Lecture Notes
Snubber Circuits
Outline
A.
Overview of Snubber Circuits
B.
Diode Snubbers
C.
Turn-off Snubbers
D.
Overvoltage Snubbers
E.
Turn-on Snubbers
F.
Thyristor Snubbers
Copyright © by John Wiley & Sons 2003
Snubbers - 1
Overview of Snubber Circuits for Hard-Switched Converters
Function: Protect semiconductor devices by:
• Limiting device voltages during turn-off transients
• Limiting device currents during turn-on transients
• Limiting the rate-of-rise (di/dt) of currents through
the semiconductor device at device turn-on
• Limiting the rate-of-rise (dv/dt) of voltages across
the semiconductor device at device turn-off
• Shaping the switching trajectory of the device as it
turns on/off
Copyright © by John Wiley & Sons 2003
Types of Snubber Circuits
1. Unpolarized series R-C snubbers
• Used to protect diodes and thyristors
2. Polarized R-C snubbers
• Used as turn-off snubbers to shape the turn-on
switching trajectory of controlled switches.
• Used as overvoltage snubbers to clamp voltages
applied to controlled switches to safe values.
• Limit dv/dt during device turn-off
3. Polarized L-R snubbers
• Used as turn-on snubbers to shape the turn-off
switching trajectory of controlled switches.
• Limit di/dt during device turn-on
Snubbers - 2
Need for Diode Snubber Circuit
di
+
V
d
-
Ls
Rs
Df
Cs
Io
i Df (t)
Io
Df
=
d t
V
d
Ls
t
I rr
Sw
v
• Ls = stray inductance
• S w closes at t =
0
• Rs - Cs = snubber circuit
•
Df
(t)
• Diode voltage
without snubber
Vd
Ls
t
di Ls
d t
diLs
Diode breakdown if Vd + Ls
> BVBD
dt
Copyright © by John Wiley & Sons 2003
Snubbers - 3
Equivalent Circuits for Diode Snubber
Ls
+
Vd
-
Diode
snap-off
cathode
• Simplified snubber the capacitive snubber
Rs
Ls
anode
+
+
v
Cs
-
Vd
i Df
-
t
• Rs = 0
• Worst case assumptiondiode snaps off instantaneously
at end of diode recovery
•v
= -v
Cs
Df
d2vCs
•
Boundary conditions - vCs(0+) = 0 and iLs(0+) = Irr
LsCs
=
Vd
Governing equation -
dt2
+
vCs
•
Copyright © by John Wiley & Sons 2003
Cs
!LsCs
Snubbers - 4
Performance of Capacitive Snubber
•
vCs(t) = Vd - Vd cos(wot) + Vd
•
•
Cbase
sin(wot)
Cs
wo =
Vcs,max =
1
LsCs
;
Ï
Ì
Vd 1!+!
Ó
È I ˘2
Í rr ˙
Cbase = Ls Í
˙
ÎV d˚
Cbase ¸
˝
1!+!
!
˛
Cs
5
4
V
Cs,max
Vd
3
2
1
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
C base
Cs
Copyright © by John Wiley & Sons 2003
Snubbers - 5
Effect of Adding Snubber Resistance
Snubber Equivalent Circuit
Ls
i(t)
-
+
V
d
-
v
Rs
Df
(t)
+
•
Governing equation
•
Boundary conditions
Cs
i(0+) = Irr
and
Ls
d2i
di
i
+ Rs
+
=0
2
dt
C
dt
s
Vd!-!IrrRs
di(0+)
=
dt
Ls
Diode voltage as a function of time
Vdf
Vd (t) = - 1 wa = wo
e-at
sin(wat - f + z) ; Rs ≤ 2 Rb
h!cos(f)
Rs
1-!(a/!wo)2 ; a = 2!L ; wo =
s
È
˘
1
Í (2-x) h ˙
-1
; f = tan Í
˙
LsCs
Î 4!-!hx2˚
Ls![Irr]2
Cs
Rs
Vd
h = C ; x = R ; Rb = I
; Cb =
; z = tan-1(a/wa)
2
b
b
rr
Vd
Copyright © by John Wiley & Sons 2003
Snubbers - 6
Performance of R-C Snubber
3
•
At t = tm vDf(t) = Vmax
•
tan-1(wa/a)
f!-!x
tm =
+ w
≥0
wa
a
•
Vmax
=1+
Vd
•
h =
•
Cs
Cbase
Ls!Irr2
Cbase =
Vd2
x=
and
R
V max
V
d
Rbase
Copyright © by John Wiley & Sons 2003
base
1
Rs
Rbase =
= 1.3
2
1!+!h-1!-!x exp(-atm)
and
R s,opt
C s = Cbase
R sI rr
V
d
Vd
Irr
0
0
1
Rs
R base
Snubbers - 7
2
Diode Snubber Design Nomogram
Wtot
2
L s I r r /2
3
WR
2
L s I r r /2
0
2
0
V max
0
0
0
Vd
00
0 0
0 0
0 0 00
0 00 0 0
1
0
0
for R
s
= R
s,opt
00
R s,op
R base
0
0
Copyright © by John Wiley & Sons 2003
1
C s / Cbase
2
3
Snubbers - 8
Need for Snubbers with Controlled Switches
Step-down converter
L1
V
d
L s di
dt
L2
i
L3
Switch current and voltage waveforms
sw
Sw
Io
i
sw
I
+
vsw
-
L s di
dt
o
Io
V
d
vsw
to t
•
I rr
L1 , L 2 , L 3 = stray inductances
1
t
t
4
3
t
5
t6
Switching trajectory of switch
•
L s = L1 + L 2 + L 3
idealized
switching
loci
i sw
t 5
t6
turn-off
to
t1
turn-on
t
• Overcurrent at turn-on due to
diode reverse recovery
4
t3
Vd
Copyright © by John Wiley & Sons 2003
• Overvoltage at turn-off
due to stray inductance
vsw
Snubbers - 9
Turn-off Snubber for Controlled Switches
i
+
V
D
f
DF
d
Turn-off
snubber
Io
Ds
S
-
Step-down converter with turn-off snubber
Rs
w
i
Cs
Cs
Equivalent circuit during switch turn-off.
Io
Df
V
d
• Simplifying assumptions
Io - i
i sw
Cs
1. No stray inductance.
sw
2. isw(t) = Io(1 - t/tfi)
3. isw(t) uneffected by snubber circuit.
Copyright © by John Wiley & Sons 2003
Snubbers - 10
Turn-off Snubber Operation
•
•
2
I ot
I ot
Capacitor voltage and current for 0 < t < tfi iCs(t) =
tfi
and v (t) =
Cs
2C t
s fi
Iotfi
For Cs = Cs1, vCs = Vd at t = tfi yielding Cs1 =
2Vd
Circuit waveforms for varying values of Cs
i
i
sw
i
sw
sw
Io
i
i
Df
tf i
i
i
Df
Df
t
tf i
fi
Cs
V
d
v
Cs
Cs
< Cs 1
Copyright © by John Wiley & Sons 2003
Cs = Cs 1
Cs > C
s
1
Snubbers - 11
Benefits of Snubber Resistance at Switch Turn-on
vs w
D
Io
f
Io
• Ds shorts out Rs
during Sw turn-off.
Rs
V
d
Sw
• During Sw turn-on,
Ds reverse-biased and
Cs discharges thru Rs.
Ds
Cs
i
D
t rr
I rr
f
i sw
Io
Vd
Rs
I rr
discharge
of C s
t rr
vs w
V
i sw
Io
d
t ri
0
t
t ri + t rr
2
• Turn-on with Rs > 0
• Turn-on with Rs = 0
• Energy stored on Cs dissipated
in Rs rather than in Sw.
• Energy stored on Cs dissipated
in Sw.
• Voltage fall time kept quite
short.
• Extra energy dissipation in Sw
because of lengthened voltage
fall time.
Copyright © by John Wiley & Sons 2003
Snubbers - 12
Effect of Turn-off Snubber Capacitance
1
Energy dissipation
W
/
total Wbase
W
0.8
WR = dissipation in
resistor
0.6
W / Wbase
R
0.4
WT / W base
W
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
Iotfi
Cs1 =
2Vd
1.4
Cs / Cs1
i
WT = dissipation in
switch Sw
Wtotal = WR + WT
sw
Io
Wbase = 0.5 VdIotfi
Cs < Cs1
RBSOA
Switching trajectory
Cs = Cs1
Cs > Cs1
V
Copyright © by John Wiley & Sons 2003
d
vs w
Snubbers - 13
Turn-off Snubber Design Procedure
Selection of Cs
• Minimize energy dissipation (WT) in BJT at turn-on
• Minimize WR + WT
• Keep switching locus within RBSOA
Snubber recovery time (BJT in on-state)
• Reasonable value is Cs = Cs1
• Capacitor voltage = Vd exp(-t/RsCs)
• Time for vCs to drop to 0.1Vd is 2.3 RsCs
• BJT must remain on for a time of 2.3 RsCs
Selection of Rs
Vd
• Limit icap(0+) = R < Irr
s
• Usually designer specifies Irr < 0.2 Io so
Copyright © by John Wiley & Sons 2003
Vd
Rs = 0.2 Io
Snubbers - 14
Overvoltage Snubber
Ls
+
D
f
Io
R
i
ov
Vd
-
kV
d
s
w
Io
Sw
Dov
C ov
• Step-down converter with
overvoltage snubber comprised
of Dov, Cov, and Rov.
• Overvoltage snubber limits
overvoltage (due to stray I
nductance) across Sw as it
turns off.
Copyright © by John Wiley & Sons 2003
v
V
d
s
w
t
o
fi
•
Switch Sw waveforms without overvoltage snubber
•
tfi = switch current fall time ; kVd = overvoltage on Sw
diLs
Io
• kVd = Ls
= Ls
dt
tfi
kVdtfi
• Ls =
Io
Snubbers - 15
Operation of Overvoltage Snubber
i
+
Ls
L
• Dov on for 0 < t <
s
V
d
-
R
Dov
C
ov
• tfi <<
+
ov
v
-
i
Cov
+
-
• Dov,Cov provide alternate path
for inductor current as Sw turns
off.
•
Switch current can fall to zero
much faster than Ls current.
•
Df forced to be on
(approximating a short ckt) by Io
after Swis off.
•
s
• Equivalent circuit while
inductor current decays to zero
+
C
ov
v
-
Cov
Ls
I
Equivalent circuit after turn-off
of Sw.
v
i
0
p!
i Ls(0+) = I o
t
(t) = Io cos[
Ls
! Ls!Cov
V
d
o
s
w
Copyright © by John Wiley & Sons 2003
v Cov (0+) = Vd
]
Discharge of C ov thru R ov
with time constant R ov C
ov
DV sw,max
Charge-up of C ov from L s
i
LsCov
2
LsCov
2
Ls
L
Vd
π
π
• Energy transfer from L s to Cov
Cov !(DV sw,max )2
Ls!(I o)2
=
2
2
Ls!Cov
4
Snubbers - 16
Overvoltage Snubber Design
• Cov =
•
•
Ls!Io2
(Dvsw,max)2
Limit Dvsw,max to 0.1Vd
Using Ls =
• Cov =
kVd!tfi
!!Io
kVdtfiIo2
!Io(0.1Vd)2
in equation for Cov yields
=
100k!tfi!Io
!!Vd
tfiIo
• Cov = 200 k Cs1 where Cs1 =
!2Vd
in turn-off snubber
which is used
• Recovery time of Cov (2.3RovCov) must be less
than off-time duration, toff, of the switch Sw.
•
Rov ≈
toff
2.3!Cov
Copyright © by John Wiley & Sons 2003
Snubbers - 17
Turn-on Snubber
+
D
V
d
I
f
Ls
o
+
f
Snubber
circuit
Ls
D
R
Ls
D
V
d
Ls
Sw
-
Io
R
D
Step-down converter
with turn-on snubber
D
Ls
Io
Ls
f
Sw
-
• Snubber reduces Vsw at switch
turn-on due drop across
inductor Ls.
• Will limit rate-of-rise of switch
current if Ls is sufficiently
large.
i sw
With
snubber
Without
snubber
Ls
Switching trajectory with and without turn-on snubber.
di sw
dt
v
Copyright © by John Wiley & Sons 2003
V
d
sw
Snubbers - 18
Turn-on Snubber Operating Waveforms
v
Small values of snubber inductance (Ls < Ls1)
disw
•
controlled by switch S w
dt
and drive circuit.
• Dvsw =
V
LsIo
tri
i
Irr reduced when Ls > Ls1 because Irr proportional to
Copyright © by John Wiley & Sons 2003
Io
s
w
t ri
i
disw
dt
t rr
I rr
s
w
reduced
V
Vdtri
• Ls1 =
Io
•
d
v
Large values of snubber inductance (Ls > Ls1)
disw
Vd
Io
•
limited by circuit to
<
dt
Ls
tri
I rr
s
w
d
Io
s
w
t
on
≈
Ls Io
V
>
ri t
rr+ t
d
Snubbers - 19
Turn-on Snubber Recovery at Switch Turn-off
+
D
Io
f
I o R Lsexp(-R Lst/L s )
Io R
Ls
is
w
V
d
-
Ls
R
Ls
D
vs
w
Ls
V
d
Io
t rv
Sw
• Switch waveforms at turn-off with turn-on snubber in circuit.
• Assume switch current fall time
tri = 0.
• Inductor current must discharge
thru DLs- RLs series segment.
• Overvoltage smaller if tfi smaller.
• Time of 2.3 Ls/RLs required for inductor current to decay to 0.1 Io
• Off-time of switch must be > 2.3 Ls/RLs
Copyright © by John Wiley & Sons 2003
Snubbers - 20
Turn-on Snubber Design Trade-offs
Selection of inductor
• Larger Ls decreases energy dissipation in switch at turn-on
• Wsw = WB (1 + Irr/Io)2 [1 - Ls/Ls1]
• WB = VdIotfi/2 and Ls1 = Vdtfi/Io
• Ls > Ls1 Wsw = 0
• Larger Ls increases energy dissipation in RLs
• WR = WB Ls / Ls1
• Ls > Ls1 reduces magnitude of reverse recovery current Irr
• Inductor must carry current Io when switch is on - makes
inductor expensive and hence turn-on snubber seldom used
Selection of resistor RLs
• Smaller values of RLs reduce switch overvoltage Io RLs at turn-off
• Limiting overvoltage to 0.1Vd yields RLs = 0.1 Vd/Io
• Larger values of RLs shortens minimum switch off-time of 2.3 Ls/RLs
Copyright © by John Wiley & Sons 2003
Snubbers - 21
Thyristor Snubber Circuit
P
Ls
- vbn +
Ls
v cn +
Ls
-
3-phase thyristor circuit with snubbers
• van(t) = Vssin(wt), vbn(t) = Vssin(wt - 120°),
vcn(t) = Vssin(wt - 240°)
1
va n +
-
5
3
A
B
i
d
C
Cs
6
4
Phase-to-neutral waveforms
• vLL(t) =
v
2
Rs
v
a
an
bn
3 Vssin(wt - 60°)
• Maximum rms line-to-line voltage VLL =
Copyright © by John Wiley & Sons 2003
3
V
2 s
v LL = v
bn
v
an=
v
ba
w t
1
Snubbers - 22
Equivalent Circuit for SCR Snubber Calculations
Assumptions
• Trigger angle a = 90° so that vLL(t) = maximum =
2 VLL
Equivalent circuit after T1 reverse recovery
• Reverse recovery time trr << period of ac waveform so that
vLL(t) equals a constant value of vba(wt1) =
• Worst case stray inductance Ls gives rise to reactance equal
to or less than 5% of line impedance.
• Line impedance =
Vs
=
2VLL
=
VLL
+
V (w t1)
ba
-
2Ia1
6Ia1
3Ia1
where Ia1 = rms value of fundamental component of the
line current.
VLL
•
wLs = 0.05
3Ia1
Copyright © by John Wiley & Sons 2003
i
2 VLL
2 Ls
Ls
P
T1 after
recovery
T 3 (on)
Cs
i
A
T1
Rs
Snubbers - 23
Component Values for Thyristor Snubber
•
•
Use same design as for diode snubber but adapt the formulas to the
thyristor circuit notation
Snubber capacitor Cs = Cbase = Ls
È
˘2
Í Irr ˙
Í
˙
ÎVd ˚
diLs
dt
•
From snubber equivalent circuit 2 Ls
•
Irr =
•
Vd =
•
Cs = C base =
•
Vd
Snubber resistance Rs = 1.3 Rbase = 1.3
Irr
•
•
diLs
trr
dt
=
2VLL
2Ls
t rr =
2VLL
0.05!VLL
2!
3!Ia1 w
=
2 V LL
trr = 25 wIa1 trr
2 VLL
Rs
=
0.05!VLL
1.3
3!Ia1w
È25!wI
˘ 2
a1trr˙
Í
=
Í
˙
Î ! 2VLL ˚
2V LL
25wIa1 trr
=
8.7!wIa1 trr
VLL
0.07!VLL
!wIa1 trr
Energy dissipated per cycle in snubber resistance = W R
•
WR =
LsIrr 2
2
Copyright © by John Wiley & Sons 2003
+
CsV d2
2
=
18 w I a1 V LL(trr )2
Snubbers - 24