Abstract:
A slotted coaxial shield for high voltage cylindrical air core transformers is described that controls the electric field stress while permitting the rapid extraction of electric energy stored in the shield to improve the output efficiency.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The conditions under which this invention was made are such as to entitle the Government of the United States under paragraph 1( a ) of Executive Order 10096, as represented by the Secretary of the Air Force, to the entire right, title and interest therein, including foreign rights. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention is in the field of dual resonant transformers used for charging pulse-forming networks, and in particular relates to a design for the improved efficiency for such transformers. 
     2. Description of the Prior Art 
     The dual resonant transformer is important in applications requiring the charging of Pulse Forming Networks (PFN) because it provides a high voltage step-up, has a high energy transfer efficiency, and is very compact and inherently well configured for megavolt level operation. The simplified circuit of a dual resonant transformer applied to a PFN charging circuit is shown in FIG.  1 . The operation consists of initially storing energy in the primary capacitor, C 1 , at a low voltage, typically on the order of 50 kV. The PFN, or other capacitive load to be charged, is connected to the secondary of the transformer. The total secondary equivalent capacitance, C 2 , consists of the PFN (or other load) capacitance, C PFN , plus the stray capacitance, C s . The primary open-circuit inductance of the transformer is L 1 , and the secondary open-circuit inductance is L 2 . The double tuned condition is implemented by satisfying the relation, L 1 *C 1 =L 2 *C 2 . The voltage ratio, that is the voltage to which C 2  (PFN and stray capacitance) is to be charged, divided by the initial voltage on C 1 , is determined by the square-root of the inductance ratio, (L 2 /L 1 ) ½ . In addition to both of these conditions the coupling coefficient of the transformer must be 0.600. That is k=M 12 /(L 1 *L 2 ) ½ , where M 12 , is the mutual inductance between L 1  and L 2 . 
     When all three of these conditions are fulfilled the initial energy in C 1  will be totally transferred to C 2  in a time duration of 1.6673*(L 1 *C 1 ) ½ =1.6673*(L 2 *C 2 ) ½ , measured from the closure of the switch connecting C 1  to the primary of the transformer. The capacitance C 2  is the total effective capacitance on the secondary of the transformer and consists of the useful load capacitance and the transformer “stray” capacitance. The normalized voltage waveforms of V 1  and V 2  are also shown in FIG.  1 . It is important to recognize that a high-energy transfer efficiency does not necessarily mean a high over-all efficiency. In applications where the useful load capacitance is on the order of, or less than, the stray capacitance, the loss of the stray capacitance energy greatly limits the efficiency of the transformer charging system. Such applications include Ultra Wide Band (UWB) generators. In UWB applications the pulse being generated typically has a voltage amplitude on the order of a megavolt and is of nanosecond or sub-nanosecond duration. Consequently the pulse has a very low energy content, typically on the order of a few joules. At megavolt operating voltages the electric field stress must be carefully managed to prevent arc down faults in the insulation. To accomplish this it is necessary to use field shaping conductors to eliminate high stress concentrations related to geometry features with small radii of curvature. 
     The effect of shielding is illustrated in FIGS. 2 a  and  2   b , both of which show a cross-section of a cylindrical coil. The ground end of the coil is to the outside and the high voltage end is to the inside. The equipotential field lines have been calculated using a computerized Laplace solver. The intensity of the electric field is indicated by the closeness or bunching of the equipotential lines. It can be seen that with “doughnut” ring shield  11 , the bunching is reduced and thus the electric field stress is lower. The introduction of ring shield  11  increases the stray capacitance of the system and also couples to the magnetic field of the transformer. The stray capacitance increases the energy storage. 
     It is the purpose of the present invention to make productive use of this increased energy storage. The coupling to the magnetic field reduces the transformer inductances and also decreases the coupling coefficient. These magnetic effects can be completely counteracted by carefull design of the field shaping conductors or shields in relation to the magnetic field of the transformer. At a voltage of 1 MV, a capacitance of 1 pF corresponds to an energy of ½ Joule. A typical transformer stray capacitance is on the order of 50 pF or 25 Joules at 1 MV, therefore, the degradation of efficiency is very significant for UWB or other low pulse energy applications. 
     FIGS. 3 a  and  3   b  show, in more detail, typical “doughnut” ring shields  11 . The shields  11  must have a gap  13  to prevent the ring from acting as a shorted turn on the transformer flux. The ring shields  11  must also be connected electrically by lead  15  to the output connection electrode or lead in order to accomplish the field grading function. The very nature of the rings as well as the electrical connections are inductive. Therefore, because of this inductance, the capacitive energy stored in the ring cannot be rapidly removed to the load. A simplified equivalent circuit illustrating this is shown in FIG.  4 . 
     The equivalent circuit in FIG. 4 shows how the capacitive energy stored in the grading rings and the transformer secondary winding must pass through the inductance of the rings and the electrical connections to be delivered to the output. In so doing, this energy is delayed by the inductance and is therefore not available as useful output energy on a fast time scale. 
     SUMMARY OF THE INVENTION 
     High voltage cylindrical air core transformers must have shields to control the electric field stress. However, the energy stored in conventional shields cannot be usefully extracted. The present invention provides for this shield by means of a new coaxial type configuration. Slots in the shield permit the normal transformer flux to couple the primary and secondary windings. This coaxial shield provides the required electric field stress control as well as the conventional shield does. In addition, the coaxial shield permits the very rapid extraction of the energy stored in the electric field, which then becomes useful output energy. The energy stored in the coaxial shield is approximately equal to that which would be stored in a conventional shield having a capacitance of typically 50 picoFarads. In applications such as UWB, the total load capacitance is also on the order of 50 picoFarads, leading to a factor of two improvement in efficiency. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The various features of novelty that characterize the invention are pointed out with particularity in the claims annexed to and forming a part of this disclosure. For a better understanding of the invention, its operating advantages, and specific objects attained by its uses, reference is made to the accompanying drawings and descriptive matter in which a preferred embodiment of the invention is illustrated. 
     FIG. 1 a  is a schematic diagram of a dual resonant charging circuit, and 
     FIG. 1 b  shows the normalized voltage waveforms V 1  and V 2  for L 1  and L 2  of FIG. 1 a . 
     FIG. 2 shows how field-shaping conductors can reduce the electric field intensity. 
     FIG. 3 a  is a cross-section of a transformer showing prior art “doughnut” ring shields, and 
     FIG. 3 b  is an enlarged end view of a prior art ring shield showing the electrical connection and the gap. 
     FIG. 4 is an equivalent circuit for the transformer of FIG. 3 a . 
     FIG. 5 is a cross-section of a transformer located inside a coaxial structure as proposed in the present invention. 
     FIG. 6 a  shows the axial slots in the outer coaxial conductor; 
     FIG. 6 b  is an end view of the outer coaxial conductor; 
     FIG. 6 c  shows the axial slots in the inner coaxial conductor; and 
     FIG. 6 d  is an end view of the inner coaxial conductor. 
     FIG. 7 is a qualitative diagram of the flux pattern with the proposed slotted coaxial shield. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Heretofore the stray energy in the transformer, as explained above, has been ignored. This was largely because previous applications dealt with load energies that were typically very large compared to the stray energy. Therefore, the impact on efficiency was not significant or at least was tolerable. The present invention provides for the beneficial use of the transformer stray energy and is, therefore, very important to applications such as UWB and other low energy per pulse loads. 
     This invention is based on the construction of the field shaping electrodes or shields formed in a coaxial configuration rather than the toroidal or “doughnut” configuration shown in FIGS. 2 a  and  2   b  and in FIGS. 3 a  and  3   b . These prior art diagrams show the cross-section of a coil, which is wound with a ribbon conductor. The ground end of the coil is located on the outer radius and the high voltage end is located at the inner radius. The field lines shown in FIGS. 2 a  and  2   b  are the equipotential lines. The closer the equipotential lines are, the greater the field enhancement and the higher the stress on the insulation. 
     The purpose of the shield is to grade the electric field in such a manner as to limit the maximum intensity to a value that is less than the breakdown value of the insulation. In general the electric field depends on the geometry. The smaller the radius of curvature of a conductor, the higher the electric field will be in the insulation near the surface of that curvature. If the strength of the electric field exceeds the breakdown stress of the insulation, the insulation will fail. 
     In the case of the “Doughnut” or ring shields  11 , the associated capacitive energy cannot be rapidly extracted, as a result of the inductive nature of the rings and electrical connections, as illustrated by the equivalent circuit diagram in FIG.  4 . 
     The present invention utilizes the principle of the coaxial conductor pair, which is modified to accomplish three key functions. The coaxial conductors must, (1) provide for the rapid extraction of the stored electrostatic energy to the load, (2) provide for the grading of the electric field intensity and, (3) not objectionably interfere with the transformer flux. 
     A coaxial pair of conductors constitutes a coaxial transmission line. The most significant parameters of such a transmission line are the characteristic impedance, the delay time or length, and the capacitance. These parameters are related to the geometry and material as follows. The characteristic impedance in Ohms is:          Z   0     =       60     ɛ            ln        (     r2   r1     )                                
     Where: r 2 =outer radius, r 1 =inner radius, and ε=relative dielectric constant between r 1  and r 2 . The delay time in seconds is:        τ   =       l        ɛ       c                            
     Where: l=length in meters, and c=speed of light.        C   =       l        ɛ         cZ   0                              
     The capacitance in Farads is: 
     The time required to extract or deliver the energy is very fast, approximately 2τ, typically on the order of a few nanoseconds. 
     The coaxial shield is used to accomplish the field grading by locating the transformer  16  inside the coaxial assembly and modifying the inner conductor  17  by rounding its ends  18 , as shown FIG.  5 . The radius of the rounding is similar to the radius used on the rings  11  in FIGS. 3 a  and  3   b  and accomplishes the same purpose for the same reason. 
     The coaxial assembly must be modified such that it does not significantly interfere with the transformer flux. The basic operation of a transformer depends upon the flux coupling or looping between the primary and secondary windings of the transformer. This coupling is the mechanism by which energy is transferred from the primary to the secondary winding and the means by which a voltage step-up is achieved. The electric field shaping electrode must be a conductor, and a time varying flux, such as in a transformer, cannot penetrate a conductor. 
     Therefore, axial slots  19  in both the inner coaxial conductor  17  and outer coaxial conductor  21 , as shown in FIGS. 6 a  and  6   c , are introduced to limit the interference of the shield with the flux coupling between primary winding  23  and secondary winding  25 . The slots are wide enough let the flux through, couple the windings, and retain the fast energy transmission properties of a coaxial assembly, yet narrow enough to be effective in grading the electric field stress. It has been estimated by calculation and verified by experiments that the optimum slot width in the inner conductor  17  should be on the order of 25% to 50% of the center-to-center slot spacing. The optimum slot width on the outer conductor  21  is larger, on the order of 50% to 75% of the center-to-center slot spacing. The optimum width of the slot  19  should be on the order of about two to four times the thickness of the inner conductor  17  and four to eight times the thickness of the outer conductor  21 . These relative dimension ranges are approximate and actual usable and successful designs may vary considerably from these guide values. Although it is not shown in the Figures, one must always radius the edges of the coaxial shields to inhibit and control the electric field enhancement. Typically one would use an edge radius of approximately one half of the material thickness. A qualitative diagram of the flux pattern  27 , which links the primary winding  23  and secondary winding  25  through the slots  19 , is shown in FIG.  7 . 
     The slotted coaxial shield configuration provides an electric shield with the proper geometry to control the enhanced stress of the electric field and permits the electric energy stored in the shield to be extracted very rapidly as useful output. Alternative modes of implementation of the shield include fabricating it from sheet stock formed into cylinders with slots and rolled or machined edges and fabricating it from machined bars or rods with associated structural parts. In all cases the coaxial nature must be preserved and the slots must be used to provide for the coupled flux. Also all edges must be rounded and smoothed to control and limit the electric field stress due to geometric enhancement.