as actual components to better illustrate the subject matter. 
     The shield capacitors serve to supply current to traces that are at a lower potential than the voltage of that shield. In this way, while the stray capacitors tend to divert current away from the capacitor string, shield capacitors tend to inject current into the capacitor string. 
       FIG. 1  shows a high voltage shield  130   a  located at the high voltage output  150 . However, other shields may also be present. For example, in this figure, a low voltage shield  130   b  is disposed at the lower voltage, which may be ground. In other embodiments, a plurality of printed circuit boards may be connected in series, and the lower voltage may be the output of the previous printed circuit board in the series and is therefore the next stage input voltage. In both cases, the low voltage shield  130   b  serves to reduce the effect of stray capacitance. An intermediate shield  130   c  is disposed at the midpoint of the capacitor string. Capacitive coupling may exist between the intermediate shield  130   c  and some of the other traces in the voltage doubler circuit  1 . For example, one such capacitive coupling is represented as shield capacitor  140   c.    
     For example, assume the capacitor string comprises 20 capacitors, where the capacitors are numbered sequentially from the lower voltage to the high voltage output. In one embodiment, an intermediate shields  130   c  may be disposed at the positive end of the 10 th  capacitor (i.e. the midpoint). 
     Of course, other embodiments are also possible. For example, intermediate shields  130   c  may be disposed at closer intervals, if desired. Intermediate shields  130   c  may be disposed at the positive end of the 5 th , 10 th , and 15 th  capacitor Alternatively, the intermediate shields  130   c  may be disposed at the positive end of the 4 th , 8 th , 12 th , and 16 th  capacitor. In certain embodiments, the intermediate shields  130   c  are equally spaced, however, in other embodiments, the intermediate shields  130   c  may not be equally spaced. Thus, the intermediate shields  130   c  may be disposed between any two adjacent capacitors in the capacitor string. In other embodiments, the intermediate shields  130   c  may be omitted. 
     The choice of the number of shields  130  and their locations may be based on a number of factors. The size of the shields  130  may be based on the amount of voltage compensation that is desired. Additionally, the amount of stray capacitance may also be a function of the geometry and material properties of the printed circuit board and the placement of the signal traces on the printed circuit board. Thus, the size and number of shields  130  may be based on the geometry and material properties of the printed circuit board and the desired voltage uniformity along the capacitor string. 
       FIG. 2  shows a representative layout of the voltage doubler circuit  1  disposed on a printed circuit board  2 . In this embodiment, there are twelve stages  200  in the capacitor string and the diode string. Each stage  200  comprises a diode  110  and a capacitor  100 . Shields  130   a ,  130   b ,  130   c  are disposed along the capacitor string. A high voltage shield  130   a  may be disposed at the positive end of the twelfth capacitor, which is electrically connected to the high voltage output. The low voltage shield  130   b  may be disposed at the negative side of the first capacitor, which is the lower voltage and may be grounded. Further, the low voltage shield  130   b  is electrically connected to the negative side of the first capacitor. An intermediate shield  130   c  may be disposed at the midpoint of the capacitor string and electrically connected to the first end of the secondary winding  30 . Thus, the voltage of the intermediate shield  130   c  may be the average of the lower voltage and the high voltage output. 
     In this embodiment, the shields  130  are shown as thick traces having a width and a length. The length of the shield may be greater than the space occupied by a stage  200 . For example, in one embodiment, the shields  130  may have a length between 40 mm and 100 mm, a width of between 3 mm and 10 mm and a thickness between 75 μm and 150 μm. In one particular embodiment, the shields  130  may have a length of 60 mm, a width of 5 mm and a thickness of 110 μm. In this way, the intermediate shield  130   c  effectively isolates the two stages  200  on opposite sides of intermediate shield  130   c . The width of high voltage shield  130   a , the low voltage shield  130   b , and the intermediate shield  130   c  may vary. In addition, there may be spacing guidelines based on the voltages of each trace which limit the width of the shields. Further, as noted above, the shield dimensions may depend on the desired voltage compensation and the geometry and material properties of the printed circuit board. 
     Thus, in this embodiment, the high voltage power supply comprises a single secondary winding  30  with two ends in communication with the voltage doubler circuit  1 . The voltage doubler circuit  1  is disposed on a printed circuit board  2 . The voltage doubler circuit  1  comprises a capacitor string, which comprises a plurality of capacitors arranged in series. The first end of the capacitor string is connected to a lower voltage, which may be ground, while the second end of the capacitor string is connected to the high voltage output. The voltage doubler circuit  1  also comprises a diode string, which comprises a plurality of diode arranged in series. The first end of the diode string is connected to the lower voltage, which may be ground, while the second end of the diode string is connected to the high voltage output. The first end of the secondary winding  30  is connected to the midpoint of the capacitor string, while the second end of the secondary winding is connected to the midpoint of the diode string. One or more shields  130  are disposed along the capacitor string. In certain embodiments, there is a high voltage shield  130   a  connected to the positive end of the last capacitor in the capacitor string connected to the high voltage output, and a low voltage shield  130   b  connected to the negative end of the first capacitor in the capacitor string connected to the lower voltage, which may be ground. One or more additional intermediate shields  130   c  may be disposed along the capacitor string between the high voltage shield  130   a  and the low voltage shield  130   b . These additional intermediate shields  130   c  are connected to a trace connecting the positive end of one capacitor and the negative end of an adjacent capacitor along the capacitor string and are biased at voltage between ground and the high voltage output. Thus, the intermediate shield  130   c  is disposed along the capacitor string, disposed between two adjacent capacitors and electrically connected to the trace connecting the two adjacent capacitors. 
     In certain embodiments, the additional intermediate shields  130   c  are equally spaced apart such that the voltage between adjacent intermediate shields is equal or nearly equal. Stated differently, there may be a constant number of capacitors disposed between any two adjacent shields. 
     The shields may be disposed on the same side of the printed circuit board as the traces and components. In other embodiments, the shields may be disposed on both sides of the printed circuit board, or on the opposite side of the printed circuit board as the traces and components. The placement of the shields  130  is selected so as to compensate for stray capacitance and allow connection to the desired voltages. 
       FIG. 3  shows a second embodiment. In this embodiment, there is an external power supply  310 , a primary winding  320  and a plurality of secondary windings  330 . Each secondary winding  330  is in communication with an associated low voltage doubler circuit  350 . Each low voltage doubler circuit  350  comprises two capacitors  360   a ,  360   b  arranged in series, and two diodes  370   a ,  370   b  arranged in series. The first end of the secondary winding  330  is in electrical contact with the trace that connects the two capacitors  360   a ,  360   b . The second end of the secondary winding  330  is in electrical contact with the trace that connects the anode of diode  370   a  to the cathode of diode  370   b . The positive end of capacitor  360   a  is electrically connected to the cathode of diode  370   a . The negative end of capacitor  360   b  is electrical connected to the anode of diode  370   b.    
     The low voltage doubler circuits  350  are connected in series to create the high voltage doubler circuit  301 . In other words, the cathode of diode  370   a  in one low voltage doubler circuit  350  is in electrical contact with the anode of diode  370   b  in the adjacent low voltage doubler circuit  350 . 
     Although not shown in  FIG. 3 , there is stray capacitance in high voltage doubler circuit  301 . As described with respect to  FIG. 1 , there is capacitive coupling between a trace and a second trace or component that is at a lower voltage. This stray capacitance tends to divert current away from the capacitors  360   a ,  360   b  in each low voltage doubler circuit  350 . 
     Therefore, as was shown in the embodiment of  FIG. 1 , shields  380  are added. In  FIG. 3 , there are a plurality of shields  380 . The high voltage shield  380   a  is electrically connected to the positive end of the most positive low voltage doubler circuit  350 . This high voltage shield  380   a  may be biased at the high voltage output. The low voltage shield  380   b  is electrically connected to the negative end of the least positive low voltage doubler circuit  350 . This low voltage shield  380   b  may be biased at a lower voltage, such as ground. There may also be additional intermediate shields  380   c  disposed between the high voltage shield  380   a  and the low voltage shield  380   b . For example, in  FIG. 3 , there is an even number of low voltage doubler circuits  350 . In this embodiment, an intermediate shield  380   c  is disposed such that there are an equal number of low voltage doubler circuits  350  between the intermediate shield  380   c  and the high voltage shield  380   a  and between the intermediate shield  380   c  and the low voltage shield  380   b . Thus, if there were 20 low voltage doubler circuits  350 , the intermediate shield  380   c  may be disposed at and connected to the trace that connects positive end of the tenth low voltage doubler circuit  350  to the negative end of the eleventh low voltage doubler circuit  350 . 
     However, the disclosure is not limited to this embodiment. There may be additional intermediate shields  380   c . For example, assuming that there are twenty low voltage doubler circuits  350 , additional intermediate shields  380   c  may be disposed at and connected to the positive ends of the 5 th , 10 th  and 15 th  low voltage doubler circuits  350 . Alternatively, additional intermediate shields  380   c  may be disposed at and connected at the positive ends of the 4 th , 8 th  12 th , and 16 th  low voltage doubler circuits  350 . 
     In certain embodiments, the additional intermediate shields  380   c  are disposed at equal intervals. 
       FIG. 4  shows a printed circuit board  402  on which the high voltage power supply is disposed. The high voltage power supply comprises a plurality of secondary windings  330 , and a corresponding number of low voltage doubler circuits  350 . As described above, each low voltage doubler circuit  350  comprises two capacitors  360   a ,  360   b  and two diodes  370   a ,  370   b . Each low voltage doubler circuit  350  is electrically connected in series to at least one other low voltage doubler circuit  350  to form the high voltage doubler circuit  301 . High voltage shield  380   a  and low voltage shield  380   b  may be disposed at the ends of the high voltage doubler circuit  301 . Additional intermediate shields  380   c  may be disposed between adjacent low voltage doubler circuits  350 , such as at the midpoint. 
     In this embodiment, the shields  380  are shown as thick traces having a width and a length. The length of the shield may be greater than the space occupied by a low voltage doubler circuit  350 . For example, in one embodiment, the shields  130  may have a length between 40 mm and 100 mm, a width of between 3 mm and 10 mm and a thickness between 75 μm and 150 μm. In one particular embodiment, the shields  130  may have a length of 60 mm, a width of 5 mm and a thickness of 110 μm. In this way, the intermediate shield  380   c  effectively isolates the two low voltage doubler circuits  350  on opposite sides of intermediate shield  380   c . The width of high voltage shield  380   a , the low voltage shield  380   b , and the intermediate shield  380   c  may be based on the available space available on the printed circuit board. In addition, there may be spacing guidelines based on the voltages of each trace which limit the width of the shields. Further, as noted above, the shield dimensions may depend on the desired voltage compensation and the geometry and material properties of the printed circuit board. 
     Thus, like the embodiment of  FIGS. 1-2 , this embodiment may comprise one or more intermediate shields disposed between elements that combine to form the high voltage doubler circuit  301 . In  FIGS. 1-2 , these elements are capacitors, while in the embodiment of  FIGS. 3-4 , these elements are low voltage doubler circuits. Further, a high voltage shield may be disposed at the high voltage end of the voltage doubler circuit and a low voltage shield may be disposed at the lower voltage end of the doubler circuit. 
       FIG. 5  shows one method that may be used to determine the placement, dimensions and number of shields that are to be included in the high voltage power supply. As shown in Box  500 , first, the stray capacitance is calculated based on the geometry and material properties of the printed circuit board design. This may be done theoretically or using an electrostatic simulation tool. As shown in Box  510 , the calculated stray capacitance is then incorporated into the electrical circuit design. Then, as shown in Box  520 , the voltage across each capacitor in the capacitor string (see  FIG. 1-2 ) or the high voltage doubler circuit (see  FIG. 3-4 ) can be calculated using electrical circuit theory, or a simulation tool, such as PSPICE. Based on this result, one or more shields may be incorporated into the design, as shown in Box  530 . The stray capacitance and the shield capacitance can then be calculated theoretically or using an electrostatic simulation tool, as shown in Box  540 . As shown in Box  550 , the calculated stray capacitance and shield capacitance is then added to the electrical circuit design. Then, as shown in Box  560 , the voltage across each capacitor in the capacitor string (see  FIG. 1-2 ) or the high voltage doubler circuit (see  FIG. 3-4 ) can be calculated using electrical circuit theory, or a simulation tool, such as PSPICE. If the resulting voltage distribution is acceptable, the process is complete. If the voltage distribution is not acceptable, the placement, number or dimension of the shields is modified by repeating Boxes  530 - 560  until the distribution is acceptable. 
     The system described herein has many advantages. Simulations were performed for a high voltage power supply having an output of 6.4 kV using 16 elements. These elements may be capacitors, such as shown in  FIG. 1  or low voltage doubler circuits, as shown in  FIG. 3 . Thus, ideally, the voltage across each element may be 400V. As shown in line  600  of  FIG. 6 , in the prior art, the distribution of voltage across the elements of the high voltage doubler circuit is not linear. Rather, the elements that are closer to the high voltage output store more voltage than those that are closer to the lower voltage. In fact, in this simulation, the voltage of the element closest to the high voltage output was calculated to be 564.8V, while the voltage of the element closest to the lower voltage was calculated to be only 237.2V. If the capacitors are rated for 400V, the voltage stress of the capacitor closest to the high voltage output is 1.412. This may result in increased stress on the elements that are disposed near the high voltage output. This may increase the component stress and lead to premature failure. In contrast, line  610  shows the distribution of voltage across the elements of the high voltage power supply comprising a high voltage shield, a low voltage shield and an intermediate shield disposed at 3.2 kV. In other words, the shields are disposed at the minimum voltage, the maximum voltage and the midpoint. Note that the amount of voltage stored by each element in the high voltage doubler circuit is nearly identical, resulting in a graph that is nearly linear. In this simulation, the voltage of capacitor closest to the high voltage output was calculated to be 424.4V, while the voltage of the capacitor closest to the lower voltage was calculated to be 384.8V. In other words, the difference between the highest capacitor voltage and the lowest capacitor voltage is less than 10%. Furthermore, if the capacitors are rated for 400V, the voltage stress of the capacitor closest to the high voltage output is reduced to 1.061, a reduction of nearly 25%. This configuration reduces stress on the components near the high voltage output and may increase the life of the high voltage power supply. 
     The present disclosure is not to be limited in scope by the specific embodiments described herein. Indeed, other various embodiments of and modifications to the present disclosure, in addition to those described herein, will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings. Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure. Furthermore, although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose, those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes. Accordingly, the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein.