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```EE462L, Fall 2011
DC−DC Buck/Boost Converter
1
Boost converter
iin + v L1 –
Iout
+
Vout
–
L1
Vin
C
Buck/Boost converter
iin
+ v L1 –
L1
Vin
+ v C1 –
Iout
+
C1
L2
v L2
–
C
+
Vout
–
+ v C1 –
+
C1
L2
v L2
–
2
Buck/Boost converter
iin
+ v L1 –
L1
Vin
+ v C1 –
Iout
+
C1
L2
v L2
–
C
+
Vout
–
This circuit is more unforgiving than the boost converter, because the
MOSFET and diode voltages and currents are higher
• Before applying power, make sure that your D is at
the minimum, and that a load is solidly connected
• Limit your output voltage to 90V
3
KVL and KCL in the average sense
I in + 0 –
L1
Vin
I in
0
+ Vin –
C1
Iout
L2
Iout
Iout
+
0
–
C
0
+
Vout
–
KVL shows that VC1 = Vin
Interestingly, no average current passes from the source side, through
C1, to the load side, and yet this is a “DC - DC” converter
4
Switch closed
assume constant
iin
+ Vin –
L1
+ Vin –
+ v D–
+
Vout
–
+
C1
Vin
Iout
L2
v L2
–
C
KVL shows that vD = −(Vin + Vout),
so the diode is open
Thus, C is providing the load power when the switch is closed
iin
+ Vin –
L1
Vin
+ Vin –
– (Vin + Vout) +
C1
–
Vin
+
L2
C
Iout
Iout
+
Vout
–
iL1 and iL2 are ramping up (charging). C1 is charging L2.
C is discharging.
5
Switch open (assume the diode is conducting because,
otherwise, the circuit cannot work)
iin
+ Vin –
– Vout +
L1
assume constant
Iout
C1
Vin
L2
+
Vout
–
C
+
Vout
–
C1 and C are charging. L1 and L2 are discharging.
KVL shows that VL1 = −Vout
The input/output equation comes from recognizing that the average
voltage across L1 is zero
VL1avg  D Vin  1  D   Vout   0
Vout  (1  D)  D  Vin
DVin
Vout 
1 D
6
Inductor L1 current rating
During the “on” state, L1 operates under the same conditions
as the boost converter L, so the results are the same
Use max
2
I L1rms 
I in
3
7
Inductor L2 current rating
Average values
I in + 0 –
0
L1
Vin
C1
I in
2Iout
Iavg = Iout
0
+ Vin –
Iout
L2
Iout
Iout
+
0
–
C
0
+
Vout
–
iL2
ΔI
2
I L22rms  I out

1
2
2I out 2  4 I out
12
3
2
I L 2rms 
I out
3
Use max
8
MOSFET and diode currents and current ratings
iin
+ v L1 –
L1
+ v C1 –
Iout
+
C1
Vin
L2
v L2
–
C
+
Vout
–
iL1 + iL2
MOSFET
2(Iin + Iout)
0
2(Iin + Iout)
0
switch
closed
Diode
iL1 + iL2
switch
open
Take worst case D for each
Use max
I rms 
2
Iin  I out 
3
9
Output capacitor C current and current rating
iC = (iD – Iout)
2Iin + Iout
0
−Iout
switch
closed
switch
open
I in 
1  D I in
DI out
, I out 
1 D
D
As D → 1, Iin >> Iout , so I Crms 
2
I in
3
As D → 0, Iin << Iout , so
I Crms  I out
 2

I Crms  max 
I in , I out 
 3

10
Series capacitor C1 current and current rating
iin
+ Vin –
L1
Vin
– (Vin + Vout) +
C1
–
Vin
+
L2
iin
– Vout +
L1
Vin
+ Vin –
C
+ Vin –
Iout
Iout
+
Vout
–
Iout
C1
L2
+
Vout
–
C
+
Vout
–
Switch closed, IC1 = −IL2
Switch open, IC1 = IL1
11
Series capacitor C1 current and current rating
Switch closed, IC1 = −IL2
iC1
2Iin
0
Switch open, IC1 = IL1
switch
closed
switch
open
−2Iout
As D → 1, Iin >> Iout , so I C1rms  2 I in
3
As D → 0, Iin << Iout , so I C1rms 
2
I out
3
2
 2

I C1rms  max 
I in ,
I out 
3
 3

12
iC = (iD – Iout)
0
−Iout
The worst case is where D → 1, where output capacitor C
provides Iout for most of the period. Then,
Q I out  T I out
V 


C
C
Cf
13
Worst case ripple voltage on series
capacitor C1
iC1
switch
open
2Iin
0
−2Iout
switch
closed
V 
I  DT I in  1  D T
 out

C1
C1
C1
Q
Then, considering the worst case (i.e., D = 1)
V 
I out
C1  f
14
Voltage ratings
+ Vin –
L1
– (Vin + Vout) +
C1
Vin
L2
C
+
Vout
–
MOSFET and diode see (Vin + Vout)
– Vout +
L1
Vin
+ Vin –
C1
L2
C
+
Vout
–
• Diode and MOSFET, use 2(Vin + Vout)
• Capacitor C1, use 1.5Vin
• Capacitor C, use 1.5Vout
15
Continuous current in L1
 Vout
A / sec
L1
iL
2Iin
Iavg = Iin
0
(1 − D)T
2 I in 
Vout
L1boundary
 1  D T 
DVin
1 D
L1boundary
 1  D T 
Vin D
L1boundary f
Vin D
L1boundary 
2 I in f
Then, considering the worst case (i.e., D → 1),
V
L1  in
2 I in f
use max
guarantees continuous conduction
16
use min
Continuous current in L2
2Iout
Iavg = Iout
 Vout
A / sec
L2
iL
0
(1 − D)T
2 I out 
Vout
L2boundary
 (1  D)T 
Vout (1  D)
L2boundary f
V (1  D)
L 2boundary  out
2 I out f
Then, considering the worst case (i.e., D → 0),
use max
V
L 2  out guarantees continuous conduction
2 I out f
use min
17
Impedance matching
I 1  D 
I out  in
D
Iin
+
Source
DC−DC Boost
Converter
Vin
Vout
−
+
DVin

1 D
−
V
I out
Iin
+
Vin
Equivalent from
source perspective
Requiv
−
1  D Vout
V
Requiv  in 
I in
D
DI out
1  D 
2
2
 1  D  Vout  1  D 


 
 D  I out  D 
18
Impedance matching
1  D Vout
V
Requiv  in 
I in
D
DI out
1  D 
2
2
 1  D  Vout  1  D 


 
 D  I out  D 
For any Rload, as D → 0, then Requiv → ∞ (i.e., an open circuit)
For any Rload, as D → 1, then Requiv → 0 (i.e., a short circuit)
Thus, the buck/boost converter can sweep the entire I-V
curve of a solar panel
19
Example - connect a 100Ω load resistor
PV Station 13, Bright Sun, Dec. 6, 2002
D = 0.88
6
D = 0.80
5
I - amps
4
3
2
D = 0.50
1
0
0
5
10
15
20
25
30
35
40
45
V(panel) - volts
With a 100Ω load resistor attached, raising D from 0 to 1 moves the solar
panel load from the open circuit condition to the short circuit condition
20
Example - connect a 5Ω load resistor
PV Station 13, Bright Sun, Dec. 6, 2002
D = 0.61
6
D = 0.47
5
I - amps
4
3
2
D = 0.18
1
0
0
5
10
15
20
25
30
35
40
45
V(panel) - volts
21
BUCK/BOOST DESIGN
Worst-Case Component Ratings Comparisons
for DC-DC Converters
Our components
9A
Converter
Type
Input Inductor
Current
(Arms)
Buck/Boost
2
I in
3
10A
250V
Output
Capacitor
Voltage
1.5 Vout
5.66A p-p
Output Capacitor
Current (Arms)
 2

max 
I in, I out 
 3

200V, 250V
Diode and
MOSFET
Voltage
2(Vin  Vout )
16A, 20A
Diode and
MOSFET
Current
(Arms)
2
Iin  I out 
3
90V
10A, 5A
40V, 90V
10A, 5A
Likely worst-case buck/boost situation
L1. 100µH, 9A
L2. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
C1. 33µF, 50V, 14A p-p
Diode D. 200V, 16A
MOSFET M. 250V, 20A
22
BUCK/BOOST DESIGN
Comparisons of Output Capacitor Ripple Voltage
Converter Type
Buck/Boost
Volts (peak-to-peak)
5A
I out
Cf
0.067V
1500µF 50kHz
L1. 100µH, 9A
L2. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
C1. 33µF, 50V, 14A p-p
Diode D. 200V, 16A
MOSFET M. 250V, 20A
23
BUCK/BOOST DESIGN
Minimum Inductance Values Needed to
Guarantee Continuous Current
Converter Type
Buck/Boost
For Continuous
For Continuous
Current in the Input
Current in L2
Inductor
V
V
40V
90V
L1  in
L2  out
2 I in f
2 I out f
200µH
450µH
2A
50kHz
2A
50kHz
L1. 100µH, 9A
L2. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
C1. 33µF, 50V, 14A p-p
Diode D. 200V, 16A
MOSFET M. 250V, 20A
24
BUCK/BOOST DESIGN
50V
14A p-p
Our components
Series Capacitor
Voltage
Series Capacitor (C1)
Current (Arms)
1.5 Vin
 2

2
max 
I in ,
I out 
3
 3

40V
10A
5A
9A
Series
Second
Capacitor (C1)
Inductor (L2)
Ripple Voltage Current (Arms)
(peak-to-peak)
2
I out
5A
I out
3
C1 f
3.0V
33µF
50kHz
5A
Likely worst-case buck/boost situation
L1. 100µH, 9A
L2. 100µH, 9A
C. 1500µF, 250V, 5.66A p-p
C1. 33µF, 50V, 14A p-p
Diode D. 200V, 16A
MOSFET M. 250V, 20A
Conclusion - 50kHz may be too low
for buck/boost converter
25
Converter
Type
Buck
Worst-Case Component Ratings Comparisons for DC-DC Converters
Output
Input Inductor
Capacitor
Output Capacitor
Diode and
Current (Arms)
Voltage
Current (Arms)
MOSFET Voltage
2
1
1.5 Vout
2 Vin
Boost
3
2
Buck/Boost
3
2
3
I out
I in
I in
Series Capacitor
Voltage
1.5 Vin
Diode and
MOSFET
Current (Arms)
2
I out
3
2
I in
3
I out
3
I out
1.5 Vout
1.5 Vout
2 Vout
 2

max 
I in , I out 
 3

2Vin  Vout 
Series Capacitor
Series Capacitor (C1)
(C1) Ripple
Current (Arms)
Voltage (peak-topeak)
 2

2
max 
I in ,
I out 
3
 3

I out
C1 f
2
3
I in  I out 
Second Inductor
(L2) Current
(Arms)
2
3
I out
26
Comparisons of Output Capacitor Ripple Voltage
Converter Type
Volts (peak-to-peak)
Buck
I out
Boost
Buck/Boost
4Cf
I out
Cf
I out
Cf
Minimum Inductance Values Needed to Guarantee Continuous Current
Converter Type
For Continuous Current
For Continuous
in the Input Inductor
Current in L2
Buck
V
L  out
–
2 I out f
Boost
V
L  in
–
2 I in f
Buck/Boost
V
V
L1  in
L2  out
2 I in f
2 I out f
27
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