An Experimental Verification and Analysis ofa Single-phase to Three-phase Matrix Converter
using PDM Control Method for High-frequency Applications
Yuki Nakata
Nagaoka University of Technology
nakata@stn.nagaokaut.ac.jp

Jun-ichi Itoh
Nagaoka University of Technology
itoh@vos.nagaokaut.ac.jp

Abstract-This paper discusses the PDM (Pulse Density
Modulation) control method for a single-phase to three-phasematrix converter (MC) in the high-frequency application. The
proposed circuit is used as an interface converter for a wirelesspower transfer system. This converter can input a several
hundred kHz frequency and outputting a low frequency, ie 50
Hz, for commercial power grid. The proposed circuit achieves
zero voltage switching (ZVS) operation by using the PDM
control method and obtains high efficiency. In this paper, thePDM control strategy is using delta-sigma conversion andimproving the PDM pattern generation method based on Space
Vector Modulation (SVM). Also, the simulation, experimental
and loss analysis results of the proposed system will bedemonstrated and discussed. As a result, the total harmonic
distortion (THD) of the input current and the output voltage are
84.6 % and 5.4 % respectively. The efficiency of 91.5% is
obtained from the prototype circuit. Additionally, the effect ofpower source side impedance for a high-frequency single-phaseto-three-phase MC is discussed. It is clear that the line-to-line
capacitance at the power source side must be kept as small as
possible in order to suppress the resonance.

to AC converter. The matrix converter (MC) has been
attracted attentions as the AC interface converter for thewireless system, because it delivers advantages in terms ofsizing and energy saving [4]. However, the implementation of
MC in the high-frequency power source has not been reported.
In this paper, the MC is structured into a single-phase to
three-phase converter. The authors propose to use the PDM[5-8] control method for the high-frequency power source [911]. The proposed circuit has an advantage that switching loss
can be decreased nearly close to zero by Zero Voltage
Switching (ZVS) operation. This paper shows the possible
applicable of the MC for the high-frequency power source
circuit. Firstly, the configurations of the proposed circuit
introduced. Secondly, the PDM control strategy using deltasigma conversion and improved PDM pattern generation
method based on the Space Vector Modulation (SVM) are
explained and simulated. Next, the converter loss is analyzed
by simulation. After that, the validity of the proposed circuit
is confirmed by the experimental results. Finally, the effect of
the impedance on the power source is analyzed.

I.

INTRODUCTION

In recent year, wireless power transfer systems have been
actively researched [1-3]. There are two types of wirelesspower systems known as electromagnetic induction andmagnetic resonant coupling. In the electromagnetic induction
type, the frequency of the coil for the transmission is low, andit can transmit high-capacity power with relative ease.
However the coupling is reduced and the transmitting
efficiency decreases with increasing of the transmission
distance. As a result, a large coupling is necessary in order toimprove the transmitting efficiency. Likewise, thetransmitting distance needs to become shorter. On the other
hand, the efficiency of the electromagnetic resonant coupling
type is over 90% in case of the intermediate distance which isabout 1m.
In the wireless power transfer system, the frequency of thegenerated voltage at the receiving coil is from tens of kHz toseveral MHz, which is identical to the power source
frequency. Accordingly, in order to connect this system to aload, an interface converter which converts the received
power into a controlled output power is required. The
characteristic of this interface converter must has a high input
frequency from several hundred kHz and able to deliver a low
output frequency (50Hz or 60Hz) suitable for commercial
power grid. The structure of the interface converter is an AC

II. CIRCUIT CONFIGURATIONS
A. Single-phase to Three-phase Matrix Converter
Figure 1 shows the circuit configuration of a single-phaseto three-phase MC. This circuit is an AC to AC directconverter which is constructed by six bidirectional switches
and it does not composed of an electrolytic capacitor in theDC link. Furthermore, the efficiency of a MC is higher than aconventional system that is constructed by a rectifier,electrolytic capacitors and a three-phase inverter because ofless switching devices in the current path.
B. Indirect Single-phase to Three-phase Matrix Converter
Figure 2 shows another circuit configuration of an indirecttype of single-phase to three-phase MC. This circuit isconstructed by a diode rectifier as an input interface and athree-phase inverter. In this circuit, the conduction loss ishigher than the single-phase to three-phase MC, because thenumbers of conduction device are larger than the single-phaseto three-phase MC as shown in Fig.2. Although the circuit
structures of these two converters are different, the control
methods are identical. In this paper, the indirect type structure
is verified and confirmed the operation in simulation andexperiment.

III. CONTROL STRATEGY
A. PDM Control using Delta-sigma Conversion
PDM controls the density and the plus/minus of theconstant-width pulse, and then these pulse signals are used as
the output unit.
Figure 3 shows the control block diagram of the proposed
circuit. The PDM signals used for the switching can beobtained by converting the delta-sigma command (vu*, vv*,vw*) value from each phase. Delta-sigma conversion is a kindof analog-digital conversion. These PDM signals are used toturn on/off each of the inverter arm at the indirect singlephase to three-phase MC circuit. However, the polar
characteristic of the input signal is changing occasionallybecause the input of this circuit is a single-phase AC voltage.
Then the functions of the upper and lower arms are inverted.
As a result, it is necessary to detect the input voltage polarity
and convert the switching signals, when the input voltage isin minus pole.
Additionally, the zero cross points exist with respect to thefrequency since the input voltage is a sinusoidal waveform.
ZVS operation is performed at every zero cross points of the
input voltage. The loss at the switching devices is reduced
drastically because the switching loss can be decreased nearly
to zero by the ZVS operation.
However, there are some parts, which refer to constantvoltage in this method. In these parts, switching loss increases
because ZVS is not achieved. The phenomenon occurs
because PDM patterns using delta-sigma conversion contains
the switching patterns, where the phase between the output
voltage and current become too large instantaneously. Whenthe phase between the current and voltage vector becomeslarger than 30 degrees, DC link current flows backward to
power source side in the inverter. As a result, DC link voltage
is equaled to snubber capacitor voltage. In order to resolve
this problem, the method based on Space Vector Modulation(SVM) is applied to the generation of PDM patterns. Thismethod is explained detail in the next chapter.
B. PDM Control based on Space Vector Modulation
The waveform is improved applying PDM patterngeneration method based on SVM. In SVM, the instantaneousvoltage vector that the phase between the output current andvoltage does not become too large rapidly is selected andoutput. Therefore, DC link current does not flow backward,
and the phase error between voltage and current does notoccur.
Figure 4 shows the PDM signal generation block based onSpace Vector Modulation. The switching signals generated
from SVM is an input to the d flip flop (D-FF), and +/detection signal from the input voltage is used to detect thezero cross points of input voltage, this signal is an input to the
CLK. The output of the D-FF, “Q” is synchronized at theedge of +/- signal, which is the zero cross point of input
voltage. As a result, the switching signals generated by SVM

Fig. 1. Single-phase to three-phase MC.

Fig. 2. Indirect single-phase to three-phase MC.

Fig. 3. PDM control block diagram using Delta-sigma Conversion.

Fig. 4. PDM signal generation block based on Space Vector Modulation.

are quantized by a pulse where the width is half cycle of the
input voltage.
In addition, the switching frequency is proportional to thecarrier frequency of SVM. A ratio between the input voltage
and carrier frequency is very important factor related toresolution of the control. Hence, decision of the carrier
frequency of SVM is significant in this method.
This method is called “Space Vector Base Pulse Density
Modulation” or “SVB-PDM” for short.

IV. SIMULATION RESULTS
The following is the simulation results using indirect typecircuit in Fig.2. As a simulation condition, a 100kHz, 400V
sinusoidal voltage is used as the input, output voltage is 50Hz,
200V, and a 300W inductive load is used as a load.
A. Simulation results of PDM using Delta-sigma Conversion
Figure 5(a) shows the operation waveforms of the proposed
circuit in the simulation with PDM using delta-sigma
conversion. From the result, 50 Hz sinusoidal waveforms are
obtained at the output voltage and current. The PDM control
operation which uses the half cycle of the input sinusoidal
waveform as the output minimum unit can be verified andconfirmed at the simulation results Fig. 5. However, there aresome inverse voltage pulses in this case. These pulses affectthe distortion of waveforms.
Figure 5(b) shows extended view of waveform of theinterval “A” in Fig. 5(a). As a result, the output line-line
voltage vuv confirms that the switching of the inverter isapproximately at each zero cross point of the 100 kHz
sinusoidal input waveform. However, there are some areas,
the constant voltage is occurring. In these areas, switchingloss increases because ZVS is not achieved.
Figure 6(a) shows the harmonics analysis of the output
voltage from simulation result with PDM using delta-sigma
conversion. From (a), the output voltage does not consist of
low-order harmonic components closely to 50 Hz and theoutput voltage THD is 11.8 %. Figure 6(b) shows the
harmonics analysis of the input current from simulation resultwith PDM using delta-sigma conversion. From (b), the input
current includes of the integral-multiple harmonic nearlyclosed to 100 kHz and therefore the input current THD is
78.8 %.
B. Simulation Results of SVB-PDM
Figure 7(a) shows the operation waveforms of the proposed
circuit in the simulation with SVB-PDM. From the result, 50
Hz sinusoidal waveforms are obtained at the output voltage
and current. The PDM control operation which uses the halfcycle of the input sinusoidal waveform as the output
minimum unit can be verified and confirmed at the simulation
results. Notice there are no inverse voltage pulses in this case.
Figure 7(b) shows extended view of waveform of theinterval “B” in Fig. 7(a). As a result, the output line-line
voltage vuv confirms that the switching of the inverter isapproximately at each zero cross point of the 100 kHz
sinusoidal input waveform. In this case, areas that contain theconstant voltage have been resolved. Therefore, switchingloss is negligible small because ZVS is achieved in this case.
Figure 8(a) shows the harmonics analysis of the output
voltage from simulation result with SVB-PDM. From (a), theoutput voltage does not consist of low-order harmoniccomponents closely to 50 Hz and the output voltage THD is
6.96 %. In this case, output voltage includes of the integralmultiple harmonic nearly to 5 kHz, which is the carrier
frequency of SVM used in this simulation. Figure 8(b) shows

Fig. 5. Operation waveforms of the proposed circuit in the simulation
with PDM using delta-sigma conversion.

Fig. 6. Harmonics analysis of output voltage and input current in thesimulation with PDM using delta-sigma conversion.

Fig. 7. Operation waveforms of the proposed circuit in the simulation
with SVB-PDM.

18
16

switching

14
12

conduction

10
8
Snubber loss
6
4
Rectifier loss

2
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Fig. 9. Converter losses vs delay time of switching with PDM using
delta-sigma conversion.
18
16

switching

14
12

conduction

10

Fig. 8. Harmonics analysis of output voltage and input current in thesimulation with SVB-PDM.

the harmonics analysis of the input current from simulation
result with SVB-PDM. From (b), the input current includes of
the integral-multiple harmonic nearly to 100 kHz andtherefore the input current THD is 78.9 %.
V. LOSS ANALYSISThe following is the loss analysis results using indirect typecircuit as shown in Fig. 2. The simulation condition is assame as the parameters discussed in chapter IV. The device
parameters are from datasheets MOSFET： IRFP460 (500V,
20A) and diode: S20L60 (600V, 20A), which are similar in
the prototype circuit[12-13].
A. Loss Analysis of PDM using Delta-sigma Conversion
Figure 9 shows result of loss analysis with PDM using
delta-sigma conversion. The figure compares the converter
loss and the time delay in switching. Rectifier loss, snubber
loss and conduction loss of the inverter are maintained
virtually constant about 7W. Switching loss of the inverterchanges accordingly to the time delay.
The frequency of the voltage which is applied to the switch
is twice input frequency of 100 kHz. On the other hand, thefrequency of the current which flows through the switch is theoutput frequency of 50 Hz. Hence, the current can beassumed constant during switching period. Additionally, thevoltage becomes the peak value when the time delay ofswitching equals to one-fourth of input cycle. Therefore, theswitching loss becomes maximum value then.
Even, the time delay t of switching is 0μs, there isswitching loss of 1.4 W occurs due to the phase error
waveforms.
B. Loss Analysis of SVB-PDM
Figure 10 shows result of loss analysis with SVB-PDM.
The characteristics of this result are same to the delta-sigma

8
Snubber loss
6
4
Rectifier loss
2
0
0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Fig. 10. Converter losses vs delay time of switching with SVB-PDM.

conversion. The difference in this case is when the time delayof switching is 0μs, there is no switching loss because phaseerror waveform does not exist. Comparing to the result from
Fig. 9, the loss is reduced by approximately 18 %.
VI. EXPERIMENTAL VERIFICATION AT LOW-ORDER VOLTAGE
In order to demonstrate the validity of the proposed circuit,a prototype circuit has been built and tested. The indirect typesingle-phase to three- phase MC was tested in the experimentwith PDM using delta-sigma conversion. A 20 kHz sinusoidal
voltage is used as the input of the circuit initially to confirm
the basic principle of the proposed circuit. Table 1 shows theexperimental conditions.
Figure 11(a) shows the operation waveforms of the
proposed circuit. From the result, 50 Hz sinusoidal
waveforms are obtained at the output voltage and current. The
PDM control operation which uses the half cycle of the input
sinusoidal waveform as the output minimum unit can beverified and confirmed at the experiment results Fig. 11.
Figure 11(b) shows the extended view of waveform of theinterval “C” in Fig. 11(a). As a result, the output line-line
voltage vuv confirms that the switching of the inverter isapproximately at each zero cross point of the 20 kHz
sinusoidal input waveform. However the switching has a 3 μs
delay due to the reasons, slow detections on the zero crosspoints and the dead time of the inverter. The delay of the zerocross point detection is approximately 2μs, and dead time of
the inverter is set to 1μs. The delay can be improved by theTable 1. Experimental parameters.

modifying the zero cross point detection circuit, and re-design
the dead time based on the device parameters. Additionally,
although the switching has a short delay, the switching loss
and surge voltage are lower than the hard switching method at
the zero cross point.
In addition, the efficiency 91.5% is obtained from theprototype circuit. This efficiency can be improved by
optimizing the dead time and criteria selection of theswitching devices.
Figure 12 shows the harmonics analysis of the output
voltage. From the result, the output voltage consists of loworder harmonic components closely to 50Hz and the output
voltage THD is 5.4 %. Figure 13 shows the harmonics
analysis of the input current. From the result, the input
current includes of the integral-multiple harmonic nearly to
20 kHz and therefore the input current THD is 84.6 %.
Based on these results, the validity of proposed circuit isconfirmed by the experiment.

Input voltage

35V

Input frequency

20kHz

Output voltage

19.5V

Output frequency

50Hz

Load

Rload=19Ω
Lload=3mH (50W)

VII. EXPERIMENTAL RESULTS USING HIGH-IMPEDANCEPOWER SOURCE
In order to consider about the effect of the impendence in a
power source, a prototype circuit has been tested using highimpedance power source. Delta-sigma conversion is used as
the modulator.
Figure 14 shows the equivalent circuit of the power source
circuit. It is constructed by a full-bridge inverter, a low passfilter (LPF) and a transformer.
Figure 15(a) shows the operation waveforms of the
proposed circuit without an input filter. From (a), there areresonance phenomena (approximately 330 kHz) occurring on
the input and output waveforms.
Figure 15(b) shows the operation waveforms of the
proposed circuit with an input filter (22 nF filter capacitor and136 Ω dumping resistance). These filter parameters aredesigned from the leakage inductance (139 μH), cut-off
frequency (approximately 90 kHz) and a damping factor(0.85). From (b), the resonance is being suppressed by adding
filter capacitance and damping resistance input side. However,the non-ZVS periods caused distortions on the operation
waveforms because of the in slow detection error.
VIII.

CONSIDERATION ABOUT EFFECT OF A POWER
SOURCE SIDE IMPEDANCE

Since the resonance phenomena (approximately 330 kHz)are found in the operation waveform as shown in Fig. 15(a),the impedance on the power source is considered as theelement to cause the resonance. In order to consider the causeof resonance, the proposed circuit is analyzed by using
simulator with the same practical parameters.
Figure 16(a) shows the simulation results of the proposed
circuit without the leakage inductance and line-to-line
capacitance of a transformer. At (a), there are no resonancephenomenon found in the operation waveforms.
Figure 16(b) shows the simulation results of the proposed
circuit with the leakage inductance and line-to-line

Fig. 11. Operation waveforms of the proposed circuit in the experiment.
101
100
10-1
10-2
10-3
10-4
50 102

103

104

105

106

Fig. 12. Harmonics analysis of output voltage.
101
100
10-1
10-2
10-3
10-4
50 102

103

104

105

Fig. 13. Harmonics analysis of input current.

Fig. 14. Equivalent circuit of source circuit.

106capacitance of a transformer. In this condition, resonancephenomena are confirmed in the operation waveforms. The
resonance frequency is about 300 kHz, and it is identical tothe experimental result. It can be considered that theresonance is caused by the leakage inductance, line-to-line
capacitance and load inductance. Additionally, when leakage
inductance of transformer changes. Thus resonance frequency
more change than when load inductance changes, and whenline-to-line capacitance transformer changes, resonancefrequency most change. The energy of the leakage inductancecan be absorbed by the filter capacitance and damping
resistance input side. However, the effect of the damping
resistance is small when the line-to-line capacitance is large
because the damping resistance is connected parallel with thecapacitance.

Fig. 15. Operation waveforms of the proposed circuit in the experimentusing high-impedance power source.

IX. CONCLUSION
A single-phase to three-phase MC using the PDM control
method for the high-frequency power source has been
proposed. The proposed circuit is able to achieve the ZVS
operation by using the PDM control method that is according
to half cycle of the input sinusoidal voltage. Then the validityof the proposed circuit is confirmed in this paper.
The loss analysis results show that the switching loss of thecase of SVB-PDM is lower than the case of PDM using deltasigma conversion.
The experimental results from prototype circuit confirmed
the following aspects; the output voltage and current aresinusoidal waveforms. Further, the switching of the inverterarm at the proximity of zero cross point is obtained.
Moreover, THD of the output voltage and the input current ofproposed circuit are 5.4% and 84.6 %. In addition, theefficiency of 91.5% is obtained.
Additionally, the effect the impedance on the input powersource is considered. It is clear that the line-to-line
capacitance at the power source side must be kept as small as
possible in order to suppress the resonance. Therefore, designof the system requires attentions in the capacitance of themagnetic coupling circuit and magnetic resonance antenna.
In future work, an experiment using SVB-PDM will be
investigated, the zero cross point detection circuit will be
improved, and tested with a higher input frequency that isequivalent to the wireless power transfer system. Also, thebidirectional switches MC will be tested.
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