开关电源深度解析：BUCK-BOOST功率级
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"buck-boost 开关型电源 功率级 控制电路 降压 升压 连续模式 非连续模式 稳态分析 小信号模型 变型 组件选择"
本文是一份关于开关型电源中BUCK-BOOST功率级的详细应用报告，由Everett Rogers撰写，最初发布于1999年3月，并在2002年11月进行了修订。报告主要聚焦于功率级本身，而不涉及控制电路部分。BUCK-BOOST功率级是一种能实现输入电压到输出电压正反向转换的非隔离拓扑结构，尤其适用于需要输出电压高于或低于输入电压的应用场景。
报告首先介绍了BUCK-BOOST功率级的基本构成，包括开关和输出滤波器，并强调了其在连续模式和非连续模式下的工作原理。在稳态分析中，详细探讨了两种模式下的电压转换和电流状态。连续导通模式（CCM）下，电感电流在整个开关周期内保持连续；而非连续导通模式（DCM）中，电感电流在开关周期内有一段时间为零。这两种模式下，功率级的性能表现和参数选择有所不同。
报告还涉及了临界电感的概念，这是介于CCM和DCM之间的一个特殊工作点，对理解和优化功率级性能至关重要。此外，报告列举了标准BUCK-BOOST功率级的不同变型，如反向（Flyback）功率级，这些变型扩展了拓扑的应用范围。
在小信号模型部分，报告详细分析了在CCM和DCM下，BUCK-BOOST功率级的动态响应，包括其传递函数，这对于设计高稳定性电源至关重要。这部分内容有助于理解功率级的瞬态响应和频率特性。
接着，报告讨论了功率级各组成部分的选择，如输出电容、电感、功率开关和输出二极管。每个组件的选取都直接影响到电源的效率、纹波、热性能和可靠性。例如，输出电容的选择要考虑纹波抑制和稳定性，而输出电感则影响电流转换和电磁兼容性。
最后，报告总结了BUCK-BOOST功率级的主要特点和设计考虑，同时提供了进一步阅读的参考文献，为电源设计师提供了全面的技术指导。这份报告对于理解BUCK-BOOST功率级的工作机制、优化设计以及解决实际工程问题具有很高的参考价值。
6
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
6
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
And, substituting T
S
for T
ON
+ T
OFF
, and using D = T
ON
/T
S
and (1−D) = T
OFF
/T
S
, the
steady-state equation for V
O
is:
V
O
V
I
V
DS
D
1 D
V
d
I
L
R
L
1 D
Notice that in simplifying the above, T
ON
+ T
OFF
is assumed to be equal to T
S
. This is true
only for continuous conduction mode as we will see in the discontinuous conduction mode
analysis.
An important observation should be made here: Setting the two values of ∆I
L
equal to each
other is precisely equivalent to balancing the volt-seconds on the inductor. The volt-seconds
applied to the inductor is the product of the voltage applied and the time that the voltage is
applied. This is the best way to calculate unknown values such as V
O
or D in terms of known
circuit parameters, and this method will be applied repeatedly in this paper. Volt-second
balance on the inductor is a physical necessity and should be comprehended at least as well
as Ohms Law.
In the above equations for ∆I
L
(+) and ∆I
L
(−), the output voltage was implicitly assumed to be
constant with no AC ripple voltage during the ON time and the OFF time. This is a common
simplification and involves two separate effects. First, the output capacitor is assumed to be
large enough that its voltage change is negligible. Second, the voltage due to the capacitor
ESR is also assumed to be negligible. These assumptions are valid because the AC ripple
voltage is designed to be much less than the DC part of the output voltage.
The above voltage conversion relationship for V
O
illustrates the fact that V
O
can be adjusted
by adjusting the duty cycle, D. This relationship approaches zero as D approaches zero and
increases without bound as D approaches 1. A common simplification is to assume V
DS
, V
d
,
and R
L
are small enough to ignore. Setting V
DS
, V
d
, and R
L
to zero, the above equation
simplifies considerably to:
V
O
V
I
D
1 D
A simplified, qualitative way to visualize the circuit operation is to consider the inductor as an
energy storage element. When Q1 is on, energy is added to the inductor. When Q1 is off, the
inductor delivers some of its energy to the output capacitor and load. The output voltage is
controlled by setting the on-time of Q1. For example, by increasing the on-time of Q1, the
amount of energy delivered to the inductor is increased. More energy is then delivered to the
output during the off-time of Q1 resulting in an increase in the output voltage.
Unlike the buck power stage, the average of the inductor current is not equal to the output
current. To relate the inductor current to the output current, referring to Figures 2 and 3, note
that the inductor delivers current to the output only during the off state of the power stage.
This current averaged over a complete switching cycle is equal to the output current because
the average current in the output capacitor must be equal to zero.
用
T
ON
+T
OFF
来替换
T
S
，
并利有
D = T
ON
/ T
S
和
(1 – D) = T
OFF
/ T
S
，
V
O
的稳态方程可变为
:
SLVA059A
6
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
And, substituting T
S
for T
ON
+ T
OFF
, and using D = T
ON
/T
S
and (1−D) = T
OFF
/T
S
, the
steady-state equation for V
O
is:
V
O
V
I
V
DS
D
1 D
V
d
I
L
R
L
1 D
Notice that in simplifying the above, T
ON
+ T
OFF
is assumed to be equal to T
S
. This is true
only for continuous conduction mode as we will see in the discontinuous conduction mode
analysis.
An important observation should be made here: Setting the two values of ∆I
L
equal to each
other is precisely equivalent to balancing the volt-seconds on the inductor. The volt-seconds
applied to the inductor is the product of the voltage applied and the time that the voltage is
applied. This is the best way to calculate unknown values such as V
O
or D in terms of known
circuit parameters, and this method will be applied repeatedly in this paper. Volt-second
balance on the inductor is a physical necessity and should be comprehended at least as well
as Ohms Law.
In the above equations for ∆I
L
(+) and ∆I
L
(−), the output voltage was implicitly assumed to be
constant with no AC ripple voltage during the ON time and the OFF time. This is a common
simplification and involves two separate effects. First, the output capacitor is assumed to be
large enough that its voltage change is negligible. Second, the voltage due to the capacitor
ESR is also assumed to be negligible. These assumptions are valid because the AC ripple
voltage is designed to be much less than the DC part of the output voltage.
The above voltage conversion relationship for V
O
illustrates the fact that V
O
can be adjusted
by adjusting the duty cycle, D. This relationship approaches zero as D approaches zero and
increases without bound as D approaches 1. A common simplification is to assume V
DS
, V
d
,
and R
L
are small enough to ignore. Setting V
DS
, V
d
, and R
L
to zero, the above equation
simplifies considerably to:
V
O
V
I
D
1 D
A simplified, qualitative way to visualize the circuit operation is to consider the inductor as an
energy storage element. When Q1 is on, energy is added to the inductor. When Q1 is off, the
inductor delivers some of its energy to the output capacitor and load. The output voltage is
controlled by setting the on-time of Q1. For example, by increasing the on-time of Q1, the
amount of energy delivered to the inductor is increased. More energy is then delivered to the
output during the off-time of Q1 resulting in an increase in the output voltage.
Unlike the buck power stage, the average of the inductor current is not equal to the output
current. To relate the inductor current to the output current, referring to Figures 2 and 3, note
that the inductor delivers current to the output only during the off state of the power stage.
This current averaged over a complete switching cycle is equal to the output current because
the average current in the output capacitor must be equal to zero.
注意在上式的化简中
，
用到了
T
ON
+T
OFF
等于
T
S
，
这只是在连续导通模式下成立的
，
在我们以后分析到
非连续导通模式下就可以看到
。
我们还发现
，
Δ
I
L
的两个值相互相等的假定
，
等同于电感上的电压
-
秒曲线的平衡
。
电感上的电压
–
秒
关系是由加载在电感上的电压和加载电压的时间来确定的
。
这是用已知的电路参数来计算像
V
O
和
D
等
未知值的最好方法
，
这种方法在本文中将经常用到
。
电感上的电压
-
秒关系平衡在物理上是必须的
，
而且就像欧姆定律一样容易理解
。
在上面关于
Δ
I
L
(+)
和
Δ
I
L
(–)
的方程中
，
输出电压默认为常数定值
，
在
ON
时间和
OFF
时间内没有交流
纹波电压
。
这是一个常用的简化
，
涉及到两方面的假设
，
首先
，
输出电容足够大
，
它上面的电压变
化可以忽略
；
其次
，
由于电容等效串联电阻
（
ESR
）
造成的电压也可以忽略
。
这些假设是合理的
，
因为设计的交流纹波电压是远小于输出电压的直流部分的
。
上面
V
O
的电压转换关系表明一个事实
，
就是可以通过调节电控比
D
来调节输出电压
。
这种关系在
D
接
近于
0
时也接近
0
，
在
D
接近
1
时逐渐增加而没有限制
。
一个常用的简化就是假定
V
DS
，
V
d
和
R
L
足够小
，
可以忽略
。
假设
V
DS
, V
d
和
R
L
等于
0
，
上面的式子就可以简单地看作为
：
一个简单定性的想象电路工作的方法就是把电感看作是一个能量储存单元
，
当
Q1
打开时
，
能量加到
电感器上
，
当
Q1
关上时
，
电感就把它储存的一部分能量输送到输出电容和负载上
。
输出电压就通过
设定
Q1
的开关时间来控制
，
例如
，
增大
Q1
开的时间
，
输送到电感的能量就增加
，
在
Q1
关时有越多
的能量输出
，
输出电压就会增加
。
不像降压
（
buck
）
功率级
，
电感电流的平均值并不等于输出电流
。
想知道电感电流和输出电流的关
系
，
可以参考图
2
和图
3
，
注意电感只有在能量级的关
（
OFF
）
态才向输出传送电流
。
这样在整个开
关周期内的电流平均值就等于输出电流
，
因为输出电容中的电流平均值必须等于
0.
Buck-Boost
级稳态分析
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