Snubber Circuits - aboutme.samexent.com

Lecture Notes
Snubber Circuits
William P. Robbins
Dept. of Electrical and Computer Engineering
University of Minnesota
Outline
A.
Overview of Snubber Circuits
B.
Diode Snubbers
C.
Turn-off Snubbers
D.
Overvoltage Snubbers
E. Turn-on Snubbers
F. Thyristor Snubbers
Snubbers -11
W.P. Robbins
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
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
W.P. Robbins
Need for Diode Snubber Circuit
d i Df
+
Vd
-
Lσ
Rs
Df
Cs
Io
i Df (t)
Io
Vd
=
d t
Lσ
t
I rr
Sw
v
• Lσ = stray inductance
• S w closes at t =
0
• Rs - Cs = snubber circuit
•
Df
(t)
• Diode voltage
without snubber
t
Vd
Lσ
di Lσ
d t
diLσ
Diode breakdown if Vd + Lσ
> BVBD
dt
Snubbers - 3
W.P. Robbins
Equivalent Circuits for Diode Snubber
Lσ
+
Vd
-
cathode
Diode
snap-off
• Simplified snubber the capacitive snubber
Rs
Lσ
anode
+
+
v
Cs
-
Vd
i Df
-
t
Cs
• Rs = 0
• Worst case assumptiondiode snaps off instantaneously
at end of diode recovery
•v
= -v
Cs
Df
d2vCs
Governing equation -
•
Boundary conditions - vCs(0+) = 0 and iLσ(0+) = Irr
LσCs
=
Vd
•
dt2
+
vCs
LσCs
Snubbers - 4
W.P. Robbins
Performance of Capacitive Snubber
•
vCs(t) = Vd - Vd cos(ωot) + Vd
•
•
Cbase
sin(ωot)
Cs
ωo =
1
LσCs
Vcs,max = Vd
;

1 + 
 I 2
 rr 
Cbase = Lσ 

Vd
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
C base
Cs
5
2
Snubbers - 5
W.P. Robbins
Effect of Adding Snubber Resistance
Snubber Equivalent Circuit
Lσ
i(t)
-
+
V
d
-
v
Rs
Df
(t)
+
Cs
•
Governing equation
•
Boundary conditions
i(0+) = Irr
and
Lσ
d2i
di
i
+ Rs
+
=0
dt
Cs
dt2
Vd - IrrRs
di(0+)
=
dt
Lσ
Diode voltage as a function of time
Vdf
Vd (t) = - 1 ωa = ωo
e-αt
sin(ωat - φ + ζ) ; Rs ≤ 2 Rb
η cos(φ)
Rs
2
1- (α/ ωo) ; α = 2 L ; ωo =
σ


1
 (2-x) η 
-1
; φ = tan 

LσCs
 4 - ηx2
Lσ [Irr]2
Cs
Rs
Vd
η = C ; x = R ; Rb = I
; Cb =
; ζ = tan-1(α/ωa)
2
b
b
rr
Vd
Snubbers - 6
W.P. Robbins
Performance of R-C Snubber
3
•
•
•
•
•
At t = tm vDf(t) = Vmax
tan-1(ωa/α)
φ - ξ
tm =
+ ω
≥0
ωa
a
Vmax
Vd
η =
=1+
Cs
Cbase
Cbase =
Ls Irr2
Vd2
x=
and
R
V max
V
d
1
Rs
Rbase
Rbase =
base
= 1.3
2
1 + η-1 - x exp(-αtm)
and
R s,opt
C s = Cbase
R s I rr
V
d
Vd
Irr
0
0
1
Rs
R base
2
Snubbers - 7
W.P. Robbins
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
V
d
0
0
00
0
00 0
00 0 0
000
1
0
0
for R = R
s
s,opt
00
R s,op
R base
0
0
1
C s / Cbase
2
3
8
Snubbers - 8
W.P. Robbins
Need for Snubbers with Controlled Switches
Step-down converter
L1
V
d
L σ di
dt
L2
i
L3
Switch current and voltage waveforms
sw
Sw
Io
i
sw
L σ di
dt
Io
+
vsw
-
I rr
Io
V
d
vsw
to t
•
L1 , L 2 , L 3 = stray inductances
•
L σ = L1 + L 2 + L 3
t
1
t
4
3
t5
t6
Switching trajectory of switch
idealized
switching
loci
i sw
t6
t5
turn-off
to
t1
turn-on
t
• Overvoltage at turn-off
due to stray inductance
• Overcurrent at turn-on due to
diode reverse recovery
4
t3
Vd
vsw
Snubbers - 9
W.P. Robbins
Turn-off Snubber for Controlled Switches
i
+
V
D
f
DF
d
Turn-off
snubber
Io
Ds
S
-
Rs
w
i
Cs
Io
Df
V
Step-down converter with turn-off snubber
Cs
Equivalent circuit during switch turn
-off. • Simplifying assumptions
1. No stray inductance.
d
Io - i
i sw
Cs
sw
2. isw(t) = Io(1 - t/tfi)
3. isw(t) uneffected by snubber circuit.
Snubbers - 10
W.P. Robbins
Turn-off Snubber Operation
•
•
I ot
I ot
Capacitor voltage and current for 0 < t < tfi iCs(t) =
tfi
2
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
Cs = Cs 1
Cs > C
s
1
Snubbers - 11
W.P. Robbins
Benefits of Snubber Resistance at Switch Turn-on
vs w
D
Io
f
• Ds shorts out Rs
during Sw turn-off.
Rs
V
d
Sw
t rr
Io
i
• During Sw turn-on, Ds reverse-biased and
Cs discharges thru Rs.
Ds
Cs
D
I rr
f
Vd
Io
i sw
Rs
I rr
• Turn-on with Rs > 0
discharge
of C s
t rr
• Turn-on with Rs = 0
vs w
V
i sw
Io
d
t ri
0
• Energy stored on Cs dissipated
in Rs rather than in Sw.
t
t ri + t rr
2
• Energy stored on Cs dissipated
in Sw.
• Extra energy dissipation in Sw
because of lengthened voltage
fall time.
• Voltage fall time kept quite
short.
Snubbers - 12
W.P. Robbins
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
WT = dissipation in
switch Sw
0
0.2
0.4
0.6
0.8
1
1.2
Iotfi
Cs1 =
2Vd
1.4
Wtotal = WR + WT
Cs / Cs1
i
Wbase = 0.5 VdIotfi
sw
Io
Cs < Cs1
RBSOA
Switching trajectory
Cs = Cs1
Cs > Cs1
V
d
vs w
Snubbers - 13
W.P. Robbins
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
Vd
Rs = 0.2 Io
Snubbers - 14
W.P. Robbins
Overvoltage Snubber
Lσ
+
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 Inductance) across Sw as it
turns off.
v
V
d
s
w
o
t
fi
•
Switch Sw waveforms without overvoltage snubber
•
tfi = switch current fall time ; kVd = overvoltage on Sw
diLσ
Io
• kVd = Lσ
= Lσ
dt
tfi
kVdtfi
• Lσ =
Io
Snubbers - 15
W.P. Robbins
Operation of Overvoltage Snubber
i
+
• Dov on for 0 < t <
Lσ
L
σ
V
d
-
R
Dov
C
ov
• tfi <<
π
π
LσCov
2
LσCov
2
+
ov
v
-
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. Snubbers - 16
W.P. Robbins
Overvoltage Snubber Design
•
Limit
vsw,max to 0.1Vd
kVd tfi
Io
• Using L
=
• Cov =
kVdtfiIo2
Io(0.1Vd)2
= Io
Lο
Cov
in above equation yields
€
=
100k tfi Io
Vd
• Cov = 200 k Cs1 where Cs1 =
tfiIo
2Vd
which is used
in turn-off snubber
• Choose Rov so that the transient recovery of Cov is critically
damped so that ringing is minimized. For a critically damped
circuit Q = 1 =
•
€
Rov =
ω o Lσ
=
Rov
Lσ 1
C ov Rov
.
0.1Vd
Io
• Check€that the recovery time of Cov (2.3L /Rov) is less
than off-time duration, toff, of the switch Sw.
•
With
choice
of
Rov from above, trecovery is
trecovery = 23 k tf i
Snubbers - 17
W.P. Robbins
Turn-on Snubber
+
D
I
f
V
d
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
Switching trajectory with and without turn-on snubber.
Ls
di sw
dt
v
V
d
sw
Snubbers - 18
W.P. Robbins
Turn-on Snubber Operating Waveforms
v
Small values of snubber inductance (Ls < Ls1)
•
disw
controlled by switch Sw
dt
and drive circuit.
• Δvsw =
V
tri
i
Io
s
w
v
disw
Vd
Io
•
limited by circuit to
<
dt
Ls
tri
•
d
LsIo
Large values of snubber inductance (Ls > Ls1)
• Ls1 =
I rr
s
w
t ri
t rr
I rr
s
w
reduced
V
d
Io
Vdtri
Io
Irr reduced when Ls > Ls1 because Irr proportional to
i
disw
dt
s
w
t
on
≈
Ls Io
V
d
>
ri t
rr+ t
Snubbers - 19
W.P. Robbins
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
Ls
vs
w
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
Snubbers - 20
W.P. Robbins
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
Snubbers - 21
W.P. Robbins
Thyristor Snubber Circuit
P
3-phase thyristor circuit with snubbers
• van(t) = Vssin(ωt), vbn(t) = Vssin(ωt - 120°),
vcn(t) = Vssin(ωt - 240°)
1
van +
Lσ
- vbn +
Lσ
v cn +
Lσ
-
5
3
A
B
-
i
d
C
Cs
6
4
2
Rs
Phase-to-neutral waveforms
• vLL(t) =
v
3 Vssin(ωt - 60°)
• Maximum rms line-to-line voltage VLL =
v
α
an
bn
3
V
2 s
v LL = v
bn
v
an=
v
ba
ω t
1
Snubbers - 22
W.P. Robbins
Equivalent Circuit for SCR Snubber Calculations
Assumptions
• Trigger angle α = 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(ωt1) =
• Worst case stray inductance Lσ gives rise to reactance equal
to or less than 5% of line impedance.
• Line impedance =
Vs
2Ia1
=
2VLL
6Ia1
=
i
2 VLL
VLL
3Ia1
+
V (ω t1)
ba
-
where Ia1 = rms value of fundamental component of the
line current.
VLL
•
ωLσ = 0.05
3Ia1
2 Lσ
Lσ
P
Cs
T1 after
recovery
T 3 (on)
i
T1
Rs
A
Snubbers - 23
W.P. Robbins
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 = Lσ
 I 2
 rr 


Vd
diLσ
dt
•
From snubber equivalent circuit 2 Lσ
•
Irr =
•
Vd =
•
Cs = Cbase =
•
Snubber resistance Rs = 1.3 Rbase = 1.3
•
•
diLσ
trr
dt
2VLL
=
trr =
2Lσ
=
2VLL
0.05 VLL
2 3 Ia1ω
2 VLL
trr = 25 ωIa1trr
2 VLL
Rs
=
0.05 VLL
3 Ia1ω
1.3
25 ωI
 2
a1trr

=


 2VLL 
2VLL
25ωIa1trr
=
8.7 ωIa1trr
VLL
Vd
Irr
0.07 VLL
ωIa1trr
Energy dissipated per cycle in snubber resistance = WR
•
WR =
LσIrr2
2
+
CsVd2
2
=
18 ω Ia1 VLL(trr)2
Snubbers - 24
W.P. Robbins