initial compensation circuitries described by j . casey et al ( particle accelerator conference 2005 ) and g . leyh ( 2005 pulsed power conference & amp ; particle accelerator conference 2007 ), as mentioned before , have an identical topology as those of main cells of marx modulators , and the charge voltage for the compensation cells is different from that of main cells , with the latter being much higher . those initial compensation cells have only one - time compensation action per cell during one voltage pulse . an example of the marx modulator , including its mmc bank and its compensation cell bank , was given by g . leyh in the citation above in which the compensation cell bank is called as a vernier cell bank . the mmc bank , comprising of a plurality of main cells , is in series with a vernier cell bank that also has a plurality of vernier cells , i . e . compensation cells . the modulator has a negative output pulse , as do the embodiments to be described below . the number of vernier cells that should be used in a vernier cell bank , i . e . a compensation cell bank can be computed according to the principle that the energy stored in a vernier cell bank should at least make up the energy difference between the ideal pulse energy and the actual , decayed pulse energy absorbed by a load . based on this principle , the following calculations yield the number of vernier cells needed : the voltage v ( t ) output by a mmc bank having a total capacitance c and a load impedance r in series with the bank attenuates in time according to : where v 0 is the initial output voltage amplitude of the mmc bank , equal to the dc charge voltage times the number of stages of the mmc erected , and t is discharging time . the output power p ( t ) of the mmc bank decays in a form of : if e ( t ) is the total energy dissipated in the load r , then : ( 2 ) energy needed by a load for an ideal rectangular voltage pulse for an ideal rectangular voltage pulse ( amplitude of v 0 ), the energy e r ( t ) of the pulse loss in the load with an impedance of r is : ( 3 ) energy stored in one vernier cell ( i . e . one compensation cell ), e v ( t ), is : where c v is the capacitance and v v is the charge voltage of the vernier cell . the electrical energy stored in the vernier cell bank should make up the difference between e r ( t ) and e ( t ). thus , the minimum number , n , of the compensation cells can be calculated from the equation below : n =( e r ( t )− e ( t ))/ e v ( t ) ( 6 ) from the above calculations , it is seen that the minimum number , n , of the compensation cells is inversely proportional to the amplitude square of the charge voltage , v v , of the compensation cells . increasing the charge voltage will greatly reduce the number of the compensation cells , thus helping to simplify the marx modulator and saving cost . in certain applications such as the international linear collider project , the flatness of an output voltage pulse of the marx modulator is required to be in a very small range , i . e . 1 % or less , which requires a very low charge voltage for a compensation cell having only one time compensation action to stay within the range . thus many compensation cells for the marx modulators are needed in this conventional scheme . the present invention , by smoothing the output voltage of the compensation cell employing solid - state switches , inductors and diodes , will greatly raise the charge voltage of a compensation cell ( as high as that of the charge voltage of the mmc ) while keeping the flattop fluctuation of the voltage pulse in the required small arrange , and thus reduce the number of compensation cells . fig1 a illustrates the first embodiment of the compensation circuitry of the present invention . it includes main switch 1 , charge switch 2 , compensation capacitor 3 , main discharge diode 4 , compensation inductor 5 , and compensation diode 6 . two other important components are added , i . e . compensation inductor 5 and compensation diode 6 . with these two critical components , the compensation cell can perform multiple compensation actions . as the voltage pulse output by the marx modulator droops , main switch 1 is turned on immediately by the feedforward correction system . the voltage across compensation capacitor 3 is added on the voltage of the mmc bank gradually because of the counteraction of inductor 5 . once the voltage of the main marx circuit recovers , main switch 1 is turned off and the magnetic energy stored in inductor 5 continues to compensate the main marx circuit through diode 6 . but the compensation voltage will diminish with time as the stored magnetic energy is depleted , and the total voltage of the marx modulator begins to droop again . when the total voltage reduces to a certain level , the compensation cycle starts over , as long as there is sufficient electrical energy stored in capacitor 3 , to compensate the voltage droop of the mmc bank . although the fall time of the voltage pulse output by the mmc bank is affected by the inductance of inductor 5 , the impact of the inductance is limited by the relatively fast compensation action . the value of the inductance needed is correlated to the switching speed of the solid - state switch . the faster the speed of the solid - state switch has , the less inductance the compensation cell needs and the less impact the inductance of the inductor 5 has . fig1 b describes an improvement of the compensation circuit in fig1 a . a third solid - state switch , load protection switch 7 , is added in the circuit for protecting the load of the marx modulator , which may be an rf load such as a klystron . switch 7 will rapidly cut off the compensation current in case of load arcing . however , the switch does not directly contribute to normal compensation functions . fig2 a is the second embodiment of the present invention . compared with the first embodiment shown in fig1 a , the second embodiment has similar topology but one more capacitor , direct compensation capacitor 8 . the first embodiment is a special case of the second one , with capacitor 8 in the second embodiment having a value of zero . the advantage of direct compensation capacitor 8 is that the capacitor can alleviate the current load from inductor 5 and diode 6 because the current of the mmc bank will pass through direct compensation capacitor 8 . separately , the second embodiment can be viewed in two parts ( see fig2 b ). the left part in fig2 b is a buck converter . when this part works in switching mode power supply ( smps ), it has a variable output voltage that is related to the voltage of the capacitor 3 and the duty cycle of the switch 1 . however , the smps mode is not used in the compensation actions . instead , in the present invention , switch 1 is triggered by a feedforward correction system whenever the compensation is needed . capacitor 3 will be charged to a high voltage , which can be identical to that of mmc , so that it stores more electrical energy to be used in the ensuing compensation actions . the right part in fig2 b is the topology of the main marx cell , whose capacitor 8 will receive the adjustable compensation energy from the left part . the compensation energy flux , and thus the voltage of capacitor 8 , are adjusted through the triggering of switch 1 . low - voltage experiments were performed for the compensation circuitry of the first embodiment ( see fig1 a ). the experimental purpose was to find the evident of the feasibility of our compensation cell design scheme , i . e . multiple compensations regulated by the solid - state switch and the inductor . for simplicity , only one compensation cell was used in the test . the charge voltage of the compensation cell was 6 v . the capacitance of the compensation cell was 30 μf . mmc bank ( its total capacitance is 3 μf ) with the output voltage from ˜ 55 v to 75 v was used . the entire experimental setup is referred to the marx modulator used by g . leyh ( particle accelerator conference 2007 ) but with a scaled down charge voltage , and is shown in fig3 when both banks of the marx modulator are erected . in the tests , switch 1 and 2 adopted igbt switches . igbt ( rated at 100v ) switches were driven by driver circuits and controlled by a single - board computer . a divider that was in series of the load was utilized to monitor the voltage change on the load and the voltage of the divider was sent to the computer for the purpose of controlling switch 1 to start the compensation actions . fig4 shows that the compensation voltage curve , output by the single cell and regulated by the computer , was observed in the experiments , where the overall voltage pulse was 1 . 7 ms long . the horizontal axis in fig4 is time ( same in the following fig5 a and 5 b ). the compensation actions ( curve 2 in fig4 ) made small ripples on the overall voltage pulse ( curve 1 in fig4 ) and maintained its level up to t = 500 μs . after that , the overall voltage pulse decayed as the stored energy of the compensation cell was exhausted , and from that time the compensation cell ( mainly , the main switch 1 ) was turned on all the way till the end of the voltage pulse . further experiments were conducted for finding the relationship of the mmc &# 39 ; s capacitance to that of compensation cell . here we define the adequate compensation period , t a , which refers to the time from the initial trigger of switch 1 to the instant that the energy in the compensation cell is no longer sufficient to compensate the voltage output by the mmc bank ( the voltage began to droop all the way from then ). at time t a , the igbt of the compensation cell would be turned on and would remain on . from the equations above , we can induce that the adequate compensation period t a should become longer when the capacitance of the mmc increases because less energy is needed to compensate the voltage droop . we have observed this phenomenon during our experiments when we varied the capacitance of the mmc bank and kept other experimental conditions nearly the same . it is shown that t a is around 240 μs for the capacitance of the mmc at 3 μf ( see fig5 a ) and around 400 μs when the value is changed to 6 μf . ( see fig5 b ). the observation agrees well with the prediction of the equations above . while the invention has been described with reference to its preferred embodiments , those skilled in the art will understand that various changes may be made and equivalents may be substituted for elements thereof without departing from the true spirit and scope of the invention . in addition , many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from its essential teachings .