A Solid-State Marx Generator with Prevention of through Current for Rectangular Pulses

: In solid-state high-voltage pulse generators, switches may be triggered on by fault due to electromagnetic interference, resulting in high through current and breakdown of switches. To generate rectangular high-voltage pulses, this paper proposes a solid-state Marx generator (SSMG) with fast recovery diodes to prevent through current. Only charging currents with the same direction flow through these fast recovery diodes breaks the short-circuit loops in and between stages. A 52-stage SSMG prototype based on the proposed circuit was developed. PSpice simulations and experiments were performed for comparison. It was found that the through current can rise to 250 A without any protection. With 10-µ H protection inductors in each state, the through current amplitude drops to 50 A. Under the same condition, there is no continuous through current with the proposed fast recovery diodes. Furthermore, 22-kV repetitive rectangular pulses were also obtained in experiments. This proved that the proposed Marx generator can prevent the through current in power cells.


Introduction
In recent years, high-voltage pulse generators have been widely used in applications such as plasma source ion implantation, material processing, and pulsed field ablation [1][2][3][4].Electrical pulses can generate more active plasma species due to their high voltage (>10 kV), fast rising edges, and short duration (<100 µs); additionally, ultrashort and high-voltage pulses can reduce muscle contractions and inflammation in the field of pulse electric field ablation.Marx generators are frequently used to generate high-voltage pulses since they charge many capacitors in parallel and discharge them in series.In this way, the low voltage can be multiplied easily.With the development of solid-state switches, various SSMGs that can flexibly adjust pulse width were developed [5][6][7][8][9][10].Unlike the conventional Marx generators shown in Figure 1a, which use gas switches, SSMGs typically use semiconductor switches such as MOSFETs and IGBTs to generate repetitive pulses [11][12][13][14].In addition, the remanent charges in the capacitive load must be truncated to obtain rectangular pulses.The charge switches in half-bridge SSMGs as shown in Figure 1b can truncate the tails of pulses [15].Therefore, half-bridge SSMGs can generate rectangular pulses which are preferred in dielectric barrier discharges [16] because the fast back edge of high-voltage pulse can excite a second DBD, which considerably improves the DBD efficiency [17].However, the risk of overcurrent faults increases significantly in the half-bridge SSMGs when through current occurs due to malfunction.The electromagnetic interference (EMI) becomes the most intensive in the front edge period of high-voltage pulses.The EMI may turn on one or more charge switches while they should be off.Once both the discharging front edge period of high-voltage pulses.The EMI may turn on one or more charge switches while they should be off.Once both the discharging switch and the charging switch are on at the same time, they provide a low-impedance loop for the capacitor, generating a transient short-circuit current which may breakdown the switches.Suppose that the total equivalent resistance in one power cell is 0.5 Ω, including the on-state resistance of both switches, and the capacitor is charged to 400 V, the short-circuit current can reach 800 A according to Ohm's law.This current is far beyond the rated current capacity of most semiconductor switches.Short-circuit faults can easily breakdown semiconductor switches and result in the failure of power systems since all these switches have a limited short-circuit withstand time (SCWT).Specifically, commercial Insulated Gate Bipolar Transistors (IGBTs) usually have a Short-circuit faults can easily breakdown semiconductor switches and result in the failure of power systems since all these switches have a limited short-circuit withstand time (SCWT).Specifically, commercial Insulated Gate Bipolar Transistors (IGBTs) usually have a typical SCWT longer than 10 µs while silicon carbide Metal-Oxide-Semiconductor Field-Effect Transistors (SiC MOSFETs) usually have a SCWT shorter than 8 µs.Therefore, the overcurrent and short-circuit protection is absolutely necessary in high voltage pulsed power systems using semiconductor switches.Otherwise, the reliability of these systems is poor and unsuitable for long-term operation.There are solutions to replace the charge switches to inductors or resistors to limit the occurrence of instantaneous short-circuits as in the SSMG shown in Figure 1c [18].Among them, the scheme using resistors can limit the short-circuit current to a very low value at the price of deterioration in the energy efficiency and charging speed.Using inductors may overcome these drawbacks, but inductors result in a boost effect and the leakage current becomes high when the pulse width is long.Therefore, it is unsuitable to generate long pulses at high-frequency.In addition, they do not help to release the residual charges in the capacitive load, resulting in relatively long tailing pulses.As shown in Figure 1d, R. L. Cassel proposed another inductor protection scheme in the half-bridge Marx generator.Though it reduces the boost effect apparently [19], the inductor can only suppress an instantaneous current in short pulse.
Another choice is using the driver circuit to timely turn the switch off when overcurrent occurs.Typically, drive-based protection circuits are classified as active or passive.Active protection circuits protect speeds up to 200 ns but require additional isolated power supplies [10,20,21].These isolated power supplies must be able to withstand the maximum output voltage, while most commercial power supplies have limited insulation voltage of a few kilovolts.This is the reason that most pulse generators cannot output high voltage over 10 kV.As a result, active protection circuits in high-voltage pulse generators are quite costly and rarely used.Passive drive protection circuits do not require an additional power supply, use of sampling resistors [22][23][24], or desaturation protection [25].The challenge is that the drive circuit with overcurrent protection should have fast response speed and high-voltage isolation in the strong electromagnetic environment.
However, all the above protection circuits aim to passively turn off the switches un-der fault conditions.Each switch requires a drive circuit with protection, which considerably increase the complexity and cost of high-voltage pulse generators which include many switches.What will happen if we break the short-circuit loops?The protection circuits in many drive circuits can be spared.To solve the through current problem in SSMGs, we propose to block the through current loop by using diodes for one-direction current conduction.Because this solution solves the internal through current problem of the discharge process by using only diodes without any energy storage or energy consumption components, it has little impact on the working performance of the circuit.Part II of this paper describes the short-circuit characteristics of switches, the overcurrent and protection principles of the half-bridge, inductor protection and diode protection schemes, as well as the selection of the protection diodes.To better present the protection effects of the proposed circuits, the simulation and analysis of three circuits are presented in Part III.While in Part IV, experiments of short-circuit faults are performed for each of the three circuits.The conclusions are given in Part V.

Working Principle of Diode Protection SSMG
Figure 2 shows the schematic diagram of the n-stage positive diode protection SSMG proposed in this paper, which consists of a DC power supply V in , a resistor, many power units with diodes, and a load.Figure 2 contains the three phases of the SSMG operation: first is the charging phase (Figure 2a), then the discharging phase (Figure 2b), and finally the overcurrent protection during the discharging phase (Figure 2c).Among them, the DC power supply V in is an LLC resonant power supply, which can provide continuously adjustable DC voltage.In addition, the maximum output current of the DC power supply can be precisely controlled.Therefore, the short-circuit of the DC power supply is not considered.A current limiting resistor, R 0 , can also be connected in series with the power supply if necessary.The driver adopts a multi-channel driver based on magnetic isolation technology, so the signals of the charge and discharge switches can be provided simultaneously.The power circuit consists of multiple stages of power cells, each of which includes an energy storage capacitor C n , a discharge switch S dn , a charging switch S cn , a charging diode D n , and a protection diode D sn .During the charging phase, all charge switches are turned on as indicated by the red arrows in Figure 2a, the discharge switches are off, and the charging diodes and the protection diodes are on, the capacitors are connected in parallel, and they are charged to the same voltage value as V in .
considered.A current limiting resistor, R0, can also be connected in series with the p supply if necessary.The driver adopts a multi-channel driver based on magnetic iso technology, so the signals of the charge and discharge switches can be prov simultaneously.The power circuit consists of multiple stages of power cells, each of w includes an energy storage capacitor Cn, a discharge switch Sdn, a charging switch charging diode Dn, and a protection diode Dsn.During the charging phase, all c switches are turned on as indicated by the red arrows in Figure 2a, the discharge swi are off, and the charging diodes and the protection diodes are on, the capacitor connected in parallel, and they are charged to the same voltage value as Vin.The discharge phase is shown in Figure 2b.During discharging, all disc switches are turned on, all the diodes but Ds0 are reversely biased and off, an capacitors discharge in series to generate a high-voltage pulse to the load.At the e discharge, as shown by the blue arrow in Figure 2a, the discharge switches are turne Afterwards, the charge switches are turned on to refresh the capacitors and releas residual charge in the load.
In the discharge phase, if a stage of the charging switch Sc2 is triggered on by mi as shown in Figure 2c, the diode Ds1 will block the through current and no short-c will occur.In this case, the discharge phase still proceeds normally.Protecting ag overcurrent in this way has many advantages.Compared with the inductor prote scheme, as there is no inductor in the main circuit, there is no induced overvoltag boost effect during high-frequency, and high-voltage long-pulse discharge.

Comparison of through Current in Different SSMGs
In this section, the through current in three different SSMGs are presented.schematics are shown in Figures 1b,d and 2a.In order to deepen the understanding role of through current under different conditions, the basic power cells of conditions were presented in Figure 3.The discharge phase is shown in Figure 2b.During discharging, all discharge switches are turned on, all the diodes but D s0 are reversely biased and off, and the capacitors discharge in series to generate a high-voltage pulse to the load.At the end of discharge, as shown by the blue arrow in Figure 2a, the discharge switches are turned off.Afterwards, the charge switches are turned on to refresh the capacitors and release the residual charge in the load.
In the discharge phase, if a stage of the charging switch S c2 is triggered on by mistake as shown in Figure 2c, the diode D s1 will block the through current and no short-circuit will occur.In this case, the discharge phase still proceeds normally.Protecting against overcurrent in this way has many advantages.Compared with the inductor protection scheme, as there is no inductor in the main circuit, there is no induced overvoltage, no boost effect during high-frequency, and high-voltage long-pulse discharge.

Comparison of through Current in Different SSMGs
In this section, the through current in three different SSMGs are presented.Their schematics are shown in Figures 1b,d and 2a.In order to deepen the understanding of the role of through current under different conditions, the basic power cells of three conditions were presented in Figure 3. Suppose that the charging switch Sc2 is turned on due to EMI interference in the discharging phase, through current may occur immediately since the discharging switch Sd2 is also in the on-state.In the half-bridge SSMG shown in Figure 3a, the through current can rise to a very high value quickly since the impedance in this loop is low.This shortcircuit current may breakdown the switches.In contrast with the inductor isolation circuit shown in Figure 3b, the inductors limit the rising rate of the through current, but it is only effective when this fault last for a very short time.If the through current lasts for longer than 5 µs, the current would still exceed the allowed maximum current and result in the breakdown of switches.Moreover, the charging current flowing through these inductors may boost the voltage over capacitors in repetitive operation, which may cause overvoltage breakdown of components [26][27][28].
As in Figure 3c, diodes Ds1 and Ds2 in the proposed SSMG with diode protection break the loop of through current.So, the occasional false turning-on of one switch will not cause through current.However, if two adjacent charge switches are falsely turned on in the discharging phase, through current or overvoltage breakdown fault may occur.Two possible faults that might occur in the proposed SSMG with diode protection are illustrated as in Figure 4, and they are possible through current loop including Ds0 (a), as well as possible overvoltage over Ds1 and Sc1 (b), respectively.In Figure 4a, when the charging switches Sc1 and Sc2 are falsely turned on, a short-circuit will form through the diode Ds0 through the loop indicated by the red arrowed dashed line.The short-circuit must include the Ds0 since other diodes break the loops of through current.But if the switches Sc2 and Sc3 are falsely turned on as shown in Figure 4b, voltage over the charging switch Sc1 and the diode Ds1 are doubled as indicated by the red arrowed dashed line.In this case, despite the risk of overvoltage, breakdown of them still exists.However, the possibility of the false turning-on of two adjacent charge switches is quite low and can be ignored.Suppose that the charging switch S c2 is turned on due to EMI interference in the discharging phase, through current may occur immediately since the discharging switch S d2 is also in the on-state.In the half-bridge SSMG shown in Figure 3a, the through current can rise to a very high value quickly since the impedance in this loop is low.This shortcircuit current may breakdown the switches.In contrast with the inductor isolation circuit shown in Figure 3b, the inductors limit the rising rate of the through current, but it is only effective when this fault last for a very short time.If the through current lasts for longer than 5 µs, the current would still exceed the allowed maximum current and result in the breakdown of switches.Moreover, the charging current flowing through these inductors may boost the voltage over capacitors in repetitive operation, which may cause overvoltage breakdown of components [26][27][28].
As in Figure 3c, diodes D s1 and D s2 in the proposed SSMG with diode protection break the loop of through current.So, the occasional false turning-on of one switch will not cause through current.However, if two adjacent charge switches are falsely turned on in the discharging phase, through current or overvoltage breakdown fault may occur.Two possible faults that might occur in the proposed SSMG with diode protection are illustrated as in Figure 4, and they are possible through current loop including D s0 (a), as well as possible overvoltage over D s1 and S c1 (b), respectively.In Figure 4a, when the charging switches S c1 and S c2 are falsely turned on, a short-circuit will form through the diode D s0 through the loop indicated by the red arrowed dashed line.The short-circuit must include the D s0 since other diodes break the loops of through current.But if the switches S c2 and S c3 are falsely turned on as shown in Figure 4b, voltage over the charging switch S c1 and the diode D s1 are doubled as indicated by the red arrowed dashed line.In this case, despite the risk of overvoltage, breakdown of them still exists.However, the possibility of the false turning-on of two adjacent charge switches is quite low and can be ignored.Suppose that the charging switch Sc2 is turned on due to EMI interference in th discharging phase, through current may occur immediately since the discharging switc Sd2 is also in the on-state.In the half-bridge SSMG shown in Figure 3a, the through curren can rise to a very high value quickly since the impedance in this loop is low.This shor circuit current may breakdown the switches.In contrast with the inductor isolation circu shown in Figure 3b, the inductors limit the rising rate of the through current, but it is onl effective when this fault last for a very short time.If the through current lasts for longe than 5 µs, the current would still exceed the allowed maximum current and result in th breakdown of switches.Moreover, the charging current flowing through these inductor may boost the voltage over capacitors in repetitive operation, which may caus overvoltage breakdown of components [26][27][28].
As in Figure 3c, diodes Ds1 and Ds2 in the proposed SSMG with diode protection brea the loop of through current.So, the occasional false turning-on of one switch will not caus through current.However, if two adjacent charge switches are falsely turned on in th discharging phase, through current or overvoltage breakdown fault may occur.Tw possible faults that might occur in the proposed SSMG with diode protection are illustrate as in Figure 4, and they are possible through current loop including Ds0 (a), as well a possible overvoltage over Ds1 and Sc1 (b), respectively.In Figure 4a, when the chargin switches Sc1 and Sc2 are falsely turned on, a short-circuit will form through the diode D through the loop indicated by the red arrowed dashed line.The short-circuit must includ the Ds0 since other diodes break the loops of through current.But if the switches Sc2 and S are falsely turned on as shown in Figure 4b, voltage over the charging switch Sc1 and th diode Ds1 are doubled as indicated by the red arrowed dashed line.In this case, despite th risk of overvoltage, breakdown of them still exists.However, the possibility of the fals turning-on of two adjacent charge switches is quite low and can be ignored.It should be emphasized that this diode protection SSMG can only block the thro current in the power cells.It can not block the short-circuit current of the load.In o words, if the load in Figure 2b is short-circuit, overcurrent through all switches still occ Therefore, a proper overcurrent protection for the load is still required.As in [2 current-limiting protection module and an automatic quick-cutting protection mo were used for the short-circuit protection at the output terminal.

Component Selection
To achieve better protection, the diode type should be selected based on characteristics of the half-bridge SSMG.First of all, the peak reverse voltage of dio should be similar to the switches.In this paper, the SiC MOFFETs with the mode C2M0080120D were selected as the power switches.The main parameters of this sw are listed in Table 1 [27].The allowed pulsed drain current is 80 A, and the drain so voltage is allowed to be 1200 V.In addition, the following simulation and analysis o switches are based on the parameters in Table 1.As for the current capability, it is not necessary to have a strong current capab because the forward time is very short and the current value is small during its opera According to its protection principle, the recovery speed of the diode directly determ whether it can quickly suppress the short-circuit current.Therefore, the widely used recovery diode FR157 with a maximum recovery time of 500 ns is selected as protection diode in this paper.Its rated voltage is 1 kV and its other main parameters listed in Table 2.One can observe that the recovery time is 500 ns and the surge forw current is up to 60 A, which completely fulfill the requirements of the present work.It should be emphasized that this diode protection SSMG can only block the through current in the power cells.It can not block the short-circuit current of the load.In other words, if the load in Figure 2b is short-circuit, overcurrent through all switches still occurs.Therefore, a proper overcurrent protection for the load is still required.As in [29], a currentlimiting protection module and an automatic quick-cutting protection module were used for the short-circuit protection at the output terminal.

Component Selection
To achieve better protection, the diode type should be selected based on the characteristics of the half-bridge SSMG.First of all, the peak reverse voltage of diodes should be similar to the switches.In this paper, the SiC MOFFETs with the model of C2M0080120D were selected as the power switches.The main parameters of this switch are listed in Table 1 [27].The allowed pulsed drain current is 80 A, and the drain source voltage is allowed to be 1200 V.In addition, the following simulation and analysis of the switches are based on the parameters in Table 1.As for the current capability, it is not necessary to have a strong current capability because the forward time is very short and the current value is small during its operation.According to its protection principle, the recovery speed of the diode directly determines whether it can quickly suppress the short-circuit current.Therefore, the widely used fast recovery diode FR157 with a maximum recovery time of 500 ns is selected as the protection diode in this paper.Its rated voltage is 1 kV and its other main parameters are listed in Table 2.One can observe that the recovery time is 500 ns and the surge forward current is up to 60 A, which completely fulfill the requirements of the present work.

Contents Value
Repetitive Peak Voltage V RRM 1 kV Average Forward Current I F(AV) 1.5 A

Simulation
To verify the above theory, the circuits were simulated using PSpice software (OrCAD 16.6).In the simulation, the charging switch S c2 was turned on constantly to simulate the false turning-on of switches in the discharge phase.All three different SSMGs presented in Figure 3 were simulated for comparison.The model element parameters refer to the corresponding datasheet to sustain the consistency.As shown in Figure 4b, voltage over the diodes was doubled in the fault condition, and the input voltage must be lower the half of the rated voltage of diodes which is 1 kV.So, the maximum input voltage was set as 420 V.The main parameters are shown in Table 3. Figure 5 shows the parameters and locations that were measured in the simulation and in the following experiments.V c refers to the capacitor voltage of the front stage of the breakdown stage.V sd is the drain-source voltage of the discharge switches.V sc is the drain-source voltage of the charging switch.V p is the voltage across the protection inductors or diodes, while in the half-bridge SSMG V p is zero.I cell refers to the internal current of the power cell measured through S c2 , and V out refers to the output voltage of pulse over the load.

Simulation
To verify the above theory, the circuits were simulated using PSpice s (OrCAD 16.6).In the simulation, the charging switch Sc2 was turned on const simulate the false turning-on of switches in the discharge phase.All three different presented in Figure 3 were simulated for comparison.The model element paramete to the corresponding datasheet to sustain the consistency.As shown in Figure 4b, over the diodes was doubled in the fault condition, and the input voltage must b the half of the rated voltage of diodes which is 1 kV.So, the maximum input volt set as 420 V.The main parameters are shown in Table 3.Based on the aforementioned modeling method, we conducted calculations model and obtained the corresponding results.Figure 6 shows the waveforms of Based on the aforementioned modeling method, we conducted calculations for the model and obtained the corresponding results.Figure 6 shows the waveforms of I cell , V out , and V c in the normal operation and in the fault stage in the simulations of three circuits when S c2 is falsely turned on.With a 3-pF light capacitive load, the small current only occurs during the rising and falling periods of pulses, as in Figure 6a.As shown in Figure 6b, the short-circuit current in the half-bridge SSMG rises to 250 A quickly.This instant high current was much higher than the allowed 80-A pulsed drain current of the switch and could easily cause the breakdown of it.Figure 6c shows the waveforms of the inductor protection SSMG.The short-circuit current was clamped to under 60 A by inductors, which indicates that these inductors can limit the overcurrent.In addition, it can be seen that the output voltage amplitude exceeded 1260 V, indicating that these inductors have already boosted the charging voltage over capacitors.The waveforms of the diode protection SSMG are shown in Figure 6d.As can be seen, there was no obvious overcurrent generated since the overcurrent loop was blocked by D s1 .Unlike in the other two cases, there was no sudden drop of the voltage across capacitor C 2 , which further proves that there is no overcurrent in this condition.The waveform of the output voltage is the same as in normal operation conditions (Figure 6a,d).Therefore, the diodes inserted into SSMGs showed the best overcurrent protection effect among the three circuits in Figure 3.
Electronics 2024, 13, x FOR PEER REVIEW 8 of 13 and Vc in the normal operation and in the fault stage in the simulations of three circuits when Sc2 is falsely turned on.With a 3-pF light capacitive load, the small current only occurs during the rising and falling periods of pulses, as in Figure 6a.As shown in Figure 6b, the short-circuit current in the half-bridge SSMG rises to 250 A quickly.This instant high current was much higher than the allowed 80-A pulsed drain current of the switch and could easily cause the breakdown of it.Figure 6c shows the waveforms of the inductor protection SSMG.The short-circuit current was clamped to under 60 A by inductors, which indicates that these inductors can limit the overcurrent.In addition, it can be seen that the output voltage amplitude exceeded 1260 V, indicating that these inductors have already boosted the charging voltage over capacitors.The waveforms of the diode protection SSMG are shown in Figure 6d.As can be seen, there was no obvious overcurrent generated since the overcurrent loop was blocked by Ds1.Unlike in the other two cases, there was no sudden drop of the voltage across capacitor C2, which further proves that there is no overcurrent in this condition.The waveform of the output voltage is the same as in normal operation conditions (Figure 6a,d).Therefore, the diodes inserted into SSMGs showed the best overcurrent protection effect among the three circuits in Figure 3.

Experimental Results and Discussion
To verify the theory and analysis above, a 52-stage SSMG was built for the experiment.All conditions were performed to be consistent with the simulation.The highest charging voltage of each stage was 420 V, and the output voltage amplitude could reach 22 kV.The load was a high-voltage probe with a capacitance of 3 pf.It can be seen as a light capacitive load.The main parameters of the circuit are shown in Table 4.The photograph of the developed 52-stage diode protection SSMG prototype is shown in Figure 7.The different components have been labeled on the diagram.The high voltage and current were measured by using a high-voltage probe (P6015A, 40 kV (pk), Tektronix, Beaverton, OR, USA) and a current monitor (Model 101, Pearson Electronics, Palo Alto, CA, USA), respectively.The experimental waveforms were captured by a digital Oscilloscope (Tektronix DPO 2104, Beaverton, OR, USA) with a sampling bandwidth of 100 MHz and a sampling frequency of 1 GHz.To verify the theory and analysis above, a 52-stage SSMG was built experiment.All conditions were performed to be consistent with the simulat highest charging voltage of each stage was 420 V, and the output voltage amplitud reach 22 kV.The load was a high-voltage probe with a capacitance of 3 pf.It can as a light capacitive load.The main parameters of the circuit are shown in Tabl photograph of the developed 52-stage diode protection SSMG prototype is sh Figure 7.The different components have been labeled on the diagram.The high and current were measured by using a high-voltage probe (P6015A, 40 kV (pk), Te Beaverton, OR, USA) and a current monitor (Model 101, Pearson Electronics, Pa CA, USA), respectively.The experimental waveforms were captured by a Oscilloscope (Tektronix DPO 2104, Beaverton, OR, USA) with a sampling bandw 100 MHz and a sampling frequency of 1 GHz.The input voltage was chosen to be no higher than 420 V to decrease the breakdown of switches.In the experiments, the charging switch Sc2 was sho purpose to simulate the false turning-on.The same parameters, including Icell, Vo as in Figure 5 in the second stage power cell, were measured.The reason for choo second stage for testing is that the lower stage power cell has lower potential and EMI during the discharge process.As we did in the simulation, the shor experiments were conducted for 5 µs in conventional unprotected half-bridge inductor protection SSMG, and diode protection SSMG, respectively.The m results are shown in Figure 8. Comparing the experimental and simulation results 6), we can see that these two trends are very consistent.The input voltage was chosen to be no higher than 420 V to decrease the risk of breakdown of switches.In the experiments, the charging switch S c2 was shorted on purpose to simulate the false turning-on.The same parameters, including I cell , V out and V c as in Figure 5 in the second stage power cell, were measured.The reason for choosing the second stage for testing is that the lower stage power cell has lower potential and weaker EMI during the discharge process.As we did in the simulation, the short-circuit experiments were conducted for 5 µs in conventional unprotected half-bridge SSMG, inductor protection SSMG, and diode protection SSMG, respectively.The measured results are shown in Figure 8. Comparing the experimental and simulation results (Figure 6), we can see that these two trends are very consistent.
A control group experiment with no fault was also carried out for comparison.Figure 8a shows the output voltage and current waveforms in normal operation conditions.It shows that the pulsed voltage amplitude was 22 kV, while the intra-stage current I cell had a high-frequency oscillation of about 100 A amplitude during turn-on and turn-off processes, respectively.This waveform also contains the EMI component due to the high dV/dt corresponding to the pulse edges.Similar high-frequency oscillation with higher amplitudes also appears in all other experiments as in Figure 8.A control group experiment with no fault was also carried out for comparison.Figure 8a shows the output voltage and current waveforms in normal operation conditions.It shows that the pulsed voltage amplitude was 22 kV, while the intra-stage current Icell had a high-frequency oscillation of about 100 A amplitude during turn-on and turn-off processes, respectively.This waveform also contains the EMI component due to the high dV/dt corresponding to the pulse edges.Similar high-frequency oscillation with higher amplitudes also appears in all other experiments as in Figure 8.
The short-circuit waveforms of the half-bridge SSMG are shown in Figure 8b.As in the simulation results, the voltage Vc across the capacitor drops to −120 V within 1 µs and the current rises quickly to 250 A. The amplitude of its through current is three times higher than the allowed pulsed drain current, 80 A, of the switch.Therefore, this fault can easily cause the breakdown of both the charging and discharge switches.
The experimental waveforms of inductor protection are shown in Figure 8c.Similar to the simulation, the voltage Vc across the capacitor drops to −50 V within 3.5 µs and the current rises to 60 A at a slower rate.The amplitude of the through current was still higher than the allowed continuous drain current of the switch.
The experimental waveforms of diode protection SSMG are shown in Figure 8d.Similar to the simulation results, the voltage Vc of the capacitor only decreased slightly The short-circuit waveforms of the half-bridge SSMG are shown in Figure 8b.As in the simulation results, the voltage V c across the capacitor drops to −120 V within 1 µs and the current rises quickly to 250 A. The amplitude of its through current is three times higher than the allowed pulsed drain current, 80 A, of the switch.Therefore, this fault can easily cause the breakdown of both the charging and discharge switches.
The experimental waveforms of inductor protection are shown in Figure 8c.Similar to the simulation, the voltage V c across the capacitor drops to −50 V within 3.5 µs and the current rises to 60 A at a slower rate.The amplitude of the through current was still higher than the allowed continuous drain current of the switch.
The experimental waveforms of diode protection SSMG are shown in Figure 8d.Similar to the simulation results, the voltage V c of the capacitor only decreased slightly and there was no through current.The amplitude of V out in diode protection SSMG was also about 200 V higher than other cases.Therefore, it can be concluded that these diodes can thoroughly block the through current.
The drain-source voltage V sd of the discharge switch and the voltage V p across the protection inductors or diodes were also measured and presented in Figure 9.As in the short-circuit stage in the half-bridge SSMG, the voltage instantly fell on the inductor L 1 and decreased gradually to zero with the increase in the through current, as shown in Figure 9a.In the fault stage in the diode protection SSMG as shown in Figure 9b, the voltage fell on the diode D s1 throughout the discharging process.So, there was no continuous through current.This further proves the successful blocking of through current by these diodes.
Electronics 2024, 13, x FOR PEER REVIEW 11 of 13 and there was no through current.The amplitude of Vout in diode protection SSMG was also about 200 V higher than other cases.Therefore, it can be concluded that these diodes can thoroughly block the through current.The drain-source voltage Vsd of the discharge switch and the voltage Vp across the protection inductors or diodes were also measured and presented in Figure 9.As in the short-circuit stage in the half-bridge SSMG, the voltage instantly fell on the inductor L1 and decreased gradually to zero with the increase in the through current, as shown in Figure 9a.In the fault stage in the diode protection SSMG as shown in Figure 9b, the voltage fell on the diode Ds1 throughout the discharging process.So, there was no continuous through current.This further proves the successful blocking of through current by these diodes.

Conclusions
To improve the reliability of half-bridge SSMGs, we proposed to block the through currents with fast recovery diodes.A 52-stage SSMG prototype was built.Simulation and experiments were carried out to verify its feasibility.Both simulating and experimental results indicated that the fault through current could rise to above 250 A when there was no overcurrent protection.With a 10-µH inductor in each stage, the fault through current dropped to 60 A. With the proposed diodes the fault through current was completely blocked.Furthermore, 22-kV rectangular pulses were also obtained.The introduction of diodes not only reserved the truncation function of charge switches, but also broke the through current loops so the overcurrent risk of switches was reduced.The proposed through current protection with fast recovery diodes helps to block the overcurrent in power cells, which considerably simplifies the design of the overcurrent protection for semiconductor switches.In combination with a proper overcurrent protection in the load loop, it can further improve the reliability of half-bridge SSMGs.

Figure 1 .
Figure 1.Several common Marx circuit topologies.(a) Classic Marx generator topology.(b) Positive SSMG based on half-bridge structure.(c) Positive SSMG with diodes and inductors in charging loops.(d) Positive SSMG with inductor protection structure.

Figure 1 .
Figure 1.Several common Marx circuit topologies.(a) Classic Marx generator topology.(b) Positive SSMG based on half-bridge structure.(c) Positive SSMG with diodes and inductors in charging loops.(d) Positive SSMG with inductor protection structure.

Figure 2 .
Figure 2. The structure of the diode protection SSMG and its operating principle.(a) Charge (truncation phase).(b) Discharge phase.(c) Partial short-circuit (charge phase).

Figure 2 .
Figure 2. The structure of the diode protection SSMG and its operating principle.(a) Charge phase (truncation phase).(b) Discharge phase.(c) Partial short-circuit (charge phase).

Figure 3 .
Figure 3. Through current loop in three basic power cells using half-bridge SSMG (a), inductor protection SSMG (b) and diode protection SSMG (c) when charging and discharge switches are on simultaneously.

Figure 3 .
Figure 3. Through current loop in three basic power cells using half-bridge SSMG (a), inductor protection SSMG (b) and diode protection SSMG (c) when charging and discharge switches are on simultaneously.

Electronics 2024 , 1 Figure 3 .
Figure 3. Through current loop in three basic power cells using half-bridge SSMG (a), inducto protection SSMG (b) and diode protection SSMG (c) when charging and discharge switches are o simultaneously.

Figure 4 .
Figure 4. Two possible faults that might occur in proposed SSMG.(a) Possible through current including Ds0.(b) Possible overvoltage over Ds1 and Sc1.

Figure 4 .
Figure 4. Two possible faults that might occur in proposed SSMG.(a) Possible through current loop including D s0 .(b) Possible overvoltage over D s1 and S c1 .

Figure 5
Figure5shows the parameters and locations that were measured in the sim and in the following experiments.Vc refers to the capacitor voltage of the front the breakdown stage.Vsd is the drain-source voltage of the discharge switches.V drain-source voltage of the charging switch.Vp is the voltage across the pr inductors or diodes, while in the half-bridge SSMG Vp is zero.Icell refers to the current of the power cell measured through Sc2, and Vout refers to the output vo pulse over the load.

Figure 5 .
Figure 5. Schematic diagram of the local short-circuit and the location of the physical q under test.

Figure 5 .
Figure 5. Schematic diagram of the local short-circuit and the location of the physical quantities under test.

Figure 8 .
Figure 8. Experimental waveforms of Icell, Vout, and Vc in the normal or fault stage in different circuits.(a) Normal operation of half-bridge SSMG.(b) Fault stage of half-bridge SSMG.(c) Fault stage of inductor protection SSMG.(d) Fault stage of diode protection SSMG.

Figure 8 .
Figure 8. Experimental waveforms of I cell , V out , and V c in the normal or fault stage in different circuits.(a) Normal operation of half-bridge SSMG.(b) Fault stage of half-bridge SSMG.(c) Fault stage of inductor protection SSMG.(d) Fault stage of diode protection SSMG.

Figure 9 .
Figure 9. Experimental waveforms of Vsd and Vp in the fault stage in different circuits.(a) Inductor protection SSMG.(b) Diode protection SSMG.

Table 3 .
Specifications of the Simulated SSMG.

Table 3 .
Specifications of the Simulated SSMG.

Table 4 .
Specifications of the developed SSMG.

Table 4 .
Specifications of the developed SSMG.