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应用报告
ZHCA041–1999
年
3
月
–2002
年
11
月修订
全面认识开关型电源中的
BUCK-BOOST
功率级
Everett Rogers
系统能源
摘要
开关电源由功率级和控制电路组成
,
功率级完成从输入电压到输出电压的基本能量转换
,
它包括开关
和输出滤波器
。
这篇报告只介绍降压
–
升压
(
buck-boost
)
功率级
,
不包含控制电路
。
详细介绍了工
作在连续模式和非连续模式下
buck-boost
功率级的稳态和小信号分析
,
同时也介绍了标准
buck-boost
功率级的不同变型
,
并讨论了功率级对组成部件的要求
。
目录
商标属于各自所有者持有。
1
简介
2
2 Buck-Boost
级稳态分析
3
2.1 Buck-Boost
稳态连续导通模式分析
3
2.2 Buck-Boost
稳态非连续导通模式分析
7
2.3 Critical Inductance 11
3 Buck-Boost
功率级小信号模型
12
3.1 Buck-Boost
连续导通模式小信号分析
13
3.2 Buck-Boost
非连续导通模式小信号分析
16
4 Buck-Boost
功率级的变型
21
4.1
反向
(Flayback)
功率级
21
5
组件选择
24
5.1
输出电容
24
5.2
输出电感
26
5.3
功率开关
27
5.4
输出二极管
28
6
总结
29
7
参考文献
31
1
全面认识开关型电源中的
BUCK-BOOST
功率级
ZHCA041–1999
年
3
月
–2002
年
11
月修订
2
全面认识开关型电源中的
BUCK-BOOST
功率级
www.ti.com.cn
ZHCA041–1999
年
3
月
–2002
年
11
月修订
1
介绍
开关电源最常见的三种结构布局是降压
(
buck
)、
升压
(
boost
)
和降压
–
升压
(
buck-boost
),
这
三种布局都不是相互隔离的
,
也就是说
,
输入级电压和输出电压是共地的
,
但是也存在这种隔离拓
扑的变型
。
电源布局主要是指这些开关
、
输出电感和输出电容怎么连接的
。
每种布局都有它独自的
特性
,
这些性能主要包括稳态电压转换比
、
输入输出电流的状态
、
输出电压的纹波特征
,
另一个主
要特性就是占空比
–
输出电压的传输函数的频率响应
。
Buck-boost
是一种流行的非隔离
、
逆功率级的拓扑
,
有时也称为升降功率级
。
电源设计者选用
buck-
boost
功率级是因为输出电压和输入电压是反向的
,
这种拓扑结构可以得到在幅度上
,
比输入电压更
高的输出电压
(
像升压
(
boost
)
功率级
),
或者更低的输出电压
(
像降压
(
buck
)
功率级
),
这就
是它名字的由来
,
但是输出电压在极性上跟输入电压是相反的
。
由于功率开关
(
Q1
)
的作用
,
buck-
boost
的输入电流是非连续的或脉冲的
,
在每个开关周期内
,
脉冲电流从
0
变化到
I
L
,
输出电流也是
非连续或脉冲的
,
这是因为输出二极管只能在开关周期内的一部分时间内导通
,
输出电容提供开关
周期内其它时间的所有负载电流
。
这篇报告描述了在给定的理想波形下
,
连续模式和非连续模式中
buck-boost
转换器的稳态工作过程
。
在介绍了脉冲宽度调制
(
PWM
)
开关模型后
,
给出了占空比
–
输出电压的传输函数
。
图
1
显示了包括
驱动电路模块在内的
buck-boost
功率级的简单原理图
,
功率开关
Q1
是以一个
n
通道的金属氧化物半导
体场效应管
(
MOSFET
),
输出二极管是
CR1
。
电感
L
和电容
C
组成了有效的输出滤波器
。
在分析过
程中
,
考虑了电容
ESR
(
等效串联电阻
)
,
R
C
,
和电感
DC
的阻抗
,
R
L
。
电阻
R
,
代表了在功率输出端的
负载
。
图
1.buck-boost
功率级原理图
在
buck-boost
功率级的正常工作中
,
Q1
在控制电路的开关时间内
,
重复的打开
、
关上
。
在
Q1
、
CR1
和
L
的连结节点处
,
开关动作产生了一个脉冲序列
。
电感
L
跟输出电容
C
相连
,
只有在
CR1
导通时
,
一
个有效的
L/C
输出滤波器才形成
,
过滤脉冲序列
,
产生直流输出电压
。
CR1
Q1
a
c
i
a
+
V
I
Drive
Circuit
p
R
L
I
L
= i
c
C
R
C
R
V
O
L
简介
3
全面认识开关型电源中的
BUCK-BOOST
功率级
www.ti.com.cn
ZHCA041–1999
年
3
月
–2002
年
11
月修订
2 Buck-Boost
功率级稳态分析
功率级可以在连续电感器电流和非连续电感器电流模式下工作
,
连续电感器电流模式在稳态工作
时
,
整个开关周期内都有电流连续通过电感器
;
非连续电感器电流模式是开关周期内的一部分时间
电感电流为
0
,
它在整个周期内从
0
开始
,
达到一个峰值后
,
再回到
0.
这两种模式稍后再详细探讨
,
在给出额定负载情况下如何选择电感值
,
来保证工作在选定模式的设
计指导书也会提供
。
对于转换器来说
,
在预期工作条件下只保持希望的工作模式是很理想的
,
因为
在两种不同工作模式下功率级的频率响应变化相差很大
。
经过这些分析发现
,
采用
n
通道的功率型金属氧化物半导体场效应管
(
MOSFET
),
驱动电路打开
场效应管
(
FET
)
时
,
Q1
的栅极和漏极间加上正的电压
V
GS(ON)
,
采用
n
通道场效应管的优势在于它的
低导致电阻
R
DS(on)
,
但是驱动电路就更加复杂
,
因为需要浮动电极
。
而同样大小的
p
通道场效应管有
较高的
R
DS(on)
,
通常也不需要浮动电极回路
。
晶体管
Q1
和二极管
CR1
画在点划线方框里面
,
终端接
口标为
a
,
p
和
c
,
这些会在
BUCK–BOOST
功率级模型部分
详细讲到
。
2.1 Buck-Boost
稳态连续导通模式分析
紧接着介绍
Buck-Boost
的稳态连续导通模式分析
,
这部分主要目的就是给出一个
Buck-Boost
稳态
连续导通模式下电压转换关系的推导
。
这是很重要的
,
因为它揭示了输出电压怎样由占空比和输入
电压决定
,
或者相反
,
怎样基于输入电压和输出电压来计算占空比
。
稳态说明输入电压
、
输出电
压
、
输出负载电流和占空比都是固定不变的
,
大写字母表示出了稳态下的变量名
。
在连续导通模式
,
buck-boost
转换器保证每个开关周期有两个功率态
,
当
Q1
是开
、
CR1
是关时
,
就
是开态
(
ON
);
当
Q1
是关而
CR1
是开时
,
就是关态
(
OFF
)。
在每个状态中
,
当回路中的开关被
等价回路所代替时
,
一个简单的线性回路可以用来表示这两种状态
,
两种状态的回路图表见图
2.
图
2.buck-boost
功率级状态图
SLVA059A
3
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
2 Buck-Boost Stage Steady-State Analysis
A power stage can operate in continuous or discontinuous inductor current mode.
Continuous inductor current mode is characterized by current flowing continuously in the
inductor during the entire switching cycle in steady-state operation. Discontinuous inductor
current mode is characterized by the inductor current being zero for a portion of the switching
cycle. It starts at zero, reaches a peak value, and returns to zero during each switching cycle.
The two different modes are discussed in greater detail later and design guidelines for the
inductor value to maintain a chosen mode of operation as a function of rated load are given.
It is very desirable for a converter to stay in one mode only over its expected operating
conditions because the power stage frequency response changes significantly between the
two different modes of operation.
For this analysis, an n-channel power MOSFET is used and a positive voltage, V
GS(ON)
, is
applied from the Gate to the Source terminals of Q1 by the drive circuit to turn ON the FET.
The advantage of using an n-channel FET is its lower R
DS(on)
but the drive circuit is more
complicated because a floating drive is required. For the same die size, a p-channel FET has
a higher R
DS(on)
but usually does not require a floating drive circuit.
The transistor Q1 and diode CR1 are drawn inside a dashed-line box with terminals labeled
a, p, and c. This is explained fully in the Buck-Boost Power Stage Modeling section.
2.1 Buck-Boost Steady-State Continuous Conduction Mode Analysis
The following is a description of steady-state operation in continuous conduction mode. The
main goal of this section is to provide a derivation of the voltage conversion relationship for
the continuous conduction mode buck-boost power stage. This is important because it shows
how the output voltage depends on duty cycle and input voltage or conversely, how the duty
cycle can be calculated based on input voltage and output voltage. Steady-state implies that
the input voltage, output voltage, output load current, and duty-cycle are fixed and not
varying. Capital letters are generally given to variable names to indicate a steady-state
quantity.
In continuous conduction mode, the buck-boost converter assumes two states per switching
cycle. The ON State is when Q1 is ON and CR1 is OFF. The OFF State is when Q1 is OFF
and CR1 is ON. A simple linear circuit can represent each of the two states where the
switches in the circuit are replaced by their equivalent circuit during each state. The circuit
diagram for each of the two states is shown in Figure 2.
a
c
i
a
+
V
I
p
R
L
L
I
L
= i
c
C
R
C
R
R
DS(on)
V
O
ON State
a
c
i
a
+
V
I
p
C
R
C
R
V
O
V
d
L
I
L
= i
c
R
L
I
O
I
O
OFF State
Figure 2. Buck-Boost Power Stage States
Buck-Boost
级稳态分析
4
全面认识开关型电源中的
BUCK-BOOST
功率级
www.ti.com.cn
ZHCA041–1999
年
3
月
–2002
年
11
月修订
开态的时间为
D
×
T
S
= T
ON
,
其中
D
为由控制回路设定的占空比
,
代表了开关在开态的时间占
整个开关周期
(
T
S
)
的比值
。
关态的时间叫
T
OFF
,
因为对于连续导通模式下在整个开关周期
中只有两个状态
,
所以
T
OFF
等于
(1 – D)
×
T
S
,
数值
(
1 – D
)
有时被成为
D
’,
这些时间与波
形一起显示在图
3
中
。
图
3.
连续模式下
buck-boost
功率级波形图
参考图
2
,
在
ON
态
,
Q1
此时为低电阻
,
R
DS(ON)
,
从漏极到源极
,
只有很小的电压降
V
DS
=I
L
×
R
DS(on)
。
同时电感器的直流电阻上的电压降也很小
,
等于
I
L
×
R
L
。
因此
,
输入电压
V
I
,
减去损
耗
(V
DS
+ I
L
×
R
L
)
,
就加载到电感器
L
两端
。
在这段时间
CR1
是关的
,
因为它是反向偏置的
。
电感电流
IL
,
从输入源
VI
流出
,
经过
Q1
,
到地
。
在开
(ON)
态
,
加在电感器两端的电压为定
值
,
等于
V
I
– V
DS
– I
L
×
R
L
。
通过改变图
2
中电流
I
L
的极性
,
电感上的电流会随着所加的电压
而增大
。
同时
,
由于加载的电压通常必须为定值
,
所以电感电流线性增加
。
图
3
描述了在
T
ON
时间内电感电流的增加
。
SLVA059A
4
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
The duration of the ON state is D × T
S
= T
ON
where D is the duty cycle, set by the control
circuit, expressed as a ratio of the switch ON time to the time of one complete switching cycle,
T
s
. The duration of the OFF state is called T
OFF
. Since there are only two states per switching
cycle for continuous conduction mode, T
OFF
is equal to (1−D) × T
S
. The quantity (1−D) is
sometimes called D’. These times are shown along with the waveforms in Figure 3.
∆I
L
T
ON
T
OFF
T
S
I
Q1
I
CR1
I
L
Solid
I
O
Dashed
V
c-p
Solid
V
O
Dashed
0
0
Figure 3. Continuous Mode Buck-Boost Power Stage Waveforms
Referring to Figure 2, during the ON state, Q1 presents a low resistance, R
DS(on)
, from its
drain to source and exhibits a small voltage drop of V
DS
=I
L
× R
DS(on)
. There is also a small
voltage drop across the dc resistance of the inductor equal to I
L
× R
L
. Thus, the input voltage,
V
I
, minus losses, (V
DS
+ I
L
× R
L
), is applied across the inductor, L. CR1 is OFF during this
time because it is reverse biased. The inductor current, I
L
, flows from the input source, V
I
,
through Q1 and to ground. During the ON state, the voltage applied across the inductor is
constant and equal to V
I
− V
DS
− I
L
× R
L
. Adopting the polarity convention for the current I
L
shown in Figure 2, the inductor current increases as a result of the applied voltage. Also, since
the applied voltage is essentially constant, the inductor current increases linearly. This
increase in inductor current during T
ON
is illustrated in Figure 3.
Buck-Boost
级稳态分析
5
全面认识开关型电源中的
BUCK-BOOST
功率级
www.ti.com.cn
ZHCA041–1999
年
3
月
–2002
年
11
月修订
SLVA059A
5
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
The amount that the inductor current increases can be calculated by using a version of the
familiar relationship:
v
L
L
di
L
dt
�I
L
v
L
L
�T
The inductor current increase during the ON state is given by:
�I
L
()
V
I
V
DS
I
L
R
L
L
T
ON
This quantity, ∆I
L
(+), is referred to as the inductor ripple current. Also notice that during this
period, all of the output load current is supplied by the output capacitor, C.
Referring to Figure 2, when Q1 is OFF, it presents a high impedance from its drain to source.
Therefore, since the current flowing in the inductor L cannot change instantaneously, the
current shifts from Q1 to CR1. Due to the decreasing inductor current, the voltage across the
inductor reverses polarity until rectifier CR1 becomes forward biased and turns ON. The
voltage applied across L becomes (V
O
− V
d
− I
L
× R
L
) where the quantity, V
d
, is the forward
voltage drop of CR1. The inductor current, I
L
, now flows from the output capacitor and load
resistor combination through CR1 and to ground. Notice that the orientation of CR1 and the
direction of current flow in the inductor means that the current flowing in the output capacitor
and load resistor combination causes V
O
to be a negative voltage. During the OFF state, the
voltage applied across the inductor is constant and equal to (V
O
− V
d
− I
L
× R
L
). Maintaining
our same polarity convention, this applied voltage is negative (or opposite in polarity from the
applied voltage during the ON time), because the output voltage V
O
is negative. Hence, the
inductor current decreases during the OFF time. Also, since the applied voltage is essentially
constant, the inductor current decreases linearly. This decrease in inductor current during
T
OFF
is illustrated in Figure 3.
The inductor current decrease during the OFF state is given by:
�I
L
()
V
O
V
d
I
L
R
L
L
T
OFF
This quantity, ∆I
L
(−), is also referred to as the inductor ripple current.
In steady state conditions, the current increase, ∆I
L
(+), during the ON time and the current
decrease during the OFF time, ∆I
L
(−), must be equal. Otherwise, the inductor current would
have a net increase or decrease from cycle to cycle which would not be a steady state
condition. Therefore, these two equations can be equated and solved for V
O
to obtain the
continuous conduction mode buck-boost voltage conversion relationship:
Solving for V
O
:
V
O
V
I
V
DS
T
ON
T
OFF
V
d
I
L
R
L
T
ON
T
OFF
T
OFF
电感电流的增加量可以由类似关系式来求得
:
SLVA059A
5
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
The amount that the inductor current increases can be calculated by using a version of the
familiar relationship:
v
L
L
di
L
dt
�I
L
v
L
L
�T
The inductor current increase during the ON state is given by:
�I
L
()
V
I
V
DS
I
L
R
L
L
T
ON
This quantity, ∆I
L
(+), is referred to as the inductor ripple current. Also notice that during this
period, all of the output load current is supplied by the output capacitor, C.
Referring to Figure 2, when Q1 is OFF, it presents a high impedance from its drain to source.
Therefore, since the current flowing in the inductor L cannot change instantaneously, the
current shifts from Q1 to CR1. Due to the decreasing inductor current, the voltage across the
inductor reverses polarity until rectifier CR1 becomes forward biased and turns ON. The
voltage applied across L becomes (V
O
− V
d
− I
L
× R
L
) where the quantity, V
d
, is the forward
voltage drop of CR1. The inductor current, I
L
, now flows from the output capacitor and load
resistor combination through CR1 and to ground. Notice that the orientation of CR1 and the
direction of current flow in the inductor means that the current flowing in the output capacitor
and load resistor combination causes V
O
to be a negative voltage. During the OFF state, the
voltage applied across the inductor is constant and equal to (V
O
− V
d
− I
L
× R
L
). Maintaining
our same polarity convention, this applied voltage is negative (or opposite in polarity from the
applied voltage during the ON time), because the output voltage V
O
is negative. Hence, the
inductor current decreases during the OFF time. Also, since the applied voltage is essentially
constant, the inductor current decreases linearly. This decrease in inductor current during
T
OFF
is illustrated in Figure 3.
The inductor current decrease during the OFF state is given by:
�I
L
()
V
O
V
d
I
L
R
L
L
T
OFF
This quantity, ∆I
L
(−), is also referred to as the inductor ripple current.
In steady state conditions, the current increase, ∆I
L
(+), during the ON time and the current
decrease during the OFF time, ∆I
L
(−), must be equal. Otherwise, the inductor current would
have a net increase or decrease from cycle to cycle which would not be a steady state
condition. Therefore, these two equations can be equated and solved for V
O
to obtain the
continuous conduction mode buck-boost voltage conversion relationship:
Solving for V
O
:
V
O
V
I
V
DS
T
ON
T
OFF
V
d
I
L
R
L
T
ON
T
OFF
T
OFF
在开态
(
ON
)
时间内电感电流的增量由下式可得
:
量
Δ
I
L
(+)
代表了电感的纹波电流
,
同时注意在此期间
,
所有的输出负载电流由输出电容
C
提供
。
参考图
2
,
当
Q1
关时
,
它的漏极和源极间有很高的阻抗
,
所以
,
流过电感
L
的电流不能瞬时的变化
,
从
Q1
转移到
CR1
。
随着电感电流的减小
,
电感两段的电压改变极性直到整流器
CR1
变为前向偏置
,
打开的时候
,
这时电感
L
两段的电压变为
(V
O
– V
d
– I
L
×
RL)
,
式中的
V
d
是
CR1
的前向电压降
。
电感电
流
IL
,
这时从输出电容和负载电阻的组合
,
经过
CR1
到地
。
注意
CR1
的方向和电感中电流的流向意味着输出电容和负载电阻中电流导致
V
O
为负电压
。
在关态
(
OFF
)
时
,
电感两端的电压为定数
,
且为
(V
O
– V
d
– I
L
×
R
L
)
,
为了保证同样极性的转换
,
这个加载
电压必须是负的
(
或者在开态
(
ON
)
时为极性相反的加载电压
),
因为输出电压为负的
。
因此
,
电
感电流在
OFF
态时是减小的
,
而且由于加载电压必须是常数
,
所以电感电流线性减小
。
T
OFF
时间内电
感电流的减小见图
3.
SLVA059A
5
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
The amount that the inductor current increases can be calculated by using a version of the
familiar relationship:
v
L
L
di
L
dt
�I
L
v
L
L
�T
The inductor current increase during the ON state is given by:
�I
L
()
V
I
V
DS
I
L
R
L
L
T
ON
This quantity, ∆I
L
(+), is referred to as the inductor ripple current. Also notice that during this
period, all of the output load current is supplied by the output capacitor, C.
Referring to Figure 2, when Q1 is OFF, it presents a high impedance from its drain to source.
Therefore, since the current flowing in the inductor L cannot change instantaneously, the
current shifts from Q1 to CR1. Due to the decreasing inductor current, the voltage across the
inductor reverses polarity until rectifier CR1 becomes forward biased and turns ON. The
voltage applied across L becomes (V
O
− V
d
− I
L
× R
L
) where the quantity, V
d
, is the forward
voltage drop of CR1. The inductor current, I
L
, now flows from the output capacitor and load
resistor combination through CR1 and to ground. Notice that the orientation of CR1 and the
direction of current flow in the inductor means that the current flowing in the output capacitor
and load resistor combination causes V
O
to be a negative voltage. During the OFF state, the
voltage applied across the inductor is constant and equal to (V
O
− V
d
− I
L
× R
L
). Maintaining
our same polarity convention, this applied voltage is negative (or opposite in polarity from the
applied voltage during the ON time), because the output voltage V
O
is negative. Hence, the
inductor current decreases during the OFF time. Also, since the applied voltage is essentially
constant, the inductor current decreases linearly. This decrease in inductor current during
T
OFF
is illustrated in Figure 3.
The inductor current decrease during the OFF state is given by:
�I
L
()
V
O
V
d
I
L
R
L
L
T
OFF
This quantity, ∆I
L
(−), is also referred to as the inductor ripple current.
In steady state conditions, the current increase, ∆I
L
(+), during the ON time and the current
decrease during the OFF time, ∆I
L
(−), must be equal. Otherwise, the inductor current would
have a net increase or decrease from cycle to cycle which would not be a steady state
condition. Therefore, these two equations can be equated and solved for V
O
to obtain the
continuous conduction mode buck-boost voltage conversion relationship:
Solving for V
O
:
V
O
V
I
V
DS
T
ON
T
OFF
V
d
I
L
R
L
T
ON
T
OFF
T
OFF
在关态
(
OFF
)
电感电流的减小可以由下式求得
:
量
Δ
I
L
(–)
也代表了电感的纹波电流
。
在稳态条件下
,
开态
(
ON
)
下的电流增加量
Δ
I
L
(+)
和关态
(
OFF
)
下的电流减小量
Δ
I
L
(–)
必须是相
等的
。
否则
,
在一个周期到下一个周期
,
电感电流就会有一个净的增加量或者减小量
,
这就不是一
个稳态了
。
所以
,
这两个方程必须相等
,
从而求出
V
O
,
得到连续导通下
buck-boost
能量转换的关系
式
:
求解出
V
O
:
SLVA059A
5
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
The amount that the inductor current increases can be calculated by using a version of the
familiar relationship:
v
L
L
di
L
dt
�I
L
v
L
L
�T
The inductor current increase during the ON state is given by:
�I
L
()
V
I
V
DS
I
L
R
L
L
T
ON
This quantity, ∆I
L
(+), is referred to as the inductor ripple current. Also notice that during this
period, all of the output load current is supplied by the output capacitor, C.
Referring to Figure 2, when Q1 is OFF, it presents a high impedance from its drain to source.
Therefore, since the current flowing in the inductor L cannot change instantaneously, the
current shifts from Q1 to CR1. Due to the decreasing inductor current, the voltage across the
inductor reverses polarity until rectifier CR1 becomes forward biased and turns ON. The
voltage applied across L becomes (V
O
− V
d
− I
L
× R
L
) where the quantity, V
d
, is the forward
voltage drop of CR1. The inductor current, I
L
, now flows from the output capacitor and load
resistor combination through CR1 and to ground. Notice that the orientation of CR1 and the
direction of current flow in the inductor means that the current flowing in the output capacitor
and load resistor combination causes V
O
to be a negative voltage. During the OFF state, the
voltage applied across the inductor is constant and equal to (V
O
− V
d
− I
L
× R
L
). Maintaining
our same polarity convention, this applied voltage is negative (or opposite in polarity from the
applied voltage during the ON time), because the output voltage V
O
is negative. Hence, the
inductor current decreases during the OFF time. Also, since the applied voltage is essentially
constant, the inductor current decreases linearly. This decrease in inductor current during
T
OFF
is illustrated in Figure 3.
The inductor current decrease during the OFF state is given by:
�I
L
()
V
O
V
d
I
L
R
L
L
T
OFF
This quantity, ∆I
L
(−), is also referred to as the inductor ripple current.
In steady state conditions, the current increase, ∆I
L
(+), during the ON time and the current
decrease during the OFF time, ∆I
L
(−), must be equal. Otherwise, the inductor current would
have a net increase or decrease from cycle to cycle which would not be a steady state
condition. Therefore, these two equations can be equated and solved for V
O
to obtain the
continuous conduction mode buck-boost voltage conversion relationship:
Solving for V
O
:
V
O
V
I
V
DS
T
ON
T
OFF
V
d
I
L
R
L
T
ON
T
OFF
T
OFF
Buck-Boost
级稳态分析
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