Abstract:
An electrical connector includes an anode assembly for conducting an electrical supply current from a source to a destination, the anode assembly includes an anode formed into a first shape from sheet metal or other sheet-like conducting material. A cathode assembly conducts an electrical return current from the destination to the source, the cathode assembly includes a cathode formed into a second shape from sheet metal or other sheet-like conducting material. An insulator prevents electrical conduction between the anode and the cathode. The first and second shapes are such as to provide a conformity of one to the other, with the insulator therebetween having a predetermined relatively thin thickness. A predetermined low-resistance path for the supply current is provided by the anode, a predetermined low-resistance path for the return current is provided by the cathode, and the proximity of the anode to the cathode along these paths provides a predetermined low self-inductance of the connector, where the proximity is afforded by the conformity of the first and second shapes.

Description:
FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
     This invention was made with government support under contract B601996 awarded by the Department of Energy. The government has certain rights in the invention. 
    
    
     BACKGROUND 
     The present invention relates to separably interconnecting power between a DC power supply and its load with minimal losses even with clocking transitions on the load current demands. More specifically, a pair of conductive plates sized for predetermined current capacity and shaped to conform to each other are separated by a thin insulator to thereby minimize both resistive and self-inductive losses. 
     In the field of electronics, and in particular in the field of high-performance computers, it is highly desirable to reduce the consumption of electrical power as much as possible. Toward this end, new generations of power supplies are designed to minimize loss, and new generations of processors and memory systems are designed to dissipate less power despite higher computational performance. An effective technique in reducing the power consumption P of electronics is to lower its operating voltage V. For CMOS circuits, P=CV 2 f, where C is the sum of all capacitances which are charged to voltage V or discharged from voltage V, at frequency f. As will be further explained, power is minimized by reducing V until any further reduction will stop the circuit from operating at frequency f. Yet, because P=VI, where I is current in amperes flowing through the electronics, reduced voltage V implies higher current I, despite reduction in power P. Thus, for such low-voltage, high-current electronics, a power connector must be capable of handling large current I. The current I must be delivered substantially at potential V from a supply terminal of the power supply to the electronics, and must be returned substantially at zero potential from the electronics to a return terminal of the power supply. The supply-terminal potential and the return-terminal potential may be referred to as “power” and “ground” respectively. Let ΔV s  be the voltage drop that occurs as current I travels from the supply terminal to the electronics; let ΔV r  be the voltage drop that occurs as current I travels from the electronics to the return terminal; and let ΔV o  be other overhead voltage drop that occurs, such as in conductors other than the connector. Let R s , R r , and R o  be the resistances corresponding to the voltage drop S  ΔV s , ΔV r  and ΔV o  respectively; that is,
 
Δ V   s   =IR   s   ;ΔV   r   =IR   r   ;ΔV   o   =IR   o .  (1)
 
     A total overhead voltage drop ΔV total  may therefore be defined as
 
Δ V   total   ≡ΔV   s   +ΔV   r   +ΔV   o   =I ( R   s   +R   r   +R   o )  (2)
 
     For electronics such as a processor and memory, another common method of power reduction is to reduce, as processor workload changes, the processor&#39;s operating voltage V and/or a clock frequency f at which the processor operates. A popular technique is called dynamic voltage-frequency scaling (DVFS), in which both V and f are dropped proportionally when workload is reduced, and raised again when workload is increased. 
     Consequently, the current I from the power supply to the processor and memory varies strongly in time. This leads to voltage fluctuation at the processor and memory, because an inductive voltage drop ΔV L  occurs across the power connector according to Faraday&#39;s Law, 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         L 
                       
                     
                     = 
                     
                       L 
                       ⁢ 
                       
                         dI 
                         dt 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     where L is a self-inductance of the power connector and 
             dI   dt         
is a change in current per unit time through the connector. Because a technique such as DVFS can produce large
 
               dI   dt     ,         
the self-inductance L of the power connector must be small, according to equation (3), to avoid large voltage fluctuations ΔV L .
 
     Consequently, for low-voltage, high-current electronics, there is a need for a power connector that simultaneously achieves
         (a) high current-carrying capacity,   (b) low connector resistance R conn ≡R s +R r , and   (c) low self-inductance L conn .       

     Some prior-art, high-current power connectors achieve (a) and (b), but fail to achieve (c). For example, a power connector comprising an array of pins, with each pin being either power or ground, has relatively high self-inductance. Other prior-art connectors, such as coaxial or stripline connectors, achieve (c) but fail to achieve (a): they are typically restricted to just a few amperes of current per contact. 
     Thus, the present inventors have recognized that it is highly desirable to find a connector structure that achieves (a), (b), and (c) simultaneously, and does so in a compact package for the purpose of reducing R o . For example, a useful target set of specifications might be:
 
 I= 100 A; R   conn   ≡R   s   +R   r ≦50μΩ; L   conn ≦500 pH,  (4)
 
where the inductance specification in (4) arises from a desire to achieve a dynamic voltage drop of at most
 
                 Δ   ⁢           ⁢     V   L       =     50   ⁡     [   mV   ]         ⁢                     with               dI   dt     =     100   ⁢       A   μs     .             
Additionally, it would be particularly useful to have the connectors to be able to mate and unmate multiple times, meaning that the connectors are selectively easily separable.
 
     SUMMARY 
     According to an embodiment of the present invention, an electrical connector is described that is capable of carrying large amounts of electrical current between two circuit boards or other entities, in both a forward direction and a reverse direction, in a manner that provides a low resistance between the two circuit boards in each of the two directions, and also provides a low self-inductance of the connector. The connector has application to delivering low-voltage, high-current power from a power supply on a first board to electronics on a second board: the low resistance minimizes voltage drop for a load current that is constant, while the low inductance minimizes voltage fluctuations due to a load current that changes. These issues are of great importance, for example, in designing high-performance computers. 
     In an exemplary embodiment, an electrical connector is described comprising
         a. An anode assembly for conducting an electrical supply current from a source to a destination, the anode assembly comprising an anode formed into a first shape from sheet metal or other sheet-like conducting material, an anode-to-source attachment means, and an anode-to-destination attachment means,   b. A cathode assembly for conducting an electrical return current from the destination to the source, the cathode assembly comprising a cathode formed into a second shape from sheet metal or other sheet-like conducting material, a cathode-to-source attachment means, and a cathode-to-destination attachment means,   c. An insulator that prevents electrical conduction between the anode and the cathode.       

     The first and second shapes are such as to provide a conformity of one to the other, with the insulator therebetween being relatively thin; the connector is attached to the source using both the anode-to-source attachment means and the cathode-to-source attachment means; and the connector is attached to the destination using both the anode-to-destination attachment means and the cathode-to-destination attachment means. In a preferred exemplary embodiment, for each of the anode assembly and the cathode assembly, at least one of the attachment means is separable even if the other is more permanent by using a press-fit or solder attachment. However, one of skill would readily recognize that the present invention is not limited by details of the attachment means, including the number of permanent/separable attachments. In the exemplary embodiment described herein, all four end attachments (e.g., anode and cathode, source and destination) are separable. A low-resistance path for the supply current is thereby provided by the anode, a low-resistance path for the return current is thereby provided by the cathode, and the proximity of the anode to the cathode along these paths provides a low self-inductance of the connector, the proximity being afforded by the conformity of the first and second shapes. 
     In one or more embodiments, the connector deliberately sacrifices ease of connection and disconnection to achieve lower inductance and lower contact resistance. For example, in one or more embodiments, connection and disconnection involves tightening and loosening screws, respectively; nevertheless, separability of the connector, and therefore serviceability of the source and the destination, is maintained. 
     In one or more embodiments, the connector provides substantial mechanical compliance between source and destination, thereby permitting the use of a plurality of the connectors in parallel between the source and the destination without fear that electrical contact at either the source or the destination will be compromised by mechanical tolerances. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a top perspective view of a power connector  100  according to a first exemplary embodiment; 
         FIG. 2  illustrates a bottom perspective view of the power connector  100 ; 
         FIG. 3  illustrates an exploded view of the power connector  100 ; 
         FIG. 4  illustrates an exploded view of an anode assembly  102  for the power connector  100 ; 
         FIG. 5  illustrates an exploded view of a cathode assembly  104  for the power connector  100 ; 
         FIG. 6  illustrates an insulator for the power connector  100 ; 
         FIG. 7  illustrates a cross-sectional view of the power connector  100 ; 
         FIG. 8  illustrates a perspective view of an assembly  800  comprising two circuit boards and two instances of the power connector  100 ; 
         FIG. 9  illustrates an exploded view of the assembly  800 ; 
         FIG. 10  illustrates an upside-down exploded view of the assembly  800 ; 
         FIG. 11  illustrates a perspective view of an assembly  1100  comprising two circuit boards and three instances of the power connector  100 ; 
         FIG. 12  illustrates the calculation of resistance and inductance for the power connector  100 ; 
         FIG. 13  illustrates nomenclature used in the calculation of inductance for two parallel plates; 
         FIG. 14  illustrates a top perspective view of a power connector  1400  according to a second exemplary embodiment; 
         FIG. 15  illustrates a bottom perspective view of the power connector  1400 ; 
         FIG. 16  illustrates an anode assembly  1402  for the connector  1400 ; 
         FIG. 17  illustrates an exploded view of the anode assembly  1402 ; 
         FIG. 18  illustrates a perspective view of a connector assembly  1800  according to a third exemplary embodiment; 
         FIG. 19  illustrates a perspective view of an assembly comprising two circuit boards and one instance of the connector  1800 ; 
         FIG. 20  illustrates a perspective view of a power connector  2000  according to a fourth exemplary embodiment; 
         FIG. 21A  illustrates a perspective view of a power connector  2100  according to a fifth exemplary embodiment; 
         FIG. 21B  illustrates a cross-sectional view of the power connector  2100 , which has angle parameters θ 1 , θ 2 , and θ 3 ; 
         FIG. 22A  illustrates a cross-sectional schematic view of the power connector  2100  with θ 1 =90°, θ 2 =180°, and θ 3 =180°; 
         FIG. 22B  illustrates a cross-sectional schematic view of the power connector  2100  with θ 1 =90°, θ 2 =270°, and θ 3 =270°; 
         FIG. 22C  illustrates a cross-sectional schematic view of the power connector  2100  with θ 1 =90°, θ 2 =180°, and θ 3 =90°; 
         FIG. 22D  illustrates a cross-sectional schematic view of the power connector  2100  with θ 1 =180°, θ 2 =180°, and θ 3 =180°; and 
         FIG. 22E  illustrates a cross-sectional schematic view of a power connector  2200 . 
     
    
    
     REFERENCE NUMERALS 
     In the following listing of component labels, the leading digit(s) of a reference numeral indicates the number of the figure whose discussion introduces it. For example, although reference numeral  402  appears on  FIG. 1 , it is introduced during the discussion of  FIG. 4 , so the leading digit is “4”.
           100  High-current, low-resistance, low-inductance connector according to a first embodiment     101  Cartesian coordinate system     102  Anode assembly for connector  100       104  Cathode assembly for connector  100       106  Insulator for connector  100       302  Coating on cathode  500  that obviates need for insulator  106       304  Coating on anode  400  that obviates need for insulator  106       400  Anode for connector  100       402  Top shim plate     404  Bottom shim plate     406  Fasteners in top flange  414  of anode  400       408  Bottom flange of anode  400       410  First angled flange of anode  400       412  Second angled flange of anode  400       414  Top flange of anode  400       416  Fastener hole     418  Fastener clearance hole     420  Locating-pin clearance hole     422  Fastener clearance hole     500  Cathode for connector  100       502  Locating Pin     506  Fastener in flange  518  of cathode  500       508  Bottom flange of cathode  500       510  First angled flange of cathode  500       512  Second angled flange of cathode  500       514  Top flange of cathode  500       516  Fastener hole     518  Top notch     520  Gap between cathode top flange and anode top shim plate     522  Bottom notch     524  Gap between cathode bottom flange and anode bottom shim plate     526  Hole in cathode for locating pin     528  Protruding portion of cathode top flange  514       530  Protruding portion of cathode bottom flange  508       608  Bottom portion of insulator  106       610  First angled portion of insulator  106       612  Second angled portion of insulator  106       614  Top portion of insulator  106       616  Fastener clearance hole     618  Top notch     620  Locating-pin clearance hole     622  Bottom notch     628  Protruding portion of top portion  614       630  Protruding portion of bottom portion  608       702  Sigma-shaped curve     800  Two-connector, board-to-board assembly     802  First printed circuit board     804  Second printed circuit board     902  Locating-pin holes in second circuit board  804  for a first instance  100 . 1  of connector  100       904  Anode pads on second circuit board  804  for the first instance  100 . 1  of connector  100       906  Cathode pad on second circuit board  804  for the first instance  100 . 1  of connector  100       908  Locating-pin holes in second circuit board  804  for a second instance  100 . 2  of connector  100       910  Anode pads on second circuit board  804  for the second instance  100 . 2  of connector  100       912  Cathode pad on second circuit board  804  for the second instance  100 . 2  of connector  100       1002  Fasteners that engage fasteners  406  of the first instance  100 . 1  of connector  100       1004  Fasteners that engage fasteners  506  of the first instance  100 . 1  of connector  100       1006  Anode pads on first circuit board  802  for the first instance  100 . 1  of connector  100       1008  Cathode pad on first circuit board  802  for the first instance  100 . 1  of connector  100       1010  Fasteners that engage fasteners  406  of the second instance  100 . 2  of connector  100       1012  Fasteners that engage fasteners  506  of the second instance  100 . 2  of connector  100       1014  Anode pads on first circuit board  802  for the second instance  100 . 2  of connector  100       1016  Cathode pad on first circuit board  802  for the second instance  100 . 2  of connector  100       1100  Three-connector, board-to-board assembly     1202  Short vertical path at top of connector  100       1204  Short vertical path at bottom of connector  100       1302  Coordinate system for  FIG. 13       1304  First parallel plate     1306  Second parallel plate     1400  High-current, low-resistance, low-inductance connector according to a second embodiment     1402  Anode assembly of connector  1400       1404  Gap between anode surface stamp and cathode for connector  1400       1600  Anode for connector  1400       1608  Bottom flange of anode  1600       1610  First angled flange of anode  1602       1612  Second angled flange of anode  1602       1614  Top flange of anode  1602       1616  Surface stamp in top flange  1614  of anode  1600       1618  Surface stamp in bottom flange  1608  of anode  1600       1800  High-current, low-resistance, low-inductance connector according to a third embodiment     1802  All-fastener-mounted anode assembly of connector  1800       1804  All-fastener-mounted cathode assembly of connector  1800       1806  All-fastener-mounted anode for connector  1800       1808  Female fastener attached to a top surface stamp  1810       1810  Top surface stamp     1812  Female fastener attached to a bottom surface stamp  1814       1814  Bottom surface stamp     1816  All-fastener-mounted cathode     1818  Female fastener attached to a top cathode flange  1820       1820  Top cathode flange     1822  Female fastener attached to a bottom cathode flange  1824       1824  Bottom cathode flange     1826  Centerline of connector assembly, parallel to xy plane     1900  Board-to-board assembly using connector  1800       1902  First printed circuit board in assembly  1900       1904  Second printed circuit board in assembly  1900       1908  Male fastener that engages female fastener  1808       1912  Male fastener that engages female fastener  1812       1918  Male fastener that engages female fastener  1818       1922  Male fastener that engages female fastener  1822       2000  High-current, low-resistance, low-inductance connector according to a fourth embodiment     2100  High-current, low-resistance, low-inductance connector according to a fifth embodiment     2102  Anode for connector  2100       2104  Cathode for connector  2100       2106  Insulating layer for connector  2100       2108  Bottom flange of anode  2102       2110  First angled flange of anode  2102       2112  Second angled flange of anode  2102       2114  Top flange of anode  2102       2116  Bottom flange of cathode  2104       2118  First angled flange of cathode  2104       2120  Second angled flange of cathode  2104       2122  Top flange of cathode  2104       2124  Surface stamp in bottom flange  2108  of anode  2102       2126  First circuit board     2128  Surface stamp in top flange  2114  of anode  2102       2130  Second circuit board     2132  Fasteners for first circuit board  2126       2134  Fasteners for second circuit board  2130       2202  First corner     2204  Second corner     2206  Third angled flange       

     DETAILED DESCRIPTION 
     With reference now to the figures, various non-limiting exemplary embodiments will now be described. 
     First Exemplary Embodiment (FIGS.  1 - 13 ) 
       FIG. 1  through  FIG. 7  illustrate a first embodiment of a high-current-capacity, low-resistance, low-inductance electrical connector  100 . Each figure shows an imaginary, Cartesian xyz coordinate system  101  comprising an x axis, a y axis and a z axis, the coordinate system thereby defining an xy plane, an xz plane and a yz plane. The coordinate system&#39;s orientation with respect to the connector is consistent on all figures, although the origin is not necessarily consistent.  FIGS. 1, 2, and 7  illustrate assembled views of the connector  100 , which comprises an anode assembly  102 , a cathode assembly  104 , and an insulator  106 . These three assemblies are illustrated on  FIG. 3 , which is an exploded diagram of the connector  100 . Other reference numerals on  FIGS. 1 through 3  are described in connection with  FIGS. 4 through 6 . 
       FIG. 4  illustrates an exploded view of the anode assembly  102 , which comprises an anode  400 , at least one top shim plate  402 , at least one bottom shim plate  404 , and at least one anode fastener  406 , such as a threaded PEM nut, well known in the art, available from Penn Engineering® of Danboro, Pa. However, one of ordinary skill in the art would readily recognize that other separable fastening means could be used other than PEM nuts and screws, such as slide-in or plug connectors or that the fastening means could be more permanent, such as press-fit or soldered connections, as long as the connector maintains sufficient mechanical compliance and the low resistance objectives are met. The anode  400 , the top shim plates  402 , and the bottom shim plates  404  are made of electrically conducting material, preferably copper or alloys of copper such as copper beryllium. The anode  400  comprises a bottom flange  408 , a first angled flange  410 , a second angled flange  412 , and a top flange  414 . The top flange  414  comprises, for each anode fastener  406 , a fastener hole  416  for receiving the anode fastener  406  and affixing it to the top flange  414 . The top flange  414  also comprises at least one fastener-clearance hole  418 . The bottom flange  408  comprises two locating-pin clearance holes  420 . 
     Each top shim plate  402  comprises at least one screw-clearance hole  422 . Each top shim plate is affixed to the positive-z-facing surface of top flange  414  in such a manner that the screw-clearance holes  422  are substantially concentric with the fastener holes  416 , and such that a low electrical resistance is achieved between each top shim plate  402  and the top flange  414 . The bottom shim plates  404  are affixed to the negative-z-facing surface of bottom flange  408  in such a manner that a low electrical resistance is achieved therebetween. The top and bottom shim plates are attached, for example, by soldering or brazing. The anode fasteners  406  are attached, for example, by swaging, as is routinely done in the attachment of PEM nuts. 
       FIG. 5  illustrates an exploded view of the cathode assembly  104 , which comprises a cathode  500 , two locating pins  502 , and at least one cathode fastener  506  such as a threaded PEM nut. The cathode  500  is made of electrically conducting material, such as copper. The cathode  500  comprises a bottom flange  508 , a first angled flange  510 , a second angled flange  512  and a top flange  514 . The top flange  514  comprises, for each cathode fastener  506 , a fastener hole  516  for receiving the cathode fastener  506  and affixing it to the top flange  514  by, for example, swaging. The top flange  514  also comprises at least one top notch  518 , each of which accommodates, in the assembly  100 , the top shim plate  402 ; as illustrated in  FIG. 1 , the top notch  518  is large enough to leave a gap  520  between the cathode&#39;s top flange  514  and three sides of the anode&#39;s top shim plate  402 . 
     Likewise, referring again to  FIG. 5 , the bottom flange  508  comprises at least one bottom notch  522 , each of which accommodates, in the assembly  100 , the bottom shim plate  404 ; as illustrated on  FIG. 2 , each bottom notch  522  is large enough to leave a gap  524  between the bottom flange  508  and three sides of the bottom shim plate  404 . The bottom flange  508  also comprises two locating-pin holes  526 , which are used to attach the locating pins  502  thereto by, for example, swaging. Protruding portions  528  of the top flange  514  are formed by the notches  518 ; likewise, protruding portions  530  of the bottom flange  508  are formed by the notches  522 . 
       FIG. 6  illustrates the insulator  106 , which comprises a bottom portion  608 , a first angled portion  610 , a second angled portion  612 , and a top portion  614 . The top portion  614  comprises, for each cathode fastener  506 , a fastener clearance hole  616 . The top portion  614  also comprises, for each top notch  518 , a corresponding notch  618 . The bottom portion  608  comprises two locating-pin clearance holes  620 , and, for each bottom notch  522 , a corresponding bottom notch  622 . Protruding portions  628  of the top portion  614  are formed by the notches  618 ; likewise, protruding portions  630  of the bottom portion  608  are formed by the notches  622 . 
     Referring to  FIG. 3 , it should be noted that the insulator  106  may not actually be a separate piece; instead, it may be pre-bonded as a first coating  302  applied to the following surfaces of the cathode  500 : the negative-z-facing surface of flange  514 , the positive-x-facing surfaces of flanges  512  and  510 , and the positive-z-facing surface of flange  508 . As a second alternative, insulator  106  may be pre-bonded as a second coating  304  applied to the following surfaces of the anode  400 : the positive-z-facing surface of flange  414 , the negative-x-facing surfaces of flanges  412  and  410 , and the negative-z-facing surface of flange  408 . As a third alternative, insulator  106  may be provided by applying both coatings  302  and  304 . 
       FIG. 7  illustrates a cross-sectional view of the connector assembly  100 , parallel to the xz plane. As shown, the anode  102 , the cathode  104  and the insulator  106  conform to each other everywhere along a sigma-shaped curve  702  comprising points A, B, C, D, E, F, G, and I; consequently, everywhere along the sigma-shaped curve  702 , the anode and cathode are separated only by a thickness T of the insulator. 
     Assuming that one or both of the pre-bonded coatings  302  and  304  are used to provide the insulator  106 , assembly of the connector  100  merely involves nesting the anode assembly  102  inside the cathode assembly  104 . To accomplish this, protrusions  528  ( FIG. 5 ) must be temporarily and elastically bent upward to allow the fasteners  506  to snap into the fastener-clearance holes  418 . Each fastener-clearance  418  hole is larger than the fastener  506  by a significant amount, in order to avoid electrical shorting of anode to cathode, so this assembly process is relatively easy to perform. To insure the proximity of anode to cathode shown in FIG.  7 , it is desirable, during this assembly process, to apply a small quantity of adhesive to the insulator-coated surfaces of the anode and the cathode. 
     The thickness of the top shim plates  402  is chosen so that, when assembly of the connector is complete, the positive-z-facing surfaces of the top shim plates  402  are substantially co-planar with the positive-z-facing surface of the top flange  514 . Likewise, the thickness of the bottom shim plates  404  is chosen so that, when assembly of the connector is complete, the negative-z-facing surfaces of the bottom shim plates  404  are substantially co-planar with the negative-z-facing surface of the bottom flange  508 . 
     Referring to  FIG. 8 , connector  100  is designed to conduct a first voltage V on the anode  400  and a second voltage V ref  on the cathode  500 , thereby to deliver electrical power from a first printed circuit board (PCB)  802 , which is in contact with the anode at upper shim plates  402  and is in contact with the cathode at the top flange  514 , to a second PCB  804 , which is in contact with the anode at the lower shim plates  404  and is in contact with the cathode at the bottom flange  508 . 
     For example, V may be a positive voltage (V&gt;0) associated with a positive terminal of a power domain, and V ref  may be a ground potential (V ref ≡0) associated with a negative terminal of the power domain. The insulator  106 , which is composed of an electrically insulating material, maintains electrical isolation between the anode and the cathode, thereby preventing voltage V from shorting to voltage V ref . 
       FIG. 8  illustrates a two-connector, board-to-board assembly  800 . This is a typical deployment of the connector assembly  100 , in which two instances thereof, denoted  100 . 1  and  100 . 2 , are used. Connector  100 . 1  transmits a first power domain, characterized by its anode-voltage V 1 , from the first PCB  802 , where voltage V 1  is generated, to the second PCB  804 , where voltage V 1  is used to power various electronic devices. Likewise, connector  100 . 2  transmits a second power domain, characterized by its anode-voltage V 2 , from the first PCB  802 , where voltage V 1  is generated, to the second PCB  804 , where voltage V 2  is used. 
       FIG. 9  is an exploded diagram of assembly  800  that illustrates an attachment of connectors  100 . 1  and  100 . 2  to PCB  804 . Locating connector  100 . 1  with respect to PCB  804  by insertion of its locating pins  502  into holes  902 , the connector  100 . 1  is soldered to an inner surface of PCB  804  using copper pads  904  and  906  printed thereon; specifically, to connect the anode of connector  100 . 1  to PCB  804 , the bottom shim plates  404  of connector  100 . 1  are soldered to the copper pads  904 , and to connect the cathode of connector  100 . 1  to PCB  804 , the bottom flange  508  of connector  100 . 1  is soldered to the copper pad  906 . Likewise, locating connector  100 . 2  with respect to PCB  804  by insertion of its locating pins  502  into holes  908 , the connector  100 . 2  is soldered to the inner surface of PCB  804  using copper pads  910  and  912  printed thereon; specifically, to connect the anode of connector  100 . 2  to PCB  804 , the bottom shim plates  404  of connector  100 . 2  are soldered to the copper pads  910 , and to connect the cathode of connector  100 . 2  to PCB  804 , the bottom flange  508  of connector  100 . 2  is soldered to the copper pad  912 . 
       FIG. 10  is an upside-down exploded diagram of assembly  800  that illustrates an attachment of connectors  100 . 1  and  100 . 2  to PCB  802 . Specifically, the attachment of connector  100 . 1  to PCB  802  is achieved with fasteners  1002  and  1004  that engage fasteners  406  and  506  of connector  100 . 1 , respectively. Tightening the fasteners  1002  achieves a low-resistance anode connection for connector  100 . 1  by pulling the top shims  402  thereof with high normal force against copper pads  1006 . Tightening the fasteners  1004  achieves a low-resistance cathode connection for connector  100 . 1  by pulling the top flange  414  thereof with high normal force against a copper pad  1008 . 
     Likewise, the attachment of connector  100 . 2  to PCB  802  is achieved with fasteners  1010  and  1012  that engage fasteners  406  and  506  of connector  100 . 2 , respectively. Tightening the fasteners  1010  achieves a low-resistance anode connection for connector  100 . 2  by pulling the top shims  402  thereof with high normal force against copper pads  1014 . Tightening the fasteners  1012  achieves a low-resistance cathode connection for connector  100 . 2  by pulling the top flange  514  thereof with high normal force against a copper pad  1016 . 
     Still referring to  FIG. 10 , the attachment of connectors  100 . 1  and  100 . 2  to PCB  802  with removable fasteners  1002 ,  1004 ,  1110 , and  1012  is advantageous because PCBs  802  and  804  may then be separated for servicing. For example, if a power-delivery component on PCB  802  fails, replacement of PCB  802  is thereby facilitated, because the fasteners  1002 ,  1004 ,  1010 , and  1012  may be easily removed, a new PCB  802  inserted, and the fasteners re-attached. 
       FIG. 11  illustrates a three-connector, board-to-board assembly  1100 . It is similar to assembly  800  except that a third instance of connector assembly  100 , denoted  100 . 3 , is added for the purpose of transmitting a third power domain from PCB  802  to PCB  804 . In such a case, where there are three or more instances of connector assembly  100  between the two PCBs, compliance in the z-direction is desirable in connector assembly  100 , to allow for mechanical tolerances where a connector height H, shown in  FIG. 7 , may differ from instance to instance of the connector. 
     For example, suppose that the heights of instances  100 . 1 ,  100 . 2  and  100 . 3  are H 1 , H 2 , and H 3  respectively. If H 2 =H 1  but H 3 &gt;H 1 , then as the fasteners such as  1002  and  1004  are tightened for all three connectors  100 . 1 ,  100 . 2  and  100 . 3 , PCBs  802  and  804  will bend toward each other at connectors  100 . 1  and  100 . 2 , which will be in tension, while connector  100 . 3  will be in compression. Consequently, solder joints at PCB  804  for  100 . 1  and  100 . 2  will be under tension. Excessive tension is undesirable, as it may lead to solder-joint failure. To avoid excessive tension as well as excessive deformation of the PCBs, it is therefore desirable that the connector assembly  100  be compliant in the z direction. This is the reason for the cross-sectional shape of the connector  100 , like an upper-case Greek “sigma”, shown most clearly in  FIG. 7 . 
     Referring to this figure, when a sigma-shaped connector is placed in compressed or tension, it flexes around the corners BC, DE, and FG, thereby allowing modulation of the height H and relieving the stress that would accrue for a simpler shape. For example, referring to  FIG. 7 , if θ 1 =θ 3 =90° and θ 2 =180°, then the connector has a “C” shape; that is the two angled flanges merge into a vertical flange. Such a C shape has less compliance than the sigma shape, because the vertical flange must buckle before it deflects, which implies a greater stress on solder joints, stress that may be problematic if the tolerance on H is appreciable. 
     Operation of the First Embodiment— FIGS. 12-13   
     Referring to  FIG. 12 , the resistance R conn  of the connector may be computed. In the anode and in the cathode, either of which may be referred to as an electrode, an electrical current flows along a sigma-shaped current path of length
 
 l   1   ≡ABCDEFGI.   (1)
 
     The cross-sectional area through which the current flows is substantially the product of an electrode thickness l 2  and an electrode width w 1 , both of which are assumed to be same for the two electrodes, whence 
                       R   conn     ≡     ρ   ⁢           ⁢       2   ⁢     ℓ   1           ℓ   2     ⁢     w   1             ,           (   6   )               
where ρ is the resistivity of the an electrode material assumed to be the same for both electrodes, and the factor of two occurs because the current travels through the anode of length l 1  and also through the cathode of length l 1 .
 
     For example, a prototype of the first embodiment, using copper electrodes (ρ=1.6×10 −5  [Ω-mm]), has the following dimensions:
 
 l   1 =62.5 [mm], l   2 =0.8 [mm], w   1 =67 [mm],  (7)
 
whence
 
 R   conn =37.3[μΩ].  (8)
 
     This meets the target resistance specified in equation (4). 
     The inductance L conn  of the connector may be computed using a well-known solution for the self-inductance of parallel plates. Referring to  FIG. 13  and a coordinate system  1302  thereon having an x direction, a y direction, and a z direction, all mutually orthogonal, thereby defining an xy plane, this solution states that, for a pair of parallel plates comprising a first parallel plate  1304  and a second parallel plate  1306  lying parallel to each other and parallel to the xy plane, each plate having dimensions d x  and d y  in the x and y directions respectively, with a gap between them of thickness d z , the gap being filled with an insulating material having a magnetic permeability close to the permeability of free space: 
                       μ   0     =     4   ⁢   π   ×       10     -   10       ⁡     [     H   mm     ]           ,           (   9   )               
and with electrical current I flowing toward the +x direction in plate  1306  and toward the −x direction in plate  1304 , the self-inductance of the parallel plates is:
 
     
       
         
           
             
               
                 
                   
                     L 
                     PP 
                   
                   = 
                   
                     
                       μ 
                       0 
                     
                     ⁢ 
                     
                       
                         
                           
                             d 
                             x 
                           
                           ⁢ 
                           
                             d 
                             z 
                           
                         
                         
                           d 
                           y 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     Referring again to  FIG. 12 , equation (10) may be applied to a sigma-shaped path ABCDEFGI to yield a first connector inductance: 
                     L   1     =       μ   0     ⁢         ℓ   1     ⁢     g   1         w   1                 (   11   )               
where
 
 l   1   ≡ABCDEFGI   (12)
 
and
 
 g   1 ≡Thickness of the insulator 106.  (13)
 
     Equation (10) may be further applied to a first short vertical path  1202  that carries current from the top PCB  802  ( FIG. 8 ) to and from the connector  100 , and also to a second short vertical path  1204  that carries current from the bottom PCB  804  ( FIG. 8 ) to and from the connector  100 . According to equation (10), each of these paths has an inductance 
                     L   2     =       μ   0     ⁢         ℓ   2     ⁢     g   2         w   2                 (   14   )               
where
 
 l   2 ≡Thickness of cathode,  (15)
 
 g   2 ≡Gap between flange cathode flange 508 and anode shim plate 402,  (16)
 
and, as shown on  FIG. 12 ,
 
 w   2 ≡Combined length of three-sided path              MN  and three-sided path            TU.   (17)
 
Consequently, the self-inductance of the connector  100  is

     
       
         
           
             
               
                 
                   
                     
                       L 
                       conn 
                     
                     ≈ 
                     
                       
                         L 
                         1 
                       
                       + 
                       
                         2 
                         ⁢ 
                         
                           L 
                           2 
                         
                       
                     
                   
                   = 
                   
                     
                       μ 
                       0 
                     
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               ℓ 
                               1 
                             
                             ⁢ 
                             
                               g 
                               1 
                             
                           
                           
                             w 
                             1 
                           
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             
                               
                                 ℓ 
                                 s 
                               
                               ⁢ 
                               
                                 g 
                                 2 
                               
                             
                             
                               w 
                               2 
                             
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     For example, a prototype of the first embodiment has the values
 
 l   1 =62.5 [mm]; g   1 =0.05 [mm]; w   1 =67.0 [mm];  (19)
 
 l   2 =0.8 [mm]; g   1 =0.5 [mm]; w   1 =66.0 [mm];  (20)
 
whence, according to equation (11), for the prototype connector,
 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           L 
                           1 
                         
                         = 
                         
                           
                             μ 
                             0 
                           
                           ⁢ 
                           
                             
                               
                                 ℓ 
                                 1 
                               
                               ⁢ 
                               
                                 g 
                                 1 
                               
                             
                             
                               w 
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               ( 
                               
                                 4 
                                 ⁢ 
                                 π 
                                 × 
                                 
                                   
                                     10 
                                     
                                       - 
                                       10 
                                     
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       H 
                                       ⁢ 
                                       
                                         / 
                                       
                                       ⁢ 
                                       mm 
                                     
                                     ] 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 62.5 
                                 ⁡ 
                                 
                                   [ 
                                   mm 
                                   ] 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 0.05 
                                 ⁡ 
                                 
                                   [ 
                                   mm 
                                   ] 
                                 
                               
                               ) 
                             
                           
                           
                             ( 
                             
                               67 
                               ⁡ 
                               
                                 [ 
                                 mm 
                                 ] 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                           
                             58.6 
                             ⁡ 
                             
                               [ 
                               pH 
                               ] 
                             
                           
                         
                         ; 
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           L 
                           2 
                         
                         = 
                         
                           
                             μ 
                             0 
                           
                           ⁢ 
                           
                             
                               
                                 ℓ 
                                 2 
                               
                               ⁢ 
                               
                                 g 
                                 2 
                               
                             
                             
                               w 
                               2 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               ( 
                               
                                 4 
                                 ⁢ 
                                 π 
                                 × 
                                 
                                   
                                     10 
                                     
                                       - 
                                       10 
                                     
                                   
                                   ⁡ 
                                   
                                     [ 
                                     
                                       H 
                                       ⁢ 
                                       
                                         / 
                                       
                                       ⁢ 
                                       mm 
                                     
                                     ] 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 0.8 
                                 ⁡ 
                                 
                                   [ 
                                   mm 
                                   ] 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 0.05 
                                 ⁡ 
                                 
                                   [ 
                                   mm 
                                   ] 
                                 
                               
                               ) 
                             
                           
                           
                             ( 
                             
                               66 
                               ⁡ 
                               
                                 [ 
                                 mm 
                                 ] 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             7.6 
                             ⁡ 
                             
                               [ 
                               pH 
                               ] 
                             
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     Consequently, the total self-inductance of the prototype connector is,
 
 L   conn   ≈L   1 +2 L   2 =58.6 [pH]+2(7.6 [pH])=73.8 [pH].  (23)
 
     This meets the target inductance specification in equation (4). In this case, the majority of the inductance in equation (23) is attributable to the first term L 1 , which corresponds to the sigma-shaped path ABCDEFGI, rather than to the second term 2L 2 , which corresponds to the short paths  1202  and  1204 . 
     Additional Exemplary Embodiments (FIGS.  14 - 22 ) 
     Second Exemplary Embodiment (Surface Stamps); FIGS.  14 - 17   
       FIG. 14  through  FIG. 17  illustrate a second exemplary embodiment of a high-current-capacity, low-resistance, low-inductance electrical connector  1400 .  FIGS. 14 and 15  illustrate assembled views of the connector  1400 , which comprises an anode assembly  1402 , the cathode assembly  104 , and the insulator  106 . That is, the second embodiment is distinguished from the first embodiment by the structure of the anode assembly  1402 . 
       FIGS. 16 and 17  illustrate unexploded and exploded views of the anode assembly  1402 , respectively. The anode assembly  1402  comprises an anode  1600  and a plurality of the fasteners  406 . The anode  1600  comprises a bottom flange  1608 , a first angled flange  1610 , a second angled flange  1612 , and a top flange  1614 . The anode  1600  of the second embodiment is distinguished from the anode  400  of the first embodiment by at least one top surface stamp  1616  formed from the top flange  1614 , and by at least one bottom surface stamp  1618  formed from the bottom flange  1608 . Referring to  FIG. 14 , these top surface stamps  1616  provide, in the second embodiment, what the top shim plates  402  provide in the first embodiment; namely, anode surfaces  1616  that are coplanar with the positive-z-facing surface of cathode flange  514 , so that metal pads such as  1006  and  1008  on the top circuit board  802  ( FIG. 8 ) come into contact with both the anode and the cathode simultaneously, by virtue of the coplanar, positive-z-facing surfaces of  514  and  1616 . 
     Likewise, referring to  FIG. 15 , the bottom surface stamps  1618  provide, in the second embodiment, what the bottom shim plates  404  provide in the first embodiment; namely, anode surfaces that are coplanar with the negative-z-facing surface of cathode flange  508 , so that metal pads such as  904  and  906  on the bottom circuit board  804  ( FIG. 8 ) come into contact with both the anode and the cathode simultaneously, by virtue of the coplanar, negative-z-facing surfaces of  508  and  1618 . 
     The advantage of using the surface stamps is that they obviate the need for the shims plates  402  and  404 , and the need to attach them, both of which reduce manufacturing cost. 
     Operation of the second embodiment is similar to that of the first embodiment. The inductance L 2  for the second embodiment is likely to be somewhat higher than for the first embodiment, depending on a surface-stamp fabrication technique. That is, referring to  FIG. 12 , the first embodiment comprises a gap g 2  whose value is constant over the length l 2 , whereas, referring to  FIG. 14 , the analogous gap for the second embodiment is a gap  1404  whose value varies over the length l 2 , and is likely to be larger than g 2  over most of this length, depending on the fabrication technique. 
     Consequently, the connector self-inductance L conn  for the second embodiment is likely to be higher than for the first embodiment. However, the inductance penalty for using the cost-saving surface stamps is likely to be small: for example, using the prototypical calculations given in equations (19) through (23), even a doubling of L 2  changes L conn  by only 20.6 percent, because L 2  is much less than L 1 . 
     Third Exemplary Embodiment (Fasteners on Both Sides); FIGS.  18 - 19   
       FIGS. 18 and 19  illustrate a third exemplary embodiment of a high-current-capacity, low-resistance, low-inductance, all-fastener-mounted electrical connector  1800 . Referring to  FIG. 18 , the third embodiment is similar to the second embodiment, except that the third embodiment comprises an all-fastener-mounted anode assembly  1802  and an all-fastener-mounted cathode assembly  1804 . The all-fastener-mounted anode assembly comprises an all-fastener-mounted anode  1806 , at least one female fastener  1808  attached to at least one top surface stamp  1810 , and at least one female fastener  1812  attached to at least one bottom surface stamp  1814 . 
     Likewise, the all-fastener-mounted cathode assembly  1804  comprises an all-fastener-mounted cathode  1816 , at least one female fastener  1818  attached to a top cathode flange  1820 , and at least one female fastener  1822  attached to a bottom cathode flange  1824 . Consequently, the connector  1800  may be completely symmetric top to bottom about a plane parallel to the xy plane that is coincident with centerline  1826 , although this symmetry is not necessary. That is, a bottom half of the connector  1800  may be, but does not have to be, a mirror image of a top half of the connector  1800 . 
     Referring to  FIG. 19 , when connector  1800  is used in a board-to-board assembly  1900  to transmit power from a first printed circuit board  1902  to a second printed circuit board  1904 , a male fastener  1908  engages each female fastener  1808 , a male fastener  1912  engages each female fastener  1812 , a male fastener  1918  engages each female fasteners  1818 , and a male fastener  1922  engages each female fastener  1822 . Engagement of the fasteners  1808  and  1908  connects the anode  1806  to the first PCB  1902 ; engagement of the fasteners  1812  and  1912  connects the anode  1806  to the second PCB  1904 ; engagement of the fasteners  1818  to  1918  connects the cathode  1816  to the first PCB  1902 ; and engagement of the fasteners  1822  to  1922  connects the cathode  1816  to the second PCB  1904 . 
     Operation of the third embodiment is similar to that of the first embodiment; however, because the connector  1800  is connected to both the first PCB  1902  and the second PCB  1904  with fasteners, both PCBs can be detached for repair. This is an advantage vis-à-vis the first and second embodiments, which are soldered to the second PCB  804 , as shown in  FIG. 9 . However, the contact resistance associated with mechanical fastening to the second PCB is likely to be higher than the soldered connection thereto, wherein the third embodiment is disadvantaged vis-à-vis the first and second embodiments. Consequently, the choice of the most appropriate embodiment is application specific. 
     Fourth Exemplary Embodiment (Shorter, Fewer Fasteners); FIG.  20   
       FIG. 20  illustrates a fourth exemplary embodiment of a high-current-capacity, low-resistance, low-inductance connector  2000 . It is similar to connector  1800 , except that is shorter in the y direction, such that only one instance of the fastener  1808  connects the anode  1806  to the first PCB  1902  (not shown in  FIG. 20 ) at surface stamp  1810 , only one instance of the fastener  1812  connects the anode to the bottom PCB  1904  (not shown in  FIG. 20 ) at the surface stamp  1812 , only one instance of the fastener  1818  connects the cathode  1816  to PCB  1902  at the top cathode flange  1802 , and only one instance of the fastener  1822  connects the cathode  1816  to PCB  1904  at the bottom cathode flange  1824 . Operation of the fourth embodiment is similar to the third embodiment, just with fewer fasteners. 
     Fifth Exemplary Embodiment (Various Shapes); FIGS.  21 - 22   
       FIGS. 21A and 21B  illustrate a fifth exemplary embodiment of a high-current-capacity, low-resistance, low-inductance connector  2100 . It is similar to connector  1800 , comprising an electrically conducting anode  2102 , an electrically conducting cathode  2104 , and an insulating layer  2106  therebetween. The anode comprises a bottom flange  2108 , a first angled flange  2110 , a second angled flange  2112 , and a top flange  2114 . Likewise, the cathode comprises a bottom flange  2116 , a first angled flange  2118 , a second angled flange  2120 , and a top flange  2122 . The anode comprises at least one bottom surface stamp  2124  in flange  2108 , thereby producing a set of bottom-aligned anode and cathode surfaces, such that a first circuit board  2126  may simultaneously make contact with the bottom-aligned surfaces when affixed thereto with fasteners  2132 , whereby electrical contact between the first circuit board  2126  and both of the electrodes, anode  2102  and cathode  2104 , is established. Likewise, the anode comprises at least one top surface stamp  2128  in flange  2114 , thereby producing a set of top-aligned anode and cathode surfaces, such that a second circuit board  2130  may simultaneously make contact with the top-aligned surfaces when affixed thereto with fasteners  2134 , whereby electrical contact between the second circuit board  2130  and both of the electrodes, anode  2102  and cathode  2104 , is established. 
     As illustrated on  FIG. 21B , let 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           θ 
                           1 
                         
                         ≡ 
                           
                         ⁢ 
                         
                           Angle 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           between 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                             
                                 
                             
                             ⁢ 
                             
                                 
                             
                           
                           ⁢ 
                           2108 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2110 
                         
                       
                     
                   
                   
                     
                       
                         ≡ 
                           
                         ⁢ 
                         
                           Angle 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           between 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2116 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2118 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           θ 
                           2 
                         
                         ≡ 
                           
                         ⁢ 
                         
                           Angle 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           between 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                             
                                 
                             
                             ⁢ 
                             
                                 
                             
                           
                           ⁢ 
                           2110 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2112 
                         
                       
                     
                   
                   
                     
                       
                         ≡ 
                           
                         ⁢ 
                         
                           Angle 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           between 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2118 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2120 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           θ 
                           3 
                         
                         ≡ 
                           
                         ⁢ 
                         
                           Angle 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           between 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                             
                                 
                             
                             ⁢ 
                             
                                 
                             
                           
                           ⁢ 
                           2112 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2114 
                         
                       
                     
                   
                   
                     
                       
                         ≡ 
                           
                         ⁢ 
                         
                           Angle 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           between 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2120 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           and 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           flange 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2122. 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
     Also define a board-to-board angle θ BB , which is the angle between circuit boards  2126  and  2130 , as 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             θ 
                             BB 
                           
                           ≡ 
                             
                           ⁢ 
                           
                             Angle 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             between 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             flange 
                             ⁢ 
                             
                               
                                   
                               
                               ⁢ 
                               
                                   
                               
                             
                             ⁢ 
                             2108 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             and 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             flange 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2114 
                           
                         
                       
                     
                     
                       
                         
                           ≡ 
                             
                           ⁢ 
                           
                             Angle 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             between 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             flange 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2116 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             and 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             flange 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2122. 
                           
                         
                       
                     
                   
                     
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     By inspection of  FIG. 21B , the board-to-board angle θ BB  is mathematically related to θ 1 , θ 2 , and θ 3  as follows:
 
θ BB =θ 1 +(180°−θ 2 )−(180°−θ 3 )=θ 1 +θ 3 −θ 2 .  (28)
 
     Previous embodiments have all shown θ 1 =θ 3 =45° and θ 2 =90°, whence θ BB =0°. However, by suitable choices of the angles θ 1 , θ 2 , and θ 3 , a variety of connector shapes may be produced to accommodate a variety of applications. 
     As a first example, consider the case shown in  FIG. 22A :
 
θ 1 =90°,θ 2 =180°,θ 3 =180°           θ BB =90°.  (29)

     This permits the connection of two circuit boards  2126  and  2130  at right angles. Because of the 180-degree angles, anode flanges  2110 ,  2112  and  2114  merge into a single flange, as do cathode flanges  2118 ,  2120 , and  2122 . 
     As a second example, consider the case shown in  FIG. 22B :
 
θ 1 =90°,θ 2 =90°,θ 3 =90°           θ BB =90°.  (30)

     This again produces a right-angle connection between the two circuit boards  2126  and  2130 , but with greater compliance than for the case shown in  FIG. 22A , because, referring to the coordinate system  101  beneath  FIG. 22B , the circuit board  2130  can move slightly in the x and z directions with respect to circuit board  2126  because the connector  2100  can flex about a first corner  2202  and a second corner  2204 , respectively. 
     As a third example, consider the case shown in  FIG. 22C :
 
θ 1 =90°,θ 2 =180°,θ 3 =90°           θ BB =0°.  (31)

     Like previous embodiments ( FIGS. 1-12 and 14-19 ), this C-shaped connector produces parallel boards (θ BB =0°). The C shape is a degenerate case of the sigma shape, due to θ 2 =180°, which causes the two angled flanges to merge into a single vertical flange. Compared to the sigma shape, the C-shape has the advantage of somewhat lower resistance and inductance because of the shorter length l 1 ; see equations (6) and (18). However, compared to the sigma shape, the C shape has low compliance in the z direction vis-à-vis the sigma shape, because the latter can flex at the three corners BC, DE, and FG illustrated in  FIG. 7 . Consequently, the C shape may be less desirable than the sigma shape for applications that demand compliance, for example, to accommodate mechanical tolerances. 
     As a fourth example, consider the case shown in  FIG. 22D :
 
θ 1 =180°,θ 2 =180°,θ 3 =180°           θ BB =180°.  (32)

     This illustrates a low-resistance, low-inductance power connection between two connect circuit boards  2130  and  2126  for applications in which the boards are substantially coplanar. 
     As a fifth example, consider a case in which a third angled flange  2206  is added to each of the electrodes (anode and cathode). Then a connector such as that shown in  FIG. 22E  may be constructed. In general, by adding various numbers of flanges at various angles, a great variety of shapes of connectors may be constructed, for a variety of applications, all within the scope of the embodiments specifically detailed herein. 
     Although the above-described exemplary embodiments described various cross-sectional shapes such as the sigma-shaped curves with relatively abrupt angles, right angles, or zero angle, it should be clear that the present invention is not limited to these cross-sectional shapes since the same principle of operation would apply with less abrupt angles such as semi-circular or other conic cross-sectional shapes. 
     Thus it can be seen that, in accordance with one or more embodiments, high-current-capacity, low-resistance, low-inductance power connectors may be constructed for a variety of applications in which two electronic entities must be connected and a large, sometimes-fluctuating current passed between them with low loss. One or both entities may be disconnected from the connector, as may be required for servicing. Construction of the connector is straightforward, and manufacturing cost is low. 
     While the above description contains much specificity, this should not be construed as limitations on the scope, but rather as an exemplification of several embodiments thereof. Many other variations are possible. For example, a connector with no fasteners may be constructed by soldering both terminations thereof. Accordingly, the scope should be determined not by the embodiments illustrated, but by the appended claims and their legal equivalents. 
     The descriptions of the various embodiments of the present invention have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.