环路补偿很容易 · 2014. 5. 15. · type ii 误差放大器 comp comp zea r c 1 ω ⋅ =...
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环路补偿很容易
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确定功率级特性����
课程的目的
说明 Type II Type II Type II Type II 补偿 –––– 电流模式����
阐述 Type III Type III Type III Type III 补偿 –––– 电压模式����
补偿电流模式降压����
找出交越频率和相位裕量����
使用 Excel Excel Excel Excel 补偿器设计工具����
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电源转换器拓扑
降压 / / / /
正激式• 降压 / / / / 隔离
升压 • 升压
降压----升压 / / / /
反激式• 反转极性 / / / / 隔离
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电源转换器拓扑
降压 / / / /
正激式
升压
降压----升压 / / / /
反激式
DVV INOUT ⋅=
LLLL
VVVVO U TO U TO U TO U TVVVVI NI NI NI N
Buck ConverterBuck ConverterBuck ConverterBuck Converter
NNNNSSSS
LLLL
Forward ConverterForward ConverterForward ConverterForward Converter
NNNNPPPPVVVVI NI NI NI N VVVVO U TO U TO U TO U TP
SINOUT N
NDVV ⋅⋅=
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电源转换器拓扑
降压 / / / /
正激式
升压
降压----升压 / / / /
反激式
VO U TV I N
Boost ConverterBoost ConverterBoost ConverterBoost Converter
L
D11VV INOUT −
⋅=
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电源转换器拓扑
降压 / / / /
正激式
升压
降压----升压 / / / /
反激式
D1DVV INOUT −
⋅=
B u c kB u c kB u c kB u c k ----Boost ConverterBoost ConverterBoost ConverterBoost Converter
Flyback ConverterFlyback ConverterFlyback ConverterFlyback Converter
NNNNSSSSNNNNPPPPVVVVI NI NI NI N VVVVO U TO U TO U TO U T
VVVVI NI NI NI N ----VVVVO U TO U TO U TO U TLLLL
P
SINOUT N
ND1
DVV ⋅−
⋅=
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极点/零点回顾
单个极点
单个零点
反相零点 (Inverted Zero)(Inverted Zero)(Inverted Zero)(Inverted Zero)
右半平面零点
共轭复极点
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Pωs1
1)s(H+
=
-60-60-60-60
-40-40-40-40
-20-20-20-20
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20202020
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)M
AGNI
TUDE
(dB)
MAG
NITU
DE (d
B)M
AGNI
TUDE
(dB)
MAG
NITU
DE (d
B)
-135-135-135-135
-90-90-90-90
-45-45-45-45
0000
45454545
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
PHA
SE (°
)PH
ASE
(°)
PHA
SE (°
)PH
ASE
(°)
单个极点
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20202020
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60606060
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)M
AGNI
TUDE
(dB)
MAG
NITU
DE (d
B)M
AGNI
TUDE
(dB)
MAG
NITU
DE (d
B)
-45-45-45-45
0000
45454545
90909090
135135135135
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
PHA
SE (°
)PH
ASE
(°)
PHA
SE (°
)PH
ASE
(°)
单个零点
1ωs1
)s(H Z+
=
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0000
20202020
40404040
60606060
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)M
AGNI
TUDE
(dB)
MAG
NITU
DE (d
B)M
AGNI
TUDE
(dB)
MAG
NITU
DE (d
B)
-135-135-135-135
-90-90-90-90
-45-45-45-45
0000
45454545
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
PHA
SE (°
)PH
ASE
(°)
PHA
SE (°
)PH
ASE
(°)
反相零点
1s
ω1
)s(H
Z+=
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0000
20202020
40404040
60606060
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)M
AGNI
TUDE
(dB)
MAG
NITU
DE (d
B)M
AGNI
TUDE
(dB)
MAG
NITU
DE (d
B)
-135-135-135-135
-90-90-90-90
-45-45-45-45
0000
45454545
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
PHA
SE (°
)PH
ASE
(°)
PHA
SE (°
)PH
ASE
(°)
右半平面零点
1ωs1
)s(H Z−
=
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共轭复极点
2O
2
OO ωs
ωQs1
1)s(H+
⋅+
=
-60-60-60-60
-40-40-40-40
-20-20-20-20
0000
20202020
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)M
AG
NIT
UD
E (d
B)
MA
GN
ITU
DE
(dB
)M
AG
NIT
UD
E (d
B)
MA
GN
ITU
DE
(dB
)
Q=2Q=2Q=2Q=2Q=1Q=1Q=1Q=1Q=0.5Q=0.5Q=0.5Q=0.5Q=0.25Q=0.25Q=0.25Q=0.25
-270-270-270-270
-180-180-180-180
-90-90-90-90
0000
90909090
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
PHA
SE (°
)PH
ASE
(°)
PHA
SE (°
)PH
ASE
(°)
Q=2Q=2Q=2Q=2Q=1Q=1Q=1Q=1Q=0.5Q=0.5Q=0.5Q=0.5Q=0.25Q=0.25Q=0.25Q=0.25
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控制环路基础知识
环路补偿介绍
理想的控制环路
实用的反馈理论
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Pow er Stage :Inductor /Transform er
Power SwitchesM odulator
C om pensation
V I N VO U T
VC
L o a d
R E F
E rro r A m p
TestSignal
环路补偿介绍
环路增益是以反馈环路
为中心的增益，
由误差放大器增益和
功率级增益部分组成。
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理想的控制环路
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80808080
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GAI
N (d
B)G
AIN
(dB)
GAI
N (d
B)G
AIN
(dB)
-45-45-45-45
0000
45454545
90909090
135135135135
180180180180
PHAS
E (°
)PH
ASE
(°)
PHAS
E (°
)PH
ASE
(°)
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实用的反馈理论
• 控制环路的带宽决定了环路对于某种瞬态状况的响应速度
• 通常都会优先选择较高的交越频率，但存在着实际的限制。经验法则是将其设定为开关频率的 1/5 至 1/10
• 0°（增益裕量） 时的衰减以及开关频率下的衰减也是很重要的
交越频率
• 需要充足的相位裕量以避免发生振荡
• 最佳的相位裕量是 52°
• 低相位裕量将导致欠阻尼的系统响应
• 较高的相位裕量则导致过阻尼的系统响应
相位裕量
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功率级回顾
电压模式降压
电流模式降压
电流模式升压
电流模式降压-升压
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-60-60-60-60
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40404040
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
电压模式降压功率级
π2ω O⋅
VCA
π2ωZ⋅
VI N
CO U T
RE S RRO U T
LVO U T
VR A M P+-
VC
P W M
Logic
OUTO CL
1ω⋅
=
OUTESRZ CR
1ω
⋅=
RAMP
INVC V
VA =
2O
2
OO
ZVC
C
OUT
ωs
ωQs1
ωs1
Av̂
v̂
+⋅
+
+⋅=
OUT
OUTO
CL
RQ =
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-60-60-60-60
-40-40-40-40
-20-20-20-20
0000
20202020
40404040
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
电流模式降压功率级
OUTESRZ CR
1ω
⋅=
OUTOUTP RC
1ω
⋅≈
LRKω imL⋅
=
SLOPE
INm V
VK ≈
i
OUTVC R
RA ≈
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
+⋅≈
LP
ZVC
C
OUT
ωs1
ωs1
ωs1
Av̂
v̂
π2ωP⋅
VCA
π2ωZ⋅
π2ωL⋅
VI N
CO U T
RE S RRO U T
LVO U T
Σ+
+
VC+- VS L OP E
P W M
Ri
Logic
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0000
20202020
40404040
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
电流模式升压功率级
OUTESRZ CR
1ω
⋅=
OUTOUTP RC
2ω⋅
≈
LRKω imL⋅
=
SLOPE
OUTm V
VK ≈
i
OUTVC R2
DRA⋅
′⋅≈
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛−
⋅≈
LP
ZRVC
C
OUT
ωs1
ωs1
ωs1
ωs1
Av̂
v̂
LDRω
2OUT
R′⋅
=
π2ωP⋅
VCA
π2ω Z⋅
π2ωL⋅
π2ωR⋅
VI N
CI N
RS
CO U T
RE S R
RO U T
LVO U T
Σ+ +
VC
Logic
VS L OP E
P W M
+-
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10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
电流模式降压-升压功率级
OUTESRZ CR
1ω
⋅=
OUTOUTP RC
D1ω⋅+≈
LRKω imL⋅
=
SLOPE
OUTINm V
VVK +≈
( ) iOUT
VC RD1DRA⋅+′⋅
≈
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛−
⋅≈
LP
ZRVC
C
OUT
ωs1
ωs1
ωs1
ωs1
Av̂
v̂
DLDRω
2OUT
R ⋅′⋅
=
V I N
CO U T
RE S RRO U T
L
-VO U T
Σ+
+
VC+- VS L OP E
Ri
P W M
L o g icπ2
ωP⋅
VCA
π2ω Z⋅
π2ωL⋅
π2ωR⋅
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误差放大器回顾
Type I Type I Type I Type I 误差放大器
Type II Type II Type II Type II 误差放大器
Type II Type II Type II Type II 跨导放大器
Type III Type III Type III Type III 误差放大器
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20202020
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10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
Type I 误差放大器
RF B T
RF B BVR E F
VF B
+
-
VO U T ′
VC
CC OM P
COMPFBTEA CR
1ω
⋅=
sω
v̂
v̂ EA
OUT
C −≈′
π2ωEA⋅
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0000
20202020
40404040
60606060
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
Type II 误差放大器
COMPCOMPZEA CR
1ω
⋅=
HFCOMP CC >> :假设
π2ω ZEA
⋅
VMAπ2
ωHF⋅
HF
ZEA
VMOUT
C
ωs1
sω1
Av̂
v̂
+
+⋅−≈′HFCOMP
HF CR1ω⋅
≈
FBT
COMPVM R
RA ≈
RF B T
RF B BVR E F
VF B
+
-VC
RC OM PCC OM P
CH F
VO U T ′
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0000
20202020
40404040
60606060
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
GAIN
(dB)
Type II 跨导放大器
COMPCOMPZEA CR
1ω⋅
=
COMPEAHFCOMP RRCC >>>> & :假设
π2ω ZEA
⋅
VMAπ2
ωHF⋅+
-
RC OM P
CC OM P
VC
RE A gm
RF B B
VO U T ′
VR E F
VF BRF B T
CH F
COMPmFBVM RgKA ⋅⋅=
EAmOL RgA ⋅=
FBTFBB
FBBFB RR
RK+
=
HF
ZEA
VMOUT
C
ωs1
sω1
Av̂
v̂
+
+⋅−≈′
HFCOMPHF CR
1ω
⋅≈
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0000
20202020
40404040
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10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)FREQUENCY (Hz)
GA
IN (d
B)
GA
IN (d
B)
GA
IN (d
B)
GA
IN (d
B)
Type III 误差放大器
RF B T
RF B BVR E F
VF B
+
-VC
RC O M PCC O M P
CH F
CF F
RF F
VO U T ′
COMPCOMPZEA CR
1ω⋅
=FFFBT
FZ CR1ω⋅
≈
FFFFFP CR
1ω⋅
=HFCOMP
HF CR1
ω⋅
≈
FBT
COMPVM R
RA ≈
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟⎠
⎞⎜⎜⎝
⎛+
⋅−=′
HFFP
FZ
ZEA
VMOUT
C
ωs1
ωs1
ωs1
sω1
Av̂
v̂
FFFBTHFCOMP RRCC >>>> & :假设
π2ωZEA
⋅
VMA
π2ωHF⋅
π2ωFZ⋅
π2ωFP⋅
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开关稳压器补偿
电流模式降压 –––– Type II Type II Type II Type II 补偿
电流模式升压 –––– Type II Type II Type II Type II 补偿
电流模式降压-升压 –––– Type II Type II Type II Type II 补偿
电压模式降压 –––– Type II Type II Type II Type II 补偿
电压模式降压 –––– Type III Type III Type III Type III 补偿
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VVVV I NI NI NI N
RC OM P
C C OM P
C O U T
Slope C om p
RE S R
R O U T
L
RF B T
RF B B
VVVVO U TO U TO U TO U T
VR E F
Σ+
+
V F BVC
+
-+-
VS L OP E
O ptim al V S L OP E = VO U T x R i / L
P W M
Ri
C H F
gm
L o g i c
输出滤波器
误差放大器
调制器
电流模式降压模型
IN
OUT
VV
D =
IN
OUTIN
VVVD −=′
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FBTVMCOMP R AR ⋅=
电流模式降压 – Type II 补偿
FBm
VMCOMP Kg
AR
⋅=或：
COMPHFHF Rω
1C⋅
=COMPZEA
COMP Rω1C⋅
=
(mod)GCω
Am
OCVM
⋅=
im R
1(mod)G =
• 选择一个大的 RFBT 阻值，介于 2 kΩ 和 200 kΩ 之间
• 找出调制器跨导（单位：A/V）
• 选择一个目标带宽，通常为 FSW/10
• 设定中频段增益 AVM 以实现目标带宽：ωC = 2·π·FC• 设定 ωZEA = 1/10 目标交越频率：ωZEA = ωC/10
• 设定 ωHF = ESR 零点频率：ωHF = ωZ
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10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
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0000
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10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
控制环路
误差放大器
功率级
电流模式降压控制环路
VCA
π2ωC⋅
π2ωP⋅ π2
ωZ⋅
π2ω ZEA
⋅ VMA π2ωHF⋅
′⋅=
′OUT
C
C
OUT
OUT
OUT
v̂
v̂v̂
v̂
v̂
v̂
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
+⋅≈
LP
ZVC
C
OUT
ωs1
ωs1
ωs1
Av̂
v̂
HF
ZEA
VMOUT
C
ωs1
sω1
Av̂
v̂
+
+⋅−≈′
π2ωL⋅
-
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31
VVVVI NI NI NI N
CI N
RS
RC O M P
CC O M P
CO U T
S lope C om p
RE S R
RO U T
L
RF B T
RF B B
VVVVO U TO U TO U TO U T
VR E F
Σ+ +
VF BVC
Logic
VS LOP E
O ptim a l V S LOP E = ( VO U T – V I N ) x R i / LW here R i = Current Sense Gain x R S
CH F
gm+
-P W M
+-
电流模式升压模型
输出滤波器
误差放大器调制器
OUT
INOUT
VVV
D−
=
OUT
IN
VV
D =′
-
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32
FBTVMCOMP R AR ⋅=
电流模式升压 – Type II 补偿
FBm
VMCOMP Kg
AR
⋅=或：
COMPHFHF Rω
1C⋅
=COMPZEA
COMP Rω1C⋅
=
(mod)GCω
Am
OCVM
⋅=
im R
D(mod)G′
=
• 选择一个大的 RFBT 阻值，介于 2 kΩ 和 200 kΩ 之间• 找出调制器跨导（单位：A/V）• 找出最小输入电压和最大负载电流条件下的 RHPZ 频率• 将目标带宽设定为 RHPZ 频率的 ¼：ωC = ωR/4• 设定中频段增益 AVM 以实现目标带宽：ωC = 2·π·FC• 设定 ωZEA = 1/10 的目标交越频率：ωZEA = ωC/10• 设定 ωHF = RHP 或 ESR 零点频率当中较低的那个：ωHF = ωR 或 ωZ
LDR
ω2
OUTR
′⋅=
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33
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0000
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0000
20202020
40404040
60606060
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
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0000
20202020
40404040
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
控制环路
误差放大器
功率级
电流模式升压控制环路
VCA
π2ωC⋅
π2ωP⋅ π2
ωZ⋅
π2ω ZEA
⋅ VMA π2ωHF⋅
′⋅=
′OUT
C
C
OUT
OUT
OUT
v̂
v̂v̂
v̂
v̂
v̂
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛−
⋅≈
LP
ZRVC
C
OUT
ωs1
ωs1
ωs1
ωs1
Av̂
v̂
HF
ZEA
VMOUT
C
ωs1
sω1
Av̂
v̂
+
+⋅−≈′
π2ωR⋅
π2ωL⋅
-
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34
VVVV I NI NI NI N
R C OM P
CC OM P
C O U T
Slope C om p
RE S R
R O U T
L
RF B T
R F B B
----VVVVO U TO U TO U TO U T
VR E F
Σ+
+
V F BVC
+
-+-
V S L OP E
O ptim al V S L OP E = VO U T x R i / L
R i
P W M
C H F
gm
L o g i c
输出滤波器
误差放大器
调制器
电流模式降压-升压模型
OUTIN
OUT
VVV
D+
=
OUTIN
IN
VVV
D+
=′
-
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35
FBTVMCOMP R AR ⋅=
电流模式降压-升压 – Type II 补偿
FBm
VMCOMP Kg
AR
⋅=或：
COMPHFHF Rω
1C⋅
=COMPZEA
COMP Rω1C⋅
=
(mod)GCω
Am
OCVM
⋅=
im R
D(mod)G′
=DLDR
ω2
OUTR ⋅
′⋅=
• 选择一个大的 RFBT 阻值，介于 2 kΩ 和 200 kΩ 之间• 找出调制器跨导（单位：A/V）• 找出最小输入电压和最大负载电流条件下的 RHPZ 频率• 将目标带宽设定为 RHPZ 频率的 ¼： ωC = ωR/4• 设定中频段增益 AVM 以实现目标带宽： ωC = 2·π·FC• 设定 ωZEA = 1/10 的目标交越频率： ωZEA = ωC/10• 设定 ωHF = RHP 或 ESR 零点频率当中较低的那个： ωHF = ωR 或 ωZ
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36
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0000
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0000
20202020
40404040
60606060
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
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0000
20202020
40404040
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
控制环路
误差放大器
功率级
电流模式降压-升压控制环路
VCA
π2ωC⋅
π2ωP⋅ π2
ωZ⋅
π2ω ZEA
⋅ VMA π2ωHF⋅
′⋅=
′OUT
C
C
OUT
OUT
OUT
v̂
v̂v̂
v̂
v̂
v̂
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛−
⋅≈
LP
ZRVC
C
OUT
ωs1
ωs1
ωs1
ωs1
Av̂
v̂
HF
ZEA
VMOUT
C
ωs1
sω1
Av̂
v̂
+
+⋅−≈′
π2ωR⋅
π2ωL⋅
-
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37
电压模式降压稳压器
VVVVI NI NI NI N
CO U T
RE S RRO U T
L
RF B T
RF B B
VVVVO U TO U TO U TO U T
VR E F
VF B
VR A M P
+
-+-
T
VC
RC O M PCC O M P
CH FCF F
RF F
Logic
P W M
输出滤波器
误差放大器
调制器
IN
OUT
VV
D =
IN
OUTIN
VVVD −=′
-
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38
FBTVMCOMP R AR ⋅=
电压模式降压 – Type II 补偿
COMPHFHF Rω
1C⋅
=COMPZEA
COMP Rω1C⋅
=
• 与高 ESR 输出电容器配合使用
• 选择一个大的 RFBT 阻值，介于 2 kΩ 和 200 kΩ 之间
• 设定中频段增益 AVM 以获得期望的带宽
• 设定 ωZEA = 输出滤波器共轭复极点 ωO• 设定 ωHF = ½ 开关频率：ωHF = 2·π·FSW/2
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39
FBTVMCOMP R AR ⋅=
电压模式降压 – Type III 补偿
COMPHFHF Rω
1C⋅
=
COMPZEACOMP Rω
1C⋅
=
• 与低 ESR输出电容器配合使用
• 选择一个大的 RFBT 阻值，介于 2 kΩ 和 200 kΩ 之间
• 设定中频段增益 AVM 以实现目标带宽：ωC = 2·π·FC• 设定 ωZEA 和 ωFZ = 输出滤波器共轭复极点 ωO• 设定 ωFP = 输出滤波器零点 ωZ• 设定 ωHF = ½ 开关频率： ωHF = 2·π·FSW/2
FBTFZFF Rω
1C⋅
=FFFP
FF Cω1R⋅
=
OVC
CVM ωA
ω A
⋅=
-
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0000
20202020
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60606060
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
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0000
20202020
40404040
10101010 100100100100 1,0001,0001,0001,000 10,00010,00010,00010,000 100,000100,000100,000100,000 1,000,0001,000,0001,000,0001,000,000
控制环路
误差放大器
功率级
电压模式降压控制环路
VCA
π2ωC⋅
π2ωO⋅
π2ωZ⋅
π2ω
&π2
ω FZZEA⋅⋅
VMA
π2ωHF⋅π2
ωFP⋅
′⋅=
′OUT
C
C
OUT
OUT
OUT
v̂
v̂v̂
v̂
v̂
v̂
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⎟⎟⎠
⎞⎜⎜⎝
⎛+⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛+
⋅−≈′
HFFP
FZ
ZEA
VMOUT
C
ωs
1ω
s1
ωs
1s
ω1
Av̂
v̂
2O
2
OO
ZVC
C
OUT
ωs
ωQs1
ωs1
Av̂
v̂
+⋅
+
+⋅≈
-
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41
误差放大器考虑因素
• 误差放大器必须驱动的阻抗
• 误差放大器的带宽
• 误差放大器的开环增益
• LC 滤波器的 Q 值
需要关注的是：
-
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42
• 需要网络分析仪以获得完整的曲线图
• 可利用普通的测试设备获得关键性的数据点
2: 伯德图
环路测量方法
测量选项
• 简单易行
• 无需专用设备
1: 瞬态响应测试
-
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43
负载阶跃分析
瞬态测试
负载阶跃实例
伯德图与瞬态
-
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44
瞬态测试 – 负载阶跃
用于瞬态测试的简单电路
针对一个从 0V 至大约比VOUT 高 5V 的脉冲幅度及 100Hz 左右的频率来设置发生器。负载将跟随发生器的上升 /下降时间。
增设用于设定最小负载的
DC 负载箱。VOUT/RLOAD 设定了 ΔI。
VOUT
GND
RLoad脉冲发生器
-
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45
负载阶跃实例
典型的瞬态响应测试
负载电流每格 1A
输出电压每格 50 mV
时标每格 100 μs
-
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46
伯德图与瞬态响应对比案例一 – 稳定的稳压器
ffffCCCC = 10 kHz, PM = 65 = 10 kHz, PM = 65 = 10 kHz, PM = 65 = 10 kHz, PM = 65°°°° 过阻尼
每格 100 mVAC 耦合
400 mA
200 mA
VOUT
IOUT
Vg = 3.6V欠冲 134 mV过冲 144 mV
每格 100 μs
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47
伯德图与瞬态响应对比案例二 – 稳定的稳压器
ffffCCCC = 36 kHz, PM = 48 = 36 kHz, PM = 48 = 36 kHz, PM = 48 = 36 kHz, PM = 48°°°° 临界阻尼
Vg = 3.6V欠冲 68 mV过冲 70 mV
400 mA
200 mA每格 100 μs
VOUT
每格 100 mVAC 耦合
IOUT
-
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48
伯德图与瞬态响应对比案例三 – 边际稳定性
ffffCCCC = 61 kHz, PM = 17 = 61 kHz, PM = 17 = 61 kHz, PM = 17 = 61 kHz, PM = 17°°°° 欠阻尼
振铃指示低相位裕量
400 mA
200 mA
每格 100 mVAC 耦合
VOUT
IOUT
Vg = 3.6V欠冲 68 mV过冲 64 mV
每格 100 μs
-
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49
伯德图与瞬态响应对比案例四 – 不稳定的稳压器
ffffCCCC = 27 kHz, PM = 8 = 27 kHz, PM = 8 = 27 kHz, PM = 8 = 27 kHz, PM = 8°°°° 不稳定的稳压器
每格 100 mVAC 耦合
VOUT
IOUT
400 mA
200 mA每格 100 μs
-
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50
环路测量
网络分析仪测量
正弦波注入
穿越频率和相位裕量
-
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51
网络分析仪测量
Loop G ainLoop G ainLoop G ainLoop G ain
⎟⎟⎠
⎞⎜⎜⎝
⎛⋅=
ν(A)ν(B)log20 10环路增益 ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
ν(A)ν(B) phase相位
NetworkAnalyzer
AC siganlAC siganlAC siganlAC siganlin jectio nin jectio nin jectio nin jectio n
Measurem entMeasurem entMeasurem entMeasurem entPo in t BPo in t BPo in t BPo in t B
Measurem entMeasurem entMeasurem entMeasurem entPo in t APo in t APo in t APo in t A
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52
正弦波注入
Pow er StagePower Switches
M odulator
CL O A DRL O A D
C om pensation
V I N VO U T
VC
L o a d
R E F
E rro r A m p
O U T
I N
Audio Transformer
L o wVoltage
S id e
10 to 100 O hm s
Connect oscilloscope channel 1 to O U T , channel 2 to IN . Both relative to the local
controller ground .
A ud ioGenerator
-
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53
穿越频率和相位裕量
24V VIN 5V VOUT 1A 负载 幅度 120 mV pk-pk 26.5 kHz 交越频率相位裕量 = 40.5°
注意光标 时间差 = 4.225 μs在 26.5 kHz，周期为 37.7 μs。(4.225/37.7)*360= 40.5
输出
输入
LM5576 LM5576 LM5576 LM5576 –––– 500 kHz 500 kHz 500 kHz 500 kHz 开关频率
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54
动手实验
采用负载阶跃补偿降压稳压器
运用信号注入得到穿越频率和相位裕量
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55
带负载阶跃的电流模式降压
VVVV I NI NI NI N
RC OM P
C C OM P
CO U T
Slope C om p
RE S RR L O A D
L
RF B T
RF B B
VVVVO U TO U TO U TO U T
VR E F
Σ+
+
V F BVC
+
-+-
VS L OP E
O ptim al V S L OP E = VO U T x R i / L
P W M
R i
C H F
gm
L o g i c
P U L S EG E N .
-
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56
单位增益和相位测量
Pow er StagePower Switches
M odulator
CL O A DRL O A D
C om pensation
V I N VO U T
VC
L o a d
R E F
E rro r A m p
O U T
I N
Audio Transformer
Low Voltage
S id e
10 to 100 O hm s
Connect oscilloscope channel 1 to O U T , channel 2 to IN . Both relative to the local
controller ground .
A ud ioGenerator
-
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57
Excel 补偿器设计工具
峰值电流模式降压 –––– Type II Type II Type II Type II 跨导放大器
峰值电流模式控制 –––– Type II Type II Type II Type II 电压放大器
电压模式降压 –––– Type III Type III Type III Type III 电压放大器
电流模式简化频率补偿
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58
电流模式降压 – Type II 跨导放大器
Compensator Design - Peak Current-Mode Buck - Transconductance AmplifierCompensator Design - Peak Current-Mode Buck - Transconductance AmplifierCompensator Design - Peak Current-Mode Buck - Transconductance AmplifierCompensator Design - Peak Current-Mode Buck - Transconductance AmplifierEnter parameters in shaded cells PCM1 Frequency Compensation Parameters PCM1 Frequency Compensation Parameters PCM1 Frequency Compensation Parameters PCM1 Frequency Compensation ParametersVersion 2.0 Vin (V) 10 Error Amplifier - Single Pole Transconductance AmplifierError Amplifier - Single Pole Transconductance AmplifierError Amplifier - Single Pole Transconductance AmplifierError Amplifier - Single Pole Transconductance AmplifierRevision date: 9 May 2010 Vout (V) 5 Reference Voltage Vref (V) 1.25 ModulatorModulatorModulatorModulator Error AmpError AmpError AmpError Amp
Load Current Iout (A) 1 Bottom Feedback Divider Rfbb (Ω) 1,250 D = 0.5000 Kfb = 0.2500Switching Frequency Fsw (kHz) 250 Top Feedback Divider Rfbt (Ω) 3,750 Rout = 5.00 Avm = 8.250Current Sense Resistor Rs (mΩ) 10.0 Modulator Scale Factor SFM (V/V) 1.00 Ri = 0.1000 khf = 1.010
Current Sense Gain A (V/V) 10 Modulator Gain Gm(mod) (A/V) 10.00 Vsl = 0.4000 wzea = 25,253Slope Comp Multiplier SLM (V/V) 1 Modulator Crossover Fc(mod) (kHz) 3.18 Km = 25.00 whf = 2,550,505
Output Inductor L (μH) 5.0 Error Amp Zero (kHz) 4.02 Kd = 3.000 wbw = 62,831,853Output Capacitor Cout (μF) 500 Target Loop Bandwidth Fc (kHz) 25.00 Av = 16.667 Slope CompSlope CompSlope CompSlope Comp
Output Capacitor ESR (mΩ) 1.0 Error Amplifier Aol (V/V) 1,000 wp = 1,200 Se = 100000Error Amplifier gm (μA/V) 1,000 Error Amplifier UGB (MHz) 10.0 wz = 2,000,000 Sn = 100000Error Amplif ier Rea (kΩ) 1,000 Error Amplif ier Cbw (pF) 16 wc = 157,080 wn = 785,398
Q = 0.6366
Control Loop Gain/Phase Control Loop Gain/Phase Control Loop Gain/Phase Control Loop Gain/Phase
-60
-40
-20
0
20
40
60
80
100
1 10 100 1,000 10,000 100,000 1,000,000
Frequency (Hz)Frequency (Hz)Frequency (Hz)Frequency (Hz)
Gai
n (d
B)
Gai
n (d
B)
Gai
n (d
B)
Gai
n (d
B)
-90
-60
-30
0
30
60
90
120
150
Phas
e (d
eg)
Phas
e (d
eg)
Phas
e (d
eg)
Phas
e (d
eg)
Modulator Gain/PhaseModulator Gain/PhaseModulator Gain/PhaseModulator Gain/PhaseVcomp to Vout Vcomp to Vout Vcomp to Vout Vcomp to Vout
-60
-40
-20
0
20
40
1 10 100 1,000 10,000 100,000 1,000,000
Frequency (Hz)Frequency (Hz)Frequency (Hz)Frequency (Hz)
Gai
n (d
B)
Gai
n (d
B)
Gai
n (d
B)
Gai
n (d
B)
-150
-120
-90
-60
-30
0
Phas
e (d
eg)
Phas
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Phas
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Phas
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59
电流模式降压 – Type II 电压放大器
Compensator Design - Peak Current-Mode Buck - Voltage AmplifierCompensator Design - Peak Current-Mode Buck - Voltage AmplifierCompensator Design - Peak Current-Mode Buck - Voltage AmplifierCompensator Design - Peak Current-Mode Buck - Voltage AmplifierEnter parameters in shaded cells PCM1 Frequency Compensation Parameters PCM1 Frequency Compensation Parameters PCM1 Frequency Compensation Parameters PCM1 Frequency Compensation ParametersVersion 2.0 Vin (V) 12 Error Amplifier - Single Pole Operational AmplifierError Amplifier - Single Pole Operational AmplifierError Amplifier - Single Pole Operational AmplifierError Amplifier - Single Pole Operational AmplifierRevision date: 9 May 2010 Vout (V) 5 ModulatorModulatorModulatorModulator Error AmpError AmpError AmpError Amp
Load Current Iout (A) 1 Reference Voltage Vref (V) 1.25 D = 0.4167 Kfb = 0.2500Switching Frequency Fsw (kHz) 250 Bottom Feedback Divider Rfbb (Ω) 1,250 Rout = 5.00 Rth = 937.5Current Sense Resistor Rs (mΩ) 10.0 Top Feedback Divider Rfbt (Ω) 3,750 Ri = 0.1000 Avm = 8.000
Current Sense Gain A (V/V) 10 Vsl = 0.4000 khf = 1.008Slope Comp Multiplier SLM (V/V) 1 Modulator Scale Factor SFM (V/V) 1.00 Km = 25.00 wzea = 27,778
Output Inductor L (μH) 5.0 Modulator Gain Gm(mod) (A/V) 10.00 Kd = 3.000 whf = 3,361,111Output Capacitor Cout (μF) 500 Modulator Crossover Fc(mod) (kHz) 3.18 Av = 16.667 wbw = 62,831,853
Output Capacitor ESR (mΩ) 1.0 wp = 1,200 Slope CompSlope CompSlope CompSlope CompError Amp Aol (V/V) 10,000 Error Amp Zero (kHz) 4.42 wz = 2,000,000 Se = 100000
Error Amp UGB (MHz) 10.0 Target Loop Bandwidth Fc (kHz) 25.00 wc = 157,080 Sn = 140000wn = 785,398Q = 0.6366
Control Loop Gain/Phase Control Loop Gain/Phase Control Loop Gain/Phase Control Loop Gain/Phase
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Frequency (Hz)Frequency (Hz)Frequency (Hz)Frequency (Hz)
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电压模式降压 – Type III 电压放大器
Compensator Design - Voltage-Mode Buck - Voltage AmplifierCompensator Design - Voltage-Mode Buck - Voltage AmplifierCompensator Design - Voltage-Mode Buck - Voltage AmplifierCompensator Design - Voltage-Mode Buck - Voltage AmplifierEnter parameters in shaded cells Frequency Compensation Parameters Frequency Compensation Parameters Frequency Compensation Parameters Frequency Compensation ParametersVersion 2.1 Error Amplifier - Single Pole Operational AmplifierError Amplifier - Single Pole Operational AmplifierError Amplifier - Single Pole Operational AmplifierError Amplifier - Single Pole Operational AmplifierRevision date: 10 May 2010 Vin (V) 12 Input Voltage Feed-Forward Kff (V/V) 0.100 ModulatorModulatorModulatorModulator Error AmpError AmpError AmpError Amp
Vout (V) 1.8 Equivalent Ramp Voltage Vramp (V) 1.200 D = 0.1500 Kfb = 0.3333Load Current Iout (A) 10 Reference Voltage Vref (V) 0.600 Rout = 0.18 Rth = 1000.0
Switching Frequency Fsw (kHz) 500 Bottom Feedback Divider Rfbb (Ω) 1,500 Km = 10.00 Avm = 1.069Top Feedback Divider Rfbt (Ω) 3,000 Gc = 1.054 khf = 1.014
Output Inductor L (μH) 1.0 wp = 44,721 wfz = 44,721Output Capacitor Cout (μF) 500 Error Amp Aol (V/V) 3,300 wc = 471,239 wzea = 44,721
Output Capacitor ESR (mΩ) 1.0 Error Amp UGB (MHz) 15.0 wz = 2,000,000 wfp = 2,000,000wsw = 3,141,593 whf = 3,141,593
Modulator Scale Factor SFM (V/V) 1.00 Target Loop Bandwidth Fc (kHz) 75.00 wbw = 94,247,780
Control Loop Gain/Phase Control Loop Gain/Phase Control Loop Gain/Phase Control Loop Gain/Phase
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电流模式简化频率补偿
• 降压（采用理想运算放大器）
• 降压（采用理想跨导放大器）
• 升压（采用理想运算放大器）
• 升压（采用理想跨导放大器）
• 降压----升压（采用理想运算放大器）
• 降压----升压（采用理想跨导放大器）
Word Word Word Word 文档 嵌入式 ExcelExcelExcelExcelCurrentCurrentCurrentCurrent----Mode SimplifiedMode SimplifiedMode SimplifiedMode Simplified Frequency Compensation Frequency Compensation Frequency Compensation Frequency Compensation
Peak CurrentPeak CurrentPeak CurrentPeak Current----ModeModeModeMode Buck Buck Buck Buck –––– Voltage Amplifier Voltage Amplifier Voltage Amplifier Voltage Amplifier
Ri = Gi*Rs Km = Vin*FmAC 1 0
V1
Vsl = Vo*Ri*T/L
V fb
Vc
Fmd
Vo = 5V
S2
U1Q
QN
S
R
10 m
Rs
S1
10Vin
1Ro
L
5u
330uCo
Vclo ck
1mRcGi
10
Vslop e
Vramp
T = 5us
Gv
47 p
Chf
1.6Vlim
3 .74 kRfbt
1 .21 kRfbb
4 .7n
Ccomp
16 k
Rcomp
1.21 5Vref
Aol = 10000UGB = 10 MHz
Vo'
Figure 1. Current -mode buck switching model.
freq / Hertz
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Peak CM Buck Control-to-Output
Phas eGain
Figure 2. Control-to-output gain and phase.
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结论
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• 采用 Excel Excel Excel Excel 补偿器设计工具
• 运用瞬态负载验证性能
• 采用信号注入进行单位增益和相位测量
概要/行动倡议
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