Abstract:
A switched-capacitor circuit has two capacitors and two MOSFETs that cross-couple the capacitors, connecting the anode of one to the cathode of the other, and vice-versa. When either MOSFET is on, the capacitors are in series; the order alternates as the MOSFETs alternate. A reversing cyclical voltage suitable as a primary drive for a transformer is generated. If the MOSFETs alternate with no dead-time, a square-wave excitation is generated. With off-time, a pwm excitation is generate. Charge is maintained on the switched-capacitors using a symmetrical common-mode inductor. A bifilar winding is center-tap as its input, and the ends of the bifilar winding are connected to the capacitors. The capacitors are effectively in parallel. Because the charging current flows and returns through each leg of the inductor equally, it cannot magnetize the inductor core or cause any flux change. Because any voltages induced in the windings are common-mode, flux change in the core does not affect the charging current. The ac voltage generated when the capacitors switch is across the full inductor. Not only does the inductance attenuate any noise, the center-tap is between equal and opposite negative and positive voltages, which cancel. There is very little noise at the input. The circuit is reciprocal, so it can be used to rectify a transformer output. Two can be used as a bi-directional transformer isolated power converter. Several modules using 1 to 1 transformers can be stacked for a power converter having a higher ratio of input to output voltage.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation in part of a provisional patent application U.S. 61/990,015 entitled “Symmetrical Transformers,” filed May 7, 2014. This provisional patent application is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to power converters, and more particularly to isolated dc to dc power converters, though an alternative embodiment of the invention is adapted for isolated ac to ac power conversion. 
     A generic block diagram of a representative isolated de to de power converter  181  is shown in  FIG. 18 . In the center is a high frequency transformer  182 . As is the nature of most transformers, the excitation is ac, and that is provided by a switching network  183 . The output of the transformer also is ac, requiring rectification to provide a dc output. The rectifier may be a synchronous rectifier  184 . Both the input switching network  183  and the rectifier  184  tend to generate significant electrical noise, so input and output inductors  185  and  186  usually are needed. Very likely, there will be an input filter capacitor  187  and an output filter capacitor  188 . 
     The symmetrical power converter builds on the teachings of the symmetrical push-pull transformer from 1990, best explained by reference to “Design and Application of Matrix Transformers and Symmetrical Converters,” a tutorial for a seminar presented at the Fifth International High Frequency Power Conversion Conference &#39;90 in Santa Clara, Calif., on May 11, 1990. The symmetrical push-pull had limited commercial success, but it is quite difficult to provide suitable drive for its semiconductor switches. 
     SUMMARY OF THE INVENTION 
     The linchpin of the symmetrical power converter is the symmetrical inductor. It is called “symmetrical” because it uses equal and opposite voltages on its output that are cancelling at the input. The symmetrical voltages also tend to cancel currents conducted through stray capacitance. A representative symmetrical inductor is shown in  FIG. 1 , and more generic versions are shown in  FIGS. 6 and 7 . 
     The symmetrical voltages on the output of the symmetrical inductor are generated with a switched-capacitor circuit, which may be operated to generate complementary square-wave voltages or they may be operated in a pulse-width-modulated (pwm) mode to generate complementary lower duty-ratio rectangular-wave excitation, as can be seen in  FIGS. 8 a    and  8   b.    
     There are nodes on the switch-capacitor circuit that provide a suitable excitation for a high frequency transformer. In the preferred embodiment of the invention, the transformer has a single turn primary and a single turn secondary arranged as coaxial conductors for minimal leakage inductance and optimum coupling. (An alternative embodiment has a split secondary so that the de output can be complementary voltages of opposite polarity.) The single turn transformer has several advantages, one being very simple construction, however a more important consideration is that the inter-winding capacitance becomes an advantage, not a problem, facilitating much higher frequency operation. 
     Using single-turn windings constrains the transformer itself to be 1 to 1 (or 1 to 1 to 1, with a split secondary). Lower duty-ratio can be used to effect a voltage reduction, but it is preferred to use a modular design, especially for larger equivalent turns-ratios. Each power converter module has a complete power converter circuit as shown in  FIG. 18 , and it has suitable isolation within the transformer to withstand the highest applied voltage differential, input to output. In the simplest embodiment of the modular power converter, n modules have their inputs in series and their outputs in parallel, so the effective turns ratio is n to 1. Transformers are reciprocal, and so can be the symmetrical power converter, by designing the switching circuits for bi-directional current flow. Operated in reverse, this scheme provides a step up in voltage. 
     The individual modules can be turned on or off. By designing a symmetrical power converter with more modules than needed for a nominal turns-ratio, the effective turns-ratio becomes variable by switching one or more module in or out of the circuit, allowing for voltage regulation. With a very low current or zero-current output, individual modules can be operated at a low duty-ratio to keep the circuit alive and maintain regulation while having a very low magnetization current and losses 
     A preferred operating mode is for the modules to be controlled as independent dual-active-bridge (dab) converters. This gives very good control of the current and some ability to control the voltage, for voltage regulation over a small range. 
     The basic symmetrical inductor can operate in either direction with either polarity of voltage. If ac switches are used, such as back-to-back MOSFETs, as an example, not a limitation, then the symmetrical power converter can operate with either polarity, or with alternating polarity as an isolated ac to ac power converter. 
     The ac to ac power converter of this invention may find application as a simplified “solid state transformer.” While it can be used for small power converters in the scale of tens to hundreds of watts, it also scales well to hundreds of kilowatts or megawatts. 
     A problem with utility scale transformers is that they are huge, very expensive, and have a long production and replacement cycle. If one is damaged or destroyed in the field, it could take many months to replace it. A comparable “solid state transformer” is inherently smaller due to its much higher operating frequency. More important for consideration of replacement time, a “solid state transformer” built using modules of this invention can be delivered by delivery truck and assembled on-site with a few days. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  shows a symmetrical inductor with its common-mode capacitors and an input capacitor. 
         FIG. 2  is the symmetrical inductor of  FIG. 1 , with load resistors 
         FIG. 3  is the symmetrical inductor of  FIG. 1  with symmetrical voltage sources applied to its output. 
         FIG. 4  is the symmetrical inductor of  FIG. 1  with symmetrical switches. 
         FIGS. 5 a , 5 b  and 5 c    show the effective connections of the common-mode capacitors of the symmetrical inductor of  FIG. 4  for three states of the switches, with reference to nodes a, b, c and d of  FIG. 4 . 
         FIG. 6  shows a generic symmetrical inductor with capacitors and switches having a common magnetic core. 
         FIG. 7  shows a generic symmetrical inductor with capacitors and switches having two magnetic cores. 
         FIGS. 8 a  and 8 b    show representative waveforms, with reference to nodes a, b, c and d of  FIG. 4 . 
         FIG. 9  shows representative stray capacitances in a conventional transformer 
         FIG. 10  shows a bead transformer having a primary turn and a secondary turn would through n cores. 
         FIG. 11  shows the stray capacitance of one element of the bead transformer of  FIG. 10 . 
         FIG. 12  shows a section through a coaxial transformer having a primary turn and a secondary turn. The very thick insulation is for high dielectric withstanding voltage. 
         FIG. 13  shows a section through a coaxial transformer having a primary turn and a plurality of secondary windings. It is contemplated that the secondary windings would be paralleled in two groups to make a split secondary winding. 
         FIG. 14  shows the schematic diagram for a transformer having a high step-down ration. 
         FIG. 15  shows how to make a modular symmetrical power converter having a high step-down ratio using n identical modules with 1:1 transformers. 
         FIG. 16  shows a schematic of a transformer which may represent a “solid state dc-dc transformer.” 
         FIG. 17  shows a schematic of a transformer which may represent a “solid state dc-dc transformer” having a split secondary. 
         FIG. 18  shows a block diagram of the parts for the “solid-state dc-dc transformer” of  FIG. 16 . 
         FIG. 19  shows a block diagram of the parts for the “solid state dc-dc transformer” of  FIG. 17 . 
         FIG. 20  shows a coupled inductor. 
         FIG. 21  shows a transformer with series inductors for a dual-active-bridge implementation of the symmetrical power converter module of  FIG. 18 . 
         FIG. 22  shows a transformer with series inductors for dual-active-bridge implementation of the symmetrical power converter of  FIG. 19 . 
         FIG. 23  shows a symmetrical inductor with capacitor switching using MOSFETs. It also shows driving the MOSFETs from ground referenced logic and drivers exploiting the common mode voltage of the symmetrical inductor windings. 
         FIG. 24  shows how to modify the symmetrical power converter module of  FIG. 23  for alternating voltage on its input by using “back-to-back” MOSFET as ac switches. 
         FIG. 25  shows a preferred embodiment of the symmetrical push-pull transformer with its associated primary switches, primary common-mode capacitors, secondary switches and secondary common-mode capacitors. 
         FIG. 26  shows the primary circuit of  FIG. 25  alone, to show it more clearly. It has two conductors, so it can be a split primary winding. 
         FIG. 27  shows the secondary circuit of  FIG. 25  alone, to show it more clearly. It has two conductors, so it can be a split secondary winding. 
         FIG. 28  shows a section of a high voltage transformer, similar to that of  FIG. 12  except that there are two primary conductors in the center and two secondary conductors around the periphery. 
         FIG. 29  shows a section of a high voltage transformer, similar to that of  FIG. 28  except that there are eight primary conductors clustered in the center and eight secondary conductors around the periphery. 
         FIG. 30  shows a section of a high voltage transformer, similar to that of  FIG. 28  except that there are 16 secondary conductors which could be connected to be the equivalent of a split secondary winding. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows a symmetrical inductor  1  comprising n magnetic cores  2   a  through  2   n , shown as an example, not a limitation as ten toroidal cores with a bifilar inductor winding  3  comprising two wires  3   a  and  3   b . The inductor winding  3  is particularly easy to make, being simply two “U” shaped wires with center-tapped terminations for an input voltage Vi. Common-mode capacitors  4  and  5  are shown on the output of the inductor, and there may be an input capacitor  6  on the input. It can be seen that the three capacitors  4 ,  5  and  6  are effectively in parallel, therefore the voltage will always be the same on all of them, a key characteristic of the symmetrical inductor circuits. 
     In connecting from the input voltage Vi to the common-mode capacitors  4  and  5 , the circuit passes through the cores  2   a  through  2   n  in opposite directions so that the currents cancel. The currents that charge the common-mode capacitors  4  and  5  do not affect the flux in the magnetic cores  2   a  through  2   n , and nothing that the flux in the cores  2   a  through  2   n  does can affect the charging current for the common-mode capacitors  4  and  5 . 
       FIG. 2  shows that resistors  22  and  23  can be added to the symmetrical inductor of  FIG. 1 , and they conduct current and dissipate power as if they were connected directly to the input voltage Vi. The currents cannot change the flux in the cores  2   a  through  2   n , and flux changes in the cores do not affect the currents that charge or discharge the common mode capacitors  4  and  5 . 
       FIG. 3  shows that symmetrical voltage sources  32  and  33  can be connected to the output of the symmetrical inductor  1  of  FIG. 1 . A ground  34  is shown for reference. If applied as a direct voltage for too long duration, the voltage sources  32  and  33  would saturate the magnetic cores  2   a  through  2   n , as in any inductor, but if the voltage sources  32  and  33  are ac voltages of sufficiently high frequency, the combined inductance of the magnetic cores  2   a  through  2   n  will limit the flow of current to the magnetization current of the magnetic cores  2   a  through  2   n , as in any inductor. 
     A feature of the symmetrical inductor  31  is that for any symmetrical voltage applied on its output, the input terminals are at the center point of cumulative inductance of the magnetic cores  2   a  through  2   n  so symmetrical voltages cancel and no noise appears on the input terminals. This is true regardless of the magnitude of the input voltage Vi and regardless of the magnitude of the symmetrical voltage sources  32  and  33 , as long as the magnetic cores  2   a  through  2   n  do not saturate. 
       FIG. 4  shows symmetrical switches  42  and  43  can be applied to the output of the symmetrical inductor  1  of  FIG. 1 . In a practical power converter, the switches  42  and  43  may be solid state switches, and methods of driving them will be shown. Reference nodes a, b, c and d are shown for future reference of the voltage thereon. 
       FIGS. 5 a , 5 b  and 5 c    show that the common-mode capacitors  4  and  5  of  FIG. 4  are effectively placed in series if either switch S 1   42  or switch S 2   43  is closed.  FIG. 5 a    shows the state with switch S 1   42  closed;  FIG. 5 b    shows the state with switch S 2   43  closed; and  FIG. 5 c    shows the state with both switches open. Note that the voltage from the nodes a to b reverses polarity, as does the voltage from nodes c to d. Either set of nodes, a and b or c and d have suitable voltage waveforms to drive a transformer, and both sets of nodes can be used to excite a transformer with a split primary. 
       FIG. 8  shows the resulting waveforms as the switches S 1   42  and S 2   43  are operated. In  FIG. 8 a   , there is an initial period when both switches are open, then they alternate with minimal dead-time. The significance is that between nodes a and b, there is generated a square-wave voltage suitable for exciting a transformer. The same voltage occurs between nodes c and d.  FIG. 8 b    is similar, but shows the case were the switches are operated with off-time between the on-times, for pulse-width-modulated (pwm) operation. 
     As will be explained, there are advantages to making the symmetrical inductor  1  of  FIGS. 1 through 4  of multiple small cores, but  FIG. 6  shows that a symmetrical inductor  61  can be wound on a single magnetic core  62 . The bifilar winding  63  comprises two wires  63   a  and  63   b , each center-tapped at the input voltage Vi. The common-mode capacitors  4  and  5  and the symmetrical switches  42  and  43  connect just as they do in  FIG. 4 , and operation is similar. 
       FIG. 7  shows that a symmetrical inductor  71  can be wound on two magnetic cores  72   a  and  72   b , with a bifilar winding  73  comprising two wires  72   a  and  72   b , each center-tapped at the input voltage Vi. Again, the common-mode capacitors  4  and  5  and the symmetrical switches  42  and  43  connect and operated just as in  FIG. 4 . 
       FIG. 9  shows a “text book” equivalent circuit of a conventional transformer  91  having a magnetic core  92  and n windings  94   a  through  94   n , four windings being shown as an example, not a limitation. Representative stray capacitances  94   a  through  94   n  represent stray capacitances between windings and between the windings and the core. As many as are shown, it is not comprehensive. Stray capacitance is a serious problem for high frequency transformers, particularly if the voltage transitions are large. 
       FIG. 10  shows a transformer  101  comprising magnetic cores  102   a  through  102   n , ten being shown as an example, not a limitation. The winding  103  comprises a primary winding  103   p  and a secondary wining  103   s , each shown as a single “U” shaped turn. The letters a 1 , b 1 , c 1 , d 1 , a 2 , b 2 , c 2  and d 2  label nodes to identify connection points when the transformer  101  is used in a symmetrical power converter. With reference to  FIG. 4  and the discussion of  FIG. 4 , for the transformer  101 , which has a single turn primary  103   p , the nodes a and b can be connected to the nodes of the symmetrical inductor  41  having the same identifying letters a and b in  FIG. 4 . Alternatively, the wires can be connected to the nodes c and d of  FIG. 4 , as both have a suitable voltage for exciting the primary of the transformer  101 . 
     As shown in  FIG. 18  and as explained in the discussion of  FIG. 18 , the symmetrical inductor  41  of  FIG. 4  is bi-directional, so that a second identical symmetrical inductor  41  can be used as a synchronous rectifier. The nodes a 2 , b 2 , c 2  and d 2  of the single turn secondary winding  103   s  of  FIG. 10  are for showing how to connect to such a synchronous rectifier. 
       FIGS. 25 through 27  show a preferred transformer  251  for use with the symmetrical inductor  41  of  FIG. 4 . As suggested by the same reference designators,  FIG. 26  show a bifilar primary winding  263  only of the transformer  251  and the transformer  251  is designated  261  when shown this way. Likewise,  FIG. 27  shows a secondary bifilar winding  273  only and the transformer  251  is designated  271  when shown this way. 
     Switches  42 - 1  and  43 - 1  and capacitors  264  and  265  duplicate the switches  42  and  43  and the capacitors  4  and  5  of  FIG. 4 . Both sets of swithes are not used; the duplication in the dashed box is for better illustration of the connections in  FIGS. 25 and 26 . The transformer  251  comprises magnetic cores  252   a  through  252   n , shown as ten cores as an illustration, not a limitation. The bifilar primary winding  263  comprises two “U” shaped conductors  263   a  and  263   b  that pass through the magnetic cores  252   a  through  252   n . The ends are designated a 1 , b 1 , c 1  and d 1  as nodes to show their connection to the nodes a, b, c and d of symmetrical inductor  41  of  FIG. 4 . 
     Similarly, the bifilar secondary winding  273  comprises two conductors  273   a  and  273   b  that pass through the magnetic cores  252   a  through  252   n . The ends are designated a 2 , b 2 , c 2  and d 2 . When the symmetrical inductor  41  of  FIG. 4  is used in reverse as a synchronous rectifier, the nodes a, b, c and d are connected to the nodes designated a 2 , b 2 , c 2 , d 2  respectively of the secondary winding  273  of  FIGS. 25 and 27 . 
       FIG. 11  shows a portion  111  of the transformer  101  of  FIG. 10 , the core  102   a  with a portion of the primary winding  103   p  and a portion of the secondary winding  103   s  passing through it.  FIG. 11  also shows the inter-winding stray capacitance  112  and the stray capacitances  114  and  113  between the primary winding  103   p  and the secondary winding  103   s , respectively, to the core  102   a . A shunt leakage capacitance  115  is shown from the core to the chassis. A similar stray capacitance may exist in the transformer  91  of  FIG. 9  but is not shown. 
     An advantage of single turn primary and secondary wings is that equal voltage are induced in all winding by the changing flux, so the differential voltage between the primary winding  103   p  and the secondary winging  103   s  ideally is zero. If there is a differential voltage between the primary winding  103   p  and the secondary winding  103   s , any current conducted through the stray inter-winding capacitance  112  is marginally helpful and not detrimental. 
     To the extent that there is capacitive coupling to the core  102   a  through the stray capacitances  113  and  114 , it is common-mode and will tend to charge the shunt capacitance  115  to the chassis equally. However, it is contemplated that the core  102   a  will be isolated from the chassis both with insulating media and distance. To the extent that there is coupling to the core  102   a , it will have no place to go. 
     Most magnetic cores are somewhat conductive. It would be possible to make the transformer  101  of  FIG. 10  using balun type cores, but that would then establish a leakage current path between parts of the core that preferably are isolated. 
       FIG. 14  shows a transformer  141  shown having a primary voltage of 13.8 kV and a secondary voltage of 480 V, as an illustration, not a limitation. These are representative voltages for a medium voltage utility transformer, and some are very large, hundreds of VA or larger. The required turns-ratio is 13,800/480, or about 28.7 to 1.27 or 28 to 1 might be used, because there will be some voltage drop through the transformer. The transformer may be a “solid-state” transformer, which is the jargon of the utilities for a transformer having solid state circuitry associated with it so that the transformer itself is excited at a frequency that is much higher than line frequency, usually to accomplish a size and weight reduction. 
     For the reasons stated above, it is desired to use a 1 to 1 transformer, such as the transformer  161  of  FIG. 16 . If the transformer  161  of  FIG. 16  is a “solid state” transformer, it may have the components shown in  FIG. 18 . The solid state transformer  181  comprises a high frequency transformer  182  that preferably is a single turn, 1 to 1 transformer as shown in  FIG. 10 . Primary switches  183  provide the excitation for the transformer  182 , and preferably are symmetrical switches  42  and  43  of  FIG. 4 . 
     A similar switching circuit can be used for the rectifier  184 . An advantage of a 1 to 1 solid state transformer module is that it can be designed for bidirectional current flow, and the same voltages and currents are present in the primary and secondary circuits, so similar components can be used. The circuit becomes symmetrical about the transformer  182 . 
     An input filter  185  filters the noise from the switching circuit  183 , and preferably is a symmetrical inductor as shown in  FIGS. 1 through 4 . Most power converters have an input filter capacitor, such as the input filter capacitor  187  of  FIG. 18 . 
     Preferably, the solid state transformer  181  has an output filter  186  and an output capacitor  188  that are the same as the input filter  183  and the input capacitor  187  so that common parts can be used. 
     The transformer  182  can have any turns-ratio to use this invention. However, a transformer  182  having a single turns for the primary and for the secondary (1 to 1) is the preferred embodiment for high frequency operation. 
       FIG. 15  shows how n modules  181  of  FIG. 18  can be stacked as an array  181   a  through  181   n  to make a symmetrical power converter  151  having a nominal input to output voltage ratio of n to 1. Each module  181   a  through  181   n  has their inputs Vi′ in series and their outputs Vo in parallel. However, modules can be effectively “removed” from the symmetrical power converter  151  through electronic switching. If the switches  183  of a module are both closed, the input Vi′ of that module is effectively short-circuited. Current can flow through it so that it does not impede the series current flow through the other modules, but it has no effect in that module. As this would otherwise present a zero voltage at the output Vo of that module, the rectifier switches  184  must both remain open. In this manner the effective ratio of the symmetrical power converter  151  is reduced by 1, to n−1 to 1. Additional modules can similarly be “removed” so that the effective ratio can be any n or any integer value less than n. 
     The switching of modules in or out of the symmetrical power converter  151 , can be modulated so that non-integer ratios can be achieved as well. Note, though, that when both switches are closed, the common-mode capacitors and any input filter capacitor are short circuited. With reference to  FIG. 4 , if S 1   42  and S 2   43  are both closed, the common-mode capacitors  4  and  5  as well as the input capacitor  6  are all short circuited. This results in significant loss each time that it is done, so it should not be done frequently. In power converters that are configured for line frequency ac input, an opportune time to adjust the effective turns-ratio of the symmetrical power converter  151  of  FIG. 15  would be at zero crossing of the voltage. 
     If the symmetrical power converter  151  of  FIG. 15  is used with a very high input voltage, it will be noted that the voltage from the primary to the secondary winding of the first module must withstand the high voltage input voltage as its working voltage. For 13.8 kV ac rms, that is nearly 20,000 volts peak. To allow for voltage regulation, transients, aging and so forth, the design dielectric needs to be much higher, perhaps in the order of 50,000 volts. Although each module could be custom-designed with progressively lower dielectric requirements depending upon its position in the stack, it is preferred that one design be used for all. They are then balanced and one part can be stocked and used to replace any module for repair. 
       FIG. 12  shows a cross section of a transformer core  121 , which could, as an example, not a limitation, be any core  102   a  through  102   n  of the transformer  101  of  FIG. 10 . A primary winding  123  passes through the center of a toroidal magnetic core  122 . The primary winding  123  may be Litz wire, to optimize the transformer for high frequency operation. The primary winding is then surrounded by a very thick primary insulation  126 , which may comprise several layers of the same or different composition as a trade-off of the design. Surrounding that is a coaxial secondary winding  125 . The secondary winding could be Litz wire as well, perhaps braided, but it is contemplated that a solid tube may be used, as the larger diameter gives it an increased surface area, so even with penetration depth effects, conduction should be sufficient. With the coaxial structure, proximity effects are not as important. 
     Outside the coaxial secondary winding is a core insulator  124 , which, optionally, can be an insulating coating on the magnetic core  122  itself. Note that the secondary winding is lower voltage, so this insulation can be much thinner. 
       FIG. 13  shows a cross section of a transformer core  131 , which could, as an example, not a limitation, be any core  102   a  through  102   n  of the transformer  101  of  FIG. 10 .  FIG. 13  shows a variant of the transformer cross-section adapted to use a split secondary winding. A plurality of wires  135   a  through  135   n  are used in place of the solid secondary winding  135  of  FIG. 12 . In theory, n wires could make a transformer having n single turn secondaries, but it is contemplated that they would be terminated as two groups of n/2 windings to make n split secondary windings. 
     The primary winding  123  also could comprise parallel wires to make a split primary as shown in  FIGS. 28, 29 and 30 . Although the primary winding needs to have very high dielectric withstanding voltage to the secondary, two halves of a split primary need to be insulated only for the working voltage within the primary, which is much lower. 
       FIG. 28  shows a cross section of a transformer core  281 , which could, as an example, not a limitation, be any core  102   a  through  102   n  of the transformer  101  of  FIG. 10 . In  FIG. 28  two primary conductors  283   a ,  283   b  are used in place of the solid primary winding  123  of  FIG. 12 . Two primary conductors are shown as an illustration, not a limitation. Two secondary conductors  285   a ,  285   b  are used in place of the single secondary winding  125  of  FIG. 12 . Each is nearly a semicircle with a small gap between them for dielectric separation. Two secondary conductors are shown as an illustration, not a limitation. The two primary windings  283   a ,  283   b  and the two secondary conductors  285   a ,  28   bn  are separated by a high voltage insulation  286 . A magnetic core  282  surrounds the respective primary and secondary conductors and may be insulated from the secondary conductors by a secondary insulator  288 . 
       FIG. 29  shows a cross section of a transformer core  291 , which could, as an example, not a limitation, be any core  102   a  through  102   n  of the transformer  101  of  FIG. 10 . In  FIG. 29  a plurality of primary conductors  293   a  through  293   n  are used in place of the solid primary winding  123  of  FIG. 12 . Eight primary conductors are shown as an illustration, not a limitation. A plurality of secondary conductors  295   a  through  295   n  are used in place of the single secondary winding  125  of  FIG. 12 . Eight secondary conductors are shown as an illustration, not a limitation. The plurality of primary windings  293   a  through  293   n  and the plurality of secondary conductors  295   a  through  295   n  are separated by a high voltage insulation  296 . The plurality of primary conductors  293   a  through  293   n  may have a core  297  of insulating material to help locate the plurality of primary conductors  293   a  through  293   n  in a circular arrangement as shown, as an illustration, not a limitation. A magnetic core  292  surrounds the respective primary and secondary conductors and may be insulated from the secondary conductors by a secondary insulator  298 . 
       FIG. 30  shows a cross section of a transformer core  301 , which could, as an example, not a limitation, be any core  102   a  through  102   n  of the transformer  101  of  FIG. 10 . In  FIG. 30  a plurality of primary conductors  303   a  through  303   n  are used in place of the solid primary winding  123  of  FIG. 12 . Eight primary conductors are shown as an illustration, not a limitation. A plurality of first secondary conductors  304   a  through  304   n  and a plurality of second secondary conductors  305   a  through  305   n  are used in place of the single secondary winding  125  of  FIG. 12 . Eight first secondary conductors and eight second secondary conductors are shown as an illustration, not a limitation. The plurality of primary windings  303   a  through  303   n  are separated from the plurality of first secondary conductors  304   a  through  304   n  and the plurality of second secondary conductors  305   a  through  305   n  by a high voltage insulation  306 . The plurality of primary conductors  303   a  through  303   n  may have a core  307  of insulating material to help locate the plurality of primary conductors  303   a  through  303   n  in a circular arrangement as shown, as an illustration, not a limitation. A magnetic core  302  surrounds the respective primary and secondary conductors and may be insulated from the secondary conductors by a secondary insulator  308 . 
       FIG. 17  shows a transformer  171  having a split secondary as might be used for domestic power in the United States, 120/240 V ac rms split phase.  FIG. 19  shows how such a transformer can be incorporated into a symmetrical power converter module  191  of this invention. A transformer  192  having a split secondary winding has a primary switching circuit  193  to provide excitation to the transformer  192 . Two separate rectifier circuits  194  and  195  respectively rectify the outputs of the transformer  192 , and separate output filters  197  and  198  attenuate noise from the respective rectifying circuits  194  and  195 . There are two separate output filter capacitors  200  and  201 . Isolation is maintained through the secondary circuits until the final output, where they can be connected in series if desired, as shown. 
     An input filter  196  filters noise from the switching circuit  193 , and there is an input filter capacitor  199 . The symmetric power converter module  191  can be incorporated into a stacked symmetric power converter as in  FIG. 15 , replacing the symmetric power converter modules  181   a  through  181   n.    
     A preferred control mode for the symmetric power converter module is as a dual-active-bridge (dab). This requires some series inductance in the transformer circuit, and often the leakage and stray inductance of the transformer is used for this purpose. Schematically, the stray and leakage inductance may be shown as a separate inductor in series with an ideal transformer, and that can be one interpretation of the transformers  211  of  FIG. 21 and 221  of  FIG. 22 . However for better parametric control it may be preferred to use a transformer with very low stray and leakage inductance with separate actual inductor components. The inductance required tends to be small, so the inductor  201  of  FIG. 20  may be suitable. It comprises a magnetic core  202 , and the transformer leads  203   a  and  203   b  pass through it. 
       FIG. 21  shows a transformer  212  having small inductors  213  and  214  respectively in series with its primary and secondary windings.  FIG. 22  shows a transformer circuit  221 , which is similar for a circuit needing a split secondary. The transformer  222  has small inductors  223 ,  224  and  225  on its respective primary and split secondary windings. 
     In theory, a dab circuit needs only one inductor, but it is preferred to maintain symmetry. In the case of the transformer circuit  221  of  FIG. 22 , if the secondary inductors  224  and  225  are included, the secondaries can be separately controlled for voltage regulation over some range of voltage. A dual-active-bridge circuit and its method of control are not novel, but using them is a preferred embodiment of the invention for many applications. 
     In operation, the symmetrical inductor  231  of  FIG. 23  is the same as the symmetrical inductor  41  of  FIG. 4 . However, MOSFETs  237  and  238  replaces the switches S 1   41  and S 2   43 . The symmetrical inductor  231  comprises a plurality of magnetic cores  232   a  through  232   n  and a bifilar winding  233  comprising a high side winding  233   a  and a low side winding  233   b . Just as in  FIG. 4 , there are common-mode capacitors  234  and  235 , and an input capacitor  236 . 
     The sources of the MOSFETs have voltages that vary substantially throughout the switching cycle, as can be seen by reference to the voltage on nodes a and b in  FIGS. 8 a  and 8 b   . One skilled in the art of power converters would know how to provide to provide a suitable gate drive, but the complexity of the gate drive is greatly simplified if the common-mode voltage through the transformer cores  233   a  through  232   n  is utilized. To do so, the low side winding  233   b  comprises hollow conductors with the gate drives passing through them. Buffer-drivers  239   a  and  239   b  provide the necessary gate drives. The advantage of this arrangement is that the buffer-drivers and their logic can be referenced to the low side of the input power Vi. 
     If used in a symmetrical power converter such as the symmetrical power converter  151  of  FIG. 15 , the low side of the respective voltage inputs Vi′ may be at elevated voltage, maybe even thousands of volts, but the voltage does not change over the switching cycle. 
       FIG. 24  shows a symmetrical inductor  241  which also is similar to the switching inductor  41  of  FIG. 4 , except that the switches S 1   42  and S 2   43  have been replaced with back to back MOSFETs  247   a ,  247   b ,  248   a  and  248   b . The symmetrical inductor  241  comprises a plurality of magnetic cores  242   a  through  242   n  and a bifilar winding  243  comprising a high side winding  243   a  and a low side winding  243   b . Just as in  FIG. 4 , there are common-mode capacitors  244  and  245 , and an input capacitor  246 . 
     As in  FIG. 23 , buffer-drivers  249   a ,  249   b ,  249   c  and  249   d  provide gate drives for the respective MOSFETs, and as in  FIG. 23 , the common-mode voltage through the magnetic cores  242   a  through  242   n  is utilized. In operation, for one polarity of input voltage, MOSFETs  247   b  and  248   b  are switched, while MOSFETs  247   a  and  247   b  are turned on continuously, and operation is just as in  FIG. 23 . If the input voltage changes polarity, then MOSFETs  247   a  and  248   a  are switched, and MOSFETs  247   b  and  248   b  are turned on continuously. 
     Neither using the common-mode through the transformer as in  FIGS. 23 and 24  nor the used of back to back MOSFETs to switch voltage that reverses polarity are novel, but they are presented as the preferred embodiment of the invention for some applications.