Gate Drive Power Supply with Low Insulation
Voltage Transformer for in-vehicle Marx Circuit
Keisuke Kusaka
Dept. of Electrical Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
kusaka@vos.nagaokaut.ac.jp

Yosuke Ouchi
Dept. of Electrical Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japans195026@stn.nagaokaut.ac.jp

Abstract—This paper proposes a gate drive circuit with a
low-insulation voltage transformer for an in-vehicle Marx
circuit. The Marx circuit will be used for NOx gas
decomposition for diesel vehicles as a part of an ozonizer. In
order to make the Marx circuit on board, it is necessary to
reduce the size and cost of the circuit, including the gate drive
circuits. One of the bottlenecks for lowering the cost and size ofthe gate drive circuit is the insulation transformers on the gate
drive circuits because the potential of each switch of the Marx
circuit dynamically changes from zero to the output voltage ofthe Marx circuit. This paper proposes and demonstrates thegate drive circuit, which receives the drive power for the
MOSFET on the n-th stage from (n – 1)-th stage through a lowvoltage transformer. Due to the configuration, the required
insulation voltage of the transformer is equal to the input
voltage. In this paper, the design procedure of the transformer
with an approximated current is described. The proposed gate
drive circuit is developed and implemented to the 4-kV Marx
circuit.
Keywords—Gate drive, Marx circuit, Insulation

I. INTRODUCTION
In recent years, reducing nitrogen oxide (NOx) gas inexhaust gas from diesel vehicles has been a critical issue tocurb global warming. Thus, the regulation of NOx gas inexhaust gas has been tightened globally. A lean NOx trap
catalyst (LNT catalyst) has been used [1–2]. The LNT catalyst
adsorbs NOx gas; however, the adsorb efficiency is degradedwhen the exhaust gas temperature is low. In order to improve
the adsorb efficiency, in-vehicle use of an ozonizer is being
considered [3–4]. The ozonizer produces ozone and adds tothe exhaust gas to reform NO into NO2. The NO2 is absorbedby the LNT catalyst with high efficiency.
The ozonizer needs a pulse power supply, such as thesolid-stage Marx circuit [5–7]. Especially, silicon carbide(SiC) MOSFETs have been used in the Marx circuit with theprogress of SiC semiconductor technology in recent years
instead of conventional silicon (Si) MOSFETs [8–10]. SiC
MOSFETs provide a fast switching with high-drain-source
voltage, such as 1.2 or 1.7 kV [11]. The fast switching
improves the production performance of the ozone.
There is a strong demand for price and volume reduction
for onboard circuits [12]. However, the Marx circuit with
MOSFETs has a bottleneck on the gate drive circuits for
reducing the volume and cost. The n-stage Marx circuit needs
2n switches and gate drive circuits. Each gate drive circuits

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

require an isolated power supply with high-withstand voltage
because the potential of MOSFETs is dynamically changed
due to the operation of the Marx circuit. The typical withstandvoltage of isolated power supplies on the market for gate driveis less than 5 kV. Thus, a custom-built isolated DC/DC
converter is required.
In order to overcome the problem mentioned above, thegate drive power supply combined with the Marx circuit is
proposed. In the proposed gate drive power supply, the drive
power for n-stage MOSFET is supplied from the (n - 1)-thstage through the low-voltage transformer, which is inserted
into the charging path of the Marx circuit [13–14]. It
contributes to reducing the cost and size of the transformer.
Besides, the inserted transformers are a help to reduce the peakof the charging current of the Marx circuit.
II. PROPOSED GATE DRIVE POWER SUPPLY
A. Marx Circuit
Figure 1 shows the Marx circuit with the proposed gate
drive power supply [12]. The Marx circuit outputs highvoltage by changing the connection of the Marx capacitor Cn.
When the switches Scn turn on, the Marx capacitors areconnected in parallel. The Marx capacitors are charged
through the diodes Dn. Each Marx capacitor is charged to the
input voltage by ignoring the forward voltage drop of thediodes. In contrast, the Marx capacitors are connected in series
when the switches SDn turn on. Because the Marx capacitors
are charged to the input voltage during the previous charging
operation, the output voltage is n times of the input voltage Vin
ideally.
Each stage of the Marx circuit has two MOSFETs and adiode. The gate drive circuit is connected to each MOSFET todrive the device. The gate drive circuit for the n-stage are
driven with the power supplied from the (n - 1) stage throughthe additional transformers Trn. The detail of the power supply
is explained in the next section.
B. Operation Principle of Gate Drive Power Supply
Figure 2 shows the proposed gate drive power supply. The
thick wire is the main circuit of the Marx circuit. The gate
drive power for SCn is supplied from the transformer Tr(n-1).
The primary side of the transformer is connected on the
charging path on the Marx circuit. During the charging path,the charging current of the Marx capacitor flows on the
primary winding. On the secondary side of the transformer,

Stage nStage (n-1)

TABLE I.

REQUIREMENTS FOR ISOLATION TRANSFORMER.
Conventional

Proposed

Maximum
primary voltage

Arbitrary

Vin – Vcj(0)Secondary voltage

Vgs

Vgs

Insulation voltage

jVin

Vin

Dn-1
Stage 1

Cn-1

Trn-1

Gate
driverVout

SD(n-1)C1
Gate
driver

Vc1
Drive
power

Power
SupplySC(n-1)Gate
driver

SD1

Vin

Load

D1

Vc(n-1)

Tr1

SC1

Gate
driverGate driver for SDn
SDn

Trn

CBn

Vg sDnGate driver for SCn
SCn
16V

Tr(n-1)

j denotes the jth stage in the Marx circuit with n stages.

gate-source voltage VDS. In the conventional system, thetransformer must ensure the high-voltage insulation jVinbecause the auxiliary power supply is grounded. Note that, jnotes the jth stage in the n stages Marx circuit.
In contrast, the difference between the input voltage Vin
and the Marx capacitor voltage Vcj(0) is applied on the primaryside of the proposed topology at the start of the charging
operation. Note that the Marx capacitor voltage is discharged
and maintained at a lower voltage than input voltage in theprevious discharging operation. The required insulation
voltage of the transformer is as same as the input voltage
because the voltage difference between the primary andsecondary sides is the Marx capacitor voltage at the maximum.

Fig. 1. Marx circuit and proposed gate drive supply.

Bootstrap diode

a.

VgsCn

Main circuit side
Fig. 2. Proposed Gate drive supply.

the voltage is induced. The induced voltage is supplied to thegate drive circuit for SCn through the full-bridge rectifier. Notethat the Zener diode is connected to clamp the gate drive
voltage at 16 V. The switch SCn turns on or off with the
supplied power. For the gate drive circuit of SDn, the bootstrap
circuit is used [15–17]. The DC line of the gate drive circuit
for SCn is connected to the gate drive circuit for SDn via thebootstrap diode. When the switch SCn turns on, the current
charges the bootstrap capacitor CBn through the bootstrap
diode, transformer Trn, and Scn. The reverse blocking voltageof the bootstrap diodes must be higher than the input voltageof the Marx circuit.
The required insulation voltage of the proposed topology
is as same as the input voltage. Thus the volume of theisolation transformer is reduced.
III. DESIGN OF ISOLATION TRANSFORMERIn this chapter, the design method of the insulationtransformer is discussed. Table I shows the requirements forthe insulation transformers for the conventional and the
proposed gate drive supply. The conventional gate drive
supply needs the transformer to supply the power from an
auxiliary power supply to the gate driver. The primary voltage
is arbitrary because it depends on the voltage of the auxiliary
power supply. The secondary voltage should be equal to the

A. Modeling of Secondary Current
In this section, the current on the transformer is analyzed
to design the transformer.
Figure 3 shows the simplified equivalent circuit at the
charging operation. The charging current must be modeled forthe transformer design because the supplied voltage on thesecondary side depends on the primary current. Moreover, theadded primary inductance also affects the charging operation.
First, the charging current i1 and i2 are calculated. From Fig. 3,
equations (1) is developed assuming the DC capacitors of therectifier is large enough to maintain the voltage VD, where Vin
is the input voltage of the Marx circuit, L1 is the primary selfinductance, L2 is the secondary self-inductance, L1leak and L2leak
are the leakage inductance of the transformer, LM is the mutual
inductance, R is the parasitic resistance of the Marx capacitor
and switches, and Cn is the Marx capacitor.
d ( i1 − i2 ) 1
di1
+ LM
+
i1dt + Ri1
Vin − VCn( 0) = L1
dt
dt
Cn 


d ( i2 − i1 )di
+ L2 2
VD = LMdtdt
 LM = k L1 L2()

The Marx capacitor voltage is charged because the Marx
capacitor was discharged to VCn(0) due to the previous
discharging operation. At t = 0, the switch turns on. Then the
charging operation starts.
The secondary current i2(t) is developed from (1).

(k Vin − kVD − VCn ( 0)



R
−
Cn  2 

2

)e

−

R
t
2

2

sin

 R 
1
kVD
−
t
 t−
 Cn  2 
L1leak + LM ()1.5

Supplied power
to the secondary side W

i2(t ) =Theoretical curve

1.0

where  = (L1leak + LM – kLM).
B. Design of Inductance for Transformer
From (2), the inductance to supply the required gate drive
power is calculated. In order to analytically solve theequation, (2) is approximated, asi2(t ) (k Vin − kVD − VCn ( 0)



R
− 
Cn  2 

2

)e

−

R
t
2

sin

1

 Cn

Simulation

0.5

0.0 0

Experimental result

5

10
15
Primary inductance µH

2520Fig. 4. Self-inductance and supplied power.

t()k (Vin − kVD − VCn (0) )( L1leak + LM − kLM )Cn 

with the assumption that the voltage drop on the on-resistanceof the MOSFETs is zero, and the second term in (2) can beignored because the first term is dominant in several
microseconds during the transient response.

Pout = f swVout

Figure 3 shows the calculation of the secondary current i2(t)expressed as (2) and (3). By the approximation, the time toreach the maximum current t2 and the time to reach the zero t1
is easily calculated with low error.

where Pout is the output power of the gate drive power supply.

t1  ( L1leak + LM − kLM )Cn 

L1 =

t2 

imax 

()( L1leak + LM − kLM )Cn 2()k (Vin − kVD − VCn (0) )L1leak + LM − kLM  R 
− 
Cn
2

2

()

Current waveforms on thesecondary windings [A]Using the approximated time t1 and t2 and peak current, thesupplied power highlighted in Fig. 3 is calculated as

6

Theoretical current waveformby Eq. (2)Approximated current waveformby Eq. (3)Integral value of current used in design

imax

4
2
0

0

t2

1

t1
Time [ms]2

Fig. 3. Marx circuit with proposed gate drive power supply.

3

L1leak + LM − kLM  R 
− 
Cn
2

2

()

Thus, the required self-inductance for the transformer isexpressed asCn RPGD 222(1 − k 2 )  4 PGD− Cn f swVD k (Vin − kVD − VCn (0) ) 



()

where PGD is the power consumption of two gate drive circuits.
C. Drive power and inductance
Figure 4 shows the relation between the supplied drive
power and the self-inductance of the transformer. The solidline is the theoretical curve calculated from (2) by a numericalanalysis. The triangles represent the calculated power by thecircuit simulation. The circle represents the experimental
results. The experimental results show good agreement withthe simulation and the theoretical curve. It implies that theeffect of the approximation on (2) is small enough to beignored.
IV. EXPERIMENTAL VERIFICATIONThe Marx circuit with the proposed gate drive power
supply is demonstrated in this chapter. Table II shows the
specifications of the prototype. The input voltage is derated
from 1 kV to 600 V due to the limitation of the power supply
in the Lab. Moreover, the number of the stage is seven.
Figure 5 shows the prototype of the Marx circuit with theproposed power supply. Fig. 4 (a) is the Marx circuit and thecapacitor load. Fig. 4 (b) is the isolation transformer for thegate drive power supply. The primary and the secondary
windings are placed with a gap of 10 mm for insulation. The
isolation transformer for the Marx circuit can be downsized
because the required isolation voltage is as same as the input
voltage. Note that the capacitor load is used as the load insteadof an ozonizer.
Figure 6 shows the output voltage of the Marx circuit. The
output voltage of 4 kV is obtained. Fig. 5 (a) and (b) showsthe expanded waveforms focusing on the positive edge and theTABLE II.

negative edge, respectively. The rise time and fall time of theoutput voltage is less than 100 ns.

SPECIFICATIONS.

Parameters

Symbols

Value

Input voltage

Vin

600 V

GDU voltage

VD

16 V

Marx capacitorCn0.22 µF

Switching frequency

fout

10 kHzon-resistance of MOSFETs

R

0.5 W

Coupling coefficient

k

0.95

Primary leakage inductance

Lleak1(1-k)L1

Secondary leakage inductance

Lleak2(1-k)L1

Primary inductor

L1

Magnetic core for trans.

Charging period

Discharging periodn

MOSFETs
Cout

10.5 µH

4 kV

7
6 µs
C3M0065100J (CREE)

1kV/div

02 µs/div

500 pF(a) Charging and Discharging opoerations.

Charging period

Main circuit

Charging period

Output voltage

PC44 (TDK)

Number of stage
Discharging time
Load

Figure 7 shows the switching waveforms from thedischarging operation and the charging operation. At the
charging operation, the secondary current flows on thetransformer and the diode bridge rectifier. The gate drive

Discharging period

Gate drive power
supplyOutput voltage

4 kV

0

400 ns/div(b) Positive edge.

Capacitor load(a) Marx circuit and capacitor load.

Discharging period

Charging period

4 kV

Output voltage

1 kV/div0

Primary Winding

400 ns/div(c) Negative edge.
Fig. 5. Output voltage of the Marx circuit.

Discharging period

10 mm

Charging period

31 mm
15V

Secondary Winding

0

250 mm(b) Insulation transformer for gate drive power supply
Fig. 7. Prototype of the Marx circuit with proposed gate drive power
supply.

Gate-source voltage VgsC2
Secondary current -i2

00

5 A/div
1kV/div

Output voltage
1 µs/div

Fig. 6. Power supply to the gate drive circuit during charging operation.

power for MOSFETs is supplied through the proposed
isolation system with a low-voltage transformer.
V. CONCLUSION
A gate drive circuit with a low-voltage transformer for an
in-vehicle Marx circuit is proposed in this paper. The
downsizing and cost reduction are required to mount the Marx
circuit on board. One of the bottlenecks of the cost reductionis the gate drive power supply because high-voltage isolationis required due to the operation of the Marx circuit. In order toreduce the cost and size of the isolation transformer, a newgate drive power supply is proposed. The gate drive power for
MOSFETs on the n-th stage is supplied from (n – 1)-th stage
via the low-voltage transformer. The proposed topology isdemonstrated with the prototype with the Marx circuit with an
output voltage of 4 kV. The output voltage of 4 kV is obtained.
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