S2PC 2019, Tokyo, Japan

Auxiliary Power Supply for Marx Circuitwith Transformers inserted into Charging Path of Marx Capacitors
Yosuke Ouchi1, Jun-ichi Itoh1, Keisuke Kusaka1
1

Nagaoka University of Technology

In this paper, an auxiliary power supply using its switching operation for gate drivers of a Marx circuit is proposed. The Marx circuit issuitable topology to supply high voltage DC with high dv / dt because of the connection of multi-stage capacitors and power devices. Thepower devices used in the Marx circuit has high voltage potential to the ground dues to the series connection of multi-stage capacitors. Thus,
the conventional gate drive power supply, which supplies power from the low-voltage side, requires large isolation distance, which typically
prevents downsizing. In this paper, an auxiliary power supply for the gate drive circuit using a transformer inserted into the Marx circuit isproposed in order to solve above problem. In a simulation executing on a system with an input voltage of 1 kV and an output power of 500
W, it is demonstrated that a drive power of 1 W or more is supplied through a transformer with a primary value of 10 µH.
Keywords Marx circuit, Pulsed power supply, gate drive, Power supplies

1. Introduction
In recent years, the Marx circuit has been studied for a power
supply of an ozonizer [1] because the ozonizer requires a pulsed
power supply with high dv / dt. The Marx circuit is suitable
topology as a pulse power supply because of its simple
configuration. However, since the power devices and the capacitor
are in a cascade configuration, the switching devices on each cell
have high voltage potential. Thus, the gate drive circuits have to bebulky due to the isolation distance between the low-voltage side andthe high-voltage side [2,3]. Moreover, the high-voltage isolated
DC-DC converter may increase the cost of the gate drivers. In thispaper, a new topology of supplying gate drive power using acharging operation of the Marx circuit through a transformer
inserted into a charging path of capacitors is proposed.

2.

Marx circuit and Gate drive power bytransformer

Figure 1 shows the operation of a two-stage Marx circuit with atransformer for auxiliary power and the Marx circuit. Note that theactual circuit is composed by many number of stages. however, thiscircuit is used for explanation simply. The auxiliary power supply
supplies power to the gate drive circuit. During the discharging
mode, S2 and S4 are turned-on, the Marx capacitors are connected
in series, and a high voltage is output to the load with high dv / dt.
In the charging mode, switches S1, S3, S5, and S6 are turned-on, theMarx capacitors are connected in parallel, and the capacitors arecharged. In order to obtain high dv / dt, the Marx circuit should nothave an inductance in the discharging path. therefore, thetransformers are inserted into the A or B. The transformers of theproposed auxiliary power supply are not inserted into the discharge
path, therefore, the proposed auxiliary power supply does not affectthe discharging operation of the Marx circuit. In the charge mode,the current flows through the inserted primary coil. A magnetic flux
Correspondence to: Jun-ichi Itoh. E-mail: itoh@vos.nagaokaut.ac.jp,
Nagaoka University of Technology.
1603-1, Kamitomioka-machi, Nagaoka, Niigata, Japan, 940-2188
Japan.

is generated by the current flowing on the primary coil, and themagnetic flux is coupled to the secondary coil to supply power. Thepower supplied by the transformer is verified by calculation andsimulation. Since the current flowing in the place where thetransformer is inserted does not change between A and B, the same
analysis is performed.

3.

Analysis of Supplied Power

Figure 2 shows the equivalent circuit during charging operation
including the transformer. When the time is 0 s, current flows inleakage inductance and mutual inductance. The secondary loadvoltage is the sum of the voltage of mutual inductance and theleakage inductance. The power supplied to the load is given by theproduct of the secondary load voltage and the current flowing
through the leakage inductance. However, the solution becomes aquartic equation under conditions where the DC voltage fluctuationon the secondary side of the circuit is large (conditions where smallk  0.95
N2Cout =470μF

N1Connect to A or B
S3
S1A
C 2 =1μF

AS4S2

R out =800Ω

C1  1μF

B

S 5 LOAD

BS6V inFig. 1. Two-stage Marx circuit.

S2PC 2019, Tokyo, Japan

capacitor is connected). Further, the secondary capacitor should beenough large because it must supply stable driving power.
Therefore, the secondary capacitor is approximated as a constantvoltage source for simplicity. The current flowing to the leakage
inductance side is represented as:

R2
 wiring tVin  V02 sinh  Rwiring   1 t  kV t ,keouti 1(t )Rwiring 2  2   C1() 2
C1t 0L1leak

L2leak i1( t )i2( t )

C1V0

di1(t )
1i 2(t )  L  L2leak dt  Vout dt .

(3)

mIf the sum of the secondary leakage inductance voltage and themutual inductance voltage is lower than the load, current does notflow through the load, so current flows through the mutual
inductance regardless of the load. When the sum of the voltage ofthe secondary side leakage inductance and the voltage of the mutual
inductance is lower than the load, the current flowing through themutual inductance is expressed byVin  V0e
Rwiring 2()C12Calculation
Simulation

200123Time [μs]Fig. 3 Current flowing in leakage inductance i1(t).
65Calculation

4Simulation

3210-1010-220304050

Time [μs]Fig. 4. Current flowing in mutual inductance i2(t).
2 Rwiring 1sin
 t .(4) C1  2 

Each voltage on the circuit is obtained by differentiating (1), (3)and (4).

4.

4Analysis of Supplied PowerThe assumed application is a 10-stage Marx circuit with an input
voltage of 1 kV and an output power of 500 W. Furthermore, thefrequency is 10 kHz. Therefore, the primary capacitor voltage dropsby 30 V from the input voltage in a single discharge operation.
Figure 3 shows the waveform of the current that flows to thesecondary leakage inductance by the calculation represented by i1(t)and simulation. Figure 4 shows the waveform of the current thatflows to the mutual inductance by the calculation and simulation
expressed by i2(t). Since the calculation results matched thesimulation, the current flowing in the Marx circuit with thetransformer that supplies the auxiliary power could be generalized.
Figure 5 shows the relationship between primary inductance andsupplied power to the gate driver. In order to supply the minimum
power required to drive the gate through simulation and calculation,
there is a use where the primary inductance value is 10 µH or more.

Power supplied to the secondary side [W]i2( t ) R
 wiring t2

current on leakage inductance i1( t ) [A]

where k is the coupling coefficient, V0 is the initial charging voltageof C1, Rwiring is the wiring resistance, Vout is the load-side voltage αis the sum of the primary and secondary leakage inductances, and β
is the sum of primary or secondary leakage inductance and mutualinductance. the current flowing to the mutual inductance side isrepresented by (2–4). The reason why there are two expressions
relating to the current flowing through the mutual inductance will
be described. A current flow to the leakage inductance side when
the sum of the voltages of the mutual inductance and the leakage
inductance on the secondary side is higher than the DC voltage on
the load side. The voltage of the mutual inductance when the current
is flowing to the leakage inductance side is given by

Fig.2. Equivalent circuit for Marx circuit charging operation includingtransformer for auxiliary power supply.

current on mutual inductance i2( t ) [A](2)

RLoadRwiring(1)  ( L1leak  L2leak ),   ( L1leak  LM )  ( L2leak  LM ) ,VoutLMVin

1.5
Gate drive power
supplied at 15V DC

1.0
Gate drive power
supplied at 20V DC

0.5

0.0036912Primary inductance[µH]1518Fig. 5 Relationship between power and inductance.

References[1] S. Dong et al: IEEE Trans., vol. 44, no. 12, pp. 3353-3360, Dec. 2016[2] Zhou, et al: IEEE Trans., vol. 44, no. 11, pp. 2779-2784, Nov. 2016.
[3] J.itoh,T.kinomae:”Experimental Verification of a one-turn Transformer Power
Supply Current for Gate Drive Unit”,EPE-PEMC,No.T9,pp59-65(2010)