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 -1 1 W.P. Robbins Overview of Snubber Circuits for Hard-Switched Converters
Function: Protect semiconductor devices by: Types of Snubber Circuits
• Limiting device voltages during turn-off transients 1. Unpolarized series R-C snubbers • Used to protect diodes and thyristors • Limiting device currents during turn-on transients
2. Polarized R-C snubbers • Limiting the rate-of-rise (di/dt) of currents through • Used as turn-off snubbers to shape the turn-on the semiconductor device at device turn-on switching trajectory of controlled switches. • Used as overvoltage snubbers to clamp voltages applied to controlled switches to safe values. • Limiting the rate-of-rise (dv/dt) of voltages across • Limit dv/dt during device turn-off the semiconductor device at device turn-off
3. Polarized L-R snubbers • Shaping the switching trajectory of the device as it • Used as turn-on snubbers to shape the turn-off turns on/off switching trajectory of controlled switches. • Limit di/dt during device turn-on
Snubbers - 2 W.P. Robbins Need for Diode Snubber Circuit
di Df Vd = d t L L σ + σ R Io s I t o i Df (t) D I Vd f Cs rr
- Sw
v (t) t Df Vd • Lσ = stray inductance
• S w closes at t = 0 • Diode voltage di L σ without snubber Lσ • Rs - Cs = snubber circuit d t
diLσ • Diode breakdown if V + L > BV d σ dt BD
Snubbers - 3 W.P. Robbins Equivalent Circuits for Diode Snubber
L σ • Simplified snubber - the capacitive snubber + R s L Diode cathode σ Vd snap-off anode - + + v Vd Cs Cs - - i Df t
• Rs = 0 • Worst case assumption- • v = -v diode snaps off instantaneously Cs Df at end of diode recovery
2 d vCs vCs Vd • Governing equation - + = dt2 LσCs LσCs
+ + • Boundary conditions - vCs(0 ) = 0 and iLσ(0 ) = Irr
Snubbers - 4 W.P. Robbins Performance of Capacitive Snubber
Cbase • vCs(t) = Vd - Vd cos(ωot) + Vd sin(ωot) Cs
2 1 Irr • ω = ; C = L o base σ V LσCs d
Cbase • Vcs,max = Vd 1 + 1 + Cs
5
4
V 3 Cs,max
Vd 2
1
0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
C base C Snubbers - 5 s 5 W.P. Robbins Effect of Adding Snubber Resistance
Snubber Equivalent Circuit
Lσ i(t) d2i di i • Governing equation L + R + = 0 + - σ 2 s dt C R s dt s V v (t) d Df • Boundary conditions + V - I R Cs + di(0 ) d rr s - + i(0 ) = Irr and = dt Lσ
Diode voltage as a function of time
Vdf e-αt (t) = - 1 - sin(ω t - φ + ζ) ; R ≤ 2 R Vd η cos(φ) a s b
R 2 s 1 -1 (2-x) η ωa = ωo 1- (α/ ωo) ; α = 2 L ; ωo = ; φ = tan σ LσCs 4 - ηx2 C R V L [I ]2 s s d σ rr -1 η = C ; x = R ; Rb = I ; Cb = 2 ; ζ = tan (α/ωa) b b rr Vd Snubbers - 6 W.P. Robbins Performance of R-C Snubber
3 • At t = tm vDf(t) = Vmax R s,opt C s = Cbase = 1.3 -1 R tan (ωa/α) φ - ξ base • t = ω + ω ≥ 0 m a a 2
V Vmax max • = 1 + 1 + -1 - x exp(- t ) η α m V Vd d
Cs Rs 1 • η = and x = Cbase Rbase R s I rr 2 V Ls Irr Vd d • C = and R = base 2 base I 0 Vd rr 0 1 R s 2 R base
Snubbers - 7 W.P. Robbins Diode Snubber Design Nomogram
Wtot 2 3 L s I rr /2
WR 2 L s I rr /2
0
2 0 V 0 max for R = R V s s,opt 0 d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 R s,op
R base
0 0 1 2 3 Snubbers - 8 C / C s base 8 W.P. Robbins Need for Snubbers with Controlled Switches
Step-down converter Switch current and voltage waveforms di Lσ L dt 1 L 2 I rr I o i sw V d di i Lσ V I sw + I o dt d o vsw S w L 3 - vsw t t t t t 3 t 5 6 o 1 4 • = stray inductances L1 , L 2 , L 3
Switching trajectory of switch • = Lσ L1 + L 2 + L3 idealized i sw switching t loci t 6 5
t turn-off o • Overvoltage at turn-off t1 due to stray inductance turn-on • Overcurrent at turn-on due to diode reverse recovery t 4 t 3 vsw Vd Snubbers - 9 W.P. Robbins Turn-off Snubber for Controlled Switches
Turn-off D snubber i f I + D o F
V d Ds Step-down converter with turn-off snubber
S R s w i - C C s s
Equivalent circuit during switch turn -off. I o D f • Simplifying assumptions
1. No stray inductance. V d I - i o sw 2. isw(t) = Io(1 - t/tfi) i sw C s 3. isw(t) uneffected by snubber circuit.
Snubbers - 10 W.P. Robbins Turn-off Snubber Operation
2 Iot I o t • Capacitor voltage and current for 0 < t < t i (t) = and v (t) = fi Cs t Cs 2C t fi s fi
Iotfi • For Cs = Cs1, vCs = Vd at t = tfi yielding Cs1 = 2Vd
Circuit waveforms for varying values of Cs
i i i sw sw sw
I o i D i i f Df Df t t fi t fi fi i C s
V d
v Cs Snubbers - 11 Cs < C Cs = Cs1 C s > C s1 s W.P. Robbins 1 Benefits of Snubber Resistance at Switch Turn-on
vsw t D I I rr f o o • D shorts out R R s s i I s D rr during Sw turn-off. f V d V • During Sw turn-on, d S I w Ds D reverse-biased and i o s sw R s C s Cs discharges thru Rs. I rr
• Turn-on with Rs > 0
discharge t rr • Energy stored on Cs dissipated of C s in Rs rather than in Sw.
• Turn-on with Rs = 0 vsw • Voltage fall time kept quite short. • Energy stored on Cs dissipated V I o d in Sw. i sw t t ri 2 • Extra energy dissipation in Sw 0 because of lengthened voltage t ri + t rr fall time. 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 WT = dissipation in W / W R base 0.4 switch Sw WT / Wbase W 0.2 Iotfi Cs1 = 2Vd 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Wtotal = WR + WT Cs / Cs1
i sw Wbase = 0.5 VdIotfi
I o
Cs < Cs1 RBSOA Switching trajectory
Cs = Cs1
Cs > Cs1
V v d sw 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 R C Selection of Rs s s
Vd • Limit i (0+) = < I cap Rs rr
Vd • Usually designer specifies I < 0.2 I so = 0.2 I rr o Rs o
Snubbers - 14 W.P. Robbins Overvoltage Snubber
L σ kV d + i D R s f I o ov w V d I V o d Sw Dov - Cov v s w t o fi • Step-down converter with overvoltage snubber comprised of Dov, Cov, and Rov. • Switch Sw waveforms without overvoltage snubber
• t = switch current fall time ; kV = overvoltage on S • Overvoltage snubber limits fi d w overvoltage (due to stray diLσ Io Inductance) across Sw as it • kVd = Lσ = Lσ turns off. dt tfi
kVdtfi • Lσ = Io Snubbers - 15 W.P. Robbins Operation of Overvoltage Snubber
π LσCov i • D on for 0 < t < Lσ ov 2 L + σ R π LσCov Dov ov • t << fi 2 V d + C v - ov 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
Lο • Limit v to 0.1V = Io sw,max d Cov
kVd tfi • Using L = in above equation yields Io € 2 kVdtfiIo 100k tfi Io • C = = ov 2 V Io(0.1Vd) d tfiIo • Cov = 200 k Cs1 where Cs1 = which is used 2Vd 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
ωoLσ Lσ 1 circuit Q = 1 = = . Rov Cov Rov
0.1Vd • Rov = 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 tfi
Snubbers - 17 W.P. Robbins Turn-on Snubber
+ Step-down converter + with turn-on snubber D D I f f o R L Ls s Io Snubber • Snubber reduces Vsw at switch D circuit Ls turn-on due drop across R V V L Ls d inductor Ls. d s D D f • Will limit rate-of-rise of switch Ls current if Ls is sufficiently Sw large. - Sw -
isw I o With Without snubber snubber Switching trajectory with and without turn-on snubber. di L sw s dt v sw V d Snubbers - 18 W.P. Robbins Turn-on Snubber Operating Waveforms
v s I Small values of snubber inductance (Ls < Ls1) rr w
disw • controlled by switch Sw dt V d and drive circuit. I o
LsIo • Δv = sw t i ri s t t w ri rr
Large values of snubber inductance (L > L ) v I rr s s1 s reduced w disw Vd Io • limited by circuit to < dt L t s ri V d I o Vdtri • L = s1 I i o s w di sw L s I o • I reduced when L > L because I proportional to t ≈ > t + t rr s s1 rr on ri rr dt V d Snubbers - 19 W.P. Robbins Turn-on Snubber Recovery at Switch Turn-off
+ I R D I o Ls f o IoRLsexp(-R Lst/Ls) i s w V I d R o V Ls d Ls v D s Ls t rv w
- Sw • Switch waveforms at turn-off with turn-on snubber in circuit.
• Assume switch current fall time • Overvoltage smaller if tfi smaller. tri = 0. • Time of 2.3 Ls/RLs required for inductor current to decay to 0.1 Io • Inductor current must discharge thru DLs- RLs series segment. • 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 2 • Wsw = WB (1 + Irr/Io) [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
1 3 5 v - an + Lσ A 3-phase thyristor circuit with snubbers v L - bn + σ B i d • v (t) = V sin(ωt), v (t) = V sin(ωt - 120°), L an s bn s - vcn + σ vcn(t) = Vssin(ωt - 240°) C
C s 4 6 2 R s
Phase-to-neutral waveforms v v α bn an • vLL(t) = 3 Vssin(ωt - 60°) 3 • Maximum rms line-to-line voltage V = V LL 2 s v = v v = v ω t LL bn an ba 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) = 2 VLL i L σ
2 L σ P • Worst case stray inductance L gives rise to reactance equal σ + T after 1 C s to or less than 5% of line impedance. recovery V (ω t ) V 2V V ba 1 i s LL LL T1 R • Line impedance = = = - T 3 (on) s 2Ia1 6Ia1 3Ia1 A where Ia1 = rms value of fundamental component of the line current. VLL • ωLσ = 0.05 3Ia1
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
2 Irr • Snubber capacitor Cs = Cbase = Lσ Vd
diLσ • From snubber equivalent circuit 2 L = 2 V σ dt LL
diLσ 2VLL 2VLL • Irr = trr = trr = trr = 25 ωIa1trr dt 2Lσ 0.05 VLL 2 3 Ia1ω
• Vd = 2 VLL
0.05 V 25 I t 2 8.7 I t LL ω a1 rr ω a1 rr • C = C = = s base V 3 Ia1ω 2VLL LL
Vd • Snubber resistance Rs = 1.3 Rbase = 1.3 Irr
2VLL 0.07 VLL • Rs = 1.3 = 25ωIa1trr ωIa1trr
• Energy dissipated per cycle in snubber resistance = WR
L I 2 C V 2 σ rr s d 2 • WR = + = 18 ω Ia1 VLL(trr) 2 2 Snubbers - 24 W.P. Robbins