Transcript A Unified Model for the ZVS DC-DC Converters with Active Clamp

A Unified Model for the ZVS DC-DC Converters
With Active Clamp
by
N.Lakshminarasamma, B. Swaminathan,
Prof V. Ramanarayanan, IISC
Department of Electrical Engineering
Indian Institute of Science
Bangalore
Linear Regulator
(1-K)Vg
Vg
+
-
R
KVg
Series Regulator Efficiency = K
 Best dynamic performance
 Very good regulation
 Poor efficiency and bulky
Switching Regulator
TON
Vg
TOFF
+
-
Switching Voltage Regulator
 Ideal losses zero
 Output discontinuous
 Smoothing filter needed
R
Typical Converter
Vg
S
C
L
Vo
 Switches control power flow
 Reactive elements smoothen power flow
 Both are non-dissipative elements
Classification of SMPS
SWITCHED MODE
POWER
CONVERTERS
HARD SWITCHED
POWER
CONVERTERS
Resonant Load
Conve rters
SOFT-SWITCHED
POWER CON VER TERS
Quasi-Resonant
Conve rters
Resonant Transition
Conve rters
Active Clamp
Conve rters
Hard Switching Converter
P
T1
T2
V
I
t
I
V
t
Soft Switching Converter
V
I
OFF/ON
Transient
ZCS
V
t
I
I
ZVS
t
ON/OFF
Transient
V
Active Clamp ZVS Buck Converter
CR
CR
V
S1
+
CR
CR
DC
CC
S2
Throw1
LR
S
LR
1
Pole
I
D
Clamp Capacitor
Clamp Switch
s2
D
Interval T1 - Zero-voltage Turn-on
CR
CR
D2
D1
VC LR i(t)
i(0) = -I*
S1
V
S2 i(T1) = I
V
i(t)   I 
t
LR
*
I
D
Vo
I  I*
T1
LR
V

T1
I* 
 I N 1



Ts
I


IN - Normalized
current
Interval T2 - Resonant Commutation
v(t)
CR
v(0) = V
v(T2) = 0
CR
D2
D1
VC LR
S1
V
D
CR
t
sin
LR
L R CR
v(t)  Vcos
I
i(0) = I
S2
i(t)  I  V
i(t)
t
L R CR
Vo
i(T2)  I  V
v(T2)  0
CR
LR
T2 

LR CR
2
f
T2  fS

 S
Ts 2 2 f R 4f R
Interval T3 - Power-on Duration
CR
CR
D2
D1
VC LR
i(t)
I
S1
V
S2
D
Vo
S1 turned off at end of T3 and CR almost instantly charges to V+VC.
CR
i(t)  I  V
LR
T1 T2  T3 DTs
T3
T1 T2
D 
Ts
Ts Ts
Interval T4 – Assisted Turn-off
CR
i(T4) = I
CR
D2
D1
VC LR
i(t)
I
S1
V
S2
i(t)  I  V
CR V  VC

t
LR
LR
i( T4)  I
Vo
D
T4 
V
CR
LR
V  VC
LR
T4 1 fS

Ts 1  2  f R
VC

V
Interval T5 – Resonant Commutation
CR
v(0) = 0
CR
D2
D1
VC LR
i(t)
I
S1
V
S2 v(T5) = V
i(t)  I   V  VC 
CR
t
sin
LR
L R CR

t
v(t)   V  VC  1  cos

LR CR




D
Vo
I(T5)  I  V 1 
V ( T5 ) = V
CR
LR
T5  LR CR cos

1
  
T5 fS

cos1 

Ts 2  fR
1



Interval T6 – Power Freewheeling Duration
CR
CR
D2
D1
VC LR
i(t)
I
S1
V
S2
D
Vo
At the end of T6 interval current i(t) has reversed and Flows through
MOSFET of S2. CR almost instantly discharges to zero. Now S1 may be
switched on with zero voltage across the same.
Theoretical Waveforms
Resonant Inductor LR Current
I
I(T5)
t
I*
kI(T5)
T1
T2
T3
T4
T5
T6
I Active Switch S1
I Freewheel Diode
t
Vg
Pole Voltage Vo
t
Clamp Ratio and Clamp Voltage
Resonant Inductor LR Current
I
I(T5)
t
I*
kI(T5)
T1
T2
T3
T4
I
T5
T6
Clamp Capacitor Current
t
kI(T5)
I T5  V CR
k2
1
I (T5)T6
VC
A
k 1 LR


I(T5)
T6
 k  1 Ts / T6
 k 1 1 
 1  T6 2  f 
R 


f 
      S 
2  fR 

Steady State Equivalent Circuit Model
(1+k)LR/Ts
1: D
Steady State Equivalent Circuit for Active
Clamp Buck converter
Vo
L I(1  k)
 D R
Vg
Vg Ts
Vo  DVg 
LR I(1  k)
Ts
Equivalent Circuit Models of Other Converters
Rd
Rd
1-D: 1
1:D
1-D: 1
Rd1
Rd2
1-D: 1
1: D
Equivalent circuits of the active clamped ZVS boost, buck-boost and
cuk converters
Spread Sheet Design
..\pesc04\work\spreadsheetdesign.xls
Table 1 : Spreadsheet Organisation for the Steady-state Performance Solution
Inductor Current
Throw Voltage
Resonant Inductor
Resonant Capacitor
Resonant Freq r/s
Resonant Freq Hz
Switching Freq
Switching Period
Switch Initial Current
Clamp Initial Voltage
Current after T6
Clamp Voltage
Duty Ratio
S1 ON Time
Dbar
Interval 1
Interval 2
Interval 3
Interval 4
Interval 5
Interval 6
Current after T5
Current Factor
Pole Voltage
Normal Current
Clamp Ratio
Voltage Ratio
I
1.95
2.4
2.8
3.2
3.5
50
50
50
50
50
LR
5.00E-06
5.00E-06
5.00E-06
5.00E-06
5.00E-06
CR
1.00E-09
1.00E-09
1.00E-09
1.00E-09
1.00E-09
wR
1.41E+07
1.41E+07
1.41E+07
1.41E+07
1.41E+07
fR
2.22E+07
2.22E+07
2.22E+07
2.22E+07
2.22E+07
0.20
fS
2.50E+05
2.50E+05
2.50E+05
2.50E+05
2.50E+05
0.15
Ts
4.00E-06
4.00E-06
4.00E-06
4.00E-06
4.00E-06
kI(T 5)
1.40
1.87
2.30
2.72
3.03
VC
4.61
6.23
7.66
9.08
10.15
kI(T 5)
1.40
1.87
2.30
2.72
3.03
VC
4.61
6.23
7.66
9.08
10.15
V
D
DT s
1-D
0.259
0.259
0.259
0.259
0.259
1.04E-06
1.04E-06
1.04E-06
1.04E-06
1.04E-06
0.741
0.741
0.741
0.741
0.741
T1
3.35E-07
4.27E-07
5.10E-07
5.92E-07
6.53E-07
T2
1.11E-07
1.11E-07
1.11E-07
1.11E-07
1.11E-07
T3
5.90E-07
4.98E-07
4.15E-07
3.33E-07
2.72E-07
T4
6.47E-08
6.29E-08
6.13E-08
5.98E-08
5.88E-08
T5
1.05E-07
1.03E-07
1.02E-07
1.00E-07
9.91E-08
T6
2.79E-06
2.80E-06
2.80E-06
2.80E-06
2.81E-06
I(T 5)
1.18
1.61
1.99
2.37
2.66
k
1.18
1.16
1.15
1.14
1.14
Vp
9.65
8.51
7.48
6.46
5.70
IN
0.05
0.06
0.07
0.08
0.09
VC/V
0.09
0.12
0.15
0.18
0.20
V/Vg
0.19
0.17
0.15
0.13
0.11
D=0.259
D=0.332
D=0.436
V/Vg
0.30
0.25
0.10
0.05
0.00
0.00
0.05
In 0.10
Conversion Ratio (In vs V/Vg)
D=0.259
D=0.332
D=0.436
Vc/Vg
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.0000
0.0500
In 0.1000
Clam p Ratio ( In vs Vc/Vg)
C onve rsion Ratio and C lamp Ratio as a function of Normaliz e d C urre nt
Steady State Definitions Of Base Voltages And
Currents
Buck Boost
Buckboost
Cuk
v
Vg
Vo
Vg+Vo
Vg+Vo
I
Io
Ig
IL
Ig + IL
Rd
M
(1  k)L R (1  k)L
R
Ts
Ts
D  (1  k) I N
1
1  D  (1  k)I N
(1  k)L R
Ts
D  (1  k)I N
1  D  (1  k)I N
(1  k)L R (1  k)L R
;
(1  D)Ts DTs
D  (1  k)I N
1  D  (1  k)I N
Dynamic Model Of Active Clamp Buck Converter
Perturbation of the nonlinear circuit averaged model about a quiescent operating point.
L
ˆ
Vg +V
g
+
+
-

 
D+dˆ I+iˆ
(1+k)L R
TS
C
+
-
 D+dˆ   Vg +Vˆ g 
Rc
1:D
ˆ
dV
g
L
D
-+
(1+k)L R
TS
C
Vˆ g
-
+
+
-
R
ˆ
dI
Rc
1:D
Small signal ac model of active clamp buck converter
Simulated Active Clamp Buck Converter
1n
Output power = 60
watts
MUR1620CT
1n
7u
Input voltage = 50
volts
150u
IRF250
S1
5u
110u
G1
50V
12
G2
IRF250
MUR1620CT
0
Output voltage = 20
volts
Switching frequency
= 250 KHz
Resonant Inductor Current Waveform
Clamp Capacitor Current Waveform
Steady State Performance Of Active Clamp Buck
Converter
EXPERIMENTAL RESULTS
D=0.259
D=0.332
D=0.436
Conve rs ion ratio
V/Vg
V/Vg
SIMULATED RESULTS
0.50
0.50
0.40
0.40
0.30
0.30
0.20
0.20
0.10
Vc/Vg
0.05
0.10
0.15
IN - Am ps
D=0.259
D=0.332
D=0.436
Clam p Ratio
0.00
0.00
Vc/Vg
0.10
0.00
0.00
0.60
0.60
0.50
0.50
0.40
0.40
0.30
0.30
0.20
0.20
0.10
0.10
0.00
0.00
D=0.259
D=0.332
D=0.436
Conversion Ratio
0.05
0.10
0.15
In- Am ps
0.00
0.00
0.05
0.10
D=0.259
D=0.332
D=0.436
Clam p Ratio
0.05
0.15
In- Am ps
0.10
0.15
In- Am ps
Experimental Waveforms Of Active Clamp Buck
Converter
Vgs and Vds of S1 showing ZVS; Vgs and Vds of S2 showing ZVS
Experimental Waveforms Of Active Clamp Buck
Converter
Pole voltage and Inductor current waveforms; Pole voltage
and Clamp capacitor current waveforms
Dynamic Performance Of Active Clamp Buck Converter
Measured output impedance of Hard-switched buck converter and Active clamp buck converter
Conclusions – Active Clamp Converters
Derived from Hard-Switched Converters by the addition of few
Resonant elements following the simple rule.
Circuit equations governing these sub-intervals are identical when
expressed in terms of pole current; throw voltage and freewheeling
resonant circuit voltage (I, V, and VC).
Steady state and Dynamic equivalent circuits are obtained from
this idealized analysis.
The resonant sub-interval introduces lossless damping in the
converter dynamics.
Advantages – Active Clamp Converter
High Efficiency - ZVS
 Simple Dynamic Model
 Wide Variety of Topologies
Thanks