Patent Publication Number: US-2002011913-A1

Title: Transformer for induction heating system

Description:
BACKGROUND OF THE INVENTION  
       [0001] 1. Field of the Invention  
       [0002] The invention relates to induction heating systems, and more particularly, to apparatus and methods for delivering optimum power to a workpiece over a wide range of operating conditions.  
       [0003] 2. Description of Related Art  
       [0004] Induction heating systems heat an electrically conductive workpiece by magnetically inducing eddy currents therein. Electrical resistance in the eddy current paths in the workpiece cause I 2 R losses, which in turn heat the workpiece.  
       [0005] One type of induction heating system includes a power supply inverter, which has an AC voltage output having a desired frequency of operation. The output of the inverter is usually connected through a step-down transformer to a pair of power supply output terminals, across which is connected the series combination of a series inductor and a resonant tank circuit. The tank circuit includes a work coil in parallel combination with a resonance capacitor. The work coil, in operation, is placed in proximity with the workpiece, and creates the oscillating magnetic field which induces the eddy currents in the workpiece.  
       [0006] Depending on the application, a wide variety of different operating conditions may be desired. For example, different applications may require different frequencies of operation. Frequencies commonly used for induction heating range anywhere from approximately 10 kHz to approximately 400 kHz. Different applications can also require different voltages across the work coil. Additionally, depending on the configuration and composition of the workpiece, the power factor of the energy delivered to the work coil could also vary widely.  
       [0007] Most induction heating systems are designed for a particular application. For example, a system designed to heat automobile bodies for the purpose of drying paint that has been applied to the surface, need only be designed to operate at one particular frequency, voltage and power factor. It is desirable, however, to provide a general-purpose induction heating system which can be used in a wide variety of applications, under a wide variety of different circumstances. For example, it would be desirable to permit a user to select the operational frequency over the full range of typical frequencies, 10 kHz-400 kHz. Adjustability within this large range of frequencies, spanning a range of 40:1, is extremely difficult to support. Even a range of 50 kHz-400 kHz (8:1) is very difficult to support. It is desirable to provide a system which supports a large range of operating conditions.  
       [0008] In addition, systems which do support a range of operating conditions typically require an operator to tune the system prior to operation. Tuning procedures for such systems are typically complicated and require a technical understanding of the principles under which the induction heating system operates. Accordingly, skilled or trained operators are usually required to operate induction heating systems intended to support a variety of operating conditions. It is therefore desirable to provide an induction heating system and method which simplifies the tuning process.  
       SUMMARY OF THE INVENTION  
       [0009] According to the invention, roughly described, induction heating apparatus has a series inductor L S  between an AC source and a parallel tank circuit. The AC source has a variable frequency inverter, and an output transformer which has a leakage inductance, viewed from the secondary, no larger than  
                 L     l                 max       =         V     L                 min            V     p                 min            PF   min         2      π                   Nf   max          P   max           ,           (   1   )                       
 
       [0010] where  
       [0011] V Lmin  is a desired minimum permitted rms voltage across the tank circuit,  
       [0012] V pmin  is a desired minimum rms input voltage to the output transformer,  
       [0013] N is the primary: secondary turns ratio of the output transformer,  
       [0014] PF min  is a desired minimum permitted power factor, measured at the input of the transformer (ignoring the effect of the magnetizing inductance),  
       [0015] f max  is a desired maximum frequency of operation, and  
       [0016] P max  is a desired maximum power output into the induction heating coil.  
       [0017] The output transformer achieves such a low leakage inductance because of its construction as inner and outer hollow windings disposed substantially coaxially with each other, the inner winding being electrically continuous through T turns, and the outer winding having S electrically broken longitudinal segments through the T turns, S&gt;1. All of the outer winding segments are connected in parallel with each other. The inner and outer windings can be made of braided stranded wire, instead of solid wire or solid tubes, and the insulation between them is made very thin. If necessary to also reduce inter-winding capacitance, the transformer can further include a core.  
       [0018] In another aspect of the invention, a very simple tuning procedure is set forth for tuning an induction heating system which has a series inductor between an AC source and a parallel tank circuit. The tuning procedure involves first selecting a preliminary series inductance and a preliminary resonance capacitance. The operator then operates the system at low power, increasing the resonance capacitance if the system is operating at a frequency that is higher than desired, and decreasing resonance capacitance if the system is operating at a frequency that is lower than desired. Once the frequency is acceptable, the operator then operates the system at full power, increasing the series inductance if the system is current limiting, and decreasing the series inductance if the system is resonance limiting. When the series inductance is acceptable, the system is ready for use. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0019] The invention will be described with respect to particular embodiments thereof, and reference will be made to the drawings, in which:  
     [0020]FIG. 1 is a partially simplified schematic diagram of an induction heating system according to the invention.  
     [0021]FIG. 2 is a perspective view of an output transformer that can be used in the system of FIG. 1.  
     [0022]FIG. 3 is a head-on front view of the transformer of FIG. 2.  
     [0023]FIG. 4 is a view of the transformer of FIGS. 2 and 3, taken from the bottom of the illustrations in FIGS. 2 and 3, looking upward.  
     [0024]FIG. 5 illustrates a cross-section (not to scale) of the coaxial cable  212  in FIGS.  2 - 4 .  
     [0025]FIG. 6 is a perspective view of another output transformer that can be used in the system of FIG. 1.  
     [0026]FIG. 7 is a cross-sectional view of the transformer of FIG. 6, taken along the sight lines A-A.  
     [0027]FIGS. 8 and 9 are charts that can be used in a simplified tuning procedure for an induction heating system such as that shown in FIG. 1. 
    
    
     DETAILED DESCRIPTION  
     [0028]FIG. 1 is a partially simplified schematic diagram of an induction heating system according to the invention. It includes an AC power source  110  having voltage outputs  112  and  114 . Connected across the outputs  112  and  114  are, in series combination, a series inductor  116  and a tank circuit  118 . The tank circuit includes a work coil  120  connected in parallel with a resonance capacitance  122 , which is implemented as two parallel-connected capacitors  124  and  126 , for reasons described hereinafter. Also shown in FIG. 1 is a load resistance  128 , shown in broken lines because it represents the resistance with which a workpiece  130  and the work coil appear to the induction heating system. The voltage output of the AC source  110  is V S , measured in volts RMS. The inductor  116  has a value L S , the work coil has an inductance L W , and the voltage across the work coil  120  and tank circuit  118  is V L . The resonance capacitance has a value C r , which is divided into two capacitors connected across either end of the load cabling  132 . The value of the capacitor nearest the AC source  110  is C s , and the value of the capacitor nearest the work coil  120  is C L .  
     [0029] AC source  110  includes a half-bridge inverter  134  having outputs  136  and  138 . The inverter includes a series pair of switches  140  and  142  connected across a series pair of DC power sources  144  and  146 , each having a voltage V dc /2. The inverter outputs  136  and  138  are connected to the junction between the two DC sources  144  and  146 , and to the junction between the two switches  140  and  142 , respectively. The switches  140  and  142  are controlled by a control unit  143 , which includes a meter  145  indicating the current frequency of operation. Note that other embodiments could use other kinds of conventional inverters, such as a full-bridge inverter.  
     [0030] Although not required in all induction heating systems, the AC source  110  of FIG. 1 includes an output transformer  148 . The transformer  148  has primary terminals connected across the outputs  136  and  138  of the inverter  134 , and further has secondary terminals which form the voltage output terminals  112  and  114  of the AC source  110 . Such an output transformer is typically included in induction heating systems for electrical isolation, step-down impedance matching, and safety reasons. There are various equivalent circuits that are used to describe the electrical performance of transformers, one of which is shown in FIG. 1. It includes an ideal transformer  150  having a primary:secondary turns ratio of N:1. Connected across the primary of the ideal transformer  150  is the inter-winding capacitance C iw . The leakage inductance L l  is shown in series with the primary, between the inter-winding capacitance and one of the primary terminals  136 , and the magnetizing inductance of the transformer  148  L M  is shown across the primary input terminals  136  and  138 . The inter-winding capacitance, leakage inductance and magnetizing inductance are shown in broken lines since they represent inherent, rather than separate, components. It will be appreciated that one or more of these components could be shown instead on the secondary side of the ideal transformer  150 , with an appropriate transposition factor related to the turns ratio of the ideal transformer  150 . For example, the leakage inductance as viewed from the secondary of transformer  148  is L l /N 2 . Also, it will be appreciated that the resistance representing the power loss in the conductors and cores of the transformer  148  are omitted for clarity of illustration.  
     [0031] The system of FIG. 1 also includes a current limit sense circuit  151 , which is connected to a current transformer  153  disposed adjacent to one of the output leads of the inverter  134 . The current limit sense circuit  151  senses the inverter output current and, when its peak reaches a preset threshold value limits the current and activates a current limit indicator  155 . The threshold is based on the current rating of the semiconductor switches  140  and  142 , among other things.  
     [0032] The system of FIG. 1 also includes a resonance limit sense circuit  161 , having a first input port connected to sense the instantaneous inverter output voltage, and a second input port connected to sense the instantaneous voltage across the resonance capacitor  122 . Where the resonance capacitor  122  is split into capacitors  124  and  126 , the second input port is connected to sense the instantaneous voltage across the capacitor nearest the AC source  110 , i.e., capacitor  124  in FIG. 1. The resonance limit sense circuit  161  compares the phases of the signals on its two input ports, and when the phase lag of the capacitor voltage relative to the inverter output voltage decreases to 90°, the circuit  161  limits the frequency or phase lag and activates a resonance limit indicator  163 .  
     [0033] The series inductance between the AC source  110  and the work coil  120  determines the power that will be delivered by the system at a specific frequency and power factor. Thus, in order to achieve maximum power output over a very large range of operational frequencies and power factors, this inductance needs to be adjustable over a wide range. In one embodiment, inductor  116  has multiple taps, permitting an operator to select an appropriate inductor value L S . In another embodiment, a pair of connector terminals is provided and the operator removes and replaces the inductor  116  with one having an appropriate value.  
     [0034] The inductance between the AC source  110  and the load coil  120  is not, however, due only to the inductor  116 . Inductance also exists in the load cabling  132  and in the leakage inductance of the transformer  148 . Transposed to the secondary, the leakage inductance of the transformer  148  has a value of L l /N 2  and appears as part of an output inductance of the AC source. In order for the induction heating system of FIG. 1 to support such a wide range of operating conditions, therefore, it is desirable that the leakage inductance of the transformer  148  be made as small as possible since even if the operator replaces the inductor  116  with a short circuit, and even if there is no other stray inductance in the system, the total series inductance between the AC source  110  and the work inductor  120  can never be less than L l /N 2 . (It is also desirable, of course, to lay out the circuit carefully in order to minimize other sources of stray inductance.)  
     [0035] The worst-case operating conditions of the system of FIG. 1 occur when the operator chooses the maximum specified operating frequency f max , the maximum available output power P max  and the minimum specified output power factor PF min . In addition, the operator chooses the minimum specified output voltage V Lmin , and the DC link voltage V dc  in the inverter  134  is at its minimum value V dcmin  (producing a minimum rms voltage into the output transformer of V pmin ). Under the worst case conditions of operation indicated above, the total series inductance from the AC source  110  to the work coil  120  should be no more than  
               L     Seff                 Max       =           V     L                 min            V     p                 min            PF   min         2      π                   Nf   max          P   max         .             (   2   )                       
 
     [0036] Thus, even when the inductor  116  in FIG. 1 is replaced by a bus bar, the leakage inductance of the output transformer  148  of the AC source  110 , when viewed from the secondary terminals  112  and  114 , must be no greater than L SeffMax . Preferably, in fact, to allow for some stray inductance in the load cabling  132  as well as to allow for some manufacturing and operating tolerances, the leakage inductance of the output transformer  148  when viewed from the secondary should no greater than approximately 0.25 L SeffMax .  
     [0037] As an example, assuming worst case operating conditions of V pmin =114V, V Lmin =57V, f max =400 kHz, P max =5 kW, and PF min =0.33, then the leakage inductance of the output transformer  148  (viewed from the secondary) should be no more than L SeffMax =42 nH, and preferably only 25% of that. Conventional transformers used in conventional induction heating systems usually cannot achieve such low leakage inductance.  
     [0038] Transformer Design  
     [0039]FIG. 2 is a perspective view of a transformer design which can achieve the required low leakage inductance. It is a coaxial transformer  210  made up of a coaxial cable  212 . FIG. 3 is a head-on front view of the transformer of FIG. 2, and FIG. 4 is a view of the transformer  210  taken from the bottom of the illustrations in FIGS. 2 and 3, looking upward. The cable actually makes eight turns, although only four turns are illustrated in FIGS. 2 and 4 for clarity of illustration. FIG. 5 illustrates a cross-section (not to scale) of the coaxial cable  212  in FIGS. 24. At the center is a non-magnetic, insulating filler core  510 , surrounded by an inner-winding conductor  512 . The inner-winding conductor  512  is electrically a hollow conductor, due to the insulating filler core  510 . Preferably, the inner conductor  512  is made of braided, stranded wire, preferably Litz wire. The use of Litz wire increases the AC current-carrying capacity of the inner conductor  512  by reducing the skin effect of the conductor.  
     [0040] Surrounding the inner conductor  512  is a layer of insulation  514 , which may for example be made of heat-shrink tubing or conventional electrical tape. Preferably, the insulator  514  is very thin, for reasons described below. Surrounding the insulator  514  is the outer coaxial conductor  516  which may, again, be constructed from braided, stranded wire, preferably Litz wire. The outer most layer  518  of coaxial cable  212  is insulation (not shown in FIGS.  2 - 4  for clarity of illustration). The inner diameter of the outer conductor  516  is ID, and the outer diameter of the inner conductor  512  is OD.  
     [0041] The cable  212  and the transformer  210  are referred to herein as being “coaxial”, but because the conductors are made of stranded braids rather than solid wire or tubes, they might not be coaxial at all positions along the length of the coax. This might be true also in embodiments where the conductors are made of tubes. The term “substantially coaxial” is used herein to accommodate manufacturing tolerances due to which the inner and outer conductors might not be exactly coaxial. Also, cables need not have a circular cross-section to be considered coaxial, as the term is used herein. Cables with rectangular cross-section conductors, for example, can be coaxial as well.  
     [0042] Referring again to FIGS. 2 and 4, it can be seen that whereas the inner conductor  512  is electrically continuous through all eight turns of the transformer (again, only four are shown in the figures), the outer conductor is electrically broken, with a longitudinal gap  214 , after every second turn. Thus, the outer conductor has been cut into four two-turn segments (only two of which,  216  and  218 , are shown in the figures). The segment  216  has a proximal end  220  and a distal end  222 , and the segment  218  has a proximal end  224  and a distal end  226 . The proximal ends  220  and  224  of each of the segments are connected together electrically and to a terminal  228 , and the distal ends  222  and  226  of each of the segments are connected together electrically and to a terminal  230 . Thus all of the segments  216  and  218  of the outer-winding  516  are connected in parallel. Since each such parallel-connected segment traverses only two turns of the coil, whereas the inner-winding  512  traverses the full eight turns, the transformer  210  effectively has a turns ratio of 4:1.  
     [0043] In the system of FIG. 1, the inner conductor  512  constitutes the primary winding of the transformer  148 , and the outer-winding  516  constitutes the secondary winding of the transformer  148 . Tabs  232  and  234  in FIGS.  2 - 4  represent the primary terminals  136  and  138  of the transformer  148 , and the tabs  228  and  230  in FIGS.  2 - 4  represent the secondary terminals  112  and  114  in the transformer  148 .  
     [0044] It will be appreciated that the same construction as that shown in FIGS.  2 - 4  can be used as a step-up transformer by using the outer conductor  516  as the primary and the inner conductor  512  as the secondary. It will also be appreciated that whereas the conductor which has been segmented and connected in parallel in the transformer of FIGS.  2 - 4  is the outer conductor  516 , in another embodiment, it could be the inner conductor  512  which is segmented and connected in parallel. In yet another embodiment, the segmented winding can even be made from the outer conductor  516  along one length of the coax, and the inner conductor  512  along a different length of the coax. Numerous other variations will be apparent.  
     [0045] In general, if the electrically continuous winding extends through T turns, and the electrically discontinuous winding is cut into S segments, each segment extending through substantially T/S of the T turns, then the resulting coaxial transformer will have a turns ratio of substantially S:1. It will be appreciated that the number of turns of the continuous winding need not be an integer, and can also be less than one. The number of segments into which the discontinuous winding is broken is an integer greater than one. The number of turns through which each segment of the discontinuous winding extends is referred to herein as being “substantially” an integer, thereby allowing for tolerance of a longitudinal gap between the distal end of one segment and the proximal end of the next, such as can be seen in FIGS. 2 and 4.  
     [0046] The leakage inductance of a coaxial transformer, measured on the primary side, is given by  
                 L   cx     =         μ   0       2      π          ln                   (     ID   OD     )                     l   c         ,           (   3   )                       
 
     [0047] where μ 0  is the permeability of free space (4π×10 −7  H/m) and l c  is the length of the cable. Thus, the leakage inductance can be minimized by keeping ID/OD very small, such as by using a very thin inter-winding insulator  514 . Preferably, the insulator  514  is heat-shrink tubing and has a thickness of no more than 0.5 mm.  
     [0048] The leakage inductance will be minimized also if the length l c  of the cable is minimized. The minimum cable length l c  is limited, however, by the magnetizing inductance required for the transformer. The magnetizing inductance L M  of an air core cylindrical coaxial transformer is given by  
                 L   M     =         (       r   t          N   t       )     2         9        r   t       +     10        l   t             ,           (   4   )                       
 
     [0049] where r t  is the radius of the cylindrical coil (inches), N t  is the number of turns of coil, and l t  is the cylindrical length of the coil (in the dimension approximately perpendicular to a plane of a turn of coil). This is an empirical equation in which one inch represents one microhenry of magnetizing inductance. With the inverter  134  in FIG. 1, the minimum required magnetizing inductance L M  is determined by the required peak magnetizing current I Mpeak  at the minimum switching frequency f min , and is given by  
               L   M     =         V   dc       8        I   Mpeak          f   min         .             (   5   )                       
 
     [0050] The derivation of the peak magnetizing current requirement is unimportant for an understanding of the invention, and it is sufficient to note herein that it is determined by the required current for zero-voltage switching of the inverter  134  and the current rating of the semiconductor switches  140  and  142 . For the example range of operating conditions set forth previously, and for I Mpeak =40A, f min =50 kHz, and V dc =320V, this formula yields a required minimum magnetizing inductance L M =20 μH. A higher magnetizing inductance would not be detrimental since it can always be reduced if desired by connecting an additional inductor across the primary terminals  136  and  138  of the transformer  148 .  
     [0051] From equation 4, it can be seen that a cylindrical coaxial transformer having N t =8 turns, a radius of r t =6 inches, and a cylindrical length of l t =7.75 inches (0.75 inch diameter cable with turns spaced apart by 0.25 inches), has a magnetizing inductance of L M =17.5 μH, which is close to the requirement. From equation 3 above, if the cable has an inter-winding insulation thickness of 0.5 mm, ID=17 mm, OD=16 mm and a coaxial length of l c =7.7 meters, such a coaxial transformer would have a leakage inductance L cx =93 nH. Transposed to the secondary, this represents a leakage inductance of only L l =5.8 nH as viewed from the secondary, which is less than the 42 nH maximum calculated above and therefore acceptable for the induction heating system to be able to support the desired range of operating conditions.  
     [0052] One problem with the air core cylindrical coaxial transformer of FIGS.  2 - 4  is that while it exhibits low leakage inductance, it also exhibits high inter-winding capacitance C iw . C iw  in a coaxial transformer (viewed from the primary) is given by  
                 C   iw     =         2                 π                   ε   0         ln                   (     ID   OD     )              l   c         ,           (   6   )                       
 
     [0053] where ε 0  is the perimittivity of free space (8.854×10 −12  F/m), and the other variables are as defined above. It can be seen that while a small ID/OD reduces the leakage inductance, it also increases the inter-winding capacitance. In the example air core coaxial transformer design set forth above, equation 6 yields an inter-winding capacitance of C iw =7 nF. Under certain circuit conditions and layouts, this capacitance will resonate with various parasitic inductances in the system and cause the circuit to oscillate. Oscillations can also vary as a function of the power factor. In such situations, it may be concluded that an air core cylindrical coaxial transformer which is large enough to achieve the required magnetizing inductance L M  cannot be constructed which has both sufficiently low leakage inductance to support the desired range of operating conditions and sufficiently low inter-winding capacitance to prevent oscillations. Under such conditions, a transformer such as that of FIGS. 6 and 7 may be used.  
     [0054]FIG. 6 is a perspective view of a transformer  610 , and FIG. 7 is a cross-sectional view of the transformer  610 , taken along the sight lines A-A. The transformer  610  is again a coaxial transformer, having four turns  612 ,  614 ,  616  and  618  of electrically continuous inner conductor acting as the primary, and the outer conductor is electrically segmented into four segments  624 ,  626 ,  628  and  630 . The proximal ends  632  of all four outer-winding segments are connected together electrically at a tab  634 , and the distal ends  636  of each of the outer conductor segments are connected together electrically at a tab  638 . Tabs  620  and  622  act as the primary terminals and tabs  634  and  638  act as the secondary terminals of the transformer  610 . All of the turns of all of the windings pass through two windows  640  and  642  formed by ferrite E-cores  644 . It can be seen from FIG. 6 that while each of the outer-winding segments of the transformer of  610  extends through more than one-half turn of the inner-winding, they do not extend through a full turn due to the large longitudinal gap between the point on each turn where the distal end of one of the outer-winding segments peels off the coax, and the point where the proximal end of the next outer-winding segment re-joins the coax. However, one effect of the cores  644  is to concentrate the flux lines, thereby giving each segment of the outer-winding almost the same effect as if it extended through a full turn of the inner-winding.  
     [0055] The construction of the coaxial cable itself is the same as that shown in FIG. 5, although the dimensions can now be made significantly different due to the presence of the cores  644 . In particular, the cores provide a very large magnetizing inductance, much larger than is required to meet the peak magnetizing current requirement set forth above. The magnetizing inductance of transformer  610  may be reduced, if desired, either by connecting another inductor across the transformer primary terminals as previously described, or by creating an appropriate air gap between the two opposing halves of the E-cores  644 .  
     [0056] Since the magnetizing inductance requirement no longer dictates a minimum coax length for the transformer, the length l c  is now dictated only by the physical size of the cores and the number of times that the coax must wrap around them to achieve the desired turns ratio (4:1 in FIG. 6). This permits a much shorter length of coax than was required for the air core coaxial transformer of FIGS.  2 - 4 . The overall size of the ferrite core transformer can also be made much smaller than that of the air-core cylindrical coaxial transformer of FIGS.  2 - 4 . As with the air core transformer, leakage inductance can be minimized by keeping the inter-winding insulation thin. This tends to increase the inter-winding capacitance, but the much shorter permissible length of coaxial cable tends to reduce the inter-winding capacitance to an acceptable level.  
     [0057] In the example above, sufficiently low-leakage inductance and inter-winding capacitance can be achieved, with sufficiently high magnetizing inductance, using an appropriate ferrite core coaxial transformer such as that shown in FIGS. 6 and 7 in which the coaxial conductors are 0.8 m in length, ID=11 mm, OD=10 mm. The number of turns of the primary winding is four, and the number of parallel-connected secondary winding segments is four, yielding a turns ratio of 4:1. Referring to equations 3 and 6 above for leakage inductance and inter-winding capacitance, it can be seen that these values yield a leakage inductance on the primary side of only 15 nH (1 nH as viewed from the secondary), and an inter-winding capacitance of C iw =470 pF. The leakage inductance is sufficiently small to permit the induction heating system to support the desired wide range of operational conditions, and the inter-winding capacitance is sufficiently small to avoid unwanted oscillation. Note that many other well-known core shapes and sizes can be used in different embodiments, other than the E-shaped cores shown in the figures herein.  
     [0058] Split Resonance Capacitance  
     [0059] Referring again to FIG. 1, as previously mentioned, the tank circuit  118  includes a work coil  120  connected in parallel with a resonance capacitance  122 . The term “capacitance” is used herein to represent a value, whereas the word “capacitor” represents a particular component having a capacitance value. In the induction heating system, the resonance capacitance is given by  
                 C   r     =         L   W     +     L   Seff         4                   π   2          f   res   2          L   W          L   Seff           ,           (   7   )                       
 
     [0060] where f res  is the resonant frequency of the tank circuit and L Seff  is the effective series inductance from the AC source  110  to the work coil  120 , including both L S  and the output inductance of the AC source  110 . Optimum efficiency of operation is achieved at the maximum power factor output of the inverter  134 , which occurs when the frequency of operation is slightly above the resonant frequency f res  of the tank, although to simplify calculations it is assumed herein that the frequency of operation is equal to f res . For certain applications, it might be desirable to place the AC source  110  at a significant distance from the working location of the work coil  120 . In this case, load cabling  132  is installed to carry the current from the AC source  110  to the work coil  120 . The series inductor  116  is connected between the AC source  110  and the proximal end of the load cabling  132 . Load cabling  132  can be expensive and difficult to install if it is required to carry a significant amount of current. Therefore, in order to minimize the current carrying requirement of the load cable  132 , the capacitance  122  is split, with one capacitor  124  mounted near the AC source  110  and the other capacitor  126  mounted near the work coil  120 . Optimally, the two capacitors are chosen such as to bring the power factor of the current in the load cable  132  to unity. If the power factor at the input of the transformer is unity, which is approximately the case under normal and typical conditions of operation, the power factor of the current in the load cable  132  achieves unity when the operating frequency f=f res , when the capacitance of capacitor  124  is  
                 C   S     =     1     4                   π   2          f   2          L   Seff           ,           (   8   )                       
 
     [0061] and when the capacitance of capacitor  126  is  
               C   L     =       1     4                   π   2          f   2          L   W         .             (   9   )                       
 
     [0062] (If the power factor at the input of the transformer is less than unity, then whereas equation 9 above for C L  remains valid, equation 8 for C S  does not. Instead, C S  can be calculated as C S =C r −C L . Note also that capacitors  124  and  126  can each be implemented with several capacitors, if desired.)  
     [0063] It can be seen also from equations 8 and 9 that when the power factor at the input of the transformer is unity,  
                 C   S       C   L       =       L   W       L   Seff               (   10   )                       
 
     [0064] Tuning the System  
     [0065] As mentioned, the system of FIG. 1 can be tuned to operate under a wide variety of operating conditions. Tuning basically involves selecting the resonance capacitance C r  and the inductance L S  of inductor  116 . The inductor  116  is chosen according to the formula L S =L Seff −L O , where L O  is the output inductance of the AC source  110 , and L Seff  is given by  
               L   Seff     ≈           V   L          V   p         2      π                 NfP       .             (   11   )                       
 
     [0066] This equation is valid for PF=1 and is most accurate when V L ≧2V p /N. The resonance capacitance is then determined according to equation 7 set forth above.  
     [0067] In accordance with an aspect of the invention, in an embodiment which does not split the capacitor  122 , a very simple procedure may be used for tuning induction heating apparatus such as that shown in FIG. 1. First, the operator selects the desired operating frequency according to the application. For example, for surface heating, the operator will choose a higher frequency of operation, whereas for deep heating, the operator will choose a lower frequency of operation. The operator also selects a desired load voltage V L . Then the operator selects a preliminary series inductance L S . The preliminary selection can be made from a table, equation or chart provided by the vendor of the induction heating system, which relates series inductance to the approximate desired load voltage for a variety of supported operating frequencies. One such chart is illustrated in FIG. 8. The preliminary series inductance L S  need not be precise at all since the subsequent steps of the tuning procedure will correct any errors.  
     [0068] The chart of FIG. 8 represents the equation  
               L   S     =         V   L          V   p         2      π                 NfP               (   12   )                       
 
     [0069] for several frequencies of operation f. The curves in the chart are independent of the Q of the load. They are also normalized for a power output rating of P=1 kW, so the inductance read from the chart should be divided by the desired kW rating. For example, for P=5 kW, the inductance value read from the chart should be divided by 5.  
     [0070] Next, the user selects a preliminary resonance capacitance C r  from another table, formula or chart provided by the vendor of the induction heating system. An example of such a chart is shown in FIG. 9. This chart relates the preliminary resonance capacitance to the desired load voltage for a variety of values of Q. Q is the quality factor, and is given by  
             Q   =         V   L   2       2      π                   L   W        fP       .             (   13   )                       
 
     [0071] Again, the preliminary capacitance value chosen need not be accurate at all since the following steps of the tuning procedure correct any errors. The chart of FIG. 9 represents the equation  
                 C   r     =       P     2      π                   fV   L              (       N     V   p       +     Q     V   L         )         ,           (   14   )                       
 
     [0072] for several values of Q. The curves in the chart are normalized for a power output rating of P=1 kW and for a frequency of operation of 1 kHz, so the capacitance read from the chart should be multiplied by the desired kW rating and divided by the resonant frequency in kHz. For example, for P=5 kW and f=100 kHz, the capacitance value read from the chart should be multiplied by 5/100.  
     [0073] The operator then turns on the system to approximately 5% or more of full power. If the frequency at which the system is operating, which appears on gauge  145  (FIG. 1), is higher than the desired frequency of operation, the operator replaces the preliminary capacitance C r  with a capacitor having a larger capacitance value. If the gauge indicates that the frequency of operation is lower than desired, the operator replaces the resonance capacitor with one having a smaller capacitance value. This step is repeated iteratively until the desired frequency of operation is reached.  
     [0074] Next, the operator turns up the system to full power. This will decrease the frequency of operation by a small amount, but not more than about 10%. If the operator finds that the system is current limited, as reported by current limit indicator  155 , then the operator increases the series inductance L S . If the operator finds that the system is resonant limited, as reported by indicator  163 , then the operator decreases L S . This step repeats iteratively until the system is neither current limited nor resonant limited. Desirably, but not essentially, the operator should choose an L S  such that the system is just out of resonance limit, since this provides optimum efficiency of operation (highest PF). At this point the system of FIG. 1 is tuned and ready for operation.  
     [0075] It can be seen that this tuning procedure is extremely simple, and allows the use of the induction heating system of FIG. 1 over a wide variety of desired operating conditions without requiring a detailed understanding of the principles of operation. The vendor of the induction heating system can easily instruct an operator on this turning procedure. The tuning procedure is not limited for use with the system of FIG. 1, but may be used with any induction heating system having the same topology (inductance in series with a parallel tank circuit), on which the series inductance and resonance capacitance can be changed or adjusted by the operator.  
     [0076] The tuning procedure just described can be extended for use in split capacitor embodiments such as that shown in FIG. 1. In particular, for the split capacitor embodiment, C r  and L S  are first determined according to the above procedure for the non-split case, with all the capacitance being placed at the load end of the load cabling  132  (i.e. in position  126 ). Capacitance is then moved from the load end of the load cabling to the source end of the load cabling (i.e. to position  124 ), until the power factor of the current carried in the load cabling  132  is at its maximum (as close to unity as possible). In one embodiment, the amount of capacitance to move can be determined from charts or by calculation:  
                 C   S     =     1     4        π   2          f   2          L   Seff           ,           (   15   )                       
 
     [0077] and all the rest of the capacitance remains at the load end of load cabling  132 . In another embodiment, the amount of capacitance to move is determined by means of a power factor meter (not shown) located the load cabling  132 . Capacitance is moved until the power factor indicated on the meter is at its maximum (as close to unity as possible).  
     [0078] In yet a third embodiment, the amount of capacitance to move is determined by means of a current meter or current pickup (not shown) responding to the amount of current in load cabling  132 . The accuracy of the measurement is not important, and any signal that is proportional to the current will suffice. According to this third embodiment, capacitance is iteratively moved from the load end of load cabling  132  to the source end of load cabling  132 . The current measured by the current meter decreases with each iteration until at some point it starts to increase. At that point the last amount of capacitance moved from the load end to the source end of load cabling  132  is returned to the load end, and the correct split has been achieved.  
     [0079] Note that whereas the procedure just described for determining the split capacitor values assumes that the total capacitance value C r  has already been determined, it will be appreciated that in another embodiment, a user can determine C S  and C L  directly from charts or equations without having to determine C r  first.  
     [0080] Final Remarks  
     [0081] The formulas set forth above are for optimum performance. It will be understood that the values used in an actual circuit might differ somewhat from those described herein, if the performance degradation caused thereby is acceptable for the purposes of the device. Also, even for optimum performance, parasitic impedances not otherwise considered herein may mandate small deviations from the formulas set forth herein.  
     [0082] As used herein, a given signal, event or value is “responsive” to a predecessor signal, event or value if the predecessor signal, event or value influenced the given signal, event or value. If there is an intervening processing element, step or time period, the given signal, event or value can still be “responsive” to the predecessor signal, event or value. If the intervening processing element or step combines more than one signal, event or value, the signal output of the processing element or step is considered “responsive” to each of the signal, event or value inputs. If the given signal, event or value is the same as the predecessor signal, event or value, this is merely a degenerate case in which the given signal, event or value is still considered to be “responsive” to the predecessor signal, event or value. “Dependency” of a given signal, event or value upon another signal, event or value is defined similarly.  
     [0083] The foregoing description of preferred embodiments of the present invention has been provided for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Obviously, many modifications and variations will be apparent to practitioners skilled in this art. In particular, and without limitation, any and all variations described, suggested or incorporated by reference in the Background section of this patent application are specifically incorporated by reference into the description herein of embodiments of the invention. The embodiments described herein were chosen and described in order to best explain the principles of the invention and its practical application, thereby enabling others skilled in the art to understand the invention for various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the following claims and their equivalents.