Frequency Multiplying Circuit Constructed from a
Multi-phase Inverter and Multi-core Transformers
Jun-ichi Itoh

Yusuke Fujita

Hideto Nishiyama

Member, IEEE
Nagaoka University of Technology
1603-1 Kamitomioka-cho Nagaoka
itho@vos.nagaokaut.ac.jp

Student Member, IEEE
Nagaoka University of Technology
1603-1 Kamitomioka-cho Nagaoka
fujita_y@stn.nagaokaut.ac.jp

Member, IEEE
Nagaoka University of Technology
1603-1 Kamitomioka-cho Nagaoka
west@stn.nagaokaut.ac.jp

Abstract— This paper discusses a frequency multiplying circuit,which consists of a multi-phase voltage-source inverter andmultiple toroidal core. The principle of the frequency multiplying
is to utilize the neutral point voltage fluctuation of the load. A
multi-core transformer is used to obtain the voltage fluctuation.
This paper discusses the design of the circuit, transformer andloss analysis of the proposed circuit. Besides, this paper clarifies
the validity of the proposed converter in terms of simulation andexperimental results.
Keywords-high-frequency power supply, neutral voltage
fluctuation, toroidal core, multiple core transformer, leakage
inductanceI.

INTRODUCTION

Recently, wireless power transmission systems are
increasingly received attentions for the application of EV
chargers [1]. There are two types of wireless powertransmission systems; the first is magnetic coupling with amagnetic core, and the second is magnetic resonance coupling
method with high frequency antenna [2-5]. The wireless powertransmission using magnetic resonance coupling is moresuitable for the EV charger in terms of the accepting wide gap
and large position error between primary coil and secondary
coil. However, the magnetic resonance coupling system
requires high frequency power supply in order to reduce size
and achieve light weight. Industry-Science-Medical (ISM)
frequency band is one of candidate for this application in
respecting to the standard of the magnetic coupling. Therefore,
13.56 MHz and several kW power supply are required for the
EV charger.
It is very difficult to realize a high frequency and highpower supply in several kW and 13.56MHz [6]. Conventional
high-frequency power supply systems use vacuum tube andhigh frequency FET, which is categorized in class C linear
amplifier. The disadvantage of this method is low efficiency.
Furthermore, the size of the systems is large because heat sinkis large.
Follow the recent technology in semiconductors device,large capacity and low loss are enabled in IGBT and MOSFET
for power conversion, especially in the implementation of highfrequency inverter such as induction heating [7-8]. However
there is a limit in high frequency operation. Because switching

speed of each semiconductor device has a limit, especially forthe large capacity application [9].
The authors propose frequency multiplying circuit, which
utilizes the neutral point voltage fluctuation of the multi-phase
inverter. A neutral point voltage of the load in the multi-phase
inverter has fluctuation to the neutral point of the DC input
voltage. The proposed converter connects a multi-coretransformer among the neutral point of the DC input and output
terminals. The proposed method uses a five-phase inverter toconfirm the principle. Then, the output frequency of five timesof the switching frequency is obtained. In this method, the highspeed switching device is not needed because the switchingfrequency for each phase is low.
This paper is organized as follows; firstly, the approach formultiplying operation is introduced. The circuit configuration
is described accordingly. Secondly, the operation principle andenergy losses are analyzed in simulation. In addition, thedesign strategy of the prototype is clarified. Finally, someexperimental results are given in order to demonstrate theadvantages of the proposed circuit.

II.

OPERATION PRINCIPLE

In the proposed method, the variation of neutral point
voltage in a voltage-type inverter is focused. When an inverterwith N phase is driven with square wave operation, the neutral
point voltage of the load is potentially fluctuated based on
neutral point of DC link voltage, which can be obtained from
(1).
vno =

1
∑ vko
N

(1)

Where vko is the output voltage based on neutral point ofeach phase DC link voltage. Then, the neutral point voltage
becomes N times frequency as larger as the switchingfrequency of inverter. The proposed multiplying circuit uses
the spoken principle. In order to pull out the output voltage
with N times frequency, a multi-phase transformer is used. As
shown in (1), the output voltage becomes 1 / N. Therefore, theproposed circuit uses series connection in secondary side of themulti-phase transformer in order to boost the voltage. It is notethat the number of phase N must be an odd number to keep thevoltage fluctuation. If N is an even number, then the voltage
fluctuation of the load is disclaimed.
Figure 1 shows the proposed circuit in a five-phase inverter
model. In the five phase voltage-type inverter, each of thevoltage phases is shifted by 72 degree and operated with squarewave modulation. The primary side of the transformer isconnected in parallel, and the secondary side is connected inseries to increase the output voltage.
Figure 2 shows the principle of the proposed frequency
multiplying method. The neutral point of load becomes squarewave of 36 degree. The output frequency on the secondary side
becomes five times of the input frequency of the square
waveform.

Figure 1. Proposed multiplying freqeuncy circuit using five-phase
inverter

The proposed method uses a lot of switching devices
compared to a conventional circuit using a H-bridge topology.
In H-bridge, the fast switching device, which operates at 13
MHz is needed, and therefore, large switching loss occurs. In
that case, it is difficult to refrigerate the junction temperature
because the thermal resistance is large. In contrast, theproposed circuit can distribute the power loss of each device.
The loss of one switching device is smaller than that in theconventional circuit. Therefore, it is easier to reduce theswitching device. Besides, the switching frequency is 1/N
times lower than the conventional circuits, as a result, low cost
power devices can be applied.

III.

CIRCUIT DESIGNIn the proposed circuit, reduction of leakage inductance isimportant because of using high frequency. Leakage
inductance of the transformer causes an increase in rise time of
the waveform and a decrease on the amplitude of the output
voltage.
Therefore, the toroidal multi-core transformer is chosen in
the proposed circuit. Toroidal core has characteristics that the
majority of the magnetic flux passes through the core with lowleakage of magnetic flux. Therefore, it shows an advantage ofgood reproducibility because it has lesser interference withadjacent device. In addition, the inductance is obtained in a
fewer number of turns. Therefore, it is possible to reduce theleakage inductance of the transformer wiring by devising thestructure of the secondary side. In addition, in this paper, ferrite
core is used as the toroidal core, because ferrite core is a low
loss element in term of high frequency.
The proposed circuit is designed as follows, the output
voltage Vout=50V, and output frequency fout=1.5MHz. When
number of transformer is n, frequency of secondly side isrelated to (2).
f out = n ⋅ f 1(2)

Therefore in the case of five phase (n=5), output to input
ratio of transformer is 1:2. In addition, operation frequency is
f1=300 kHz.

Figure 2. Principle of the proposed circuit

The design of the transformer winding is obtained by (3).
The ratio of voltage determines the winding of secondly sideN2. (3)N1 =Vin D
ΔB ⋅ S ⋅ f 1(3)

B is the magnetic flux density, and S is the effective crosssection of core of transformer, and D is the duty ratio perphase.
Table 1 shows the specification of transformer. The
primary winding N1=2 is calculated from this table. Therefore
secondly winding N2=4 is calculated by (4).

N2 =

Vin 2
N1
Vout

(4)

Figure 3 shows the diagram of a multi-core transformer forthe proposed circuit. In order to reduce the wiring inductanceof the circuit, the transformer cores of each phase are placed in
the pentagon. Then, the primary-side winding of thetransformer is wound concentrated on the each of core. The

neutral point is connected to the midpoint of DC capacitor. The
secondary-side winding of the transformer is wound withpenetrating to the entire core. In addition, the element islocated very close to the core, the power lines are placed insideand outside by using a double-sided board. The upper sideswitch of each arm is implemented in the front side of the
Figure 3 (a). The lower side switch of each arm is implemented
in the back side of the Figure 3 (a). It aims to reduce theleakage inductance of the transformer and to reduce the wiring
inductance of the high frequency part. In addition, the skineffect is bigger on high frequencies above 1MHz. Therefore, italso aims to reduce the losses that occur in the circuit. Using
this method, the parameters of multi-core transformer is asshown in table 2.

TABLE I.

SPECIFICATIONS OF TRANSFORME

Parameter
Primary Voltage
Secondary Voltage
Primary Number of Turn
Secodary Number of TurnPrimary Frequency
Primary Frequency
Duty cycle
Flux density
Cross-sectional area

Symbol
V1
V2
N1
N2
f1
f2
D
Bm
S

Rating
25
50
2
4
300
1.5
0.5
0.3

Unit
V
V
turns
turns
kHz
MHz

112×10-6

m2

T

A. Loss analysis
Loss is analyzed to clarify the loss distribution of the
proposed circuit. The proposed method is composed of themulti-core transformer and the voltage inverter. Therefore, themajor loss is separated into two parts, the inverter andtransformer. The following formula is used to calculate thelosses.
The loss of inverter PLoss is obtained by (5). The inverter
loss is the sum total of Pcon conduction loss, PSw switching loss
and PRec loss of recovery. In addition, the conduction loss Pcon
can be separated into PFET and PFWD, where PFET is the on
resistance that occurs regularly, PFWD is the loss offreewheeling diode FET (FWD). This relationship is shown inequation (6).
PLoss = PCon + PSw + PRec

(5)

PCon = PFET + PFWD

(6)

(a)

Top view of the circuit(b)Side view of the circuit

B. Steady loss
PCon conduction loss of five phase inverter is obtained byintegrating the (7). PFET conduction losses of the FET and
PFWD conduction losses of the FWD are obtained from(8),(9).Where ID is drain current, IF is current of FWD, RON is
the on resistance.

PCon =

12π

3π
15 I 2RD
ON dt +
0
2π

∫

2
π
5 I 2R
F
ON dt
0

∫

(7)
Figure 3.

1
PFET = I D 2 RON
3

(8)

1 2
I F RON
6(9)

PFWD =

Implementation of the proposed circuit

TABLE II. SPECIFICATIONS OF TRANSFORMEC. Switching loss
Equation (10) shows the switching loss PSw, where POn is
the turn on loss, and POff is the turn off loss, which are obtainedin (11) and (12). EOn is the on voltage, EOff is the off voltage,
and fc is the switching frequency. In addition, the recovery loss
PRec is obtained in (13). Where Irr is the recovery current, Vcc is
the DC link voltage, and trr is the recovery time.

PSw = POn + POff

POn = E On f c

POff = E Off f c

PRe c =

1

π
1

π

1
I rrVcc t rr f c
8

(10)

(11)
Figure 4. Relation between the number of phase and totalloss(semiconductor part)(12)
TABLE III.

SIMULATION CONDITIONS.

(13)

Figure 4 shows the results of loss analysis that is calculatedusing the above equations. The analysis conditions are 200V
DC voltage, load resistance is 50Ω, and the output frequency is
set to 2.079MHz. Comparison of loss is performed withchanging the numbers of phase of the inverter. In this case,load is given with a5% inductance.
From the result as shown in Figure 4, the loss is constanteven if the numbers of phase of the inverter has increased. Thisshows that the loss of each device is reduced by increasing thenumbers of phase. However, the loss due to change on thenumbers of phase is only changed slightly because there are a
lot of switching devices. In addition, the conduction loss is
expected to increase slightly with an increase in the numbers ofphase because excitation current flows in the actual circuit.

25
0
-25
25
0
-25
25
0
-25

U phase voltage

V phase voltage

W phase voltage

X phase voltage25
0-25
Y phase voltage
25
0
-25

Transformer secondary voltage

25
0
-25

IV.

SIMULATION OF THE PROPOSED CIRCUIT

Table 2 shows the simulation parameters. These
parameters are identical to the experimental parameters.
However, an ideal transformer is used in simulation forsimplicity. The basic operation of the proposed circuit can be
confirmed in the simulation results shown in Figure 5. The
result shows that the transformer secondary voltage has avoltage fluctuation that is five times the frequency of the
primary side. Figure 6 shows the voltage and current
relationship between the primary and secondary sides of thetransformer. The result shows that the primary side current isturned on and off repeatedly with the same period to thesecondary side current. In addition, the current flows througheach switching devices has fluctuation, which is the same tothe secondary side of the transformer.
Table 3 shows another simulation parameters. These
parameters include magnetizing inductance and leakage

Figure 5. Operation waveforms in Simulation:each phase voltage andoutput voltage of the transformer.
TABLE IV.

SIMULATION CONDITIONS.

inductance. The results obtained from this simulation
parameter are differed to Figure 6. Figure 7 shows thesimulation results, which using ideal transformer and parameterfrom the magnetizing inductance. In this figure, the current
flows through switching device is compared. The current
amplitude is larger than that of without magnetizing inductance.
In addition, the current amplitude becomes smaller in order toincrease the magnetizing inductance.
Figure 8 shows simulation result, which using idealtransformer and parameter from the leakage inductance. As
compared to previous result, the current waveform becomes atriangular wave. This is because the leakage inductances areconnected in series in the circuit. The current ripple becomes
smaller value because impedance becomes larger. Figure 9shows the current waveform which is given magnetizing
inductance and leakage inductance. In addition, it also changes
the maximum value of the current flowing through the device
by changing the inductance value for each case.
Figure 10 shows a graph that plots the maximum value ofthe current flowing through the switching devices to change thevalue of magnetizing inductance while maintaining a constantratio of the magnetizing inductance and leakage inductance.
These show that the breakdown current value of the switching
device could be reduced by increasing the magnetizing
inductance. Here, increasing the number of turns can increase
the magnetizing inductance. However, it is not possible toincrease the magnetizing inductance in this circuit. In order toachieve it is necessary to reduce the number of turns of thetransformer. In a transformer which has a large number ofwinding, leakage inductance value is smaller than compared tomagnetizing inductance. However, transformer has a small
number of winding in this circuit. Therefore, the ratio ofleakage inductance versus magnetizing inductance can bepredicted to be small. Based on Figure 10, the ratio of leakage
inductance versus magnetizing inductance is desirable larger
than 1:10. In addition, the ratio must be a practical value.
Therefore, as shown in Table 2, actual parameter of thetransformer is suitable to apply in this experiment.

Figure 6. Operation wavefoms in simulation:voltage and current inswitching device and transformer.
Drain-source voltage[V]500Magnetization inductance 0[ H]S1 drain current[A]40-2
S2 drain current[A]40-2Transformer primary current[A]40-2Magnetization inductance 20[ H]S1 drain current[A]40-2
S2 drain current[A]
4
0
-2

V.

EXPERIMENTAL RESULTThe prototype is created to confirm the effectiveness of the
proposed circuit. Table 2 shows the experimental conditions.
MOSFET (manufactured by IR, IRFR3911) is used as theswitching device of main circuit. The DC voltage for inverter is50V, and the switching frequency is 300 kHz. In addition,phase number of the multi core transformer is five which isbased on the design described in section 3. The primarywinding is 2T and the secondary winding is 4T.
A. Characteristics of no-load test
Figure 11 shows the experimental result in a no-load
operation. From the result, the output waveform is a squarewave that has peak voltage 50V. This value is consistent with
the input voltage. In addition, frequency of the secondary sideis 1.5 MHz which is five times of switching frequency.

Transformer primary current[A]40-2Magnetization inductance 60[ H]S1 drain current[A]40-2
S2 drain current[A]40-2Transformer primary current[A]
4
0
-2

2

4

[ sec]

6

8

Figure 7. Simulation result of varying parameter of magnetizationinductance.

In addition, the secondary side of transformer U-phase
output voltage is confirmed that twice the voltage of the
primary side of the transformer, which is determined by theturns ratio. However, the transformer secondary winding is apenetrating wound. As therefore, measuring the phase voltageof the secondary side of the transformer becomes impossible.
Therefore, the secondary side voltage of the transformer ismeasured by using auxiliary winding that has the same numberof turns to the secondary side.
B. Characteristics of the load test
Figure 12 shows the experimental result with 10Ω load.
Comparing this result with Figure 6 (no-load test), oscillation
occurs on the output waveform. The output voltage has been
reduced from 50V to 25V. In addition, the output current is atriangular wave. Therefore, the load power factor isapproximately 0.1, which is a very low value. This inductancevalue is large to use in 1.5MHz.

Drain-source voltage[V]500Leakage inductance 0[ H]S1 drain current[A]20-2
S2 drain current[A]20-2Transformer primary current[A]20-2
Leakage inductance 1[ H]S1 drain current[A]20-2
S2 drain current[A]
2
0

VI.

CONCLUSION

A frequency multiplying circuit which consists of a multiphase voltage-source inverter and multiple toroidal core is
proposed in this paper. It is possible to make a high frequency
power source without using exclusive element that corresponds
to the high frequency from the proposed method.
The experimental result confirms the operation at 1.5MHz
square wave output voltage. However, high efficiency power
conversion is failed on the load experiment. This is because theload power factor is affected by leakage inductance coincide
within the transformer and load inductance.
In the future work, a low leakage inductance fortransformer will be designed to achieve high efficiency.

REFERENCES
[1]

[2]

[3]

[4]

[5]

[6]

Y. Hori, “Future Vehicle Society based on Electric Motor, Capacitor andWireless Power Supply,” Power Electronics Conference (IPEC), pp.
2930-2934, 201
J. O. Mur-Miranda, G. Fanti. F. Yifei, K. Omanakuttan, R. Ongie, A.
Setjoadi, N. Sharpe, “Wireless power transfer using weakly coupledmagnetostatic resonators,” IEEE Energy Conversion ongress andExposition (ECCE), pp. 4179-4186, 2010
B. L. Cannon, J. F. Hoburg, D. D. Stancil, S. C. Goldstein, “Magnetic
Resonant Coupling As a Potential Means for Wireless Power Transfer toMultiple Small Receivers,” Power Electronics, IEEE Transactions on ,Vol. 24, No. 7, pp. 1819-1825, 2009
S. Cheon, Y. Kim, S. Kang, M. Lee, J. Lee, T. Zyung,“CircuitModel-Based Analysis of a Wireless Energy-Transfer System
via Coupled Magnetic Resonances,” Industrial Electronics, IEEE
Transactions on , Vol. 58, No. 7, pp. 2906-2914, 2011
A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, M.
Soljacic, “Wireless Power Transfer via Strongly Coupled Magnetic
Resonances,” Science, Vol. 317, No. 5834, pp. 83-86, 2007
M.P. Theodoridis, S.V. Mollov, "Improved gate driver for a 13.56 MHz
resonant inverter," Power Electronics, Machines and Drives, 2004.
(PEMD 2004). Second International Conference on (Conf. Publ. No.
498) , Vol.1 pp.143 - 148 , 2004

-2
Transformer primary current[A]20-2
Leakage inductance 2[ H]S1 drain current[A]20-2
S2 drain current[A]20-2Transformer primary current[A]
2
0
-2

2

4

[ sec]

6

8

Figure 8. Simulation result of varying parameter of leakage inductance

Figure 9. Simulation result of given magnetization inductance andleakage inductance.

[7]

[8]

[9]

D. Goodman, A. Bortkiewicz, G. Alley, and W. Holber, “RF Power
Supply With Integrated Matching Network,” U.S. Patent 6 887 339, Sep.
20, 2001.
R. Frey, “500 W, class E 27.12 MHz amplifier using a single plastic
MOSFET,” Advanced Power Technology Application Note APT9903,
1999, Advanced Power Technology, Bend, OR
D. J. Perreault, J. Hu, J. M. Rivas, Y. Han, O. Lietermann, R. Pilawa, A.
Sagneri, and C. Sullivan, “Opportunity and challenges in very highfrequency power conversion,” in Proc. 24th Annu. IEEE Appl. PowerElectron. Conf. Expo., 2009, pp. 1–14

Figure 10. Current characteristics for the magnetizing inductanceelement

Figure 11. Oparation waveforms of the proposed cicruit at no-load;eachleg operates 300 kHz, then output frequency of 1.5MHz is obtained.).

Figure 12. Operation waveforms at with 10 ohm resitive load