Gate Drive Power Supply for On-board Marx
Circuit Using only Charging Path of Marx Capacitor
Keisuke Kusaka
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japan
kusaka@vos.nagaokaut.ac.jp

Yosuke Ouchi
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japanyosuke0113@stn.nagaokaut.ac.jp

Jun-ichi Itoh
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

Abstract— This paper proposes a gate drive power supply
method for a Marx circuit with high-voltage output. The
conventional gate drive power supply method has a
disadvantage that the gate drive requires expensive and huge
DC-DC converters to secure the insulation distance because of
the high-voltage operation of the Marx circuit. In this paper, thegate drive power is supplied through a transformer inserted into
the charging path of the Marx capacitor in order to overcome
these problems. The inserted transformer also plays a role in
suppressing the rush current during the charging operation of
the Marx circuit. The proposed power supply method reduces
the gate circuit volume and improves efficiency. In this paper,
the parameter design for obtaining the desired gate drive poweris explained. Then, it is verified that a driving power of 1 W ormore is obtained by simulation and prototype. The charging
current flowing during charging is suppressed by 75%, and theloss during charging was reduced.

on-resistance of the power devices. Therefore, the powerdevice may be damaged due to an excessive rush current. In
particular, improving the efficiency of the Marx circuit byusing SiC or GaN devices is expected as a recent trend.
However, the reduced on-resistance of the device will increase
the rush current.

Keywords—Marx circuit, Gate drive circuit, Power supply
method,Regarding the gate drive circuit of the Marx circuit, theMarx circuit uses three power devices in each stage. The onboard Marx circuit needs 10 or more stages. All that device
requires expensive and large isolated DC-DC converters.
Therefore, the gate circuit area must be large. In order toreduce the area of the gate drive circuit of the Marx circuit, amethod of transmitting the gate signal and the drive power at
the same time has been studied [12-13]. The system is useful
because the signals of the Marx circuit are synchronized.
However, since power is supplied to multiple devices, there
are concerns about power imbalance. In [14-15], a method has
been proposed in which gate drive power is supplied from themain circuit using a transformer. The use of this method in the
Marx circuit has the effect of suppressing the rush current.
Therefore, The gate circuit is miniaturized.[16-18]

I.

INTRODUCTION

In recent years, regulations on NOx gas emissions havebeen tightened in each country to prevent global warming. The
popularization of EVs, which has no emission of NOx gas, is
one of the solutions against global warming. However,vehicles with gasoline or diesel engines are still mainstream
since the energy density of batteries is lower than fossil fuels.
For gasoline or diesel engines, NOx emission reduction isessential to comply with the regulations. In order to reduce theNOx emission, a catalyst has been used. However, it will not
be enough to comply with the regulations, which will become
stricter in the future.
The Marx circuit, as a pulse power source, has been widely
studied for medical purposes, sterilization, and NOx reduction
applications [1-15]. The plasma generated by the Marx circuit
produces ozone. The NOx gas emission is suppressed byreacting the ozone generated by the Marx circuit with the NOxgas. For automotive applications, the Marx circuit should be
mounted on the vehicle.
This paper focuses on a pulse power supply for an exhaustgas treatment system for vehicles with a diesel engine. As
requirements for ozonizers, lighter weight, smaller size, andhigher efficiency are required. However, rush current occurs
during charging. The heat occurs by the rush current prevents
miniaturization. [2]. The rush current occurs in the circuit
when the capacitor in the Marx circuit discharges andrecharges. The equivalent circuit of the Marx circuit during
the charging operation is a series circuit of the input power
supply, the capacitors connected in multiple stages, and the

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

There are some literatures that employs a current source as
the input power supply for a Marx circuit to suppress rushcurrent or adding resistance and inductance to the path [3-11].
However, the rush current occurs in the circuit due to thevoltage fluctuation of the capacitors on each stage. The
additional components must increase the volume of the Marx
circuit. However, rush current occurs between each stage due
to variations in the capacitor capacitance of each stage.
Therefore, the suppression of rush current is not sufficient in[3-11].

In this paper, the circuit configuration for the power supplyof the gate driver using the transformer in the charging path of
the Marx circuit is proposed. The rush current is suppressedby the proposed power supply method. Since the current
flowing through the inserted transformer is used to supply
power to the gate drive unit (GDU), the number of isolated
DC-DC converters for gate drivers is reduced. This featurescontribute to miniaturize the Marx circuit. Further, it ispossible to suppress the rush current between the capacitors
connected in multiple stages, which is a problem in the Marx
circuit.
II.

GATE DRIVE POWER SUPPLY FOR MARXCIRCUIT

A. Circuit Configuration
Figure 1 shows the operation of the Marx circuit with atransformer for an auxiliary power supply and the Marx circuit.

The first stage of the Marx circuit has switches S1, S2, and S6,and C1 Marx capacitors. Supplied power circuit shows theconfiguration of the GDU in the proposed power supply
method in fig .2. The Marx circuit is a stack of stages with thesame structure. In this paper, the two-stage Marx circuit isexplained for simplicity, however, the proposed power supply
method will be applied to also a Marx circuit with a higher
number of stages. The auxiliary power supply supplies power
to the gate drive circuit. The two modes of the Marx circuit:
discharging mode and charging mode, are explained. In the
discharging mode, the switches S2 and S4 are turns on. Then,
Marx capacitors are connected in series, and a high voltage
with high dv/dt is applied to the load. During the charging
mode, the switches S1, S3, S5, and S6 turns on. The Marx
capacitors are connected in parallel, and the Marx capacitors
are charged. In order to obtain high dv/dt, the Marx circuit
should not have an inductance in the discharging path.
However, in order to suppress the rush current, inductance isnecessary for the charging path. The proposed power supply
method has a transformer inserted into the charging path, so it
does not affect the discharging operation. During the charging
mode, the current flows through the inserted primary coil. A
magnetic flux is generated by the current flowing on the
primary coil, and the magnetic flux is coupled to the secondary
coil to supply power.
Figure 2 shows an equivalent circuit of the Marx circuitand the gate drive supply during the charging operation. In thispaper, analysis and simulation are performed using the circuit
shown in Fig. 2. The equivalent circuit consists of a T-type
equivalent circuit of the transformer, a rectifier, and a Marx
capacitor C1. The resistance R is the sum of the on-resistanceof the MOSFETs and the wiring resistance of the charging
current path. In this study, the gate drive voltage is constant at
16 V. The analysis is performed by assuming the output
voltage of the rectifier is constant for simplicity. The Marx
capacitor C1 is discharged from the input voltage during thedischarge operation (t < 0). The transformer is designed byassuming that the voltage of the Marx capacitors drops by V
due to the discharging operation. At t = 0, the charging
operation starts by turning on the switch. The current flows
through the primary winding of the transformer and the Marx
capacitor. During the charging operation, the secondary
current flows into the rectifier.
B. Transformer design
In this section, the transformer of the proposed power
supply method is designed. First, the power applied to thesecondary side is expressed as (1).

Pout  f swVout  i2(t ) dt

(1),
Where Pout is the supplied gate drive power, Vout is gate drive
voltage of secondary side, fsw is the switching frequency of theMarx circuit, and i2(t) is the current on the secondary side. The
discharge operation causes the voltage drop on the Marx
capacitor C1. In the charging operation, current flows in order
to compensate for the voltage drop from the input power
supply. Then, a current flow on the secondary side of thetransformer. A GDU is connected to the secondary side of thetransformer and clamped by the gate drive voltage. Therefore,
the electric power obtained by one charging operation is the
product of the gate drive voltage and the integrated value ofthe current flowing through the secondary side of thetransformer. This operation occurs in every discharge cycle.

16V GDU

Cout

N2

VGS

N1
Connect to 

supplied power circuit

S3

Charging path

Duscharging path

C2
S1

C1

S4

S2

S 5 LOAD



S6



V in

Fig. 1. Two stage Marx circuit and places to insert atransformer for obtaining gate drive power.

t 0

L1leakVin  1000V

L2leak i2( t )

Vout  16V

LM

GDU

R
V0  970V

C1

Fig. 2. Equivalent circuit during charging operation.

The switching frequency and the gate voltage are arbitrarily
determined. The current flowing on the secondary side i2(t) is
given by the circuit equation expressed as (2),k Vin  kVout  V0   2R t
 R 
1
kVout
i2(t ) 
e
sin

t
 t
2

C
2

L


1
1leak  LM RC1  2 
2

(2),
(3)
  (L1leak  LM  kLM )where Vin is the input voltage, C1 is the Marx capacitor, V0 is
the initial voltage of the Marx capacitor, R is the resistancecomponent including wiring resistance and on-resistance of
MOSFETs, k is the coupling coefficient of the transformer,
L1leak is the primary leakage inductance, and Vout is the DC
voltage of the gate driver.
Figure 3 shows the waveform of the current flowing on thesecondary side of the transformer of (2) in the red line. Also,
the simplified current waveform shown in (4) is shown by ablack line. The integral value of the current flowing on thesecondary side of the transformer shown in the (1) isapproximated to a triangle and shown in Fig. 3.
i2( t ) k Vin  kVout  V0 
L1leak  LM  kLM  R 
 
C1
2

2

sin

1
( L1leak  LM  kLM )C1

t

(4).

Note that the time t1 and t2 are approximately calculated
where the vibration term in (3) is zero and one. Therefore, it
is expressed as shown below.
t1  ( L1leak  LM  kLM )C1 (5)( L1leak  LM  kLM )C1 

t2 

(6)

2

imax 

k Vin  kVout  V0 
L1leak  LM  kLM  R 
 
C1
2

2

(7)
According to the above equations, the primary and thesecondary inductance should be designed with
L

2

C1RP
2
2

(1  k ) 4 P  C1 f swVout k Vin  kVout  V0  





2



(8).

Note that there is an error in the output power due to theapproximation, as shown in Fig. 3. Therefore, it is necessary
to design the inductance with a margin, and it is necessary toincrease the inductance in order to obtain higher power.
Finally, the voltage drop of the Marx capacitor in one
discharging operation is described. The energy consumed by
the Marx capacitor in one discharge operation is expressed as(9).

Current waveforms flowing
to the secondary side

Equation (2) is simplified as (3) due to the transformer
design. For simplicity, the on-resistance of the MOSFETs are
ignored. When the on-resistance is small enough to beignored, the damping by the exponential function is ignored.
The same applies to the part containing the on-resistance ofthe sine function term. Terms containing the on-resistance ofthe sine function is ignored. The third term of (1) is also
ignored because the time interval of the current flowing during
the charging period is much smaller than the first term. The
integrated value of the current of (1) is obtained from thesimplified current waveform of (3). At this time, the integrated
value is calculated as the area of the triangle in Fig. 3.

6

imax

Theoretical current waveform
Approximate current waveform

4Integral value of current used in design

2
0

t2

0

1

t1

2

3

Time [s]Fig. 3. Waveform approximating the current flowing in thesecondary transformer.
Table. 1 Simulation conditions.
Variableparameter

Value

Input voltage

1000 V

Marx capacitor voltage

960 V

Marx capacitor capacity

0.22 µF

Gate drive voltage

16 V

Primary inductanceof transformer

10.5 µH

Secondary inductanceof transformer

10. 5 µH

Coupling coefficient

0.95

ON resistance

0.2 W

Wiring inductance

100 nH

III. EXPERIMENTAL VERIFICATION
A. Suppression of rush current
In this section, the validity of simulations, theoreticalformulas, and approximated formulas are verified using a
prototype. First, the effect of suppressing the rush current isevaluated.

(9),

Figure 4 shows the prototype. Fig. 4(b) is the transformer
for the gate drive power supply. This transformer is connectedto  in Fig. 1 to supply power to the gate circuit. In theexperiment, the resistive load is used.

where Poutmarx is output power of the Marx circuit, Edrop is thepower that the Marx capacitor of each stage is discharged by
one discharge operation, N is the number of stages that makeup the Marx circuit. Therefore, the voltage drop of the Marx
capacitor is expressed by (10).

Table 2 shows the experimental conditions. The input
voltage Vin is 100 V, and the voltage of the C1 capacitor dropsby 30 V during the discharge mode. A primary inductance ofthe transformer must be 10 H or more, according to (7).

P
Edorp  outmarx
Nf sw

1
1
2
CmarxVin2  CmarxVdorop Edrop2
2(10),

Where Vdrop is the voltage of the Marx capacitor in one
discharge operation. Therefore, the voltage after discharge isrepresented as (11),Vdrop  Vin2 

2 Edrop
Cmarx

(11),

Figure 5 shows the effect of suppressing the rush current by
the proposed power supply method. The charging current thatflows in the first stage is indicated. Fig. 5(a) shows the
charging current generated in the Marx circuit without atransformer for an auxiliary power supply in the charging path.
The waveforms are the gate signal of S1 (charging signal ofMarx circuit), charge current, and output voltage from the top.
The charging current reaches to 40 A. When the Marx circuit
consists of N stages, N times larger charging current for thecapacitors on each stage will flow through S1 and S6 at thebottom. The charging current will exceed an absolute
maximum rating of the power devices. The rush current mustbe suppressed for avoiding the circuit from the breakdown.

Load

S1 gate source voltage (charge signal)

Main circuit

16V

0V
Rush current
about 40A

Charging current for one stage

0A
20A/div

GDU unit
DC/DC Converter

4µs/div

100V/div0V(a) Without a transformer
S1 gate source voltage (charge signal)(a) Main Circuit

0A

Secondary Winding

16 V

0V

Primary Winding

310 mm0V

Charging current for one stage

5 A/div

Rush current
about 10 A

10 µs/div

100 V/div(b) 10.5 µH
S1 gate source voltage (charge signal)
250 mm(b) Transformer for auxiliary power supply
Fig. 4. Prototype of Marx circuit and auxiliary power supply.

0V

Table. 2. experimental condition.

0A

Variableparameter

Value

Input voltage

100 V

Marx capacitor voltage

70 V

Marx capacitor capacity

0.22 µF

Gate drive voltage

16 V

Primary inductanceof transformer

10.5 µH,23.7 µH

Secondary inductanceof transformer

10.5 µH,23.7 µH

Coupling coefficient

0.95

ON resistance

0.04 W

Continuous Drain Current

60 A

Drain - Source Voltage

1200 V

Figure 5(b) shows the waveforms when a transformer witha primary inductance of 10.5 µH is inserted into the  shownin Fig. 1. Similarly, Fig. 5(c) shows the waveform when atransformer with a primary inductance of 23.7 µH is used.
Experimental results show that the proposed power supply
method suppresses the peak of the charging current to 10 A
approximately. The charging current is suppressed to 75%
using the proposed power supply method. Note that too muchlarge primary inductance causes a problem in the operation of
the Marx circuit. The charging period becomes longer when a

0V

16 V

Charging current for one stage

5 A/div

Rush current
about 8 A

10 µs/div

100 V/div(c) 23.7 µH
Fig. 5. Suppression effect of charging current by the
proposed circuit.

transformer with a large primary inductance. The Marx
capacitor C1 will not be fully charged during the charging
period. It will affect the discharge operation, so there is alimitation on the primary inductance. In other words, themaximum power obtained from the Marx circuit is limited.
B. Gate drive in the proposed power supply method
Figure 6 shows the operation waveforms of the proposed
power supply method. In the experiment, the two transformers
are tested. The primary inductances are 10.5 µH or 23.7 µH,
the turn ratio is N1 = N2. The waveforms are the gate signal of
S1 (charging signal of Marx circuit), the current through thesecondary side of the transformer, output voltage, and thevoltage of the Marx capacitor of the first stage. The peakcurrent flowing on the secondary side of the transformer isabout 8 A. The convergence time is about 1.6 µs. This isconsistent with the simulation shown in Fig. 3. During thedischarge period, the proposed gate drive power supply does
not affect the operation of the Marx circuit. In the current
waveform of Fig. 6(b), the current peak is 8 A and it takes 2µs to converge. As inductance increases, more power isdelivered since the period of the oscillation term in (4)becomes slower, then the integrated value of the current
increases. Note that the increase in the inductance has alimitation because a long oscillation period causes a problem
that the next discharging operation will start before theprimary current converges to zero. It means that the Marx
circuit shuts the inductor current off at the start of discharging
mode.
Figure 6 (c) shows the experimental waveform when the
proposed circuit is operated in a steady state. The waveforms
are the gate signal of S6, the gate signal of S1, the current
waveform flowing to the secondary side during charging
operation, and the load voltage from the top. The proposed
gate drive system supplies the power to the switch S1. Fromthe experimental results, stable driving power is supplied
during the charging operation.
Figure 7 shows the relationship between the primary
inductance value of the transformer and the output power. In
this graph, the inductance values of the primary side and thesecondary side of the transformer are the same, and the turnratio is N1 = N2. The validity of (8) is shown from the resultsof experiments and theoretical calculation. Fig. 7 shows thatthe supplied power increases as the inductance on the primaryside and the secondary side increases. Moreover, since thepower required for gate drive is about 1 W when the gate
voltage is 16 V, the power required for gate drive is suppliedby the proposed power supply method. However, if the gate
voltage is 20 V, sufficient power cannot be obtained. This is
explained by the decrease in the current peak shown at (7).
Therefore, to obtain more power, it is necessary to increase theoutput of the Marx circuit and reduce the capacitor capacity
and insert a transformer with a large primary inductance value.
Figure 8 shows operation waveforms when the input
voltage Vin is increased from zero to 100 V. The DC voltageof the gate driver of S1 is automatically charged through theproposed system by the switching of low-side switches S2 andS6. It takes 50 ms for the voltage of the gate driver to rise fromzero to 16 V with a smoothing capacitor of the gate driver Coutof 20 F. After 50 ms from the start of the system, theproposed gate circuit operates stably. The starting timedepends on the capacitance of the smoothing capacitor. It
takes 160 ms when the capacitance Cout of the smoothing
capacitor is 320 µF. From Fig. 8, the proposed system does
not need an additional circuit to help the start-up.
From the experimental results, GDU is driven by the
proposed power supply method.
IV.

CONCLUSIONSIn this paper, an auxiliary power supply for the gate driveusing a transformer during the charging operation of the Marx
circuit has been proposed. First, the design of the transformer
inserted into the proposed circuit is described in this paper.
Then, we confirmed the validity of the design method of thesystem through simulations and experiments. The gate drive
power of 1 W or more is supplied using the designed
transformer. Therefore, it is found that the gate drive isperformed without the additional DC-DC converter.
Moreover, the proposed system has an additional role as
suppressing the rush current, which occurs during thecharging operation of the Marx circuit. The proposed system
supplies the power to the gate driver without an effect on the
discharge operation of the Marx circuit. The rush current

generated during the charging operation is suppressed with theproposed Marx circuit. It is confirmed that the rush current issuppressed by 75% as compared with the conventional
configuration without the auxiliary power supply. As futureplans, further suppression of rush current, experiments at ratedload, and volume comparison will be performed.

chargeperiodchargeperioddischarge
period

S1 gate source voltage

16V

0V
5A/div0A

1.6µs
50V/div

Current flowing
to the secondary side i2( t )Vload
100V/div

0V

2µs/div

C1 voltage(a) Operating waveform when a 10.5 µH transformer
is inserted
chargeperiodchargeperioddischarge
period

S1 gate source voltage

16V

0V
5A/div

2µs

0A

Current flowing
to the secondary side i2( t )50V/div

Vload
100V/div

0V

2µs/div

C1 voltage(b) Operating waveform when a 23.7 µH transformer
is inserted
S6 Gate source waveform
S1 Gate source waveform using propse method
16V

0V
0V
0A

i1( t )

15V
10A
15V
200V

Vload

Charging
current

5A

i2( t )
2µs/div

100V

0V

100V/div

100µs/div

load Voltage(c) Gate signal waveform during stable operation and current
waveform flowing on the secondary side of the transformer
Fig. 6. Experimental results in the proposed power
supply method.

[2]

1.5
Power supplied
to the secondary side [W]Experimental result
Theoretical curve

1.0
Simulation

Gate drive power
supplied at 16 V DC

0.5
Gate drive power
supplied at 20 V DC

Theoretical curve

0.0

0

5

10
15
Primary inductance[µH]2025Fig. 7. Relationship between obtained power.
S6 gate source voltage Output 16V
16V

0V

S1 GDU voltage supplied propose method
16V

50 ms

0V

100V

0V
Vin voltage

20ms/div(a)Initial charging operation(b)Stable operating area(a) Cout=20 F
S6 gate source voltage Output 16V
16V

0V

0V

S1 GDU voltage supplied propose method
16V

160 ms100V

0V

Vin voltage

40ms/div(a)Initial charging operation(b)Stable operating area(a) Cout=340 F
Fig. 9. Operation waveform from initial state.

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