it has already been demonstrated that , by using a bi - directional converter , the output voltage , v out may be forced to follow the equation ( see fig1 ): in the preferred embodiment , this is accomplished by a combination of frequency and pulse width modulation , the frequency modulation being used to obtain a desired waveform and to control the instantaneous value of the output voltage , whereas pulse width modulation is used to satisfy the requirement of constant pulse energy . it is assumed for the present demonstration that the output desired from the invention is a sine wave . it has already been demonstrated that by setting k = k 1 sin 2 ωt a sine wave may be generated by modulating f such that : function generator 12 has an output f 1 = k 1 sin 2 ωt which satisfies the requirements of equation 21 for generating a sine wave . a second output , f 2 simulates the average current flowing into the filter capacitor 72 . the actual current is not used since it contains a large amount of high frequency components which will distort the output waveform . ## equ5 ## outputs f 1 and f 2 are inputted to computing circuit 16 at inputs d and b respectively . according to equation 21 besides k which is available at input d , and e o which is available at input b , in order to generate frequency f 1 , the output voltage v out and the output current , i out must be sampled . output voltage is sampled by output voltage sensing circuit 18 and fed to input c of computing circuit 16 . likewise , output current is sampled by output sensing circuit 20 and fed to input a of computing circuit 16 . computing circuit 16 has an output voltage at output e which is proportional to the frequency , f , desired . this is accomplished in the computing circuit 16 by using the algorithm : where a , b , c , d and e are the inputs and outputs already described . also , since the value of 0 / 0 is mathematically undefined , the circuit is preprogrammed to assign 0 / 0 the value of unity . since the output e , which is proportional to the frequency may be either positive or negative depending upon whether the converter is supplying energy or sinking energy and since voltage - to - frequency converter 22 only responds to positive voltage an absolute value circuit is used to determine the absolute value of output e as an input for voltage - to - frequency converter 22 . since a bi - directional converter requires operation of two separate switches under conditions of power supply and power sink , the output of voltage - to - frequency converter 22 , which is a string of pulses of frequency proportional to e , must be directed by single pole , double throw switch 26 to the appropriate switch drivers . a polarity detector 28 determines the polarity of output e and directs output pulse from the voltage - to - frequency converter 22 , via switch 26 to either pulse distributor 30 or pulse distributor 32 . when the inverter is supplying energy , pulse distributor 32 is activated . for increased output power , a number of converters may be paralleled , therefore the positive pulse distribution circuit 32 has n 1 + n 2 outputs , each one activating n positive drive circuits of n 1 + n 2 converters . the negative pulse distribution circuit 30 has n 1 outputs , each one activating n 1 negative drive circuits of n 1 converters . from the above it follows that only a fraction of the paralleled converters are bi - directional , since the maximum amount of average negative power that has to be handled by an inverter is only 31 . 8 % of the rated output power ; the maximum amount occurs at zero power factor , requiring that only one third or less of the converters have to be bi - directional and 0 & lt ; n 2 ≦ 1 / 3 n 1 . equation ( 17 ) requires the energy delivered by each pulse , e o , to be constant . this is accomplished by modulating the &# 34 ; on &# 34 ; time of the input pulses . the pulse width of pulses from pulse distributor 30 are modulated in width by negative converter drive circuit 34 . similarly , the pulse width of pulses from pulse distributor 32 are modulated in width by positive drive converter circuit 36 . output voltage is sensed by voltage output sensing circuit 18 and compared to a predetermined reference voltage 38 at the input of error amplifier circuit 40 . the output of error amplifier 40 is sent to the b input of both negative driver circuit 34 and positive driver circuit 36 . both of these drive circuits will initiate switch conduction at the arrival of a pulse from the respective pulse distributor 32 or 36 and terminate conduction when current in the switch ( converted to a voltage ) reaches a value equal to the output voltage of the error amplifier 40 . a deviation of the output voltage from the desired value due to slow drift of any of the system &# 39 ; s constants will cause a change in output voltage of amplifier ( 40 ), which in turn will affect the value of ipk , resulting in the corrective action described previously . unless disabled by magnetization sensing circuit 42 , which senses demagnetization under conditions of overload , gate 1 , numeral 50 , will pass switch operating pulses to switch 1 , numeral 44 ; and , likewise , gate 2 , numeral 50 , will pass switch operating pulses to switch 2 , numeral 46 . the function of the demagnetization sensing circuits is to protect the converters in case of a shorted output , by forcing the converters to operate in the discontinuous mode under any load condition . as the familiar with the art will recognize , bi - directional flyback converter 52 includes an energy storage inductor having a primary winding 56 , a secondary winding 54 , primary switch 44 , secondary switch 46 , diodes 66 and 64 , and filter capacitor 72 . the converter delivers energy from the input source ( battery 62 ) to the load connected across capacitor 72 as switch 46 is cycled , &# 34 ; on &# 34 ; and &# 34 ; off &# 34 ;. during the &# 34 ; on &# 34 ; time , a current builds in winding 56 . when switch 56 turns off , the current in winding 56 , is interrupted . as the field in core 60 collapses a current appears in winding 54 and flows through diodes 66 to the load and capacitor 72 . diode 66 blocks the flow of current in winding 54 during the &# 34 ; on &# 34 ; time of switch 46 . diode 64 &# 34 ; is permanently off .&# 34 ; the transfer of energy from the load side to the battery 62 is done similarly , with functions of windings 54 , 56 switches 44 and 46 and diodes 66 and 64 reversed . undirectional converters will lack diode 64 , switch 46 , and the associated drive circuitry . as already discussed , the output of the converters is a full wave rectified sine wave . in order to generate the desired alternating sinusoidal output , a switching bridge is employed consisting of four single pole single throw switches in a bridge configuration . by alternately opening and closing switches located on opposing bridge legs , inversion may be accomplished . this switching is accomplished by a bridge drive circuit 70 , driven by the output f 3 of function generator 12 . since this output is of the form : the bridge switches in bridge 68 will flip - flop in synchronism with the desired sine wave . prior to inversion , most high frequency ripple is removed by the filter capacitor 72 . the output from bridge 68 is further filtered by low pass filter 74 and the sine wave output of the inverter is at 76 . in fig2 it may be seen how a large number of converters n 1 + n 2 may be paralleled for increased output power and reduced ripple . the outputs of converter 1 , numeral 80 , through converter n 1 + n 2 , numeral 85 are paralleled . the number of converters is unlimited . each of the converters are fused as indicated by fuses 86 , 88 , 90 and 92 . in a system where n is a large number , the failure of any one or several converters will have little impact on the output power or waveform . the pulse distribution circuit sends the pulses from the voltage - to - frequency converter sequentially to each converter in order to guarantee a high ripple frequency with its consequent reduction in size and weight of filter components . converters 80 and 82 are part of a group of bi - directional converters which total n 1 units . converters 84 and 85 are part of a group of uni - directional converters which total n 2 units . the operation of the described circuit may be represented mathematically as follows : where e o is the energy transferred to the output or from the output by one pulse of the bi - directional flyback converter . if i pk has a constant value , then the value of e o will also be constant . assuming for clarity that the conversion factor of the voltage to frequency converter equals unity , the frequency f will be according to algorithm ( 23 ): where i out is the current delivered to the load and f 2 represents the current i cf flowing in the filter capacitor 72 . the converters &# 39 ; output power is also equal to the sum of the powers delivered to the filter capacitor and the load : solving for v out yields : ## equ6 ## which is a full wave rectified sine wave , whose amplitude is independent of the input source voltage or the load current , an important object of the invention . it is apparent from the above that any output waveform can be generated by making f 1 equal to the square of a replica of the wanted output voltage and f 2 equal to the current forced into the filter capacitor by the wanted output voltage . while certain novel features of this invention have been shown and described and are pointed out in the annexed claims , it will be understood that various omissions , substitutions and changes in the forms and details of the device illustrated and in its operation can be made by those skilled in the art without departing from the spirit of the invention . it is also understood that a person skilled in the art can devise a computing circuit capable of forcing condition ( 1 ) on a converter having a topology other than flyback , in order to obtain the same operational characteristics .