Patent Publication Number: US-8995621-B2

Title: Compact X-ray source

Description:
BACKGROUND 
     A desirable characteristic of some high voltage devices, such as x-ray sources, especially portable x-ray sources, is small size. An x-ray source is comprised of an x-ray tube and a power supply. Transformers and a high voltage sensing resistor in the power supply can significantly cause the power supply to be larger than desirable. 
     An x-ray source can have a high voltage sensing resistor used in a circuit for sensing the tube voltage. The high voltage sensing resistor, due to a very high voltage across the x-ray tube, such as around 10 to 200 kilovolts, can have a very high required resistance, such as around 10 mega ohms to 100 giga ohms. The high voltage sensing resistor can be a surface mount resistor and the surface of the substrate that holds the resistor material can have surface dimensions of around 12 mm by 50 mm in some power supplies. Especially in miniature and portable x-ray tubes, the size of this resistor can be an undesirable limiting factor in reduction of size of a power supply for these x-ray tubes. 
     X-ray tubes can have a transformer (“filament transformer”) for transferring an alternating current signal from an alternating current (AC) source at low bias voltage to an x-ray tube electron emitter, such as a filament, at a very high direct current (DC) voltage, or bias voltage, such as around 10 to 200 kilovolts. A hot filament, caused by the alternating current, and the high bias voltage of the filament, relative to an x-ray tube anode, results in electrons leaving the filament and propelled to the anode. U.S. Pat. No. 7,839,254, incorporated herein by reference, describes one type of filament transformer. 
     X-ray tubes can also have a transformer (called a “high voltage transformer” or “HV transformer” herein) for stepping up low voltage AC, such as around 10 volts, to higher voltage AC, such as above 1 kilovolt. This higher voltage AC can be used in a high voltage generator, such as a Cockcroft-Walton multiplier, to generate the very high bias voltage, such as around 10 to 200 kilovolts, of the x-ray tube filament or cathode with respect to the anode. The size of both the high voltage transformer and the filament transformer can be a limiting factor in reduction of the size of the x-ray source. 
     SUMMARY 
     It has been recognized that it would be advantageous to have a smaller, more compact, high voltage device, such as an x-ray source. The present invention is directed towards a more compact, smaller high voltage device, including smaller, more compact x-ray sources. 
     In one embodiment, the present invention is directed to a circuit for supplying AC power to a load in a circuit in which there is a large DC voltage differential between an AC power source and the load. Capacitors are used to provide voltage isolation while providing efficient transfer of AC power from the AC power source to the load. The DC voltage differential can be at least about 1 kV. In an x-ray source, these capacitors can replace the filament transformer. This invention satisfies the need for a compact, smaller high voltage device, such as a compact, smaller x-ray source. 
     The present invention can be used in an x-ray tube in which (1) the load can be an electron emitter which is electrically isolated from an anode, and (2) there exists a very large DC voltage differential between the electron emitter and the anode. AC power supplied to the electron emitter can heat the electron emitter and due to such heating, and the large DC voltage differential between the electron emitter and the anode, electrons can be emitted from the electron emitter and propelled towards the anode. 
     In another embodiment of the present invention, only one transformer for an electron emitter and a high voltage generator, is needed, by connecting a first alternating current source for the electron emitter or filament in parallel with the input to the high voltage generator thus reducing size and cost by using a the high voltage generator for voltage isolation rather than using a separate transformer for voltage isolation. Thus the capacitors of the high voltage generator provide isolation between the electron emitter or filament, at very high DC voltage, and the alternating current source for the electron emitter or filament, which is at a low DC voltage potential. 
     In another embodiment of the present invention, two different circuits can utilize the same transformer core, thus reducing size and cost by utilizing one core instead of two. Each can have a different frequency in order to avoid one circuit from interfering with the other circuit. The input circuit for each can have a frequency that is about the same as the resonant frequency of the output circuit. 
     In another embodiment of the present invention, the high voltage sensing resistor can be disposed directly on the cylinder of the x-ray tube. Thus by having the high voltage sensing resistor directly on the cylinder of the x-ray tube, space required by this resistor is negligible, allowing for a more compact power supply of the x-ray source. An additional possible benefit of the sensing resistor can be improved tube stability due to removal of static charge on the surface of the x-ray tube cylinder that was generated by the electrical field within x-ray tube. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic of a circuit for supplying alternating current to a load, with a high voltage DC power source on the load side of the circuit, in accordance with an embodiment of the present invention; 
         FIG. 2  is a schematic of a circuit for supplying alternating current to a load, with a high voltage DC power source on the AC power source side of the circuit, in accordance with an embodiment of the present invention; 
         FIG. 3  is a schematic of a circuit for supplying alternating current to a load, with a high voltage DC power source connected between the load side of the circuit and the AC power source side of the circuit, in accordance with an embodiment of the present invention; 
         FIG. 4  is a schematic cross-sectional side view of an x-ray tube utilizing a circuit for supplying alternating current to a load in accordance with an embodiment of the present invention; and 
         FIG. 5  is a flow chart depicting a method for heating an electron emitter in an x-ray tube in accordance with an embodiment of the present invention. 
         FIG. 6  is a schematic cross-sectional side view of a power source in which a high voltage multiplier is used to separate an alternating current source, at low or zero bias voltage, from a load at a very high bias voltage, which load is powered by this alternating current source; 
         FIG. 7  is a schematic cross-sectional side view of a power source for an x-ray tube electron emitter in which a high voltage multiplier is used to separate an alternating current source, at low or zero bias voltage, from the electron emitter at a very high bias voltage, which electron emitter is powered by this alternating current source; 
         FIG. 8  is a schematic cross-sectional side view of a Cockcroft-Walton multiplier; 
         FIG. 9  is a schematic cross-sectional side view of an alternating current source and step-up transformer for supplying alternating current to a high voltage generator; 
         FIG. 10  is a schematic cross-sectional side view of a multiple channel transformer in which two circuits utilize the same transformer core; 
         FIG. 11  is a schematic cross-sectional side view of a multiple channel transformer in which two circuits utilize the same transformer core, one of these circuits is used to supply power to an x-ray tube electron emitter and the other is used to supply power to a high voltage generator; 
         FIG. 12  is a schematic cross-sectional side view of an x-ray tube cylinder with multiple wraps of a first resistor, used as a high voltage sensing resistor, in accordance with an embodiment of the present invention; 
         FIG. 13  is a schematic cross-sectional side view of an x-ray tube cylinder and a first resistor disposed on the cylinder in a zig-zag shaped pattern, used as a high voltage sensing resistor, in accordance with an embodiment of the present invention; 
         FIG. 14  is a schematic cross-sectional side view of an x-ray tube cylinder with multiple wraps of a first resistor, used as a high voltage sensing resistor, and a second resistor across which voltage drop is measured, in accordance with an embodiment of the present invention. 
       DEFINITIONS 
       As used in this description and in the appended claims, the following terms are defined
         As used herein, the term “substantially” refers to the complete or nearly complete extent or degree of an action, characteristic, property, state, structure, item, or result. For example, an object that is “substantially” enclosed would mean that the object is either completely enclosed or nearly completely enclosed. The exact allowable degree of deviation from absolute completeness may in some cases depend on the specific context. However, generally speaking the nearness of completion will be so as to have the same overall result as if absolute and total completion were obtained. The use of “substantially” is equally applicable when used in a negative connotation to refer to the complete or near complete lack of an action, characteristic, property, state, structure, item, or result.   As used herein, the term “about” is used to provide flexibility to a numerical range endpoint by providing that a given value may be “a little above” or “a little below” the endpoint.   As used herein, the term “capacitor” means a single capacitor or multiple capacitors in series.   As used herein, the term “high voltage” or “higher voltage” refer to the DC absolute value of the voltage. For example, negative 1 kV and positive 1 kV would both be considered to be “high voltage” relative to positive or negative 1 V. As another example, negative 40 kV would be considered to be “higher voltage” than 0 V.   As used herein, the term “low voltage” or “lower voltage” refer to the DC absolute value of the voltage. For example, negative 1 V and positive 1 V would both be considered to be “low voltage” relative to positive or negative 1 kV. As another example, positive 1 V would be considered to be “lower voltage” than 40 kV.       

     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made to the exemplary embodiments illustrated in the drawings, and specific language will be used herein to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended. Alterations and further modifications of the inventive features illustrated herein, and additional applications of the principles of the inventions as illustrated herein, which would occur to one skilled in the relevant art and having possession of this disclosure, are to be considered within the scope of the invention. 
     Capacitor AC Power Coupling Across High DC Voltage Differential 
     As illustrated in  FIG. 1 , a circuit, shown generally at  10 , for supplying AC power to a load  14 , includes an AC power source  13  having a first connection  13   a  and a second connection  13   b , a first capacitor  11  having a first connection  11   a  and a second connection  11   b , and a second capacitor  12  having a first connection  12   a  and a second connection  12   b . The first connection of the AC power source  13   a  is connected to the first connection  11   a  on the first capacitor  11 . The second connection  13   b  of the AC power source  13  is connected to the first connection  12   a  on the second capacitor  12 . The AC power source  13 , the first and second connections  13   a  and  13   b  on the AC power source  13 , the first connection  11   a  on the first capacitor  11 , and the first connection  12   a  on the second capacitor  12  comprise a first voltage side  21  of the circuit  10 . 
     The circuit  10  for supplying AC power to a load  14  further comprises the load  14  having a first connection  14   a  and a second connection  14   b . The second connection  11   b  of the first capacitor  11  is connected to the first connection  14   a  on the load  14  and the second connection  12   b  of the second capacitor  12  is connected to the second connection  14   b  on the load  14 . The load  14 , the first and second connections  14   a  and  14   b  on the load  14 , the second connection  11   b  on the first capacitor  11 , and the second connection  12   b  on the second capacitor  12  comprise a second voltage side  23  of the circuit  10 . 
     The first and second capacitors  11 ,  12  provide voltage isolation between the first and second voltage sides  21 ,  23  of the circuit  10 , respectively. A high voltage DC source  15  can provide at least 1 kV DC voltage differential between the first  21  and second  23  voltage sides of the circuit. 
     As shown in  FIG. 1 , the high voltage DC power source  15  can be electrically connected to the second voltage side  23  of the circuit  10 , such that the second voltage side  23  of the circuit  10  is a substantially higher voltage than the first voltage side  21  of the circuit  10 . Alternatively, as shown in  FIG. 2 , the high voltage DC power source  15  can be electrically connected to the first voltage side  21  of the circuit  20 , such that the first voltage side  21  of the circuit  20  has a substantially higher voltage than the second voltage side  23  of the circuit  20 . As shown in  FIG. 3 , the high voltage DC power source  15  can be electrically connected between the first  21  and second  23  voltage sides of the circuit  30  to provide a large DC voltage potential between the two sides  21  and  23  of the circuit  30 . 
     The DC voltage differential between the first  21  and second  23  voltage sides of the circuit can be substantially greater than 1 kV. For example the DC voltage differential between the first and second voltage sides  21  and  23  of the circuit  30  can be greater than about 4 kV, greater than about 10 kV, greater than about 20 kV, greater than about 40 kV, or greater than about 60 kV. 
     The AC power source  13  can transfer at least about 0.1 watt, at least about 0.5 watt, at least about 1 watt, or at least about 10 watts of power to the load  14 . 
     Sometimes a circuit such as the example circuit displayed in  FIGS. 1-3  needs to be confined to a small space, such as for use in a portable tool. In such a case, it is desirable for the capacitors  11  and  12  to have a small physical size. Capacitors with lower capacitance C are typically smaller in physical size. However, use of a capacitor with a lower capacitance can also result in an increased capacitive reactance X c . A potential increase in capacitive reactance X c  due to lower capacitance C of the capacitors can be compensated for by increasing the frequency f supplied by the AC power source, as shown in the formula: 
     
       
         
           
             
               X 
               c 
             
             = 
             
               
                 1 
                 
                   2 
                   * 
                   π 
                   * 
                   f 
                   * 
                   C 
                 
               
               . 
             
           
         
       
     
     In selected embodiments of the present invention, the capacitance of the first and second capacitors  11  and  12  can be greater than about 10 pF or in the range of about 10 μF to about 1 μF. In selected embodiments of the present invention the alternating current may be supplied to the circuit  10  at a frequency f of at least about 1 MHz, at least about 500 MHz, or at least about 1 GHz. 
     For example, if the capacitance C is 50 pF and the frequency f is 1 GHz, then the capacitive reactance X c  is about 3.2. In selected embodiments of the present invention, the capacitive reactance X c  of the first capacitor  11  can be in the range of 0.2 to 12 ohms and the capacitive reactance X c  of the second capacitor  12  can be in the range of 0.2 to 12 ohms. 
     It may be desirable, especially in very high voltage applications, to use more than one capacitor in series. In deciding the number of capacitors in series, manufacturing cost, capacitor cost, and physical size constraints of the circuit may be considered. Accordingly, the first capacitor  11  can comprise at least 2 capacitors connected in series and the second capacitor  12  can comprise at least 2 capacitors connected in series. 
     In one embodiment, the load  14  in the circuit  10  can be an electron emitter such as a filament in an x-ray tube. 
     As shown in  FIG. 4 , the circuits  10 ,  20 ,  30  for supplying AC power to a load  14  as described above and shown in  FIGS. 1-3  may be used in an x-ray tube  40 . The x-ray tube  40  can comprise an evacuated dielectric tube  41  and an anode  44  that is disposed at an end of the evacuated dielectric tube  41 . The anode  44  can include a material that is configured to produce x-rays in response to the impact of electrons, such as silver, rhodium, tungsten, or palladium. The x-ray tube  40  further comprises a cathode  42  that is disposed at an opposite end of the evacuated dielectric tube  41  opposing the anode  44 . The cathode  42  can include an electron emitter  43 , such as a filament, that is configured to produce electrons which can be accelerated towards the anode  44  in response to an electric field between the anode  44  and the cathode  42 . 
     A power supply  46  can be electrically coupled to the anode  44 , the cathode  42 , and the electron emitter  43 . The power supply  46  can include an AC power source  13  for supplying AC power to the electron emitter  43  in order to heat the electron emitter  43 , as described above and shown in  FIGS. 1-3 . The power supply  46  can also include a high voltage DC power source  15  connected to at least one side of the circuit and configured to provide: (1) a DC voltage differential between the first and second voltage sides  21  and  23  of the circuit; and (2) the electric field between the anode  44  and the cathode  42 . The DC voltage differential between the first and second voltage sides  21  and  23  of the circuit can be provided as described above and shown in  FIGS. 1-3 . 
     Thus, the capacitors  11 - 12  can replace a transformer, such as a filament transformer in an x-ray source. This invention satisfies the need for a compact, smaller high voltage device, such as a compact, smaller x-ray source. 
     Methods for Providing AC Power to a Load 
     In accordance with another embodiment of the present invention, a method  50  for providing AC power to a load  14  is disclosed, as depicted in the flow chart of  FIG. 5 . The method  50  can include capacitively coupling  51  an AC power source  13  to a load  14 . A high voltage DC power source  15  can be coupled  52  to one of the load  14  or the AC power source  13  to provide a DC bias of at least four kilovolts (kV) between the load  14  and the AC power source  13 . An alternating current at a selected frequency and power can be directed  53  from the AC power source  13  across the capacitive coupling to the load  14 . 
     The high voltage DC power source  15  can provide a DC voltage differential between the load  14  and the AC power source  13  that is substantially higher than 1 kV. For example the DC voltage differential can be greater than about 4 kV, greater than about 20 kV, greater than about 40 kV, or greater than about 60 kV. 
     In various embodiments of the present invention, the power transferred to the load  14  can be at least about 0.1 watt, at least about 0.5 watt, at least about 1 watt, or at least about 10 watts. In various embodiments of the present invention, the AC power source  13  can be capacitively coupled to the load  14  with single capacitors or capacitors in series. The capacitance of the capacitors, or capacitors in series, can be greater than about 10 pF or in the range of about 10 pF to about 1 μF. In embodiments of the present invention the selected frequency may be at least about 1 MHz, at least about 500 MHz, or at least about 1 GHz. 
     In the above described methods, the AC power coupled to the load  14  can be used to heat the load  14 . The load  14  can be an x-ray tube electron emitter  43 , such as a filament. 
     Load Driven by HV Multiplier Capacitors 
     As illustrated in  FIG. 6 , a power source  60  is shown comprising a first alternating current source  64   a  connected in series with a first capacitor  61   a . The first alternating current source  64   a  can be configured to operate at a first amplitude or peak voltage of about 10 volts. In one embodiment, the first amplitude can be less than about 20 volts. The first alternating current source  64   a  can have a bias voltage of 0 so that for example the voltage can alternate between about +10 and −10 volts. The first alternating current source  64   a  can be configured to be operated at a first frequency. In one embodiment, the first frequency can have a value of greater than about 10 megahertz. In another embodiment, the first frequency can have a value of greater than about 100 megahertz. 
     The power source  60  further comprises a second alternating current source  64   b  connected in parallel with the first alternating current source  64   a  and the first capacitor  61   a . The second alternating current source  64   b  can be configured to operate at a second amplitude or peak voltage of about 100 volts. In one embodiment, the second amplitude can be greater than about 1 kilovolts DC. The second alternating current source  64   b  can have a bias voltage of 0 so that for example the voltage can alternate between about +100 and −100 volts. The second alternating current source  64   b  can be configured to be operated at a second frequency. In one embodiment, the second frequency can have a value of between about 10 kilohertz to about 10 megahertz. 
     The power source  60  further comprises a high voltage generator  67  having two connection points at a low voltage end  62  and two connection points at a high voltage end  63 . The high voltage generator  67  can develop a voltage differential between the low voltage end and the high voltage end of greater than about 10 kilovolts. The first alternating current source  64   a  and the first capacitor  61   a  and the second alternating current source  64   b  can be connected in parallel with the two connection points  62  at the low voltage end of the high voltage generator  67 . 
     The power source  60  further comprises a load  66  connected in parallel with the two connection points  63  at the high voltage end of the high voltage generator  67 . A second capacitor  61   b  can be connected in series with a load  66 . 
     In one embodiment, the first frequency can have a value that is at least 3 times greater than the second frequency. In another embodiment, the first frequency can have a value that is at least 10 times greater than the second frequency. It can be desirable to have a very large difference between the first and second frequency. A relatively lower second frequency can result in a high impedance to the alternating current from the second alternating current source  64   b  at the first capacitor  61   a  and at the second capacitor  61   b . This minimizes any influence from the higher amplitude second alternating current source  64   b  on the first alternating current source  64   a  and load  66 . A higher first frequency allows the alternating current from the first alternating current source  64   a  to pass the first capacitor  61   a  and the second capacitor  61   b  with smaller voltage drop. 
     In one embodiment, the second amplitude can have a value that is at least 3 times greater than the first amplitude. In another embodiment, the second amplitude can have a value that is at least 10 times greater than the first amplitude. It can be desirable for the first amplitude to be lower because alternating current from the first alternating current source  64   a  can be used for heating the x-ray tube filament and a lower amplitude, such as around 10 volts, can be sufficient for this purpose. Also, a lower first amplitude can result in minimal effect on the high voltage generator  67  from the first alternating current source  64   a . It can be desirable for the second amplitude to be higher because alternating current from the second alternating current source  64   b  can be used for generating a high bias voltage through the high voltage generator  67  and a higher amplitude, such as greater than around 100 volts, may be needed for this purpose. 
     As shown in  FIG. 7 , the power source  60  described previously can be used to supply power to an x-ray source  70 . The x-ray source  70  can comprise an x-ray tube  40  with an insulative cylinder  41 , an anode  44  disposed at one end of the insulative cylinder  41 , and a cathode  42  at an opposing end of the insulative cylinder  41  from the anode  44 . The cathode  42  can include an electron emitter  43 , such as a filament. The electron emitter  43  and the second capacitor  61   b  can be connected in series to each other and parallel to the connection points  63  at the high voltage end of the high voltage generator  67 . The anode  44  can be electrically grounded to ground  72 . The first alternating current source  64   a  can drive alternating current and power at the electron emitter  43 . The second alternating current source  64   b  can create high voltage at the high voltage generator  67 , creating a voltage differential between the cathode  42  and the anode  44  of greater than about 10 kilovolts. The voltage differential between the cathode  42  and the anode  44  and the alternating current at the electron emitter  43  can cause electrons to be emitted from the electron emitter  43  and propelled towards the anode  44 . 
     As shown in  FIG. 8 , the high voltage generator  67  can be a Cockcroft-Walton multiplier  80  with capacitors C 1 -C 12  and diodes D 1 -D 12 . Diodes D 1 -D 12  in the Cockcroft-Walton multiplier  80  can have a forward voltage of greater than about 10 volts. Diode D 1 -D 12  forward voltage can be higher than the first amplitude such that alternating current from the first alternating current source  64   a  will not cause any substantial amount of current to pass through these diodes D 1 -D 12 . 
     Shown in  FIG. 9 , the second alternating current source  64   b  can comprise an alternating current source  91  connected in series with input windings  94  on a step-up transformer  92 . Output windings  95  on the step-up transformer  92  can be connected in parallel, at connection points  93   a - b , with the first alternating current source  64   a  and the first capacitor  61   a . In one embodiment, this configuration can allow use of an alternating current source  91  which can supply AC at an amplitude of around 10 volts to be used, along with the step-up transformer  92 , to supply alternating current, at an amplitude of around 100 to 1000 volts, to the high voltage generator  67 . 
     Capacitance of the first and second capacitors  61   a  and  61   b  can be chosen by balancing the desirability of higher capacitance for less power loss with lower capacitance for smaller physical size and lower cost. For example, the first capacitor  61   a  can have a capacitance of between about 10 picofarads to about 10 microfarads and the second capacitor  61   b  can have a capacitance of between about 10 picofarads to about 10 microfarads. 
     Multiple Channel Transformer 
     As illustrated in  FIG. 10 , a multiple channel transformer  100  is shown comprising a single transformer core  101  with at least two input circuits  102   a - b  and at least two output circuits  102   c - d.    
     A first input circuit  102   a  can be wrapped  103   a  at least one time around the single transformer core  101  and configured to carry an alternating current signal at a first frequency F 1 . A first output circuit  102   c  comprises a first output winding  103   c . The first output winding  103   c  can be wrapped at least one time around the single transformer core  101 . 
     A second input circuit  102   b  can be wrapped  103   b  at least one time around the single transformer core  101  and configured to carry an alternating current signal at a second frequency F 2 . A second output circuit  102   d  comprises a second output winding  103   d . The second output winding  103   d  can be wrapped at least one time around the single transformer core  101 . 
     The first output circuit  102   c  has a resonant frequency which can be the about the same as the first frequency F 1 . The second output circuit  102   d  has a resonant frequency which can be about the same as the second frequency F 2 . Circuit design resulting in substantially different resonant frequencies between the two output circuits  102   c - d  can result in (1) the first input circuit  102   a  inducing a current in the first output circuit  102   c  with negligible inducement of current from the second input circuit  102   b , and (2) the second input circuit  102   b  inducing a current in the second output circuit  102   d  with negligible inducement of current from the first input circuit  102   a . For example, the first frequency F 1  can be ten times or more greater than the second frequency F 2 , F 1 ≧10*F 2 . The first frequency F 1  can be at least 10 to 1000 times greater than the second frequency F 2 . Alternatively, the second frequency F 2  can be ten times or more greater than the first frequency F 2 , F 2 ≧10*F 1 . The second frequency F 2  can be 10 to 1000 times greater than the first frequency F 1 . Alternating current sources  104   a - b  can provide alternating current at the desired frequencies. 
     In one embodiment, the resonant frequency of the first output circuit  102   c  can be between about 1 megahertz to about 500 megahertz and the resonant frequency of the second output circuit  102   d  can be between about 10 kilohertz to about 1 megahertz. In another embodiment, the resonant frequency of the second output circuit  102   d  can be between about 1 megahertz to about 500 megahertz and the resonant frequency of the first output circuit  102   c  can be between about 10 kilohertz to about 1 megahertz. 
     The first output circuit  102   c  can further comprise a first output circuit capacitor  105   c , having a first output capacitance C o1 , in parallel with the first output winding  103   c . The first output winding  103   c  can have a first output inductance L o1 . The second output circuit  102   d  can further comprise a second output circuit capacitor  105   d , having a second output capacitance C o2 , in parallel with the second output winding  103   d . The second output winding  103   d  can have a second output inductance L o2 . In order to minimize inducement of current in the second output circuit  102   d  from the first input circuit  102   a , and to minimize inducement of current in the first output circuit  102   c  from the second input circuit  102   b , an inverse square root of the product of the first output capacitance C 01  and the first output inductance L 01  does not equal an inverse square root of the product of the second output capacitance C 02  and the second output inductance L 02 , 
     
       
         
           
             
               1 
               
                 
                   
                     C 
                     
                       0 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   * 
                   
                     L 
                     
                       0 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                 
               
             
             ≠ 
             
               
                 1 
                 
                   
                     
                       C 
                       
                         0 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     * 
                     
                       L 
                       02 
                     
                   
                 
               
               . 
             
           
         
       
     
     The first frequency F 1  can equal the inverse of the product of two times π times the square root of the first output inductance L o1  times the first output capacitance C o1 , 
               F   1     =       1     2   *   π   *         L   01     *     C   01             .           
The second frequency F 2  can equal the inverse of the product of two times π times the square root of the second output inductance L o2  times the second output capacitance C o2 ,
 
     
       
         
           
             
               F 
               2 
             
             = 
             
               
                 1 
                 
                   2 
                   * 
                   π 
                   * 
                   
                     
                       
                         L 
                         02 
                       
                       * 
                       
                         C 
                         
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                     
                   
                 
               
               . 
             
           
         
       
     
     The first output circuit  102   c  can supply power to a load  106 . The second output circuit can supply power to a high voltage generator  107 . High DC voltage potential from the high voltage generator  107  can supply high DC voltage potential to the alternating current signal at the load  106  on the first output circuit  102   c . A resistor  108  can be used in the connection between the high voltage generator  107  and the first output circuit  102   c . In this and other embodiments, the high voltage generator  107  can be a Cockcroft-Walton multiplier  80  as shown in  FIG. 8 . 
     The various embodiments of the multiple channel transformer  100  described previously can be used in an x-ray source  110 , as illustrated in  FIG. 11 . The x-ray source  110  can comprise a multiple channel transformer  100  and an x-ray tube  40 . The x-ray tube  40  can comprise an insulative cylinder  41 , an anode  44  disposed at one end of the insulative cylinder  41 , and a cathode  42  disposed at an opposing end of the insulative cylinder  41  from the anode  44 . The cathode  42  can include an electron emitter  43 , such as a filament. 
     The first output circuit  102   c  can provide an alternating current signal to the electron emitter  43 . The second output circuit  102   d  can provide alternating current to a high voltage generator  107 . The high voltage generator  107  can generate a high DC voltage potential. The high DC voltage potential can be connected to the first output circuit  102   c , thus providing a very high DC bias to the filament while also providing an alternating current through the electron emitter  43 . The anode  44  can be connected to ground  72 . 
     A voltage differential of at least 10 kilovolts can exist between the anode  44  and the cathode  42 . Due to this large voltage differential between the anode  44  and the cathode  42 , and due to heat from the alternating current through the electron emitter  43 , electrons can be emitted from the electron emitter  43  and propelled towards the anode  44 . 
     High Voltage Sensing Resistor 
     As illustrated in  FIG. 12 , an x-ray source  120  is shown comprising an x-ray tube  40  and a line of insulative material, comprising a first resistor R 1 . The x-ray tube  40  comprises an insulative cylinder  41 , an anode  44  disposed at one end of the insulative cylinder  41 , and a cathode  42  disposed at an opposing end of the insulative cylinder  41  from the anode  44 . The first resistor R 1  has a first end  124  which is attached to either the anode  44  or the cathode  42 , and a second end  125  which is configured to be connected to an external circuit. In  FIG. 12 , the first end  124  of the first resistor R 1  is shown attached to the anode  44 . In  FIG. 13 , the first end  124  of the first resistor R 1  is shown attached to the cathode  42 . In all embodiments herein, the first end  124  of the first resistor R 1  may be attached to either the cathode  42  or to the anode  44 . 
     A resistance r 1  across the first resistor R 1  from one end to the other end can be very large. In one embodiment, a resistance r 1  across the first resistor R 1  from one end to the other end can be at least about 10 mega ohms. In another embodiment, a resistance r 1  across the first resistor R 1  from one end to the other end can be at least about 1 giga ohm. In another embodiment, a resistance r 1  across the first resistor R 1  from one end to the other end can be at least about 10 giga ohms. In another embodiment, a resistance r 1  across the first resistor R 1  from one end to the other end can be at least about 100 giga ohms. 
     As illustrated in  FIG. 12 , the first resistor R 1  can wrap around a circumference of the insulative cylinder  41 , such as about four times shown in  FIG. 12 . In one embodiment, the first resistor R 1  can wrap around a circumference of the insulative cylinder  41  at least one time. In another embodiment, the first resistor R 1  can wrap around a circumference of the insulative cylinder  41  at least twenty-five times. 
     The first resistor R 1  can be any electrically insulative material that will provide the high resistance required for high voltage applications. In one embodiment, the first resistor R 1  is a dielectric ink painted on a surface of the insulative cylinder  41 . MicroPen Technologies of Honeoye Falls, N.Y. has a technology for applying a thin line of insulative material on the surface of a cylindrical object. An insulative cylinder  41  of an x-ray tube  40  can be turned on a lathe-like tool and the insulative material is painted in a line on the exterior of the insulative cylinder  41 . 
     As shown in  FIG. 12 , the second end  125  of the first resistor R 1  can be attached to a second resistor R 2 , such that the two resistors R 1  and R 2  are connected in series. Voltage ΔV can be measured across the second resistor R 2  by a voltage measurement device connected across the second resistor R 2 . Voltage V across the x-ray tube  40  can then be calculated by the formula 
               V   =         V   2     *     (       r   1     +     r   2       )         r   2         ,         
wherein V is a voltage across the x-ray tube  40 , V 2  is a voltage across the second resistor R 2 , r 1  is a resistance of the first resistor R 1 , and r 2  is a resistance of the second resistor R 2 .
 
     The second resistor R 2  can have a lower resistance r 2  than the first resistor R 1 . In one embodiment, the second resistor R 2  can have a resistance r 2  of at least 1 kilo ohm less than a resistance r 1  of the first resistor R 1 . In another embodiment, the second resistor R 2  can have a resistance r 2  of at least 1 mega ohm less than a resistance r 1  of the first resistor R 1 . In one embodiment, the second resistor R 2  can have a resistance r 2  of less than about 1 mega ohm. In another embodiment, the second resistor R 2  can have a resistance r 2  of less than about 1 kilo ohm. In another embodiment, the second resistor R 2  can have a resistance r 2  of less than about 100 ohms. 
     The first resistor R 1  need not wrap around the cylinder but can be disposed in any desired shape on the cylinder, as long as the needed resistance from one end to another is achieved. For example, as shown on x-ray source  130  in  FIG. 13 , the first resistor R 1  is disposed in a zig-zag like pattern on the insulative cylinder  41 . 
     As shown on x-ray source  140  in  FIG. 14 , the second resistor R 2 , like the first resistor R 1 , can be disposed on the insulative cylinder  41 . In one embodiment, the second resistor R 2  can wrap around the insulative cylinder  41  at least one time. In another embodiment, the second resistor R 2  can be disposed on the insulative cylinder  41  in a zig-zag like pattern or any other pattern. The second resistor R 2  can be a dielectric ink painted on a surface of the insulative cylinder  41 . 
     In one embodiment, the first resistor R 1  and/or the second resistor R 2  can comprise beryllium oxide (BeO), also known as beryllia. Beryllium oxide can be beneficial due to its high thermal conductivity, thus providing a more uniform temperature gradient across the resistor. 
     The second resistor R 2  can be connected to ground or any reference voltage at one end and to the first resistor R 1  at an opposing end. 
     A method for sensing voltage across an x-ray tube  40  can comprise: 
     a) painting insulative material on a surface of an insulative cylinder  41 , the insulative material comprising a first resistor R 1 ; 
     b) connecting the first resistor R 1  to a second resistor R 2  at one end  125  and to either a cathode  42  or an anode  44  of the insulative cylinder  41  at an opposing end  124 ; and 
     c) measuring a voltage ΔV across the second resistor R 2 ; and 
     d) calculating a voltage V across the x-ray tube  40  by 
               V   =         V   2     *     (       r   1     +     r   2       )         r   2         ,         
wherein V is a voltage across the x-ray tube  40 , V 2  is a voltage across the second resistor, r 1  is a resistance of the first resistor, and r 2  is a resistance of the second resistor.
 
     U.S. patent application Ser. No. 12/890,325, filed on Sep. 24, 2010 (now U.S. Pat. No. 8,526,574), and U.S. Provisional Patent Application Ser. No. 61/420,401, filed on Dec. 7, 2010, are hereby incorporated herein by reference in their entirety. 
     It is to be understood that the above-referenced arrangements are only illustrative of the application for the principles of the present invention. Numerous modifications and alternative arrangements can be devised without departing from the spirit and scope of the present invention. While the present invention has been shown in the drawings and fully described above with particularity and detail in connection with what is presently deemed to be the most practical and preferred embodiment(s) of the invention, it will be apparent to those of ordinary skill in the art that numerous modifications can be made without departing from the principles and concepts of the invention as set forth herein.