Analysis and Optimization Design of Snubber Cricuit
for Isolated DC-DC Converters in DC Power Grid
Koji Orikawa

Jun-ichi Itoh

Nagaoka University of Technology
Nagaoka, Japanorikawa@stn.nagaokaut.ac.jp

Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

Abstract—This paper clarifies the principle of the surge voltage
in the diode rectifier that is connected to the transformer in theisolated DC-DC converter. In addition, the design method of the
RC snubber circuit is discussed by using the equivalent circuitthat is consisting of the transformer, the snubber circuit and thediode. Finally, the experimental results are provided to validate
the design method.

the snubber circuit is basically depending on the experiences ofdesigners.

Keywords-component; Smart grid; DC power grid; Isolated DCDC converters; Rectifier diode; Surge voltage; Snubber circuit

I.

INTRODUCTION

Recently, the DC interface converters for the smart grid
have attracted large attentions in community. The size andefficiency of high power DC-DC converters become
particularly important especially for the photovoltaic
generation and battery storage system. On the other hand, thedeveloping of wide-gap semiconductor such as silicon carbide(SiC) and gallium nitride (GaN), which is the high switchingfrequency semiconductor devices, have been actively
progressing. Therefore, packaging technologies for power
converters that feature small size and high-density are highly
researching [1]-[2]. However, the occurrence of surge voltage
during high frequency switching in the semiconductor
switching devices is one of the known problems. The surge
voltage induces problems such as overvoltage and highfrequency noises in the semiconductor switching devices. As
the result, breakdown and malfunction in the semiconductor
switching devices could be happen in the power converters
such as the high power DC-DC converters for the smart grid.
Therefore, the suppression on the surge voltage is an important
aspect to study in order to offer high reliability in a power
supply system.
Isolated DC-DC converters using transformers have been
studying actively [3]. Because the transformer can insulatetransform voltage into an AC voltage easily. The surge voltage
generally occurs in the output rectifier diodes that is connectedto the output of transformer. It is known that the surge voltage
in the output rectifier diode is caused by the leakage inductanceof the transformer, and a parasitic capacitance of the diode.
However, there have been few quantitative discussions only on
the design of the snubber circuit based on the principle of thesurge voltage in the diode [4]-[6]. As the result, the design ofThis paper clarifies the principle of the surge voltage in the
output diode rectifier that is connected to the isolated DC-DC
converters with consideration of the design method in the RC
snuber circuit, which is connected to the secondary side of thetransformer. A theoretical equation of the surge voltage isderived from the equivalent circuit. Snubber circuit parameters
are designed based on a parasitic capacitance and the power
consumption of the snubber circuit. At the end, the validity ofthe design method is confirmed from the experimental results.
II.

PRINCIPLE OF SURGE VOLTAGE ON DIODE

Fig. 1 shows a circuit diagram of the isolated DC-DC
converter which is investigated in this paper. This circuit
consists of a single phase inverter, a high frequency
transformer, a diode rectifier and a R load. In this experiment,
the inverter is operated with the square waveform drive.
A. Equivalent Circuit
Fig. 2(a) shows the equivalent circuit when the surge
voltage occurs in the diode D1 after the overlapping period
during commutation from D3 to D1. The current path isillustrated with a dot line. R is a wiring resistance of thetransformer. L is a leakage inductance of the transformer. Fig.
2(b) and (c) show simulation waveforms of Fig. 2(a). The valueof wiring resistance and leakage inductance of the primary sideof the transformer is converted to the secondary side of thetransformer. In addition, the characteristic of the actual diode isdemonstrated with the ideal diode, on resistance Ron, off
resistance RDoff, the forward voltage VF and the parasitic
capacitance C. The output current cannot change rapidly
because of a smooth inductance Lout. As the result, the rushcurrent flows through the parasitic capacitance. In addition, thevibrational current flows through the leakage inductance which

Figure 1. Full bridge isolated DC-DC converter.

results the reverse electromotive voltage occurs in the leakage
inductance. That is, the reverse electromotive voltage of theleakage inductance becomes the surge voltage. Therefore, thesurge voltage does not occur when the ideal transformer which
has no leakage inductance is used.
From the principle which is mentioned above, in order toreduce the surge voltage, it is needed to suppress the rushcurrent in the parasitic capacitance. An energy buffer is aneffective method to suppress the rush current in the parasitic
capacitance.
B. Theoretical Analysis of Surge Voltage
Theoretical equation of the surge voltage is derived fromthe equivalent circuit as shown in Fig. 2(a). Table 1 shows theconditions of the simulation circuit. The theoretical equation of
the surge voltage is given by (1).

{}vD1max = I st RDoff 1 + e −τ / (2 fvib ) − VF .

(1)where Ist is the steady current of the diode when diode isturned off, τ is the damping time constant and fvib is thevibrational frequency of the surge voltage. Ist, τ and fvib are
given by (2), (3), (4).

()

I st = {Vse − I out (R + RDon )}/ 2 R + RDon + RDoff .

τ = {CRR Doff + (CR Don R Doff ) / 2 + L}/ (2 LCR Doff ) .

(

)(

)

f vib = 2 R + RDon + RDoff / 2 LCRDoff − τ 2 / (2π ) .

(2)

(3)

(4)

where Vse is the secondary side voltage of the transformer
and Iout is the output current. From (1), it is confirmed that thesurge voltage depends on (2), (3) and (4) which are changed by
the parameters; the wiring resistance, the leakage inductanceand the parasitic capacitance.
In order to confirm the validity of the equations which are
shown in (1) and (4) respectively, the calculation results of (1)and (4) are shown in Fig. (3) and Fig. (4) in the case that theleakage inductance L and the parasitic capacitance C arechanged respectively.
Fig. 3 shows the theoretical waveforms of the diode voltage
and the surge voltage in the case that the leakage inductance L
is changed. From Fig. 3, it is confirmed that the vibrationalfrequency decreases and the surge voltage is reduced according
to increment of the leakage inductance L. The reason that thesurge voltage reduced are follows; by increasing the leakage
inductance, the impedance of the series circuit which consistsof the leakage inductance and the parasitic capacitance are
increased. As a result, the rush current of the parasitic
capacitance is reduced which also reduce the surge voltage.
This means the damping time constant and vibrationalfrequency that is shown in (3) and (4) are changed, then the(a) When surge voltage occur in D1.

50
0
-50
10
0
30

Vp

0.1
Fig. 2
(a)

iD1

0
-0.1
30

iD1

vD1

iD3

0
-9.8

vD1

0
15
0
-15
40

iL

vL

0
0

iL

-10
-10.2
10
0
-10
20
13

10
Time ( s) Fig. 2 (c)(b) Voltage and current waveforms.

vL

14 15
Time ( s)16(c) Enlarged waveforms.

Figure 2. Equivalent circuit of secondary part in Fig.1.
TABLE I.

CONDITIONS OF SIMULATION CIRCUIT

Input voltage Vin
Output current source Iout
Output inductance Lout
Output capacitance
Switching frequency fsw
Winding resistance R
Leakage inductance L
Turn ratio nParasitic capasitance C
On resistance RDon
Off resistance RDoff
Forward voltage VF

48 (V)
10 (A)
0.5 (mH)
2200 (μF)
20 (kHz)53 (mΩ)8.6 (μH)
n=N1/N2=15/6=2.5
200 (pF)
0.086 (Ω)
1 (kΩ)
0.86 (V)power of an exponential in (1) will increase by increasing of
the leakage inductance. As a result, the diL/dt of the leakage
inductance current decreases, and the reverse electromotive
voltage occurs in the leakage inductance is reduced. Therefore,
the surge voltage is reduced.
Fig. 4 shows theoretical waveforms of the diode voltage
and the surge voltage in the case that the parasitic capacitance
C is changed. From Fig. 4, it is confirmed that the vibrationalfrequency decreases and the surge voltage is reduced according
to increment of the parasitic capacitance C. This reason is thatthe impedance of the series circuit which consists of theleakage inductance and the parasitic capacitance are increase.
As a result, the rush current of the parasitic capacitancebecomes larger. That is the diL/dt of the leakage inductancecurrent increases which result the reverse electromotive voltage
occurs in the leakage inductance increases. Therefore, the surge
voltage increases.
III.

SURGE VOLTAGE IN THE EXPERIMENTIn order to confirm the validity of the theoretical analysis,
the surge voltage in the diode of the prototype circuit ismeasured and compared with the theoretical analysis.

Fig. 5(a) shows the experimental waveforms consists of thefollowing, the primary side voltage of the transformer, thediode current and the diode voltage without the snubber circuit.
After the primary side voltage of the transformer changes froma positive value to a negative value, the overlapping period
occurs in the commutation. Also, it is confirmed that the surge
voltage occurs in the diode. Fig. 5(b) shows the waveforms ofthe diode current and diode voltage in the case that the leakage
inductance L is changed. From Fig. 5(b), it is seen that thevibrational frequency and the surge voltage decreases
according to the increment of the leakage inductance L.
Fig. 6 shows the comparison between the theoretical andexperimental values, which are subjected to the ratio between
the surge voltage and steady voltage. In the case of theexperiment, the characteristic of the vibrational frequency andthe surge voltage are similar to the theoretical value. Therefore,
the experimental results can confirm that the investigation in
the equivalent circuit is valid.
B. Changes of Parastic CapasitanceIn this experiment, the parasitic capacitance is changed byconnecting the capacitance to the diode in parallel.
Fig. 5(c) shows the waveforms, the diode current and diodevoltage in the case that the parasitic capacitance C is changed.
From Fig. 5(c), it can be seen that the vibrational frequency andthe surge voltage decreases according to increment of theparasitic capacitance C.
Fig. 7 shows the comparison between the theoretical andexperimental values which are subjected to the ratio between
the surge voltage and steady voltage. In the case of theexperiment, the characteristic of the vibrational frequency issimilar to the theoretical value. On the other hand, thecharacteristic of the surge voltage which is based on thetheoretical is different from the experimental results as seen in
Fig. 7 (b). This reason is that the capacitance which isconnected to the diode in parallel and its wiring resistanceworks as the snubber circuit. As a result, in contrast to the(b) Surge voltage of the diode.

Figure. 3. Voltage waveforms and surge voltage(L is variable).

(a) Voltage waveform of the diode.

Voltage (V)A. Changes of LeakageIinductanceIn this experiment, the air-core reactor which has same
resistance but different inductance, are connected to thesecondary side of the transformer in series. By using thismethod, the damping effect by the winding resistance R can beneglected. The effect of the leakage inductance on the surge
voltage only can be measured.

(a) Voltage waveform of the diode.

(b) Surge voltage of the diode.

Figure. 4. Voltage waveforms and surge voltage (C is variable).

theoretical analysis, the surge voltage can be suppressed in theexperiment.
In according to the considerations which are mentioned
above, the required conditions for suppressing the surge
voltage by reducing the rush current of the parasitic
capacitance are shown below.
1) Winding resistance of the transformer : Large
2) Leakage inductance of the transformer : Large
3) Parasitic capacitance of the diode: Small

However, in general the winding resistance of thetransformer is low in order to reduce the copper loss. The
leakage inductance is also low except the application which theleakage inductance is used in a positive way. Therefore, a
trade-off relationship that is subjected to reduce the surge
voltage is established between i) to achieve a low wiring
resistance and ii) to achieve a low leakage inductance. On theother hand, the parasitic capacitance depends on the rating of
the voltage and current. Therefore, it is difficult to always
select the diode which has a small parasitic capacitance.

Frequency fvib (MHz)(a) Voltage and current waveform (L:8.6μH, C:200pF).
(a) Vibrational frequency as a function of the leakage inductance.

(b) Enlarged waveform of Fig. 5 (a) (L:8.6μH, C:200pF).
(b) Ratio between surge voltage and steady voltage.

0(ID1)

ID1

200(mA)

VD1

R: 53(m ) L: 8.6( H)
Iout: 10(A)

5(V)

0(VD1)

200(ns)(d) Enlarged voltage and current waveform (L:8.6μH, C:2020pF).

Figure. 5 .Experimental waveforms.

IV.

DESIGN METHOD OF SNUBBER CIRCUIT

As mentioned above, there are limitations to suppress thesurge voltage by reducing the rush current of the parasitic
capacitor from the design of transformer and selection of diode.
Therefore, the snubber circuit is connected to the diode inparallel. It consists of the snubber resistance and the snubber
capacitance which has a larger value than that of the parasitic
capacitance. By using the snubber circuit, the surge voltage canbe reduced by reducing the rush current of the parasitic
capacitance. This paper describes the design of a RC snubber
circuit which is connected to the secondary side of thetransformer.
Fig. 8 shows the equivalent circuit of Fig. 2(a) in case thatthe common snubber circuit is connected to the secondary sideof the transformer. The snubber circuit is designed based on
Fig. 8. In particular, Fig. 8 is divided into two parts: the dottedline region which consists of the transformer and the snubber
circuit and the equivalent circuit of the diode. Firstly, the peak(a) Vibrational frequency as a function of the parasitic capacitance.

2.0
VD1max/Vst(c) Enlarged voltage and current waveform (L:15.9μH, C:200pF).

Frequency fvib (MHz)Figure. 6. Theoretical value and experimental value of thesurge voltage and the vibrational frequency (L is variable).

1.5

Experimental value ( )Theoretical value( )1.0No surge voltage line
0.5
R: 53(m ) L: 8.6( H)
00
500 1000 1500 2000 2500 3000
Parasitic capacitance C (pF)(b) Ratio between surge voltage and steady voltage.

Figure. 7. Theoretical value and experimental value of thesurge voltage and the vibrational frequency(C is variable).

value of the step response in the dotted line circuit is calculated.
After that, subtracting the voltage drop of the diode from it,these calculation results become the designed value of thesurge voltage VD1snmax. The coefficient that the designed valueof the surge voltage divided by the steady voltage Vst is givenby (5).

[]

V D1sn max / V st = V se 1 + e − k / V st − (I out R Don + V F ) / V st .

(5)

where Vst is the steady voltage, k is a constant value. k isgiven by (6).

k=

(

)

⎡
⎤
2
2 ⎫
2 ⎞
⎧
⎛
⎢ tan −1 ⎪⎨ 1 − ζ 1 − 4ζ ⎪⎬ − tan −1 ⎜ 1 − ζ ⎟ + π ⎥
2
⎥
⎜⎜ ζ
⎟⎟
1 − ζ 2 ⎢⎣⎪⎩ ζ 3 − 4ζ
⎪⎭
⎝
⎠
⎦

ζ

(

)

(6)

From (5), the surge voltage will be determined in case thatthe output current and the parameters of the diode are known.
In addition, the relationship among the snubber resistance Rsn,
the snubber capacitance Csn and the damping coefficient ξ aregiven by (7).
R sn = 2ζ

L / C sn .

(7)

From (7), the snubber resistance Rsn can be designed after
the snubber capacitance Csn is determined. However, thenumber of the combination of two parameters is infinity. In thissection, Csn is designed based on the relationship among thesnubber capacitance, the parasitic capacitance and the snubber
loss. In the end, Rsn is designed using by (7).
In the case of the smaller snubber capacitance, theimpedance of the snubber circuit increases, which results thesnubber circuit does not work. Therefore, the snubber circuitcannot suppress the surge voltage. On the other hand, in case of
the larger snubber capacitance, the impedance of the snubber
circuit decreases. As a result, the snubber circuit can suppress
the surge voltage. However, the snubber current and the power
consumption of the snubber circuit increases. Therefore, theoptimum value of the snubber capacitance needs to be
identified according to the parasitic capacitance. The power
consumption of the snubber circuit Psn is given by (10) in thecase that the dotted line region only is considered in Fig. 8.

Psn =

R sn
R0

2

∑

ωn 2 / ω0 2

(1 − ω / ω ) + (ω / ω )(R
2 2

2

n

0

2

n

2

0

2
sn

/ R0

2

)

Eq. (5),(6)Start

VD1snmax
Iout
RDon
VF

Csn
Eq. (7)
Rsn

C

Eq. (8)

L

Psn

Pasn

Psn < Pasn

Csn
No :Decreased

Yes
End
Figure. 9. Flowchart for design of snubber circuit.

2(a) C/Csn=10-3.

R0 = L / Csn (10)Fig. 9 shows a flowchart of the snubber circuit design.
Required parameters for the design of the snubber circuit aredesigned surge voltage VD1snmax, the output current Iout, on
resistance RDon, the forward voltage VF, the parasitic
capacitance C, the leakage inductance L and an allowancesnubber loss Pasn. First, the damping coefficient ζ is decided byparameters which are mentioned above. Then, the snubber
resistance Rsn is calculated by (7). In the end, if a calculated
snubber loss Psn is less than the allowance snubber loss, thenthe design of the snubber circuit is completed.
V.

Input

V se (ω n ) (8)where ωn is a n-order natural angular frequency of thesecondry side voltage in the transormer. ωn and R0 are given by(9), (10).
ω0 = 1 / LCsn (9)Figure. 8. Equivalent circuit of the transformer with the RC
snubber circuit.

EXPERIMENTAL RESULTS WITH SNUBER CIRCUIT

Fig. 10 shows waveforms, the diode voltage and the currentof the snubber circuit in the case that the ratio between the(b) C/Csn=3×10-2
Figure. 10. Waveforms of the diode and the current of the snubber.

parasitic capacitance and the snubber capacitance is changed
under a constant damping coefficient. It can be seen that thesurge voltage is almost same and the current of the snubber
circuit increase according to the increment of the parasitic
capacitance. Therefore, it is confirmed that the experimental
results is well agreed with the theoretical analysis which are
mentioned in the chapter IV.
Fig. 11(a) shows the designed value, the simulation results,
and the experimental results in terms of the ratio between thesurge voltage and steady voltage of the diode. Fig. 11(b) showsVD1max/Vst(a) With RC snubber (ζ:0.1).

(a) Ratio between surge voltage and steady voltage.

(b) With RC snubber (ζ:0.82).

VD1max/Vst

Figure. 12. Voltage waveforms of the diode without snubber
and with snubber using designed parameter.

(b) Snubber loss.

Figure. 11. Ratio between surge voltage and steady voltage
and snubber loss as a function of ratio between parasitic
capacitance and snubber capacitance.

the calculation result which is obtained by (8), the simulation
result is obtained by adding the RC snubber circuit to Fig. 2(a),and the experimental result is obtained from Fig. 10 in terms of
the power consumption of the snubber circuit. From Fig. 11(a),it is confirmed that the snubber capacitance should be designed
from 10 to 30 times larger than the parasitic capacitance. In
addition, it is seen that the calculation result is larger than thesimulation result. In other words, the worst case of the power
consumption of the snubber circuit can be calculated by using(8)
Fig. 12 shows the experimental waveform with snubber
circuit in the case that C/Csn=0.03. From Fig. 12, it isconfirmed that surge voltage is suppressed below than thedesigned value.
Fig. 13 shows the comparison between the designed andexperimental values that are subjected to the ratio between thesurge voltage and steady voltage. From Fig. 13, it is confirmed
the tendency of the designed and experimental values is closed.
VI.

CONCLUSION

This paper clarifies the principle of the surge voltage on thediode in the isolated DC-DC converter and also the design
method of the snubber circuit that is connected to thesecondary side of the transformer. It is confirmed that the surge
voltage depends on the wiring resistance, the leakage
inductance and the parasitic capacitance, based on theexperimental results obtained from the equivalent circuit. In
addition, it is confirmed that the surge voltage is suppressed

Figure. 13. Ratio between the surge voltage and the steady
voltage.

below the designed value with the snubber circuit which has alow snubber loss. In the end, the validity of the analysis results,
which is based on the equivalent circuit, has been confirmed byexperimental results.
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[3]

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