Such a method and a suitable device are known from CH 664,660 A5.  The known device has been used in practice for many years to inductively heat metallic or magnetic workpieces.  In addition, it generally can also be used for resistive heating of workpieces.  In the case of inductive heating, the heating current flows through an inductance arranged in the transverse branch of the H-bridge circuit, called the inductor.  The heating current produces an alternating magnetic field in the inductor, which gives rise to induced currents in the workpiece to be heated (either directly or by means of an intermediate transformer).  These induced currents cause heating as a result of the ohmic losses in the workpiece.  By contrast, in the case of resistive heating the heating current would be passed directly through the workpiece. 
The speed and the degree of heating can be adjusted selectively using the inverter.  This is typically accomplished by pulse-width modulation and/or frequency modulation of the heating current.  In other words, the pulse/space ratio and/or the frequency of current pulses in the transverse branch of the inverter are varied in this way. 
To achieve this, the four switching elements of the inverter are switched on and off again in groups, wherein the switching elements diagonally opposite one another are switched simultaneously in each case.  The resulting currents are described below using FIGS.  3 and 4 to better elucidate the invention. 
Another generic arrangement is known from DE 195 27 827 C2, wherein the inverter is represented only symbolically in this document.  In order to achieve effective operation, this document proposes compensating the reactive power that arises in the vicinity of the inductor in a capacitance placed ahead of the inverter.  Specifically, in this case the purpose is to transfer to the capacitor the energy that is stored in the inductor when the inverter is commutated, since the current through the inductor cannot abruptly change (“jump”) when the switching elements are commutated.  Accordingly, the size of the capacitance should be based on the amount of energy to be absorbed (called reactive power in DE 195 27 827 C2), wherein a large capacitance on the order of 1 to 15 mF is proposed. 
The frequencies at which the heating current is commutated in the inductor can be in the range of 50 Hz to 100 KHz, for example.  Accordingly, it is not only necessary for the upstream compensation capacitor to be adequately rated with regard to its size, but it must also be suitable for HF use.  Suitable capacitors are quite expensive. 
Another problem with the known circuit is that the switching elements in the inverter can be destroyed if the compensation capacitor is not adequately rated.  The risk of destruction arises in particular when the heating circuit is operated with no load, i.e. without a workpiece to be heated.  Accidentally turning on the heating circuit without a workpiece can thus lead to destruction of the switching elements in the inverter under unfavorable conditions. 
A third problem with the known arrangement is high frequency interference, which can arise through abrupt commutation of the switching elements in the inverter and can feed back into the input-side line voltage.  In view of the increasingly stringent requirements with respect to electromagnetic compatibility (EMC), expensive filter circuits on the line input side are needed to suppress this interference.