Present induction cooktop designs (mainly but not only for domestic use) implement a “concentrated hobs” topology: similar to gas cooktops, there are a number of main heating sources, typically four, (with different maximum power levels in general to simulate the different gas outlets) and the cooking utensil, e.g. a pan or pot, is heated only if put in the proper position above one of the heating sources, typically disposed under a glass cooktop plate.  Each heating source or hob is realized by a coil which, driven by a series resonant converter running at several tens kHz, couples electromagnetic energy with the cooking utensil (which must have a metallic, e.g., ferromagnetic base), thus heating it by inducing electrical currents in the cooking utensil.  By changing the frequency according to a reference power signal, the actual power delivered to the coil (and to the cooking utensil) is changed accordingly. 
To work properly, the relative position between the coil and the utensil must be defined.  Otherwise, electromagnetic coupling will be weak and the resonant converter will be overstressed without delivering the proper power to the utensil. 
According to another concept, called the “distributed” induction heating concept, the utensil is to be heated independently from its position over the cooktop glass plate.  This requires the use of a large number of smaller coils, whose number defines the “resolution” of the cooktop versus the size of the utensil, each coil driven by a properly sized adjustable high frequency power source, and an intelligent utensil detection system, which activates only those coils which are covered by the utensil.  This poses the issue of how many electrical power sources are needed and how they should be connected to the coils.  The number of electrical power sources and their connections to the coils must be made in accordance with the following requirements:                a) The heating sources (hobs) must be activated in any possible subset configuration, except that in each subset the elements (coils) are contiguous to each other; the subset number may vary from 1 to a maximum.  In fact, the utensil can be square or round or long or of any other shape.         b) Connections must be achieved with the minimum possible number of “switching” elements (arranged or not arranged in a switching matrix).         c) Each subset, constituted by “M” elements, must be independently controllable in power level.         d) The cost of the power conversion must be minimized.         
The simplest way to achieve goals a) to c) is to have one power converter driving each coil; in this case no switching matrix is needed on the power side, and each converter would be optimized to drive the coil and to control it, and the coil power control could be simply realized through a low level reference signal network arranged in a switching matrix (for an N×N coil set, 2×N lines would be sufficient, for example, for ON/OFF control and another 2×N lines for fine power tuning) and controlled by a centralized controller.  This solution has possibly never been described but it may be very expensive, so its industrial validity is questionable. 
Another possible solution would be to use a single converter sized for the maximum whole cooktop power, while a switching matrix properly connects the various coils to the converter's outputs. 
Since such a switching matrix should act directly on the power connections of the coils, very expensive high power relays or high power solid state switches would be needed.  Such a solution, described for example, in U.S. Pat.  No.  5,714,739 for the case of 4 hobs, has several drawbacks.  In particular, such an optimized switching matrix (hence having a “minimum number of switches”) would put the coils in parallel to each other as the cooking utensil's size increases.  This means the “equivalent” inductance seen by the converter would go down as the number of coils increases, (which also means a higher power level is required from the converter).  In turn, this would result in an increase of the switching frequency of the converter as the power level increases, which is not acceptable. 
Furthermore, to independently control the power of more subsets each composed by “m1”, “m2” . . . “ mn” coil elements, low frequency PWM operation through the switching relays would be required, as described in previous patents, having the converter tuned to the overall load at the maximum power.  However, this would mean the converter would be connected to a dynamically changing load, i.e., every time a number of relays is commutated to select a new load or simply to PWM an activated load, the equivalent load seen by the converter would change. 
The relays in such a design would have a very limited lifetime, due to the enormous number of operations required (for example, switching at a period of 2.5 sec, and considering an average cooktop utilization of 4 hours/day×365 days/year×10 years, the relays would be required to perform 30 million operations). 
The number of subsets of independent coils would reduced in such a system.  It can be shown that only the elements above (or below) the center diagonal of the rectangular matrix of coils may be independently controlled through the action of the relays, and, in fact, not in all cases.  If the elements above the center diagonal are independently controllable, the elements below the center diagonal of the matrix would receive a non controllable amount of power; i.e., with 2×N relays, for a square N×N matrix, a maximum of 2N−1 elements can be independently controlled.  In a rectangular matrix, the number of independently controllable coils is N+M−1, where N+M equal the total number of converters (N=number of columns, M=number of rows).