Snubber Circuit - RC Snubber Design Using TRIACs
Snubber Circuit - RC Snubber Design Using TRIACs
Snubber Circuit - RC Snubber Design Using TRIACs
Application note
Introduction
When a TRIAC controls inductive loads, the mains voltage and the load current are not in
phase. To limit the slope of the reapplied voltage and ensure right TRIAC turn-off, designer
usually used a snubber circuit connected in parallel with the TRIAC. This circuit can also be
used to improve TRIAC immunity to fast transient voltages.
The subject of this paper is, first of all, to analyze the snubber circuit functions and to
propose a method for snubber circuit design in order to improve turn-off commutation.
Contents
3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Revision history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
dV/dtOFF
VT (50 V/div)
Recovery current
IT (10 mA/div)
IT (10 mA/div) dI/dtOFF
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AN437 Snubber circuit functions and drawback
Figure 3. (dI/dt)c versus (dV/dt)c curve for Z01 standard TRIACs and snubber
circuit impact
Area of spurious
Load
firing at
C IT commutation
VMains VT
R
Safe area
Operating point
with RC snubber Operating point
An RC snubber circuit must be used when there is a risk of TRIAC spurious triggering, i.e.
when the dI/dtOFF - dV/dtOFF couple, measured in the application, is higher than the TRIAC
datasheet values, (dI/dt)c at a given (dV/dt)c.
Figure 4 shows the turn-off behavior of a Z0103 standard TRIAC which controls a 26 W
drain pump. Without snubber circuit and for the maximum junction temperature (110° C), a
spurious triggering appears at turn-off. Indeed, the measured (dI/dt)OFF and (dV/dt)OFF
values, equal respectively to 0.13 A/ms and 10 V/µs, are higher than the guarantee (dI/dt)c -
(dV/dt)c point (only 7 V/µs @ 0.13 A/ms, see Figure 3).
Thanks to an RC snubber circuit (10 nF and 2.7 kΩ), the slope of the reapplied voltage can
be limited to 1.5 V/µs and thus spurious triggering at turn-off can be avoided (see Figure 3
and Figure 4).
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Snubber circuit functions and drawback AN437
Figure 4. Z0103 TRIAC turn-off on inductive load without and with snubber circuit
(C = 10 nF and R = 2.7 kΩ)
:dV/dtOFF
Without snubber
IT (50 mA/div)
With snubber
VT (100 V/div)
The snubber circuit design, detailed in Section 2: How to design snubber circuit for turn-off
improvement, is a trade-off between the maximum peak off-state voltage under pulse
conditions (VDSM / VRSM), the critical slope of reapplied voltage ((dV/dt)c) and the turn-on
stress (dI/dt). When low load inductances are controlled or, low damping factor or low slope
of reapplied voltage are considered, the snubber circuit design can lead to choose a low
snubber resistance value. To reduce the snubber capacitance discharge at turn-on, the
resistance value is limited to a minimum value (refer to Section 1.4).
VM = 660 V
VM = 140 V
IH
With snubber
VT (100 V/div)
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AN437 Snubber circuit functions and drawback
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Snubber circuit functions and drawback AN437
IT (1 A/div)
dI/dtON = 50 A/µs
IMax.
VT (100 V/div)
VMax. = 320 V
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AN437 How to design snubber circuit for turn-off improvement
L R L R IT
IT RS RS
VMains ≈E
VT VT
IG CS CS
G VCs VCs
For a second order linear differential equation with a step function input, the voltage
variation across the snubber capacitance (VCs(t)) and the TRIAC (VT(t)) is given by:
Equation 1
2 .ξ dV Cs ( t )
2
1 d V Cs ( t )
· + · + V Cs ( t ) = E
ω0
2
dt
2
ω0 dt
Equation 2
dV Cs ( t )
VT ( t) = R S · C S · + V Cs ( t )
dt
Equation 3
(R S + R )(Ω ) CS (F )
ξ= ·
2 L(H )
Equation 4
1
ω 0 ( rad / s ) =
L ( H ) ·C S ( F )
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How to design snubber circuit for turn-off improvement AN437
Equation 5
L·ω
E= 2 · VRMS · sin( ϕ ) with sin( ϕ ) =
R + (L · ω ) 2
2
Equation 6
RS
M =
RS + R
By solving the second order linear differential equation according to the damping factor and
initial conditions (refer to Appendix A: RLC series circuit step response explanation), two
diagrams can be defined. These diagrams give the slope of the voltage rise (dV/dtOFF) and
the peak voltage (VP) according to the damping factor (ξ) and the load resistance (M) (refer
to Figure 8).
The voltage rise slope (dV/dtOFF) is defined as the maximum instantaneous voltage rise
slope.
K = dV/dtOFF/(E x ω0)
2.2
2
1.8
1.6
1.4
M=1
1.2 M = 0.75
1 M = 0.5
0.8 M = 0.25
M=0
0.6
0.4 M decreases
0.2
Damping factor: ξ
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
As shown on these two diagrams, the load resistance (R) helps to reduce dV/dtOFF and VP.
The load impact is significant if the damping factor is higher than 0.2.
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AN437 How to design snubber circuit for turn-off improvement
Equation 7
⎛ ξ·ω 0 ⎞ - ξ·ω ·t
VT ( t ) = E - E·⎜ cos( ωp ·t ) + · sin( ωp ·t ) ⎟ .e 0
⎜ ω ⎟
⎝ p ⎠
Equation 8
ωp = ω0 . 1 - ξ
2
For example, in the case of a 26 W drain pump (L = 2.4 H and R = 190 Ω at 50 Hz)
controlled by a Z0103 TRIAC (CT = 12 pF), the damping factor is close to zero (ξ = 2.1 x 10-
4).
For low damping factor, the normalized voltage rise slope K is equal to 1 (refer to Figure 8,
lower graph). The maximum slope of reapplied voltage across the TRIAC is then:
Equation 9
2 · VRMS ( V ) · sin( ϕ ) -6
dV / dt OFF ( V / µ s ) = · 10
L ( H ) ·C T ( F )
According to this formula, the estimated dV/dtOFF is equal to 59 V/µs without snubber circuit.
As shown in Figure 9, the measured dV/dtOFF is in fact about 10 V/µs.
The error between the Equation 9 result and real value is due to the fact that we didn’t take
into account the load inductance saturation (real value is higher at low current), the parallel
parasitic capacitor of the load, the recovery current and the load resistance increase with
frequency. Moreover, the turn-off measurement is done with a voltage probe which adds a
12 pF capacitor across the TRIAC. So, the measured dV/dtOFF is always lower than the
theoretical value, given by Equation 9.
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How to design snubber circuit for turn-off improvement AN437
Figure 9. Z0103 TRIAC turn-off on inductive load (26 W drain pump) without
snubber circuit and in transient operating
dV/dtOFF = 10 V/µs
VT (100 V/div)
IT (10 mA/div)
An RC snubber circuit must be used when there is a risk of TRIAC spurious triggering, i.e.
when the measured dI/dtOFF and dV/dtOFF values are higher than the specified (dI/dt)c and
(dV/dt)c values.
In our application case and for the worst case load conditions (transient operating), the
measured (dI/dt)OFF and (dV/dt)OFF values are equal respectively to 0.13 A/ms and 10 V/µs.
These values are higher than the specified (dI/dt)c and (dV/dt)c values, see Section 1.1.2.
Thanks to an RC snubber circuit, rated in the next paragraph, the slope of the reapplied
voltage could be limited and thus spurious triggering at turn-off could be avoided.
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AN437 How to design snubber circuit for turn-off improvement
Equation 4 modified
1 dV / dt OFF
CS = with ω0 =
2
ω0 · L E ·K
Where K is the normalized voltage rise slope (refer to the lower graphic in Figure 8).
Equation 3 modified
L
CS = 4 · 2
· ξ2
(R + R S )
From the two previous equations, the ratio between the normalized voltage rise slope (K)
and the damping factor (ξ) is given by Equation 10. Figure 10, derived from the lower graph
in Figure 8 gives the variation of this ratio with ξ:
Equation 10
K L dV / dt OFF
= 2· ·
ξ RS + R E
For the drain pump controlled (L = 2.4 H and R = 190 Ω at 50 Hz) and by using Equation 5,
the final voltage value E is:
E = 306 V for VRMS = 230 V and with ϕ ≈ 76°
To avoid spurious triggering with Z0103 TRIAC, the dV/dtOFF is fixed to 2 V/µs (lower than
maximum allowed (dV/dt)c, see Figure 2).
Thus according to Equation 10, the ratio between the normalized voltage rise slope and the
damping factor is equal to 38. Figure 10 gives then the damping factor value (ξ = 0.026).
Figure 10. Ratio between normalized voltage rise slope (K = dV/dtOFF / (E x ω0)) and
damping factor (ξ) according to the damping factor (ξ)
K/ξ
100
38
10
M decreases M=1
M = 0.75
M = 0.5
M = 0.25
1
M=0
Damping factor: ξ
0.1
0.01 ξ = 0.026 0.1 1 10
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How to design snubber circuit for turn-off improvement AN437
The peak voltage is given in the upper graphic of Figure 8. A component with a 600 V
capability will be suitable.
VP = 1.92 · E ≈ 607 V with ξ = 0.026.
4. RC snubber circuit validation
The turn-off and turn-on behaviors must be checked experimentally to validate the designed
RC snubber circuit.
For turn-off commutation, the measured slope of the voltage rise is 1.7 V/µs (Figure 10) and
is very close to the theoretical slope (2 V/µs). The measured peak voltage (520 V) is lower
than the calculated value (607 V) due to the RLC model approximations (refer to
Section 2.2.1).
Figure 11. Z0103 TRIAC turn-off on inductive load with snubber circuit
(C = 10 nF and R = 620 Ω)
IT (10 mA/div)
VP = 520 V
dI/dtOFF
VT (100 V/div)
The second method of RC snubber circuit design allows a quicker snubber capacitor choice.
The capacitor is directly chosen from the load rms current (refer to Figure 12). Pure
inductive loads are considered and the slope of the reapplied voltage is fixed to 2 V/µs.
For a given rms load current and according to the snubber resistance used (47 Ω or 620 Ω),
the ratio between the normalized voltage rise slope (K = dV/dtOFF / (E · ω0)) and damping
factor (ξ) is defined (refer to Equation 11). Then, as in the first snubber design method, the
damping factor is given by Figure 10, the capacitor value by Equation 3 modified and the
peak voltage by the upper graph of Figure 8.
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AN437 How to design snubber circuit for turn-off improvement
Equation 11
K L dV / dt OFF VRMS
= 2· · with L =
ξ RS + R E IRMS · 2 · π · f
Figure 12. Snubber capacitor value and normalized peak voltage (Z = VP/E)
according to the rms load current (assumptions: (dV/dt)OFF = 2.0 V/µs
and pure inductive load (worst case))
Snubber capacitor value (nF)
130
120
110
100
90
RS = 47 ohm
80
70
60
50 RS = 620 ohm
40
30
20
10 Load rms current: IRMS (A)
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4
Note: For inductive load with rms current higher than 4 A, Snubberless TRIACs are
recommended.
In the case of a 26 W drain pump, the rms load current is 0.3 A in transient operating (worst
case). The corresponding snubber capacitor value is about 10 nF, like defined previously.
The estimated peak voltage is 613 V. The estimated peak voltage is 20% higher than the
measured value due to the RLC model approximations (refer to Section 2.2.1) and because,
in the application, the load is not purely inductive and the peak voltage is limited by the load
resistance.
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Conclusion AN437
3 Conclusion
An RC snubber circuit is often used with TRIACs and presents different functions:
● Aid circuit for turn-off commutation
● Fast transient voltage suppressor
● Overvoltage limiter at turn-off commutation in case of inductive load with low rms
current
The RC snubber circuit drawback is the turn-on stress induced by the capacitor discharge.
Thanks to the high voltage capability of TRIACs, the snubber circuit design can be optimized
in order to reduce the capacitor value and, in the same way, reduce the snubber circuit cost.
Nevertheless, when low load inductances are controlled or, low damping factor or low slope
of reapplied voltage are considered, the snubber circuit design can lead to choose a low
snubber resistance value. To limit the snubber capacitor discharge through the TRIAC at
turn-on, the resistor value must be higher than a minimum value (typically 47 Ω for most
TRIACs and ACSTs).
14/18
AN437 RLC series circuit step response explanation
The RSCS snubber circuit and the load, L and R, make up a resonant circuit.
The electrical circuit analyzed in this Appendix is shown in Figure 13
Figure 13. Application circuit and its equivalent diagram at turn-off commutation
L R L R IT
IT RS RS
VMains
VT ≈E
CS VT
IG CS
G VCs
Note: In this Appendix the equations 1 to 6 are reproduced here with the same numbering to
facilitate use of this application note.
For a second order linear differential equation with a step function input, the voltage
variation across the snubber capacitance (VCs(t)) and the TRIAC (VT(t)) is given by:
Equation 1
2 .ξ dV Cs ( t )
2
1 d V Cs ( t )
· + · + V Cs ( t ) = E
ω0
2
dt
2
ω0 dt
Equation 2
dV Cs ( t )
VT ( t) = R S · C S · + V Cs ( t )
dt
Equation 3
(R S + R )(Ω ) CS (F )
ξ= ·
2 L(H )
Equation 4
1
ω 0 ( rad / s ) =
L ( H ) ·C S ( F )
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RLC series circuit step response explanation AN437
Equation 5
L·ω
E= 2 · VRMS · sin( ϕ ) with sin( ϕ ) =
R + (L · ω ) 2
2
Equation 6
RS
M =
RS + R
The voltage variation (VT(t)) across the TRIAC depends on the damping factor coefficient.
For each damping factor, the initial conditions to solve the differential equation are the same:
At t = 0
Equation 12
⎛ dV T ⎞ E·R S
⎜⎜ ⎟⎟ =
⎝ dt ⎠0 L
At t = ¥
Equation 13
VT ( ∞ ) = E
Note: The recovery current due to the storage charge is not considered in the initial conditions.
● Underdamped oscillating circuit: 0 ≤ ξ ≤ 1
Equation 14
⎛ ξ.ω0 ⎞ - ξ·ω ·t
VT ( t ) = E - E·⎜ cos( ωp ·t ) + ( 2·(1 - M) - 1)· · sin( ωp ·t ) ⎟ ·e 0
⎜ ωp ⎟
⎝ ⎠
Equation 15
2
ω p = ω 0 . 1 −ξ
Equation 16
- ω 0 ·t
VT ( t ) = E - E·(1 + ( 2·(1 - M ) - 1)·ω0 ·t ) ·e
Equation 17
ωp = ω0
16/18
AN437 Revision history
Equation 18
⎛ ξ.ω0 ⎞ - ξ·ω ·t
VT ( t ) = E - E·⎜ cosh( ωp ·t ) + ( 2 ·(1 - M) - 1)· · sinh( ωp ·t ) ⎟ .e 0
⎜ ωp ⎟
⎝ ⎠
Equation 19
2
ωp = ω0 . ξ −1
Thanks to these three equations and their derivatives, the variation between the peak
voltage and the slope of the voltage rise can be defined according to the damping factor and
the resistive load.
The damping factor determines the shape of the voltage wave (refer to Figure 14).
Figure 14. Voltage waves (VT(t)) for different damping factors (ξ) (assumption M = 1)
600
î=0
500
î = 0.25
400 î = 0.5
î = 0.75
300 î=1
î = 1.5
200 E = final value
ξ decreases
100
Time: t (µs)
0
0 0.25 0.5 0.75 1 1.25 1.5
When ξ is lower than 0.5, the voltage shape is not exponential and the maximum
instantaneous slope of voltage rise occurs at a time later than t = 0.
When ξ is equal and higher than 1, some overshoots occur even if the oscillating circuit is
damped and overdamped.
Revision history
17/18
AN437
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