Download 全面认识开关型电源中的 BUCK-BOOST 应用报告 ZHCA041–1999年3月–2002年11月修订

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
1 简介
2
2 Buck-Boost级稳态分析
2.1 Buck-Boost 稳态连续导通模式分析
2.2 Buck-Boost 稳态非连续导通模式分析
2.3 Critical Inductance
3
3
7
11
3 Buck-Boost功率级小信号模型
3.1 Buck-Boost 连续导通模式小信号分析
3.2 Buck-Boost非连续导通模式小信号分析
12
13
16
4 Buck-Boost功率级的变型
4.1反向(Flayback)功率级
21
21
5 组件选择
24
5.1输出电容
5.2输出电感
5.3功率开关
5.4输出二极管
24
26
27
28
6 总结
29
7 参考文献
31
商标属于各自所有者持有。
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
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简介
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buckboost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，buckboost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IL，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）,RC ,和电感DC的阻抗，R L 。电阻R ，代表了在功率输出端的
负载。
a
CR1
Q1
p
VO
ia
VI
+
Drive
Circuit
C
c
L
IL = ic
R
RC
RL
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。
2
全面认识开关型电源中的BUCK-BOOST功率级
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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
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inductor during the entire switching cycle in steady-state operation. Discontinuous
inductor
级稳态分析
Buck-Boost
current mode is characterized by the inductor current being zero for a portion of the switching
cycle.
It starts at功率级稳态分析
zero, reaches a peak value, and returns to zero during each switching cycle.
2
Buck-Boost
The two different modes are discussed in greater detail later and design guidelines for the
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
inductor
value to maintain a chosen mode of operation as a，
function
of rated load are given.
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
It is，very desirable for a converter to stay；in one mode only over its expected operating
电感电流为because
达到一个峰值后
conditions
the power stage
frequency
response
changes
significantly between the
，再回到
0，它在整个周期内从
0开始，
0.
two different modes of operation.
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
For
this analysis, an n-channel power MOSFET is used and a positive voltage, VGS(ON) , is
计指导书也会提供
因为
。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
applied from the Gate
to the Source
terminals of Q1 by the drive circuit to turn ON the，FET.
在两种不同工作模式下功率级的频率响应变化相差很大
。 RDS(on) but the drive circuit is more
The
advantage of using an n-channel FET is its lower
complicated because a floating drive is required. For the same die size, a p-channel FET has
a经过这些分析发现
higher RDS(on) ，
but
usually
does not require a floating drive circuit.
采用
（MOSFET），驱动电路打开
n通道的功率型金属氧化物半导体场效应管
场效应管
的栅极和漏极间加上正的电压
（FET）
，Q1
，采用n通道场效应管的优势在于它的
VGS(ON)
The
transistor
Q1时and
diode
CR1 are drawn inside a
dashed-line
box with terminals labeled
低导致电阻
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
，
，
。
R
a, p, and c. This
section.
DS(on) is explained fully in the Buck-Boost Power Stage Modelingp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
详细讲到
功率级模型部分
口标为a，p和c，
这些会在BUCK–BOOST
。
Buck-Boost
Steady-State
Continuous
Conduction
Mode
Analysis
2.1
The following is a description of steady-state operation in continuous conduction mode. The
2.1 Buck-Boost
main goal of稳态连续导通模式分析
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
紧接着介绍
的稳态连续导通模式分析
稳态
，这部分主要目的就是给出一个
Buck-Boost
Buck-Boost
how
the
output
voltage
depends
on
duty
cycle
and
input
voltage
or
conversely,
how
the
duty
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
cycle can be calculated based on input voltage and output voltage. Steady-state implies that
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
the input voltage, output voltage, output load current, and duty-cycle are fixed and not
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。
varying.
Capital letters are generally given to variable names to indicate a steady-state
quantity.
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
In
continuous
conduction mode, the buck-boost converter assumes two states per switching
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
cycle. The ON State is when Q1 is ON and CR1 is OFF. The OFF State is when Q1 is OFF
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.
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.
OFF State
ON State
p
a
ia
VI
+
RDS(on)
L
c
ia
IO
IL = ic
C
RC
R
Vd
a
VO
VI
p
VO
c
+
L
IL = ic
IO
C
RC
R
RL
RL
Figure 2. Buck-Boost Power Stage States
图2.buck-boost功率级状态图
ZHCA041–1999年3月–2002年11月修订
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
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级稳态分析
Buck-Boost
SLVA059A
开态的时间为
代表了开关在开态的时间占
，其中isD为由控制回路设定的占空比
T S =ON
TONstate
The
durationDof×the
D × TS = TON where D is，the
duty cycle, set by the control
关态的时间叫
整个开关周期
因为对于连续导通模式下在整个开关周期
circuit,
expressed
as的比值
a ratio
the switch ON
time
to the time of one complete switching cycle,
。of
（T S）
TOFF ，
T中只有两个状态
theTOFF
OFF
state
is called
TOFF
Since
there
are only
two states
per switching
等于
有时被成为
× TS ，
数值.（1
所以
这些时间与波
s . The duration，of
(1 – D)
D ’，
– D）
cycle
for
continuous
conduction
mode,
T
is
equal
to
(1−D)
×
T
.
The
quantity
(1−D) is
OFF
S
形一起显示在图3中。
sometimes called D’. These times are shown along with the waveforms in Figure 3.
IQ1
ICR1
IL Solid
IO Dashed
∆IL
0
Vc-p Solid
VO Dashed
0
TON
TOFF
TS
图3.
连续模式下buck-boost
功率级波形图
Figure 3.
Continuous
Mode Buck-Boost
Power Stage Waveforms
Referring
to ON
Figure
2, 此时为低电阻
during the ON
Q1 presents a low resistance, RDS(on) , from its
参考图2，在
态，Q1
，Rstate,
DS(ON) ，从漏极到源极，只有很小的电压降V DS=I L ×
drain to source and exhibits a small voltage drop of VDS =IL × RDS(on) . There is also a small
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
voltage
drop across the dc resistance of the inductor equal to IL × RL . Thus, the input voltage,
耗(V DS + IL × RL) ，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。
VI , minus losses, (VDS + IL × RL ), is applied across the inductor, L. CR1 is OFF during this
电感电流
，经过Q1，
。在开
(ON) 态，
IL ，从输入源
VI 流出biased.
time
because
it is reverse
The 到地
inductor
current,
IL ,加在电感器两端的电压为定
flows from the input source, VI ,
值，等于Q1
电感上的电流会随着所加的电压
× RL 。通过改变图
中电流
V I –and
VDS –toILground.
I L 的极性
through
During the2ON
state,
the ，
voltage
applied across the inductor is
constant
and
equal
to
V
−
V
−
I
×
R
.
Adopting
the
polarity
convention
for the Tcurrent
IL
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
I
DS L
L
ON
shown
in Figure 2, the。inductor current increases as a result of the applied voltage. Also, since
时间内电感电流的增加
the applied voltage is essentially constant, the inductor current increases linearly. This
increase in inductor current during TON is illustrated in Figure 3.
4
4
全面认识开关型电源中的BUCK-BOOST功率级
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
ZHCA041–1999年3月–2002年11月修订
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SLVA059A
SLVA059A
the
SLVA059A
SLVA059A
The amount that the inductor current increases can be calculated by using a version of
familiar
relationship:
The
amount
that the inductor current increases can be calculated by using a Buck-Boost
version of 级稳态分析
the
The amount
that the inductor current increases can be calculated by using a version of the
familiar
relationship:
di
familiar
relationship:
电感电流的增加量可以由类似关系式来求得
: v L � �T
v L � L � di L � �I L �
vL
dt
v L � L � di L � �I L � v L � �T
v LL � L � dtLL � �I L � LLL � �T
dt
L
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The inductor current increase during the ON state is given by:
The
inductor
current increase during the ON state
is given by:
在开态
（ON）时间内电感电流的增量由下式可得
:�
V I � �during
V DS �the
IL �
R Lstate
The inductor current increase
ON
is given by:
�I L(�) � V � �V
� T ON
�
�
I
�
R
I
L
DS L L
� � T ON
�I L(�) � V � �V
I
DS L� I L � R L
This quantity,�I
∆ILL(�)
(+), �
is referred to as the inductor
� ripple
T ON current. Also notice that during this
L
period,
all of the
load current
supplied
byripple
the output
capacitor,
C. that during this
This quantity,
∆ILoutput
(+), is referred
to asisthe
inductor
current.
Also notice
This quantity,
∆ILoutput
(+), is referred
to asisthe
inductor
current.
Also notice
period,
all of the
load current
supplied
byripple
the output
capacitor,
C. that during this
Referring
to
2, when
is
OFF,
it
presents
a
high
impedance
from
its drain
to source.
period,
ofFigure
the output
loadQ1
current
is
supplied
by
the
output
capacitor,
C.
量ΔIL(+)all
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
Therefore,tosince
the
flowing
inductor
L cannot
change
instantaneously,
the
Referring
Figure
2, current
when Q1
is OFF,initthe
presents
a high
impedance
from
its drain to source.
Referring
tosince
Figure
2, current
when
Q1
is OFF,
itthe
presents
a high
impedance
from
its
drain across
to source.
current
shifts
fromthe
Q1
to CR1.
Due
to in
the
decreasing
inductor
current,
the
voltage
Therefore,
flowing
inductor
L cannot
change
instantaneously,
the
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，
Therefore,
since
flowing
inductor
L cannot
change
instantaneously,
the
inductor
reverses
polarity
until
rectifier
CR1
becomes
forward
biased
and
turnsacross
ON. The
current
shifts
fromthe
Q1current
to CR1.
Due
to in
thethe
decreasing
inductor
current,
the
voltage
从
转移到
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
变为前向偏置
，
，
Q1
CR1。
CR1
current
shifts
from
Q1
to
CR1.
Due
to
the
decreasing
inductor
current,
the
voltage
across
the
voltage applied
across
L becomes
(VO −CR1
Vd −becomes
IL × RL ) where
thebiased
quantity,
Vd turns
, is theON.
forward
inductor
reverses
polarity
until rectifier
forward
and
The
打开的时候
这时电感
两段的电压变为
是
的前向电压降
电感电
×
式中的
，of CR1.
。
L L becomes
CR1 and
(VO−CR1
–VV
ILL × Rflows
RL)
Vdbiased
inductordrop
reverses
polarity
until rectifier
forward
The
The
inductor
current,
fromthe
the
output
capacitor
and
load
voltage
applied
across
(VO
Inow
where
quantity,
Vd turns
, is theON.
forward
dIdL−–, becomes
L) ，
voltage
applied
across
L becomes
(VO，to
−经过
V
−
I
×
R
)
where
quantity,
V
,
is
the
forward
resistor
combination
through
CR1 and
ground.
Notice
that
the
orientation
of
CR1
and
the
drop
of CR1.
The
inductor
current,
I
,
now
flows
from
the
output
capacitor
and
load
流IL，这时从输出电容和负载电阻的组合
到地
。
CR1
dL L
L
d
voltage
drop
of
CR1.
The
inductor
current,
I
,
now
flows
from
the
output
capacitor
and
load
direction
of
current
flow
in
the
inductor
means
that
the
current
flowing
in
the
output
capacitor
resistor
combination
through
CR1
and
to
ground.
Notice
that
the
orientation
of
CR1
and
the
L
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
VO 为负电压 。 在关态
resistor
combination
through
CR1
and
to
ground.
Notice
that
the
orientation
of
CR1
and
the
and
load
resistor
combination
causes
V
to
be
a
negative
voltage.
During
the
OFF
state,
direction
of，
current
flow in the inductor
means
the current flowing in the output capacitor
O(VO – Vdthat
电感两端的电压为定数
（OFF）时
，且为
– IL × RL) ，为了保证同样极性的转换，这个加载
direction
of
current
flowthe
in the
inductor
the
current
inILthe
output
capacitor
voltage
across
inductor
is constant
and
equal
to
(Vflowing
−V
×the
R
). Maintaining
and
loadapplied
resistor
combination
causes
Vmeans
a negative
voltage.
During
state, the
d−
LOFF
O to bethat
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
），O
。因此，电
and
loadapplied
resistor
combination
causes
VO to
be and
a negative
voltage.
During
the
OFF
state,
our
same
polarity
convention,
this
applied
voltage
isequal
negative
(or
opposite
in
polarity
from the
voltage
across
the inductor
is constant
to
(V
−
V
−
I
×
R
).
Maintaining
O
d L
L
时间内电
感电流在
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
，voltage
。
T
OFF
OFF from
voltage
applied
across
the，ON
inductor
isbecause
constant
andis
equal
to (V
−
V
−
I
×
R
).
Maintaining
applied
voltage
during
the
time),
the
output
V
is
negative.
Hence,
our
same
polarity
convention,
this
applied
voltage
negative
(or
opposite
in
polarity
the
O Od L
L
感电流的减小见图
3.
our
same
polarity
convention,
this
applied
voltage
is
negative
(or
opposite
in
polarity
from
inductor
current
decreases
during
the
OFF
time.
Also,
since
the
applied
voltage
is
essentially
applied voltage during the ON time), because the output voltage VO is negative. Hence, the
applied
voltage
during
the
ON
time),
theAlso,
output
voltage
Vin
is negative.
the
constant,
the inductor
current
decreases
Thissince
decrease
during
inductor
current
decreases
during
thebecause
OFFlinearly.
time.
the applied
voltagecurrent
is Hence,
essentially
O inductor
inductor
current
decreases
during
the
OFF
time.
Also,
since
the
applied
voltage
is
essentially
T
is
illustrated
in
Figure
3.
constant,
the
inductor
current
decreases
linearly.
This
decrease
in
inductor
current
during
OFF
constant,
the inductor
current
T
in Figure
3. decreases linearly. This decrease in inductor current during
OFF is illustrated
The
inductor
current
decrease
在关态
电感电流的减小可以由下式求得
（OFF）
: state is given by:
T
is
illustrated
in
Figure
3. during the OFF
OFF
The inductor current decrease during the OFF state is given by:
The inductor current decrease
during
OFF
� is given by:
� �V O �
V d �the
IL �
R Lstate
�I L(�) � � �V � V � I � R � � T OFF
dL
L
O
L
�I L(�) � � �V O � V d � I L � R � � T OFF
L
dL
L
O
� T OFF
This quantity,�I
∆ILLL(�)
(−),�
is also referred to as the inductor
ripple current.
L
量ΔIL(–) 也代表了电感的纹波电流。
This quantity, ∆IL (−), is also referred to as the inductor ripple current.
duringcurrent.
the ON time and the current
In steady
state∆Iconditions,
currenttoincrease,
∆IL (+), ripple
This
quantity,
referred
as the inductor
L (−), is alsothe
decrease
during
the（ON）
OFF time,
∆IL (−), must
equal.
Otherwise,
inductor
current
would
(+),
during
thethe
ON
time and
current
In
steady state
conditions,
the current
increase,
∆I
在稳态条件下
下的电流增加量
ΔIbe
和关态
下的电流减小量
Δ
，开态
（OFF）
(+)
I Lthe
(–) 必须是相
L
L
(+),
during
the
ON
time
and
the
current
In
steady
state
conditions,
the
current
increase,
∆I
have
a
net
increase
or
decrease
from
cycle
to
cycle
which
would
not
be
a
steady
state
decrease
during
the
OFF
time,
∆I
(−),
must
be
equal.
Otherwise,
the
inductor
current
would
L
等的。否则，在一个周期到下一个周期
L ，电感电流就会有一个净的增加量或者减小量
，这就不是一
decrease
during
the OFF
time,
must
betobe
equal.
Otherwise,
the not
inductor
would
condition.
Therefore,
these
two∆I
equations
can
equated
and
solved
forbeV a current
to
obtain
the
have
a net
increase
or
decrease
from
cycle
cycle
which
would
steady
state
L (−),
个稳态了
。所以
，这两个方程必须相等
，从而求出
VO ，得到连续导通下buck-boostO能量转换的关系
have
a netTherefore,
increase or
decrease
from cycle
which
would
notforbeVOa to
steady
continuous
conduction
mode
buck-boost
voltage
conversion
relationship:
condition.
these
two
equations
cantobecycle
equated
and
solved
obtainstate
the
式:
condition.
equationsvoltage
can beconversion
equated and
solved for VO to obtain the
continuousTherefore,
conductionthese
modetwo
buck-boost
relationship:
Solving
for V
continuous
conduction
mode buck-boost voltage conversion relationship:
O:
求解出VOfor
: VO :
Solving
Solving for VO :
�T
T
T
V O � � �V I � V DS� � T ON � V d � I L � R L � T ON � T OFF
T ON
T OFFOFF
V O � � �V I � V DS� � TOFF
� V d � I L � R L � T ON �
T OFF
T
T OFF
ON
ON
V O � � �V I � V DS� � OFF � V d � I L � R L �
T OFF
T OFF
��
�
ZHCA041–1999年3月–2002年11月修订
OFF
OFF
��
�
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost
Buck-Boost Power
Power Stages
Stages in
in Switch
Switch Mode
Mode Power
Power Supplies
Supplies
Understanding
全面认识开关型电源中的BUCK-BOOST功率级
www.BDTIC.com/TI
5
5
5
5
5
And, substituting TS for TON + TOFF, and using D = TON /TS and (1−D) = TOFF /TS , the
steady-state equation for VO is:
D � V � IL � RL
www.ti.com.cn
d
1�D
1�D
And, substituting TS for TON + TOFF, and using D = TON /TS and (1−D) = TOFF /TS , the
steady-state equation for VO is:
Notice
in simplifying
the
TOFF
is /assumed
to be equal to: TS . This is true
用TON+Tthat
TS ，并利有
D =above,
TON / TS T和
(1 +– D)
= TOFF
TS ，VO 的稳态方程可变为
ON
OFF 来替换
only for continuous conduction mode as we will see in the discontinuous conduction mode
analysis.
I � RL
V O � � �V I � V DS� � D � V d � L
1�D
1�D
An important observation should be made here: Setting the two values of ∆IL equal to each
other is precisely equivalent to balancing the volt-seconds on the inductor. The volt-seconds
Notice that in simplifying the above, TON + TOFF is assumed to be equal to TS . This is true
applied
to the inductor
is the
product
ofTthe
voltage applied and the time，
that
the voltage is
注意在上式的化简中
用到了
在我们以后分析到
，这只是在连续导通模式下成立的
TON
+T
OFF 等于
only
for continuous，
conduction
mode
asSwe
will see in the discontinuous conduction
mode
applied. This is the best way to calculate unknown values such as VO or D in terms of known
非连续导通模式下就可以看到。
analysis.
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
我们还发现
，等同于电感上的电压
，Δ
I L 的两个值相互相等的假定
-秒曲线的平衡
–秒
An
important
observation
should be made
here: Setting the two
values of 。
∆I电感上的电压
as
Ohms
Law.
L equal to each
other
is precisely equivalent to balancing the volt-seconds
on the inductor. The volt-seconds
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
VO 和D等
applied
to
the
inductor
is
the
product
of
the
voltage
applied
and
the
time
that
the
voltage
is
未知值的最好方法
电感上的电压
，这种方法在本文中将经常用到
，
In
the above equations
for ∆IL (+) and ∆IL (−), the。output
voltage-秒关系平衡在物理上是必须的
was implicitly assumed to be
applied.
This is the best way to calculate unknown values such as VO or D in terms of known
而且就像欧姆定律一样容易理解
。
constant
with no AC ripple voltage
during the ON time and the OFF time. This is a common
circuit parameters, and this method will be applied repeatedly in this paper. Volt-second
simplification and involves two separate effects. First, the output capacitor is assumed to be
balance on the inductor is a physical necessity and should be comprehended at least as well
large
enough
itsΔvoltage
change
is negligible. Second, ，
the
voltage
due
the capacitor
在上面关于
ΔI Lthat
在ON
时间和
，输出电压默认为常数定值
(+) 和
I L(–) 的方程中
OFFto时间内没有交流
as
Ohms Law.
ESR
is
also
assumed
to
be
negligible.
These
assumptions
are
valid
because
the
AC ripple
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
voltage is designed to be much less than the DC part of the output voltage.
化可以忽略
其次，由于电容等效串联电阻
造成的电压也可以忽略
；equations
（ESR）
。这些假设是合理的
，
In
the above
for ∆IL (+) and ∆IL (−),
the output
voltage was implicitly
assumed to be
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
。and the OFF time. This is a common
constant with no AC ripple voltage during the ON time
The above voltage conversion relationship for VO illustrates the fact that VO can be adjusted
simplification and involves two separate effects. First, the output capacitor is assumed to be
by adjusting the duty cycle, D. This relationship approaches zero as D approaches zero and
large
that its voltage change
is negligible. Second, Dthe
voltage due 。
to这种关系在
the capacitor
上面Venough
来调节输出电压
，就是可以通过调节电控比
O 的电压转换关系表明一个事实
increases
without bound as D approaches
1. A common simplification
is to assume
VDS , D
Vd接,
ESR
is
also
assumed
to
be
negligible.
These
assumptions
are
valid
because
the
AC
ripple
近于R
足够小，
。一个常用的简化就是假定
0时也接近
0，在
D接近1时逐渐增加而没有限制
VDS ，
Vd 和RLequation
and
are small
enough
to ignore. Setting VDS
, Vd , and RL to zero, the
above
L is
voltage
designed to be much less than the DC
part of the output voltage.
可以忽略
假设
和
等于
上面的式子就可以简单地看作为
：
simplifies。considerably
VDS, Vd Rto:
0，
L
SLVA059A
Buck-Boost级稳态分析
VO � �
��
�
�
�
V I � V DS� �
The above voltage conversion relationship for VO illustrates the fact that VO can be adjusted
D relationship approaches zero as D approaches zero and
by adjusting theVduty
� V I D.
� This
O �cycle,
1�D
increases without bound as D approaches 1. A common simplification is to assume VDS , Vd ,
and
RL are small
enough
Setting
VDS ,operation
Vd , and R
zero, the
above
equation
A simplified,
qualitative
waytotoignore.
visualize
the circuit
isLtotoconsider
the
inductor
as an
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
打开时
simplifies
considerably
，当Q1
energy
storage
element.to:
When Q1 is on, energy is added to the inductor.
When
Q1，is能量加到
off, the
电感器上delivers
电感就把它储存的一部分能量输送到输出电容和负载上
，当Q1关上时
。输出电压就通过
inductor
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
设定Q1的开关时间来控制
例如，D
增大
，输送到电感的能量就增加
，在Q1关时有越多
Q1开的时间
V Odelivered
� � VI �
amount
of
energy
to
the
inductor
is
increased.
More
energy
is
then
delivered
to the
1�D
的能量输出，输出电压就会增加。
output during the off-time of Q1 resulting in an increase in the output voltage.
A simplified, qualitative way to visualize the circuit operation is to consider the inductor as an
不像降压
功率级，
电感电流的平均值并不等于输出电流
（buck）
。想知道电感电流和输出电流的关
energy
storage
element.
When
Q1 is on, energy is added to the
inductor. When Q1 is off, the
Unlike
the
buck
power
stage,
the
average
of
the
inductor
current
is not equal。to
the output
系，可以参考图
注意电感只有在能量级的关
态才向输出传送电流
这样在整个开
2和图
3，of
inductor
delivers
some
its energy to the output（OFF）
capacitor
and load. The output
voltage is
current. To relate the inductor current to the output current, referring to Figures 2 and 3, note
controlled
by setting the on-time of Q1.
For example, by increasing the on-time of Q1, the
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
that the inductor delivers current to ，
the output only during the off state of0.the power stage.
amount of energy delivered to the inductor is increased. More energy is then delivered to the
This current averaged over a complete switching cycle is equal to the output current because
output during the off-time of Q1 resulting in an increase in the output voltage.
the average current in the output capacitor must be equal to zero.
Unlike the buck power stage, the average of the inductor current is not equal to the output
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.
6
current. To relate
the inductor
current
to theMode
output
current,
referring
Understanding
Buck-Boost
Power Stages
in Switch
Power
Supplies
6
6
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
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
www.BDTIC.com/TI
www.ti.com.cn
SLVA059A
Buck-Boost级稳态分析
The relationship between the average inductor current and the output current for the
在buck-boost
功率级的连续导通模式中
电感电流的平均值和输出电流的关系有下式给出
:
continuous
mode
buck-boost power，stage
is given by:
I L(Avg) �
T OFF
� I L(Avg) � (1 � D) � � I O
TS
或者 or
I L(Avg) �
� IO
(1 � D)
Another important observation is that the average inductor current is proportional to the
output current, and since the inductor ripple current, ∆IL , is independent of output load
另外一个重要的现象就是电感电流的平均值跟输出电流是成比例的
，因为电感纹波电流
I L 是跟输
current,
the minimum and the maximum values of the inductor
current track theΔaverage
出负载电流无关的
，电感电流的最大值和最小值精确的跟随电感电流的平均值变化
。例如
inductor
current exactly.
For example, if the average inductor current decreases
by ，
2 当电感
A due
电流的平均值由于负载电流降低而减小
时，电感电流的最大值和最小值也会随着减小
假定一
to
a load current decrease, then the2A
minimum
and maximum values of the inductor
2A（current
decrease
by 2 A (assuming
直保持在连续导通模式下
）。 continuous conduction mode is maintained).
The forgoing analysis was for the buck-boost power stage operation in continuous inductor
现在就停止对
能量级在连续导通模式下电感电流的分析了 在接下来的部分描述在非连
current mode.buck-boost
The next section is a description of steady-state ，
operation in discontinuous
续模式下的稳态工作
主要任务是
能量级在非连续导通模式下电压转换关系的推导
，
。 for
buck-boost
conduction mode. The main result is a derivation of the voltage conversion relationship
the discontinuous conduction mode buck-boost power stage.
2.2 Buck-Boost 稳态非连续导通模式分析
2.2
现在我们研究当导通模式从连续变为非连续
，负载电流降低时会发生什么
，回想连续导通模式
，电
Buck-Boost
Steady-State Discontinuous
Conduction Mode
Analysis
感平均电流跟随输出电流变化，也即是，如果输出电流减小，电感电流平均值也会减小。此外，电
We now investigate what happens when the load current is decreased and the conduction
感电流的最大值和最小值也会准确的随着电感电流平均值变化。
mode changes from continuous to discontinuous. Recall for continuous conduction mode,
the average inductor current tracks the output current, i.e. if the output current decreases,
如果输出负载电流减小到临界电流水平以下
在开关周期的一部分时间内电感电流就会变为
0。从
then
so does the average inductor current.，In
addition, the minimum and maximum peaks
of
图3inductor
的波形图中可以明显看出来这点
the
current follow the average
inductor current exactly.
，因为纹波电流的峰峰值幅度并不随着输出负载电流变化
。在
buck-boost 能量级 ， 如果电感电流试图减低到 0 以下时 ， 它会停在 0（ 因为 CR1 只能有单向电流通
If过the
output load current is reduced below the critical current level, the inductor current will
），并保持为0直到下一个开关周期的开始。这个工作模式就叫做非连续导通模式。一个工作在
be zero for a portion of the switching cycle. This should be evident from the waveforms shown
非连续导通模式下的功率级在一个开关周期内有三个状态，相比下连续导通模式只有两个状态。功
in Figure 3, since the peak to peak amplitude of the ripple current does not change with output
率级在连续模式和非连续模式的分界处电感电流的条件见图
这也是电感电流突然降到
0，而且在
load
current. In a buck-boost power stage, if the inductor4，
current
attempts to fall below
zero,
和IO(Crit)
的绝对值
。注意
，图flow
，因为
0时并马上开始下个开关周期的地方
4中显示的是
IL
it电流降到
just stops
at zero (due to the unidirectional
current
in CR1)IOand
remains
there
untilIO和
the
有相反的极性
beginning
of。the next switching cycle. This operating mode is called discontinuous
conduction mode. A power stage operating in discontinuous conduction mode has three
unique states during each switching cycle as opposed to two states for continuous
conduction mode. The inductor current condition where the power stage is at the boundary
between continuous and discontinuous mode is shown in Figure 4. This is where the inductor
current just falls to zero and the next switching cycle begins immediately after the current
reaches zero. Note that the absolute values of IO and IO(Crit) are shown in Figure 4 because
IO and IL have opposite polarities.
ZHCA041–1999年3月–2002年11月修订
Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级
Power Stages in Switch Mode Power Supplies
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7
7
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Buck-Boost
SLVA059A 级稳态分析
IL Solid
|IO| Dashed = |IO(Crit)|
∆IL(max)
0
TON
TOFF
TS
Figure 4. Boundary Between Continuous and Discontinuous Mode
图4.连续模式和非连续模式的分界线
Further reduction in output load current puts the power stage into discontinuous conduction
mode.
This condition is illustrated in Figure 5. ，
The
mode
power stage
输出负载电流的继续下降把功率级变为非连续导通模式
在图discontinuous
。非连续导通模式的
5中说明这种情况
frequency
response is quite different from the continuous
mode
frequency
response
and is
功率级频率响应跟在连续导通模式下的频率响应非常不一样
这会在
功率级模型部分给
，
buck-boost
given
in
the
Buck-Boost
Power
Stage
Modeling
section.
Also,
the
input
to
output
relationship
出；而且，输入到输出的关系也非常不一样，会在下面的推导中看出来。
is quite different as shown in the following derivation.
IL Solid
|IO| Dashed
∆IL
0
DTs
D3Ts
D2Ts
TS
图5.Discontinuous
非连续电流模式Current Mode
Figure 5.
To
begin the derivation of the discontinuous conduction mode buck-boost power stage
在开始推导 buck-boost 功率级非连续导通模式下电压转换比之前 ， 先回想一下在非连续导通模式
voltage conversion ratio, recall that there are three unique states that the converter assumes
下工作的转换器的三种状态 。 在 Q1 开 ，CR1 关时 ， 是开态 （ON）； 在 Q1 关 ，CR1 开时 ， 是关态
during
discontinuous conduction mode operation. The ON State is when Q1 is ON and CR1
前两种状态跟连续模式下的是一样的
（OFF）；
，是空闲态
（IDLE）。
，图Q1
Q1和State
CR1都关时
2中
is
OFF. The在OFF
is when
Q1 is OFF
and CR1
is ON. The IDLE state is when both
显示的电路也适用
只是first
≠ (1–
开关周期的剩余时间就是空闲
态。case
此外，
输
（IDLE）
TOFF two
D) ×are
TS 。
and
CR1 are OFF.，The
states
identical
to those of the continuous
mode
and
the
circuits of Figure
2 are applicable except that TOFF ≠ (1−D) × TS . The remainder
of the
出电感的直流阻抗
开
、输出二极管的前向电压降和功率型金属氧化物半导体场效应管
（MOSFET）
switching
cycle
is
the
IDLE
state.
In
addition,
the
DC
resistance
of
the
output
inductor,
the
态下的电压降都足够小，可以忽略。
output diode forward voltage drop, and the power MOSFET ON-state voltage drop are all
assumed to be small enough to omit.
开态（ON）的时间TON = D × TS ，D为占空比，由控制电路来设定，表征开关开态内的时间与开关
周期总时间TS的比值。关态（OFF）的时间T = D2 × TS ，空闲态（IDLE）的时间就是开关周期内
The duration of the ON state is TON = D OFF
× TS where D is the duty cycle, set by the control
× TS 。ON
的剩余时间
在图time
，即为Tas
TONratio
– TOFF
D3switch
6中给出这三种时间和响应的波形
S –a
circuit,
expressed
of =the
to the time of one complete。
switching cycle,
Ts . The duration of the OFF state is TOFF = D2 × TS . The IDLE time is the remainder of the
跟前面一样cycle
switching
and is given as T，
− TON − TOFF = D3 × TS . These times are
，没有进行详细的解释
。 shown with the
S 电感电流增加和减少的方程直接在下面给出
waveforms in Figure 6.
Without going through the detailed explanation as before, the equations for the inductor
current increase and decrease are given below.
8
8
全面认识开关型电源中的BUCK-BOOST功率级
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
ZHCA041–1999年3月–2002年11月修订
www.BDTIC.com/TI
www.ti.com.cn
SLVA059A
Buck-Boost级稳态分析
SLVA059A
SLVA059A
SLVA059A
在开态
内电感电流的增加为
（ON）current
:
The
inductor
increase during
the ON state is given by:
The inductor current increase during the ON state is given by:
The
during
The inductor
inductor current
current increase
increase
duringVthe
the ON
ON state
state is
is given
given by:
by:
V
�I L(�) � V I � T ON � V I � D � T S � I PK
LI T � VLI � D � T � I
�I L(�) � V
VLII �
ON � V
S � I PK
(�)
�
D
�
�I
LII �
� L�
�T
T ON
�(+),
�
Dalso
�T
Tthe
I PK
�I LL(�)magnitude,
S
PK inductor current, I
ON
S �peak
L
The ripple current
∆I
is
L
L L
pk because in
Δ
也是峰值电感电流
纹波电流幅度
因为在非连续模式下
每个周期内电流都是从
，
，
I
(+)
I
0开始的。
The
ripple
current
magnitude,
∆I
(+),
is
also
the
peak
inductor
current,
I
because
in
discontinuous mode,
the current starts
L
pk at zero each cycle.
L (+),
The
ripple
current
magnitude,
∆I
is
also
the
peak
inductor
current,
IIpk
because
in
L
pk
The
ripple
current
magnitude,
∆I
(+),
is
also
the
peak
inductor
current,
because
in
L
pk
discontinuous mode, the current starts
at zero each cycle.
discontinuous
mode,
the
current
starts
at
zero
each
cycle.
discontinuous
mode,
the
current
starts
at
zero
each
cycle.
The
inductor
current
decrease during
the OFF state is given by:
在关态
内电感电流的减小为
（OFF）
:
The inductor current decrease during the OFF state is given by:
The
during the OFF state
is given by:
The inductor
inductor current
current decrease
decrease
� V O during the OFF
� V Ostate is given by:
�I L(�) � � V � T OFF � � V � D 2 � T S
L O�T
� �LV O
�D �T
�I L(�) � �
�LV
VO
O � T OFF � �LV O
O � D2 � TS
(�)
�
�I
(�)
�
�
T
�
� D 22 �increase,
T SS
�I
L
OFF
L
L
OFFcase, L
As in the continuous
conduction
mode
the current
∆IL (+), during the ON time
L
L
As
the current
continuous
conduction
mode
current
increase,
∆IL (+),
during the
ON time
andinthe
decrease
during
the case,
OFF the
time,
∆IL (−),
are equal.
Therefore,
these
two
As
in
the
continuous
conduction
mode
case,
the
current
increase,
∆I
(+),
during
the
ON
time
L
As
in
the
continuous
conduction
mode
case,
the
current
increase,
∆I
(+),
during
the
ON
time
and
the
current
decrease
during
the
OFF
time,
∆I
(−),
are
equal.
Therefore,
these
two
L
equations can be equated and solved for VO to obtain
the first of two equations to be used
L (−),
and
the
current
decrease
during
the
OFF
time,
∆I
are
equal.
Therefore,
these
two
跟在连续导通模式下一样
开态
的电流增量
Δ
Δ
是相
和关态
的电流减小
L
and
the
current
decrease
during
the
OFF
time,
∆I
(−),
are
equal.
Therefore,
these
two
，
（ON）
，
（OFF）
I
I
(+)
(–)
L
L
L the first of two equations to be used
equations
equated
and solved
for VO to obtain
to
solve forcan
thebe
voltage
conversion
ratio:
equations
can
be
equated
and
solved
for
V
to
obtain
the
first
of
two
equations
to
be
used
O
equations
can
be
equated
and
solved
for
V
to
obtain
the
first
of
two
equations
to
be
used
等的
从而由这两个方程中第一个来解出电压转换比
。所以这两个方程相等
，解出VO ，ratio:
：
to
solve
for the voltage conversion
O
to
ratio:
to solve
solve for
for the
the voltage
voltage conversion
conversion
T ON ratio:
� � VI � D
VO � � VI � T
ON
T
2
� � V � DD
VO � � VI � T
TOFF
ON
D
ON � � V I � D
D2
�
�
V
�
V
T
�
�
V
�
�
�
V
�
VO
I
I
OFF
I
I
O
D2
T
T OFF
Now we calculate the output current
VO divided by the output load R). It
2
OFF (the outputDvoltage
Now
calculate
theone
output
currentcycle
(the of
output
voltage Vcurrent
by the
load R).
It
is thewe
average
over
switching
the inductor
during
theoutput
time when
CR1
O divided
Now
we
calculate
the
output
current
(the
output
voltage
V
divided
by
the
output
load
R).
It
现在我们来计算输出电流
输出电压
除以负载电阻
它是在
导通时间内
×
整个
（
）。
（D2
）
O
V
R
CR1
T
Now
we
calculate
the
output
current
(the
output
voltage
V
divided
by
the
output
load
R).
It
O
S
is
the
average
over
one
switching
cycle
of
the
inductor
current
during
the
time
when
CR1
O
conducts (D2 × TS).
is
the
average
over
one
switching
cycle
of
the
inductor
current
during
the
time
when
CR1
is
the
average
over
one
switching
cycle
of
the
inductor
current
during
the
time
when
CR1
开关周期上的电感电流的平均值
。
conducts (D2 × TS).
conducts
).
conducts (D2
(D2 ×
×T
TS
S).
VO
� I PK
1
VRO � I O � T1 � �2I PK � D 2 � T S
V
� I � 1S � �
�D �T
VRO
�2II PK
O � I O � T1
PK � D 2 � T S
�
�
I
�
�
� D2 � TS
O
S
2
O
R
T
R relationship
T SS for I 2 (∆I (+)2 ) intoS the above equation to obtain:
Now, substitute the
PK
L
Now, substitute the relationship for IPK (∆IL(+) ) into the above equation to obtain:
把 IPK substitute
，可以得到
(ΔIL(+) ) 的关系代入上式
: (∆I (+)
Now,
the
for
) into the above equation to obtain:
Now,
substitute
the relationship
relationship
for IIPK
PK (∆IL
L(+) ) into the above equation to obtain:
VO
1 � ( � 1) � V I � D � T � D � T
1
2
VRO � I O � T1 � 1
S
S
VLI
V
S� 2
( � 1) � V
�
I
�
�
�
D
�
T
�
D
�
T
VRO
V
1
I
1
2
O
S
S
O � I � T1 � 2
I�D�T
�
� IO
� TS � 1
� ((�
�1
1)) �
� L
� D � T SS �
�D
D 22 �
�T
T SS
2
O
R
L
2
R
L
TS
VO
� V I �SD � D 2 � T S
�
VRO
�LD 2 � T S
� V I � 2D�
V
�
D
�
�
V
�
VRO
�
D
�LD
D 22 �
�T
T SS
�
V
I
I
O�
2�
�
R
2
�
L
We now have two
equations,
the
one
for
the
output current (VO divided by R) just derived and
R
2�L
We
now for
have
equations,
theboth
oneinforterms
the output
divided
R) just
derived
and
the one
thetwo
output
voltage,
of VI , current
D, and (V
D2O. We
nowby
solve
each
equation
We
now
have
two
equations,
the
one
for
the
output
current
(V
divided
by
R)
just
derived
and
O
We
now
have
two
equations,
the
one
for
the
output
current
(V
divided
by
R)
just
derived
and
O
the
one
for
the
output
voltage,
both
in
terms
of
V
,
D,
and
D
.
We
now
solve
each
equation
for
D2 and set the ，
two
equations equal to each
other.
Using
the resulting
an
I , OD,
2 .一个就是用
现在我们有两个方程
一个就是刚得到的输出电流
除以
和D 2equation
来表示的
（V
R），
V I ， each
Dequation,
the
one
for
the
output
voltage,
both
in
terms
of
V
and
D
We
now
solve
I
2
the
one
for
the
output
voltage,
both
in
terms
of
V
,
D,
and
D
.
We
now
solve
each
equation
for D2 and for
setthe
theoutput
two equations
equal
to
each
other.
Using
the
resulting
equation,
an
I
2
expression
voltage,
V
,
can
be
derived.
O
输出电压
。 从每个方程中解出
， 再解这个方程就可以得到输出电压的表达式
D 2 ， 然后令它们相等
for
D
and
set
the
two
equal
to
each
other.
Using
the
resulting
equation,
an
for
D2
setthe
theoutput
two equations
equations
to
each
other.
Using
the
resulting
equation,
an
2 and for
expression
voltage,
Vequal
,
can
be
derived.
O
expression
for
,, can
be
derived.
VO。
expression
for the
the output
output voltage,
voltage, V
VO
can
be
derived.
O
��
�
��
�
ZHCA041–1999年3月–2002年11月修订
��
�
��
�
��
�
��
�
Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级
Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
Understanding
Understanding Buck-Boost
Buck-Boost Power
Power Stages
Stages in
in Switch
Switch Mode
Mode Power
Power Supplies
Supplies
www.BDTIC.com/TI
9
9
9
9
9
www.ti.com.cn
SLVA059A 级稳态分析
Buck-Boost
The
discontinuous
conduction mode buck-boost voltage conversion relationship is given by:
非连续导通模式下
buck-boost功率级电压转换关系为:
VO � � VI � D
�K
Where K is defined as
其中K定义为
K� 2�L
R � TS
The above relationship shows one of the major differences between the two conduction
从上面的关系式可以看出两种导通模式的主要不同
对于非连续导通模式
，电压转换关系是输入电
modes.
For discontinuous conduction mode, the，voltage
conversion relationship
is a function
压、
功率级电感
、开关频率和输出负载的方程
；而对于连续导通模式
，电压转换关系只是
of
the占空比
input、voltage,
duty
cycle, power stage inductance,
the switching frequency,
and the
output
load
resistance.
For
continuous
conduction
mode,
the
voltage
conversion
relationship
取决于输入电压和占空比。
is only dependent on the input voltage and duty cycle.
IQ1
ICR1
IL Solid
IO Dashed
∆IL
VC-P Solid
VO Dashed
0
D3×TS
D × TS
D2×TS
TS
Figure 图
6.6.Discontinuous
Mode
Buck-Boost
Converter Waveforms
非连续导通模式下
转换器波形图。
buck-boost
In
typical applications,
the功率级或者工作在连续导通模式
buck-boost power stage is，operated
in either continuous
在典型的应用中
或者工作在非连续导通模式
，buck-boost
。而对
conduction
mode
or
discontinuous
conduction
mode.
For
a
particular
application,
one
于一些特殊的应用，选定一个导通模式后，功率级就会维持在这种相同的模式工作
下一部分会给
。
conduction
mode is chosen
and the power stage is designed to maintain the same mode. The
出功率级的电感关系
，在已知给定的输入电压、输出电压和输出负载电流的范围内，让它工作在一
next section gives inductance relationships for the power stage that allow it to operate in only
种导通模式。
one conduction
mode, given ranges for input and output voltage and output load current.
10
10
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
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
www.BDTIC.com/TI
2.3
2.3
2.3
SLVA059A
SLVA059A
Critical Inductance
Critical Inductance
Critical
Inductance
The
previous
analyses for the buck-boost converter have been for continuous and
The previous
discontinuous
www.ti.com.cn
analyses for
the buck-boost
converter
haveThe
been
for continuous
and
conduction
modes
of steady-state
operation.
conduction
mode of
a
The previous analyses for the buck-boost converter have been for continuous
and
级稳态分析
Buck-Boost
discontinuous
conduction
modes
of
steady-state
operation.
The
conduction
mode
of
a
converter is a function of input voltage, output voltage, output current, and the value of the
discontinuous conduction modes of steady-state operation. The conduction mode of a
converterAisbuck-boost
a function of
input voltage,
voltage,
output current,
and the
value
the
inductor.
converter
can beoutput
designed
to operate
in continuous
mode
forofload
converter is a function of input voltage, output voltage, output current, and the value of the
inductor. above
A buck-boost
can5%
be to
designed
to operate
in continuous
load
2.3 关键电感
currents
a certainconverter
level, usually
10% of full
load. Usually,
the input mode
voltagefor
range,
inductor. A buck-boost converter can be designed to operate in continuous mode for load
currents
above
a certain
level,current
usuallyare
5%defined
to 10% by
of full
Usually,
the input voltage
range,
the
output
voltage,
and load
theload.
converter
specification.
This。leaves
前面对
转换器的分析主要是在连续导通模式下和非连续导通模式下的稳态工作
转换器
buck-boost
currents
above a certain
level, usually 5% to 10% of full load. Usually, the input voltage
range,
the output
voltage,
and
load
current
are
defined
by
the
converter
specification.
This
leaves
inductor value as the design parameter to maintain continuous conduction mode.
的导通模式是输入电压
输出电流和电感值的函数
转换器设计时
一般都
the
output voltage, and 输出电压
load current
are defined by the converter
specification.
This，leaves
。Buck-boost
the inductor value as 、
the design、
parameter to maintain continuous
conduction mode.
the
inductor
value
as
the
design
parameter
to
maintain
continuous
conduction
mode.
设定工作在连续导通模式下
，负载电流都高于某个一定的水平
，这个水平通常是全负载电流的
5%
The
minimum value of inductor
to maintain continuous conduction
mode can be determined
到10%。
输入电压范围
输出电压和负载电阻通常都是由转换器规格来确定
，这样电感值就成了让
The
minimum
value
of、inductor
to maintain continuous conduction mode
can be determined
by
the
following
procedure.
The minimum value of inductor to maintain continuous conduction mode can be determined
by
the following procedure.
转换器工作在连续导通模式的可设计参数
。让转换器工作在连续导通模式的电感的最小值可以由下
by the following procedure.
First,
define IO(Crit)
面的过程来确定
。 as the minimum output current to maintain continuous conduction mode,
First,
define
I
output current
to maintain
continuous
mode,
normally referred toasasthe
theminimum
critical current.
This value
is shown
in Figureconduction
4. Since we
are
First, define IO(Crit)
as the minimum output current to maintain continuous conduction mode,
O(Crit)
normallytoward
referred
to as the critical
current.
This value
is shown
in Figure 4.toSince
we are
working
a minimum
value for
the inductor,
it is more
straightforward
perform
the
normally
referred to as the critical current. This value is Ishown
in Figure 4. Since，we
are
首先，定义保持转换器工作在连续导通模式下的最小输出电流
通常是一个临界电流
这个值
，
O(Crit)
working
toward
minimum
value
for the
inductor,
it isaverage
more
straightforward
to perform
the
derivation
usingathe
inductor
current.
The
minimum
inductor current
to maintain
working
toward。a因为我们要得到电感的最小值
minimum value for the inductor,
it is more straightforward 。
to perform the
在图4中给出了
，所以用电感电流的推导更加直接
derivation
using
the inductor
current.
The minimum
average inductor current保持连续导通
to maintain
continuous
conduction
mode is
given by:
derivation
using the inductor current. The minimum average inductor current to maintain
模式的电感电流平均值的最小值由下式给出
continuous
conduction mode is given by:：
continuous conduction mode is given by:
�I
I L(min�avg) � �I L � I O(crit)
2L � I
I L(min�avg) � �I
I L(min�avg) � 2 L � I O(crit)
O(crit)
2 above
Second, calculate L such that the
relationship is satisfied. To solve the above equation,
Second,
calculate L∆I
such
above
is Lsatisfied.
To solve
the above
equation,
either
relationship,
(+)that
or ∆Ithe
(−)
may relationship
be used for ∆I
. Note also
that either
relationship
for
L
L
Second,
calculate L such that
the
above relationship
is satisfied.ΔTo
solve
the
above
equation,
第二is，independent
计算满足上述关系的
为了解出上面的方程
关系式中的
Δ
都可以看作是
和either
，
L。
I
I
(+)
(–)
either
relationship,
∆I
(+)
or
∆I
(−)
may
be
used
for
.
Note
also
that
relationship
for
∆I
of
the
output
current
level.
Here,
∆I
(+)
is
used.
The
worst
case
condition
L
L
L
L
L
L
either
relationship, ∆IL (+) or ∆IL (−) may be used for ∆IL . Note also that either relationship for
∆I
independent
of
the
output
current
level.
Here,
∆I
(+)
is
used.
The
worst
case
condition
ΔLI Lis
Δ
的两个关系式都跟输出电流水平无关
这里
采用
Δ
最差情况
给
(giving
the largest L，
)
is
at
maximum
input
voltage
because
this
gives
the
maximum
∆I
，
，
。同时还要注意
。
（
I
I
(+)
L
L
min
L.
∆IL is independent of
the
output current level. Here, ∆IL
The worst
case condition
L (+) is used.
(giving
the
largest
L
)
is
at
maximum
input
voltage
because
this
gives
the
maximum
∆I
.
ΔIL 。
出最大的
）就是在最大输入电压下
，因为这时有最大的
Lminlargest
(giving
the
Lmin
) is at maximum
input voltage because
this gives the maximum ∆IL
.
min
L
Now, substituting and solving for Lmin :
Now, substituting and solving for Lmin :
Now,
substituting
现在代换并解出
： solving for Lmin :
Lminand
T ON(min)
L min � 1 � �V I(max) � V DS � I L � R L� � T ON(min)
1 � �V
O(crit)
� V DS � I L � R L� � TION(min)
L min � 2
2 � �V I(max)
� V DS � I L � R L� � I O(crit)
L min � 1
I(max)
2
I O(crit)
The above equation can be simplified by ignoring minor parasitic
resistances and diode
通过忽略小寄生电阻和二极管电压降
上面的方程可以化简为
： parasitic resistances and diode
The
above
equation
can be simplified
by
ignoring
voltage
drops,
and rearranged
for，
ease
of use
to: minor
The above equation can be simplified by ignoring minor parasitic resistances and diode
voltage drops, and rearranged for ease of use to:
voltage drops, and rearranged for ease of use to:
V I (max)
�V �T
V I (max)
L min � � V O � T S �
V I (max)
S
2�
I O(crit)
�
T
VO
L min � �
�
L min � 2 �OI O(crit)S � V O � V I (max)
2 � I O(crit)
V O � V I (max)
V O � V I (max)
Using
the
inductor
value
just
calculated
will guarantee continuous conduction mode
利用刚计算的电感值，就可以保证转换器工作在连续导通模式下，而且输出负载电流高于临界电流
Using thefor
inductor
value
just calculated
guarantee
continuous
operation
output load
currents
above the will
critical
current level,
IO(crit) .conduction mode
Using
the
inductor value just calculated will guarantee continuous
conduction mode
水平IO(crit)
。for
operation
output load currents above the critical current level, IO(crit) .
operation for output load currents above the critical current level, IO(crit) .
�
��
ZHCA041–1999年3月–2002年11月修订
�
��
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
11
11
11
全面认识开关型电源中的BUCK-BOOST功率级
11
www.BDTIC.com/TI
www.ti.com.cn
功率级小信号模型
Buck-Boost
SLVA059A
3
Buck-Boost Power Stage Small Signal Modeling
功率级小信号模型
3 Buck-Boost
We now switch gears, moving from a detailed circuit oriented analysis approach to more of
功率级的分析从面向细节电路的分析方法转向系统级别的分析研究
，功率
a现在把我们对
system levelbuck-boost
investigation
of the buck-boost power stage. This section presents techniques
to
assist the power supply designer
in
accurately
modeling
the
power
stage
as
a
component
级设计者在模型中把功率级作为
功率源控制环路的一部分
文章这部分主要提供了针对
，
buck-boost
of
the control ，
loop
of a buck-boost power
supply. The three major components
of 、
the
power
这些设计者的
在精确模拟时的辅助技术
脉冲宽度
。功率源控制环路的三个主要部分
（即功率级
supply
control loop (i.e., the power stage, the pulse width modulator, and the error amplifier)
调制器和误差放大器）见图7中表格所示。
are shown in block diagram form in Figure 7.
VI
Power Stage
VO
Duty Cycle
d(t)
Pulse-Width
Modulator
Error
Amplifier
Error Voltage
VE
Reference Voltage
Vref
Figure 7. Power
Supply Control Loop Components
图7.功率源控制环路部件图
Modeling the power stage presents one of the main challenges to the power supply designer.
，在模型设计中常用的技术只有
A对功率源进行建模模型分析是那些功率源设计者面临的最大的挑战
popular technique involves modeling only the switching elements
of the power stage. An
功率级的开关部分
，称为脉冲宽度调制
（PWM）
，其中
equivalent
circuit 。
for这部分相同的电路可以推导出来
these elements is derived and
is called the PWM
Switch开关模型
Model where
PWM
is
the
abbreviation
for
the
pulse
width
modulated.
This
approach
is
presented
here.
是脉冲宽度调制的缩写
现在介绍这种方法
，
。
PWM
As
shown in Figure 7, the power stage has two inputs: the input voltage and the duty cycle.
如图7所示，功率级有两个输入量：输入电压和占空比。占空比是控制输入，也就是说这个输入是用
The duty cycle is the control input, i.e., this input is a logic signal which controls the switching
来控制功率级的开关动作和输出电压的逻辑信号。大多数的功率级具有非线性的电压转换比和占空
action
of the power stage and hence the output voltage. Most power stages have a nonlinear
比的关系conversion
功率级的电压转换比
。为了显示这种非线性
，图duty
8给出了工作在连续导通模式下
voltage
ratio versus
cycle. To illustrate this buck-boost
nonlinearity,
a graph of the
与稳态占空比voltage
和CR1
的开关动作造成的
。非线性特征是由功率级中开关部件
，可
D的函数关系图
steady-state
conversion
ratio for a buck-boost power Q1
stage
operating
in continuous
conduction
mode as
a function of steady-state duty cycle,
D, is shown in Figure 8. 。同样参
以参考文献【5】，
只有功率级中的非线性部分是开关部件
，电路其它部分由线性元件组成
考文献【5】可以发现，对于只有非线性部分的线性模型可以在整个开关周期内通过平均跟非线性部
The nonlinear characteristics are a result of the switching action of the power stage switching
件相关的电压和电流来得到。在分析完整的功率级的时候，就可以用这个模型来代替原始的电路，
components, Q1 and CR1. It was observed in reference [5] that the only nonlinear
这样就得到了开关器件的模型，称为脉冲宽度调制(PWM)开关 模型。
components
in a power stage are the switching devices; the remainder of the circuit consists
of linear elements. It was also shown in reference [5] that a linear model of only the nonlinear
components could be derived by averaging the voltages and currents associated with these
nonlinear components over one switching cycle. The model is then substituted into the
original circuit for analysis of the complete power stage. Thus, a model of the switching
devices is given and is called the PWM switch model.
12
12
全面认识开关型电源中的BUCK-BOOST功率级
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
ZHCA041–1999年3月–2002年11月修订
www.BDTIC.com/TI
www.ti.com.cn
SLVA059A
Buck-Boost功率级小信号模型
10
Buck-Boost Power Stage Gain
9
8
7
6
5
4
3
2
1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.8
0.9
1
Duty Cycle
图8.功率级增益
-占空比图
Figure 8. Buck-Boost
Power
Stage Gain vs Duty Cycle
The basic objective behind modeling power stages is to represent the non-linear behavior of
对功率级进行模型设计的基本目标就是像工作点的线性一样，来表征功率级的非线性行为。我们希
power stages as linear about an operating point. We want linearity so that we can apply the
望是线性的，这样就可以应用很多已经有的用在线性系统的分析工具。再次参考图8，如果我们选
many
analysis tools available for linear systems. Referring again to Figure 8, if we choose
择工作点在
的地方画出一条原始曲线的切线
，这就是工作点的线性性的描
D为
0.7 ，of就可以在
the
operating
point
D = 0.7,D=0.7
a straight
line can be constructed that
is tangent to the original
述，这种技术可以用推导脉冲宽度调制开关模型
定性的，可以看到
，如果占空比的变化量保持很
curve
at the point where D = 0.7. This is an 。
illustration
of linearization
about an operating
point,
a
technique
used
to
derive
the
PWM
switch
model.
Qualitatively,
one can see that if
小，现在分析的功率级的非线性行为就可以用线性模型来精确表征。
the variations in duty cycle are kept small, a linear model accurately represents the nonlinear
behavior
of the power stage being analyzed. 即连续导通模式
由于功率级可以工作在两种不同的导通模式下
和非连续导通模式
，
（CCM）
（DCM），这样脉冲宽度调制开关模型就也有两种导通模型。非连续导通模式脉冲宽度调制开关模
Since a power stage can operate in one of two conduction modes, i.e., continuous conduction
型（DCM PWM）在这里推导。连续导通模式脉冲宽度调制（CCM PWM）开关模式的推导请参考
mode
(CCM) or discontinuous conduction mode (DCM), there is a PWM switch model for the
应用报告
《buck功率级开关模式功率源的综合分析
》 ，TI文献号为
SLVA057。
two conduction
modes. The DCM PWM switch model
is derived
here. The CCM PWM switch
model is derived in the Application Report Understanding Buck Power Stages in Switchmode
Power Supplies,
TI Literature Number SLVA057.
连续导通模式小信号分析
3.1 Buck-Boost
为工作在连续导通模式下的 buck-boost 功率级建立模型 ， 我们采用了应用报告《buck 功率级开关
3.1
SLVA057。）
Buck-Boost Continuous Conduction
Mode Small-Signal Analysis
模式功率源的综合分析》 （TI 文献号为
中推导的连续导通模式脉冲宽度调制 （CCM
开关模型
通过替换开关元件
把脉冲宽度调制开关模型加入到功率级电路中
。
，
。CCM
PWM）
To
model
the
buck-boost
power
stage
operation
in
CCM,
we
use
the
CCM
PWM
switch
model
PWM 开关模型见图9，这个模型在确定功率级的直流工作点和交流传输函数上很有用。
derived in the Application Report Understanding Buck Power Stages in Switchmode Power
Supplies, TI Literature Number SLVA057. The PWM switch model is inserted into the power
功率晶体管
和二极管
都画在点画线盒子里。这些部件将要由脉冲宽度调
再次参考图
stage circuit1，
by replacing Q1，
the switching CR1，
elements. The CCM PWM Switch model is shown in
制开关等效电路来代替
脉冲宽度调制开关模型中用到的终端编号分别为
。
a（a有源极
Figure 9. This model is useful for determining the dc operating point of
power），p（
stage 无源
and
极
和
公共极
）
）。
c（
for finding ac transfer functions of a power stage.
Referring again to Figure 1, the power transistor, Q1, and the catch diode, CR1, are drawn
inside a dashed-line box. These are the components that will be replaced by the PWM switch
equivalent circuit. Terminal labels a (active), p (passive), and c (common) are used for the
PWM switch model.
ZHCA041–1999年3月–2002年11月修订
Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级
Power Stages in Switch Mode Power Supplies
www.BDTIC.com/TI
13
13
SLVA059A
SLVA059A 功率级小信号模型
Buck-Boost
Vap
D
a
ia
∧
d
www.ti.com.cn
c
− +
Vap ∧
d
D
− ∧+
Ic d
a
ia
D
1
D
1
∧
Ic d
c
ic
ic
p
Figure 9. DC and Small Signalp CCM PWM Switch Model
The a terminal is the terminal connected to the active switch. The p terminal is the terminal
of the passive
switch.
terminal
is the
terminal
is common
to both the active and
9.The
DCc and
Small
Signal
CCMthat
PWM
Switch Model
图Figure
直流和小信号的连续导通模式脉冲宽度调制开关模型
9.
passive switches. The three commonly used power stage topologies all contain active and
The
a terminal
is the
terminal
connected
the activecan
switch.
The p
the terminal
passive
switches,
and
the above
terminaltodefinitions
be used.
Interminal
addition,issubstituting
the
终端
是有源开关和无源开关共有的端
，pc是无源开关的端
，c
。三种通常使用的
a是连接有源开关的端
of
the
passive
switch.
The
terminal
is
the
terminal
that
is
common
to
both
the
anda
PWM switch model (that we will derive) into other power stage topologies also active
produces
passive
switches.
Theparticular
three commonly
used
power
topologies
contain
activepower
and
功率级拓扑布局都包含了有源开关和无源开关
此外
，使用了上面相同的终端定义
。
，in把脉冲宽度调
valid model
for that
power stage.
To usestage
the PWM
switchall
model
other
passive
and the
above
terminal
used.
In addition,
the
制开关模型
替代进其它的功率级拓扑也可以得到其它特殊功率级的正确模型
为
（我们将要推导
）
。
stages,switches,
just
substitute
the
model
showndefinitions
in Figure 9can
intobethe
power
stage insubstituting
the appropriate
PWM
switch
model
(that
we
will
derive)
into
other
power
stage
topologies
also
produces
a
了在其它的功率级中使用脉冲宽度调制开关模型
orientation.
，只需要把图9中显示的模型替换为特定应用的功率
valid model for that particular power stage. To use the PWM switch model in other power
级。
stages,
just substitute
the model
shown
in Figure
9 intooccurrences
the power stage
the appropriate
In the PWM
switch model
of Figure
9 and
subsequent
of theinmodel,
the capital
orientation.
letters indicate steady-state (or dc) quantities dependent on the operating point of the circuit
在图9中的PWM开关模型和替代模型中，大写字母显示的稳态（或直流）参量取决于需要研究的电
under study. The lowercase letters indicate time varying quantities and can indicate a quantity
In
the aPWM
model
9，and
subsequent
occurrences
theamodel,
the
capital
路的工作点
小写字母显示了时间变量
也显示了跟直流部分和交流部分有关的参量
头上有线的
；switch
with
dc component
andofanFigure
ac component.
The lowercase
letters of
with
caret；
(hat)
indicate
letters
indicate
steady-state
(orparticular
dc) quantities
on the D
operating
point
the circuit
小写字母显示了特定可变的小的交流变量
；例如
，dependent
， 代表了占空比的小的交
D 代表了稳态的占空比
the small
ac variations
of that
variable.
For example,
represents
theofsteady-state
under
study.
The
lowercase
letters
indicate
time
varying
quantities
and
can
indicate
a quantity
流变量，d 或者^d(t) 就代表了包括任何直流部分和交流部分的全部的占空比。
dutya cycle,
d represents
small
ac variations
of lowercase
the duty cycle,
and
da
orcaret
d(t) represents
the
with
dc component
and an
ac component.
The
letters
with
(hat) indicate
complete
duty
cycle
including
any
dc
component
and
ac
variations.
the small ac variations of that particular variable. For example, D represents the steady-state
^
duty cycle, d represents small ac avariations of the duty cycle, and d or d(t) represents the
complete duty cycle including any dc component and ac variations.
ia
ia
+
VI
VI
a
Vap ∧
d
D
Vap ∧
d
D
∧
Ic d
−
+
1 ∧
Ic d
−
+
c 1
+
c
RL
L
VO
D
DIL = ic
L
p
IL = ic
p
C
RC
C
R VO
R
RC
RL Small Signal AC Power Stage Model
Figure 10. CCM Buck-Boost
图10.连续导通模式下buck-boost小信号交流功率级的模型
Figure 10. CCM Buck-Boost Small Signal AC Power Stage Model
14
14
14
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
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
www.BDTIC.com/TI
SLVA059A
SLVA059A
An example dc analysis is given to illustrate how simple power stage analysis becomes with
www.ti.com.cn
^
is an open.功率级小信号模型
Then by
the PWM switch model. For dc analysis, d is zero, L is a short and C Buck-Boost
An example dc analysis is given to illustrate how simple power stage analysis becomes with
a simple loop equation we get:
^
下面给出一个直流分析的例子来说明运用
开关模型以后分析功率级变得多么简单
。对于直流
PWM
zero, L is a short and C is an open.
Then by
the
PWM switch model. For dc analysis,
d is
a分析
simple
loop
we
get:
V 是断路的
是短路的，C
， 为
。这时我们就可以得到一个简单的回路方程：
0，Lequation
� V I � ac � V O �
0
D
V ac
� V I �relationships
� VO � 0
By using the following
D
利用下面的关系式
IO
By
using the following�
relationships
IL �
1�D
� IO
IL �
1V� D
IO � O
R
VO
I O �loop to solve for V , we get:
and writing another
CP
R
and
another loop to solve for VCP, we
R L get:
写出writing
VCP的另一个回路，我们得到:
V cp � � V O � 1 �
R � (1 � D)
RL
V cp � � V O � 1 �
(
R �them
1 � to
D)get the steady-state voltage conversion
Using the two loop equations, we solve
relationship for the buck-boost power stage operating in CCM and taking the inductor dc
利用这两个回路方程
我们解得了工作在连续导通模式下
功率级的稳态电压转换关系
，
Using
the two
equations,
we solve them to getbuck-boost
the steady-state
voltage conversion
resistance,
RL,loop
into ，
account:
relationship
for the buck-boost power stage operating
in
CCM
and
taking
the
inductor
dc
这个过程中我们考虑了电感的直流电阻和负载电阻
RL:
resistance, RL, into account:
D
1
�
VO � � VI �
1�D
RL
1�
D
1
2
�
VO � � VI �
R�(R
1�D)
1�D
L
1�
The above equation is usually expressed asR�
a ratio
of) 2the output voltage, VO , to the input
(1�D
voltage, VI , and is usually called M as shown below:
The
above equation is usually expressed as a ratio of the output voltage, V , to the input
上面的方程通常用来描述输出电压VO 对输入电压VI 的比值，就像下面说的通常称为MO:
V
voltage, VI , and is usually
called M as shown below:
1
M� O�� D �
1�D
VI
R
VO
1� 1 L
D
2
M�
��
�
R��R
1�D�
1�D
VI
L
1�
2
�1�D
� steady-state I/O transfer function
Which, when RL = 0, as assumed earlier, is R�
equal
to the
previously calculated. With the PWM switch parameters Vap and Ic determined from the dc
Which,
RLanalysis
= 0, as can
assumed
earlier,
isFor
equal
to the steady-state
I/Otransfer
transfer
function
当RL为0when
时an
得到的
传递函数
有了由直流分析
analysis,
ac
performed.
ac analysis,
theI/O
following
functions
（就像前面假定的
）be
，就等于之前计算的稳态下的
。
previously
calculated.
PWM switch parameters
Vap and
Ic determined
from output
the dc
can
bePWM
calculated:
open-loop
line-to-output,
open-loop
input
impedance,
open-loop
决定的
开关参数
和I c ，the
就可以进行交流分析
。对于交流分析
，可以计算得到下面几个传递函
VapWith
analysis,
an
ac
analysis
can
be
performed.
For
ac
analysis,
the
following
transfer
functions
impedance,
and
open-loop
control-to-output.
The
control-to-output,
or
duty-cycle-to-output,
数：开环的线-输出、开环的输入阻抗、开环的输出阻抗和开环的控制-输出。控制-输出，或者占空
can
betransfer
calculated:
open-loop
line-to-output,
open-loop
impedance,
output
is比the
function
most used
for control loop
analysis.input
To determine
thisopen-loop
transfer function,
为了确定这个传递函数，首先利用直流分析得到
。
-输出是在控制环路分析中用到最多的传递函数
impedance,
and
open-loop
control-to-output.
The
control-to-output,
or
duty-cycle-to-output,
first use the results from the dc analysis for operating point information. This information
这些信息决定了相关源的参数值
，
；例如
，sources;
is工作点的信息
the transfer
function
mostvalues
used for
loop
analysis.
To determine
this transfer function,
determines
the
parameter
of control
the dependent
for example,
first use the results from the dc analysis for operating point information. This information
determines the V
parameter
values
sources; for example,
(1–M)
V �ofVthe
�dependent
ap � V �
�
�
I
and 和
and
O
�
�
I
( –V )
V ap � V I � V–I
–M � V I
OO� V I � 1–M
O
�
�
Ic � IL �
1�D
R � (1 � D)
R � (1 � D)
–I O
–V O
–M � V I
�
�
Ic � IL �
1�D
R � (1 � D)
R � (1 � D)
ZHCA041–1999年3月–2002年11月修订
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
15
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
15
全面认识开关型电源中的BUCK-BOOST功率级
15
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The above two equations are then used with loop equations to derive the duty-cycle-to-output
voltage transfer function. Then set the input voltage equal to zero because we only want the
ac component
of the transfer function. Without going through all the details, it can bewww.ti.com.cn
shown
SLVA059A
功率级小信号模型
Buck-Boost
that the transfer function can be put in the following form:
The above two equations are then used with loop equations to derive the duty-cycle-to-output
利用上面的两个方程和环路方程 可以导出占空比-输出电压的传递函数，然后设定输入电压为0，
voltage transfer function. Then，
set the input voltage equal to zero because we only want the
因为我们只希望得到传递函数的交流部分
。在不需要细节的情况下
，传递函数可以表示为下面的形
ac component of the transfer function.sWithout
goingsthrough all
the details, it can be shown
1
�
�
1
�
^
� z2
式：the transfer
v O function can be put�inz1the following
that
form:
(s) � G do �
^
2
d
1� s � s
� o�Q � 2
o
Where:
1 � �s � 1 � �s
^
V
vO
z1
z2
G do(s)�� G I �
2
^
do
2
(1 � D )
d
1� s � s
� o�Q � 2
o
1
这里Where:
:
s z1 �
V
R �C
G do � C I
22
((11 �
�D
D)) � R
s z2 �
1D � L
s z1 �
R �C
� o � 1C� D
�L � C 2
(1 � D ) � R
s z2 �
D�
(1 � D)
�LR
Q�
L
�o � 1 � D
�L �C
C
�
� �
�
�
� �
�
�
Q�
3.2
(1 � D) � R
�L
Buck-Boost Discontinuous
Conduction Mode Small-Signal Analysis
C
We now continue our discussion of modeling the power stage when it is operating in
discontinuous conduction mode (DCM). This mode is quite different from continuous
conduction
mode
just covered. We
begin with the
derivation
of the PWM
switch model for
非连续导通模式小信号分析
3.2
3.2 Buck-Boost
Buck-Boost
Discontinuous
Conduction
Mode
Small-Signal
Analysis
DCM for the buck-boost power stage. This derivation can also be found in [4]. The waveforms
现在我们继续讨论工作在非连续导通模式下（DCM）功率级的模型，这个模型非常不同于刚才讲到
that
voltage across
Q1, vacthe
, thepower
voltage
across
CR1,it vis
, the current
We are
nowaveraged
continue are
ourthe
discussion
of modeling
stage
when
in
cp operating
的连续导通模式下的模型
从
功率级的
下的脉冲宽度调制开关模型的推导开始
。
，这
buck-boost
DCM
in
Q1, ia and the
current in CR1,
. The waveforms
areisshown
Figure 6.from continuous
discontinuous
conduction
modeip(DCM).
This mode
quite indifferent
个也可以在【4】
两端的电压
两端的电压
。平均后的波形是
Q1with
CR1上的电流
vac ，CR1of
i a 和switch
p。
conduction
mode中找到
just covered.
We begin
the derivation
the PWM
model i for
波形如图
所示
。
DCM
for 6the
buck-boost
power
stage. This that
derivation
can also
be foundThe
in [4].
The waveforms
We
first
state
some basic
relationships
are used
repeatedly.
terminal
currents
that are averaged
the voltage
Q1, by:
vac , the voltage across CR1, vcp , the current
averaged
over oneare
switching
cycleacross
are given
in
Q1, ia and the current in CR1, ip . ，
The
waveforms are shown in Figure 6. ：
我们首先给出了这个重复用到的关系式
整个开关周期内的终端平均电流由下式给出
i pk
We first state some
that are used repeatedly. The terminal currents
�i a� �basic
�relationships
d
2
averaged over one switching cycle are given by:
i
�ip� � i pk � d2
2
�i a� � pk � d
2
括号里的变量
代表了在整个开关周期内取均值的量
（像<i
。
where
variables
ina>）
brackets
(e.g., 〈ia〉) represent quantities
that are averaged over one
i pk
switching cycle.
�ip� � � d2
2
16
Understanding
Buck-Boost
Power Stages
Mode Power
Supplies
where variables
in brackets
(e.g.,in〈iSwitch
〉) represent
quantities
switching cycle.
16
16
a
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
全面认识开关型电源中的BUCK-BOOST功率级
that are averaged over one
ZHCA041–1999年3月–2002年11月修订
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SLVA059A
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Buck-Boost功率级小信号模型
SLVA059A
Since the average over one switching cycle of the voltage across the inductor is zero, the
following
relationships
hold:
Since
theaverage
averagevoltage
over
one
switching cycle
the voltage across the
因为在整个开关周期内
下面的电压均值关系成立
，电感上的电压均值为
： inductor is zero, the
0，of
following average voltage relationships hold:
�v ac
ac� � V II � �i cc � R LL�
�v ac� � V I � �i c � R L�
�v cp� � � V O � �i c � R L�
L
O
�v cp� � � V O � �i c � R L�
Since the value of icc RL
L is small compared to VII and VO
O , ignore these values for modeling the
由于
的值相比于
和
很小
所以在做模型时就忽略了这些值以便方程更容易处理
，
。在时d ×the
i
R
V
V
power
stage
to
make
the
formulae
much
easier
to
manipulate.
Duringvalues
the time
period
Tss
L
I
O small compared to V and V , ignore these
Sincec the
value of ic R
for modeling
L is
I
O
the
current
i
starts
at
a
value
of
zero
and
ends
at
the
value
of
i
.
And
since
the
voltage
across
间d × stage
电流
，停止于
，且有
Ts 内，
ia 从0值开始
ipk ，因为在这段时间内电感上的电压是常数
VI =d × Ts
power
make
the formulae
much
easier to manipulate.
period
a to
pk During the time
the
inductor
during
this
time
is
constant
and
equal
to
V
=
〈v
〉,
the
following
holds:
current
i
starts
at
a
value
of
zero
and
ends
at
the
value
of
i
.
And
since
the
voltage
across
I
ac
〈vac〉，所以有下式成立
：
I
ac
a
pk
the inductor during this time is constant and equal to VI = 〈vac〉, the following holds:
i pk
i pk
�i a
pk
pk
�
VI � L a � L � i
� �v ac
�
L
�
ac
i pk
I
�i
pkT ss
�ta
d �
d
�
T ss
VI � L
�L�
� �v ac� � L �
�t
d � Ts
d � Ts
Similarly, during the time period d2 Tss , the current ip
p starts at a value of ipk
pk and ends at zero.
Also
since
the
voltage
across
the
inductor
is
equal
to
−V
=
〈v
〉,
the
following
holds:
类似的，在时间
电流iad2
从ipk
同样因为在这段时间内电感上的电压是
×time
Similarly,
duringd2the
period
Ts值开始
, the current
ip0，
starts
of ipk and ends
at zero.–
，停止于
Ts 内，
Oat a value
cp
O
cp
Also
since
the
voltage
across
the
inductor
is
equal
to
−V
=
〈v
〉,
the
following
holds:
所以有下式成立
：
VO = 〈vcp〉，
O
cp
� i pk
i pk
�i pp
pk
pk
�L� �i
� �v cp
VO � L
cp� � L �
i pk T s
�i
�tp
d2 �pkT ss
d2
�
s
�L�
� �v cp� � L �
VO � L
�t
d2 � T s
d2 � T s
With the above four equations, we begin with the derivation of the input side (vac
ac side) of the
PWM
switch
model.
With the above four equations, we begin with the derivation of the input side (vac side) of the
有了上面的四个方程
PWM
switch model.，我们从脉冲宽度调制开关模型的输入边（vac 边）开始推导。解方程（3）得
VI =就可以得到
〈vac〉, then
We
solve
ipk and use
到ipk ，利用equation
然后代入方程
〉，for
（1）
： substitute into equation (1) to get:
VI = 〈vac(3)
We solve equation (3) for ipk and use VI = 〈vac〉, then substitute into equation (1) to get:
d 2 � T SS
�i aa� � V I � 2
d �T
�i a� � V I � 2 � LS
2�L
ZHCA041–1999年3月–2002年11月修订
Understanding
Understanding Buck-Boost
Buck-Boost Power
Power Stages
Stages in
in Switch
Switch Mode
Mode Power
Power Supplies
Supplies
全面认识开关型电源中的BUCK-BOOST功率级
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
www.BDTIC.com/TI
17
17
17
17
SLVA059A
SLVA059A
SLVA059A
SLVA059A
www.ti.com.cn
We
note
We功率级小信号模型
note that
that the
the average
average current
current flowing
flowing into
into terminal
terminal a
a is
is proportional
proportional to
to the
the input
input voltage,
voltage,
Buck-Boost
V
.
We
define
an
effective
resistance
as
follows:
We
note
that
the
average
current
flowing
into
terminal
a
is
proportional
to
the
input
voltage,
I
VII . We define an effective resistance as follows:
VI . We define an effective resistance as follows:
我们注意到流进终端a的电流均值与输入电压VI 成正比，有效阻抗定义如下：
V
2�
V II
�L
L
R
R eee �
� �V I� �
� d222 �
i
2�T
I�
2
LSS
T
d
�
a
i
Re � a
�
�i aa� d 2 � T SS
Once
Once the
the input
input looks
looks like
like an
an equivalent
equivalent resistance,
resistance, we
we can
can also
also talk
talk about
about an
an apparent
apparent input
input
2
2
power
of
V
/R
which
will
be
used
next.
Once the
input
likewill
anbe
equivalent
resistance, we can also talk about
an apparent input
III2 /Rlooks
e
power
of
V
which
used
next.
2
e
e ，我们就可以得到将要在下一步用到的表征输入功率VI /Re。
当输入像等效阻抗时
power of VI2 /Re which
will be used next.
side), we start with equation (4), solve equation
To
begin
the
derivation
of
To begin the derivation of the
the output
output side
side (v
(vcp
cp
cp side), we start with equation (4), solve equation
边
的推导
我们从方程
开始
解得i pk ，(4),
为了开始输出边
再代回方程
(3)
for
i
and
substitute
back
into
equation
(4),
we
get:
）
，
（4）
，从方程
（3）
（
（4），
v
side),
start with
equation
solve equation
To
begin
the
derivation
of
the
output
side
(v
cp
cp (4),
(3) for ipk
back into equation
wewe
get:
pk
pk and substitute
(3)
for ipk and
就可以得到
： substitute back into equation (4), we get:
��v ac�� � d
v ac � d .
�
�vvcp
�
�v ac
�
�
.
cp
cp
�vcp� � acdd222� d .
d2
and
substitute
into
equation
(2) and
also
iipk
[from
We
next
solve
the
above
equation
for d
substitute
into （3）
equation
and
also use
use（2），
We
next
solve
the
above
equation
d2
2
pk
再解上面的方程得到d 2 ，代入到方程for
再利用
得到(2)
代回到方程
经
（2），
），
i pk （由方程
2 and
pk [from
equation
(3)]
and
substitute
into
equation
we
get
after
rearranging:
substitute
into equation
(2) and also use ipk [from
We
next solve
the above
equation
for d2 and(2),
equation
(3)]
and
substitute
into
equation
(2),
we
get
after
rearranging:
过整理我们得到：
equation (3)] and substitute into equation (2), we get after rearranging:
2
��v ac�� 22 � d 222 � T s
v ac
��iipp�� �
ac 2 � d � T ss
p � �v�ac� �� d 2 � T s
��2�L
�ip� � �vvcp
cp � 2 � L
�vcp
cp� � 2 � L
Finally,
〉 = V
Finally, we
we use
use 〈v
〈vac
VIII and
and substitute
substitute in
in the
the above
above equation
equation to
to get
get the
the output
output side
side
ac
ac〉 =代入上面的方程
得到输出边的关系
最后
我们用
，
：
，
〈v
〉
V
=
relationship:
Finally,
we use ac〈vac〉 =I VI and substitute in the above equation to get the output side
relationship:
relationship:
2
2
V
2
2
d
T
V II2
2�
s
2
d
�
T
s
2
��iipp�� �
��vcp�� �
s � V I2 .
V2 � 2
�
.
�
T
p � v cp
cp � V III2 � d 2
�
L
�ip� � �vcp� � V � 2 � L s � RRIeee .
2�L
Re
I
This
equation
shows
that
the
average
output
current
the average output voltage is
This
equation shows that the average output current times
times
这个方程显示输出电流均值乘以输出电压均值等于表征输入功率
。 the average output voltage is
equal
to
the
apparent
input
power.
This equation
shows that
average output current times the average output voltage is
equal
to the apparent
inputthe
power.
equal to the apparent input power.
现在我们可以把上面的输入和输出关系应用到等效的电路模型
Now
we
into
。这个模型在确定功率源的直流工作
Now
we can
can implement
implement the
the above
above input
input and
and output
output relationships
relationships
into an
an equivalent
equivalent circuit
circuit
model.
This
model
is
useful
for
determining
the
dc
operating
point
of
a
power
supply.
The
input
Now
we
can
implement
the
above
input
and
output
relationships
into
an
点很有用
输入端口可以简化模型为电阻
输出端口简化为一个从属的功率源
这个功率源输送
。 model is useful for determining
，
Re ，the dc operating point of a powerequivalent
model. This
supply.
Thecircuit
input
port
is
simply
modeled
with
a
resistor,
R
.
The
output
port
is
modeled
as
a
dependent
power
model.
This model
is
determining
the dc
operating
point
of a power
supply. Thepower
input
消耗的功率
所示
的功率等于输入电阻
。这个等效电路的构成见图
。
port
is simply
modeled
with for
a resistor,
Re
.
The
output
port
is
modeled
as
a
dependent
11
Reuseful
e
e
source.
This
source
power
equal
to
dissipated
by
the
resistor,
R
.
port is simply
modeled
with delivers
a resistor,
Re. The
output
port
is modeled
dependent
power
source.
This power
power
source
delivers
power
equal
to that
that
dissipated
byas
thea input
input
resistor,
Re
e
e.
The
equivalent
circuit
can
be
constructed
as
shown
in
Figure
11.
source.
This
power
source
delivers
power
equal
to
that
dissipated
by
the
input
resistor,
R
e.
The equivalent circuit can be constructed as shown in Figure 11.
The equivalent circuit can be constructed as shown in Figure 11.
a
a
a
a
p
p
p
p
p(t)
p(t)
p(t)
p(t)
R
R
e
Re
e
Re
c
c
c
c
图11.非连续导通模式脉冲宽度调制开关模型
Figure
Figure 11.
11. DCM
DCM PWM
PWM Switch
Switch Model
Model
Figure 11. DCM PWM Switch Model
18
18
18
18
18
Understanding
Understanding
Buck-Boost
Power
Stages
in
Switch
Mode
Power
Supplies
Understanding Buck-Boost
Buck-Boost Power
Power Stages
Stages in
in Switch
Switch Mode
Mode Power
Power Supplies
Supplies
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
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
www.BDTIC.com/TI
SLVA059A
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SLVA059A
Buck-Boost功率级小信号模型
To illustrate discontinuous conduction mode power supply steady-state analysis using this
To illustrate discontinuous conduction mode power supply steady-state analysis using this
为了用这个模型来描述非连续导通模式下功率级的稳态分析
这
model,
we examine the buck-boost converter. The analysis
proceeds likebuck-boost
the CCM转换器
case. The
，我们研究这种
model, we examine the buck-boost converter. The analysis
proceeds like the CCM case. 。
The
equivalent
circuit
is
substituted
into
the
original
circuit.
The
inductor
is
treated
as
a
short
个分析过程跟之前的连续导通模式
是一样的circuit.
电感看作是短路
，等效电路带进原始电路
，
equivalent
circuit is substituted （CCM）
into the original
The inductor is ，
treated
as a short
circuit
and the capacitor
is
treated
as
an
open
circuit.
The
DCM
buck-boost
converter
model
电容看作是断路
非连续导通模式下的
转换器的原理图如图
所示
。
。 converter model
12
circuit and the capacitor
is treated asbuck-boost
an open circuit. The DCM buck-boost
schematic is shown in the Figure 12.
schematic is shown in the Figure 12.
p
p
a
a
p(t)
p(t)
Re
Re
+
+
VI
VI
VO
VO
C
C
R
R
c
c
L
L
图12.Figure
非连续导通模式下的
转换器原理图
12. DCM Buck-Boost
Converter
Model
buck-boost
Figure 12. DCM Buck-Boost
Converter Model
The apparent power dissipated in Re is determined as:
The
apparent power dissipated in Re is determined as:
R 上消耗的表征功率由下式决定：
e
V2
V2
P Re � II .
P Re � R e .
Re
The
dependent power source delivers the above amount
of power to the output load resistor,
这个从属功率源传送上面数量的功率到输出负载电阻
R，我们可以通过令下面两个功率相等来计算
The
dependent power source delivers the above amount
of power to the output load resistor,
R.
We can calculate
gain as a function of D by equating the two powers as shown:
电压增益关于
： voltage
D的函数the
R.
We can calculate
the
voltage gain as a function of D by equating the two powers as shown:
V2
V2
V2
O
I � V2
O
I
Re � R
Re
R
VO
V O ��
V I ��
VI
�
�RRRR
(choose the negative root)
e (choose the negative root)
e
R�T
R
� D R � T ss
R
�
�RRRR �� �D2�L
2�L
�T
e
e
�D
D2
�T
D 2�T ss
�
� 22 �� LL
转换器的电压转换关系由下式给出
： buck-boost is given by:
DCMvoltage
buck-boost
The
conversion
relationship for the DCM
The voltage conversion relationship for the DCM buck-boost is given by:
VO
VO � � D
VI � � D
VI
�
�RR22����TTLL
s
s
回想前面的:
Recall from earlier that:
Recall from earlier that:
�L
K� 2
�L
K � R2�
T
R � T ss
and
making the substitution
in the above equation, the稳态非连续导通模式分析部分中利用平衡
result is identical to that obtained by
将这个式子代入上面的方程
，得到的结果跟在
and
making the substitution
in the above equation,
the result is identical to that obtained by
buck-boost
balancing the inductor volt-seconds in the buck-boost steady-state discontinuous conduction
balancing
inductor volt-seconds
电感电压
秒关系得到的结果一样
。 in the buck-boost steady-state discontinuous conduction
–the
mode
analysis
section.
mode analysis section.
ZHCA041–1999年3月–2002年11月修订
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SLVA059A
SLVA059A 功率级小信号模型
Buck-Boost
SLVA059A
The
The steady
steady state
state voltage
voltage conversion
conversion relationship
relationship for
for the
the DCM
DCM buck-boost
buck-boost becomes:
becomes:
The
steady state voltage conversion
relationship for the DCM buck-boost becomes:
非连续导通模式下
buck-boost的稳态电压转换关系变为：
V
VO
O�� D
� � �D
VV
�K
K
VOII
�� D
�
VI
K
Now,
Now, to
to derive
derive the
the small
small signal
signal model,
model, the
the circuit
circuit of
of Figure
Figure 12
12 is
is perturbed
perturbed and
and linearized
linearized
following
the
procedure
similar
to
the
one
in
the
CCM
derivation.
To
see
the
detail
of
following
the
procedure
similar
to
the
one
in
the
CCM
derivation.
To
see
the
detail
of the
the
Now,
to derive the small，signal
model, the （CCM）
circuit of 中的推导过程一样
Figure 12 is perturbed
and
linearized
现在为了推导小信号模型
跟在连续导通模式
中的电路
， 扰动图
，
12
derivation,
the
reader
is
directed
to
reference
[4]
for
details.
The
resulting
small
signal
model
derivation,
the
reader
is
directed
to
reference
[4]
for
details.
The
resulting
small
signal
model
following
the
procedure
similar
to
the
one
in
the
CCM
derivation.
To
see
the
detail
of
the
并线性化
中的细节
，想了解推导的详细过程
，读者可以参考
【4】
。这个工作在非连续导通模式下
for
the
power
stage
in
is
shown
in
Figure
13.
for
the buck-boost
buck-boost
power
stage operating
operating
in DCM
DCM
isdetails.
shownThe
in the
the
Figuresmall
13. signal model
derivation,
the
reader
is
directed
to
reference
[4]
for
resulting
buck-boost功率级的小信号模型如图13所示。
for the buck-boost power stage operating in DCM is shown in the Figure 13.
∧
∧
v
vII
∧
vI
+
+
+
R
Re
e
2
2 ⋅⋅ V
VII
Re
D ⋅⋅ R
D
2 ⋅ Ve
I
D ⋅ Re
∧
∧
∧
0
vO
0 ⋅⋅ v
O
∧
0 ⋅ vO
⋅⋅ ∧dd
∧
⋅d
2
2
⋅⋅ ∧∧vvII
M
Re
M ⋅⋅2 R
e ∧
⋅ vI
M⋅R
e
2
2 ⋅⋅ V
VII
⋅⋅ M
M ⋅⋅R
R
D
D2
⋅ VI ee
D ⋅ M ⋅R e
∧
⋅⋅ ∧dd
∧
⋅d
2
M
M2 ⋅⋅ R
Re
e
M2 ⋅ Re
Re
∧
∧
v
vO
O
∧
vO
C
C
R
R
C
R
Figure
13.
DCM
Power
Figure
13. Small
Small Signal
Signal buck-boost
DCM Buck-Boost
Buck-Boost
Power Stage
Stage Model
Model
图13. 非连续导通模式下
功率级的小信号模型
Figure 13. Small Signal DCM
Buck-Boost
Power Stage power
Model
The
The duty-cycle-to-output
duty-cycle-to-output transfer
transfer function
function for
for the
the buck-boost
buck-boost power stage
stage
工作在非连续导通模式下
功率级的占空比-输出传递函数由下式给出：
buck-boost
operating
in
DCM
is
given
by
operating
in
DCM
is
given
by
The duty-cycle-to-output transfer function for the buck-boost power stage
operating
in DCM is given by
vv^^ O
1
O�G �
1
^^ � G do �
ss
do
v^d
1
�
1
�
1�
dO � G �
�p
p
^
do
1 � �s
其中 Where d
p
Where
V
V
Where G
O
� O
G do
do � VD
DO
G do �
D
�
D
D�
��
�M
M�
� �K
K
�
D��M� K
V
VO
M
M�
� VO
VV I
M � OI
VI
2�
�L
L
K
K�
� R2�
T
ss
R2�
T
还有：and
K� �L
and
R � Ts
2
and
�
� 2
�p
p�R
C
R�
�
C
�p � 2
R�C
:
Gdo 的表达式可以简化为下面形式
The
can
be simplified to the following:
The expression
expression for
for G
Gdo
do can be simplified to the following:
The expression for Gdo can be simplified to the following:
R�T
��
�V
VI �
� R � T ss
G do �
G
I
�
do
2�
� TL
Ls
R2
G do � � V I �
2�L
�
�
20
20
20
Understanding
全面认识开关型电源中的BUCK-BOOST功率级
Understanding Buck-Boost
Buck-Boost Power
Power Stages
Stages in
in Switch
Switch Mode
Mode Power
Power Supplies
Supplies
20
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Buck-Boost功率级的变型
4
Buck-Boost功率级的变型
4.1
反驰式（Flyback）功率级
传统buck-boost功率级的变压器耦合的变型是反驰式功率级。这种功率级像传统的buck-boost功率
级一样的工作，除了把单一的线圈电感替换为两个（或者更多）的线圈耦合电感。功率开关Q1，见
图14，把输入电压加载到耦合电感的主线圈上（LPRI），能量储存直到Q1关上。接着从耦合电感的
副线圈（LSEC）通过输出二极管将能量传送到输出电容和负载电阻的组合上。这种功率级提供了输
入电压和输出电压间的电隔离，除了之外，隔离变压器还可以对输入电压进行降压（或升压）。通
过设计变压器的变换比得到合适的占空比，从而得到几乎任何的输入电压/输出电压的组合，以避免
出现极大或极小的占空比值。
这种反向功率级还可以消除两种有时会让标准buck-boost功率级变得不理想的缺点，即输出电压与
输入电压的极性相反和功率开关需要浮动驱动。除了提供隔离，耦合电感副线圈相连还可以用来产
生正极性的或者负极性的输出电压。此外，功率开关跟耦合电感的主线圈串联，可以连接功率开关
让源极为参考地，而不是像标准的buck-boost功率级一样，把漏极连接到输入电压。
反驰式功率级在48V输入电信应用和输出功率高到大约50瓦的110V交流或220V交流的离线应用上非
常流行。反驰式功率级的精确额定功率是由输入电压/输出电压组合、工作环境和许多其它因素来决
定的。通过在增加输出二极管和输出电容的同时，简单增加耦合电感的另一个线圈就可以很容易地
产生额外的输出电压。用单一的功率级得到多个输出电压是反向功率级的另一个优势。
带有驱动电路模块的反向功率级的简单原理图如图14所示，图中，连接耦合电感的副线圈用来产生
一个正极性的输出电压。功率开关Q1是一个n通道的金属氧化物半导体场效应管（MOSFET）。二
极管 CR1 通常叫做输出二极管 。 副线圈的电感 LSEC和电容 C 组成了滤波器 。 电容 ESR（ 等效串联电
阻）RC未包括。电阻R代表了功率源的输出负载。
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Buck-Boost功率级的变型
SLVA059A
SLVA059A
CR1
Vb
VI
VI
+
LPRI
b
LVSEC
+
LPRI
Va
LSEC
Drive
Circuit
Drive
Circuit
VO
CR1
VO
Va Q1
C
R
C
R
Q1
Figure 14.图Flyback
Power Stage Schematic
14. 反向功率级的原理图
Figure
The important waveforms
for14.
theFlyback
flyback Power
power Stage
stage Schematic
operating in DCM are shown in
工作在非连续导通模式下反向功率级的重要波形图如图
所示。
Figure
15.
The
important
waveforms for the flyback power 15
stage
operating in DCM are shown in
Figure 15.
IQ1
IQ1
ICR1 Solid
IO Dashed
ICR1
Solid
IO Dashed
Vb Solid
VO Dashed
Vb Solid
VO Dashed
0
0
Va
Va
0
0
D3*TS
D*TS
D*TS
D3*TS
D2*TS
D2*TS
TS
TS
Figure 15. Discontinuous Mode Flyback Waveforms
Figure 15.
Discontinuous
Mode Flyback Waveforms
图15.
非连续模式下飞驰功率级的波形图
22
22
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Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
22
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Buck-Boost功率级的变型
SLVA059A
SLVA059A
工作在连续导通模式下
反向功率级的简化电压转换关系
忽略寄生效应
）由下式给出
:工作在连续
The
simplified voltage（CCM）
conversion
relationship for the flyback（
power
stage operating
in CCM
The
simplified voltage
conversion relationship for the flyback
power stage由下式给出
operating in CCM
导通模式下
反向飞驰式功率级的简化电压转换关系
忽略寄生效应
（CCM） is given by:
（
）
:
(ignoring parasitics)
(ignoring parasitics) is given by:
N
V O � V I � N ss � D
D
VO � VI � Np � 1 �
D
Np 1 � D
工作在非连续导通模式下
The
simplified voltage conversion
relationship for the flyback power
stage operating
in DCM
（DCM）反向功率级的简化电压转换关系
（忽略寄生效应
）由下式给出
:
The simplified voltage conversion relationship for the flyback power stage operating in DCM
(ignoring parasitics) is given by:
(ignoring parasitics) is given by:
N
V O � V I � N ss � D
V O � V I � N p � �DK
N p �K
Where
K is defined
as:
其中
K定义为
:
Where
K is defined
as:
2�L
K � 2 � L SEC
K � R � SEC
T
R � T ss
The simplified duty-cycle-to-output transfer function for the flyback power stage operating in
The simplified duty-cycle-to-output transfer function for the flyback power stage operating in
工作在连续导通模式下
（CCM）反向功率级的简化占空比-输出传输函数由下式给出:
CCM
is given by:
CCM is given by:
��
式中
:
Where:
Where:
�� ��
��
1 � �ss � 1 � �ss
1 � � z1 � 1 � � z2
v^^ O
NS
v O (s) � G � N S �
z1
z2
^ (s) � G do � N �
2
s
s
do
d^
2
NP
1 � � s�Q � s
d
P
1 � � o�Q � � 2
2
o
�o
o
VI
VI
G do �
G do �
2
(1 � D ) 2
(1 � D )
1
� z1 �
� z1 � R 1� C
RC
C � C2
(1 � D ) 2 � R
� z2 � (1 � D) � R
� z2 � D � L
D � L SEC
SEC
1�D
�o �
1
�
D
� o � �L
�C
�LSEC
SEC � C
(1 � D) � R
Q � (1 � D) � R
Q�
L SEC
L SEC
C
C
�
�
The simplified duty-cycle-to-output transfer function for the flyback power stage operating in
The simplified duty-cycle-to-output transfer function for the flyback power stage operating in
DCM is given by:
DCM is given by:
工作在非连续导通模式下（DCM）反向功率级的简化占空比-输出传输函数由下式给出:
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23
1��
d
Where:
组件选择
and
SLVA059A
N
G do � V I � S �
NP
p
�
R � TS
2 � L SEC
www.ti.com.cn
2
R
�
C
vO
1
�
G
�
^
do
1 � �s
d
�p �
^
5
55
5.1
5.1
Component
式中：
Where:
p
Selection
�
NS
R�T
ThisGsection
presents
a discussionSof the function of each of the main components of the
�
V
�
�
do
I
2�
L SEC requirements and applied stresses are given for each
buck-boost powerNstage.
The
electrical
P
和：
and
power stage component.
�p � 2
R �power
C
The completed
supply, made up of a power stage and a control circuit, usually must
meet a set of minimum performance requirements. This set of requirements is usually
referred to as the power supply specification. Many times, the power supply specification
determines
individual component requirements.
Component
Selection
部件选择
This
section presents
a discussion
of the function of each
of the main components of the
这部分主要讨论
功率级每个主要组成部件的功能
。给出了功率级中每个部件的电子性能需求和压
buck-boost
buck-boost
power
stage.
The
electrical
requirements
and
applied
stresses are given for each
力。
5.1
Output
Capacitance
power
stage component.
一个完整的功率源
，由一个功率级和一个控制电路组成，通常满足最小的性能要求。这些要求通常是参考
In
switching
power
supply power stages, the output。capacitance stores energy in the electric
功率源的规格。很多时候
，功率源的规格决定了每个部件的需求
The completed
power
supply,
made
up ofThus,
a power
stage andthe
a control
circuit,
usually must
field due
to the
voltage
applied.
qualitatively,
function
of a capacitor
is to attempt
meet a set
of minimum
performance
to maintain
a constant
voltage.requirements. This set of requirements is usually
输出电容 to as the power supply specification. Many times, the power supply specification
referred
determines
requirements.
Theindividual
value of component
output
capacitance
of a buck-boost power
stage is generally
selected to limit
在开关功率源的功率级中
，由于加载电压输出电容在电场储存能量
，所以定性的说
，电容的功能就是试图
output voltage 。
ripple to the level required by the specification. The series impedance of the
保持一个固定不变的电压
capacitor and the power stage output current determine the output voltage ripple. The three
elements
of the capacitor that contribute to its impedance (and output voltage ripple) are
Output
Capacitance
通常选取Buck-boost功率级的输出电容值使得把输出电压的纹波电压限制在规格要求的水平。电容的串联
equivalent series resistance (ESR), equivalent series inductance (ESL), and capacitance
阻抗和功率级的输出电流决定了输出电压的纹波
和输出电压纹波
。导致电容产生阻抗
（
）的三个元素是等
In
switching
supply power
the for
output
capacitance
energy in the
electric
(C).power
The following
gives stages,
guidelines
output
capacitorstores
selection.
field
due
to
the
voltage
applied.
Thus,
qualitatively,
the
function
of
a
capacitor
is
to
attempt
效串联电阻（ESR）、等效串联电感（ESL）和电容（C）。下面给出了选择输出电容的原则。
to maintain
constant voltage.
Foracontinuous
inductor current mode operation, to determine the amount of capacitance
needed as a function of，output
load current,
IO , switching frequency, fS , and
对于连续电感器电流模式下的工作
为了确定电容值
开关频率output
，需要知道它一个关于输出负载电流
I O 、desired
fS、
The
value
of
output
capacitance
of
a
buck-boost
power
stage
is
generally
selected
to
limit
voltage
ripple,
∆V
,
the
following
equation
is
used
assuming
all
the
output
voltage
ripple
要求的输出纹波电压ΔVO 的函数
O ，在假定所有的输出电压纹波都是由电容器的电容产生的情况，使用下面 is
output voltage
ripple
to the levelcapacitance.
required by This
the specification.
The
series
impedance
of thethe entire
due
to
the
capacitor’s
is because the
output
capacitor
supplies
的方程。这是因为在功率级开态（ON），输出电容器提供了所有的输出负载电流
。
capacitor
and
the
power
stage
output
current
determine
the
output
voltage
ripple.
The
three
output load current during the power stage ON state.
elements of the capacitor that contribute to its impedance (and output voltage ripple) are
equivalent series resistance (ESR), equivalent series inductance (ESL), and capacitance
I O(Max) � D Max
(C). The following gives guidelines
for output capacitor selection.
C�
f S � �V O
For continuous inductor current mode operation, to determine the amount of capacitance
Where
IO(Max)
is the maximum
output
current and
DMax is the
maximum
cycle.
needed as
a function
of output
load current,
IO , switching
frequency,
fS , and
desiredduty
output
voltage ripple, ∆VO , the following equation is used assuming all the output voltage ripple is
due
the是最大输出电流
capacitor’s capacitance.
This is。
because the output capacitor supplies the entire
式中to
，DMax是最大占空比
IO(Max)
24 load
Understanding
Buck-Boost
Power Stages
Switch
Mode Power Supplies
output
current during
the power
stage in
ON
state.
C�
I O(Max) � D Max
f S � �V O
Where IO(Max) is the maximum output current and DMax is the maximum duty cycle.
24
24
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Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
ZHCA041–1999年3月–2002年11月修订
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SLVA059A
组件选择
SLVA059A
SLVA059A
For discontinuous inductor current mode operation, to determine the amount of capacitance
For
discontinuous inductor current ，
mode
operation, to determine
the amount of capacitance
对于非连续电感器电流模式下的工作
为了确定需要的电容值
，在假定所有的输出电压纹波都是由电容器
needed,
the following
equation
is used,
assuming
all
the
output
voltage
ripple
due to the
For
discontinuous
inductor
current
mode
operation,
to
determine
the amount
of is
capacitance
needed,
the following
equation is used, assuming all the output voltage
ripple
is
due to the
的电容产生的情况
，使用下面的方程
。
capacitor’s
capacitance.
needed,
the
following
equation
is
used,
assuming
all
the
output
voltage
ripple
is
due to the
capacitor’s capacitance.
capacitor’s capacitance.
�� �� ��
2�L
I O(Max) � 1 �
2�L
I O(Max) � 1 � R�T
2�Ls
I O(Max) � 1 � R�T
R�T ss
C�
C�
f S � �V O
f S � �V O
C�
f S � �V O
However, in many practical designs, to get the required ESR, a capacitor with much more
However,
in many practical
designs, to get the required
ESR, a通常都要选择比我们计算出来的电容
capacitor with much more
但是在很多实际的设计中
，为了得到需要的等效串联电阻
（ESR），
capacitance
than ispractical
needed designs,
must be selected.
However,
in many
to get the required ESR, a capacitor with much more
capacitance
than
is
needed
must
be
selected.
值大的电容器than
。 is needed must be selected.
capacitance
For continuous inductor current mode operation and assuming there is enough capacitance
For continuous inductor current mode operation and assuming there is enough capacitance
such
that the ripple
due to
the，capacitance
can beand
ignored,
the ESR
to limit
the ripple
For
continuous
inductor
current
mode operation
assuming
thereneeded
is enough
capacitance
对于连续电感器电流模式工作
假定有足够的电容使得电容导致的纹波可以忽略不计
用来把限制纹波在
，
such
that the ripple
due to
the capacitance
can be ignored,
the ESR
needed
to limit
the ripple
to
∆V
V
peak-to-peak
is:
such
that
the
ripple due
to
theESR
capacitance
can be ignored, the ESR needed to limit the ripple
Δ∆V
而需要的
为:
VO O
(V
peak-to-peak)
to
V
peak-to-peak
is:
to ∆VO
O V peak-to-peak is:
�V O
�V O
ESR �
�V
ESR � I
ESR � IO(Max) O �I
�I L
I O(Max) � �I L
� 2L
1�D
O(Max)
1�D Max
� 2
2
1�D Max
Max
For discontinuous inductor current mode operation and assuming there is enough
For discontinuous inductor current mode operation and assuming there is enough
capacitance
such that
the ripple
due tomode
the capacitance
ignored, the
ESRisneeded
to
For
discontinuous
inductor
current
operation can
andbe
there
enough
对于非连续电感器电流模式工作
，假定有足够的电容使得电容导致的纹波可以忽略不计
，用来把限制纹波
capacitance
such that
the ripple
due to the capacitance
can
beassuming
ignored, the
ESR needed
to
limit
the ripple
to ∆V
V
simply:
capacitance
such
that
thepeak-to-peak
ripple due tois
the
capacitance can be ignored, the ESR needed to
O 而需要的
limit
the
ripple
to
∆V
V
peak-to-peak
is
simply:
在ΔV
为
(
V
peak-to-peak)
ESR
:
O
limit the
ripple to ∆VO
O V peak-to-peak is simply:
�V O
ESR � �V
O
ESR � �V
�I O
ESR � �I L
�I L
L
Ripple current flowing through a capacitor’s ESR causes power dissipation in the capacitor.
Ripple current flowing through a capacitor’s ESR causes power dissipation in the capacitor.
This
power
dissipation
causesaacapacitor’s
temperature
increase
the capacitor.
Ripple
current
flowing through
ESR
causesinternal
power to
dissipation
in theExcessive
capacitor.
This
power
dissipation
causes
a temperature
increase
internal
to
the capacitor.
Excessive
纹波电流流过电容器的
造成在电容器上的功率损耗
，这个功率损耗会导致电容器内部的温度升高
，
ESR，
temperature
can seriously
shorten
the expected
life of internal
a capacitor.
Capacitors
have
ripple
This
power
dissipation
causes
a
temperature
increase
to
the
capacitor.
Excessive
temperature
can
seriously
shorten
the
expected
life
of
a
capacitor.
Capacitors
have
ripple
过高的温度会严重缩短电容器的预计寿命
。 电容器有取决于周围温度的额定纹波电流
， 而且不能超过
。
current
ratings
that
are dependent
on ambient
temperature
and should
not behave
exceeded.
temperature
can
seriously
shorten the
expected
life of a capacitor.
Capacitors
ripple
current
ratings
that
are
dependent
on
ambient
temperature
and
should
not
be
exceeded.
参考图 3，
输出电容器纹波电流等于电感器电流
流过输出电容器的纹波电流均方根值
I O。
I L减去输出电流
Referring
to
Figure
thedependent
output capacitor
ripple
current is the
inductor
current,
IL,exceeded.
minus the
current
ratings
that 3,
are
on ambient
should
not be
Referring
to Figure
3,
the output capacitor
ripple temperature
current is theand
inductor
current,
IL, minus the
由下式给出
（RMS）
（连续电感器电流模式
）：
output
current,
IO. The
value
of the
ripplecurrent
current flowing
in thecurrent,
output capacitance
Referring
to Figure
3,
theRMS
output
capacitor
the inductor
L, minus the
output
current,
IO. The
RMS
value
of theripple
ripple currentisflowing
in the output Icapacitance
(continuous
inductor
current
mode
operation)
is
given
by:
output
current,
I
.
The
RMS
value
of
the
ripple
current
flowing
in
the
output
capacitance
O
(continuous inductor
current mode operation) is given by:
(continuous inductor current mode operation) is given by:
D
I C RMS � I O �
D
I C RMS � I O � 1 �
DD
D
I C RMS � I O � 1 �
1�D
ESL can be a problem by causing ringing in the low megahertz region but can be controlled
ESL can be a problem by causing ringing in the low megahertz region but can be controlled
等效串联电感
但是可以通过选择低
（ESL）
（兆赫兹
）区产生阻尼振荡的问题
ESL的电容器
by
choosing
ESL 有在低频
capacitors,
limiting
lead
length
(PCB and，capacitor),
one 、限
ESL
can be alow
problem
by causing
ringing
in the
low megahertz
region butand
can replacing
be controlled
by choosing
low
ESL capacitors,
limiting
lead
length
(PCB and capacitor),
and
replacing
one
large
device
with
several
smaller
ones
connected
in
parallel.
by
choosing
low
ESL
capacitors,
limiting
lead
length
(PCB
and
capacitor),
and
replacing
one
制引线长度
印刷电路板
和电容器
和并联更大的器件代替几个小器件等方法来控制这个问题
（
）
PCB
large device with several smaller ones connected in parallel.
large device with several smaller ones connected in parallel.
��
��
�
�
�
ZHCA041–1999年3月–2002年11月修订
Understanding Buck-Boost 全面认识开关型电源中的BUCK-BOOST功率级
Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
www.BDTIC.com/TI
25
25
25
25
www.ti.com.cn
组件选择
制作电容器的三种技术：低阻抗铝、有机半导体和固态钽主要用于廉价的商业应用中。低阻抗铝电解电容
器最便宜，可以在很小的体积提供很高的电容值，但是等效串联电阻（ESR）都比其它两种高。有机半导
体电解电容器，像三洋（Sanyo）OS-CON系列，在最近几年功率源工业中非常流行，他们是世界上最好的
电容器，在整个温度范围稳定的低ESR和小体积提供大电容，大部分OS-CON电容器都是采用引线安装的辐
射形封装，也提供表面贴装器件，但是牺牲了很多体积和性能的优势。固态钽片电容器对于那种只能选用
表面贴装器件的情况是最好的选择。像AVX TPS系列和Sqrague 593D系列的产品就主要开发来用在功率源
上的。这些产品有很多优点：在温度范围内相对稳定的ESR、高的纹波电流容限、低的ESL、浪涌电流测试
和很高的电容体积比。
5.2
输出电感
在开关功率源的功率级中，电感器的功能是储存能量，电流流过时能量会以磁场的方式储存下来，所以定
性的说，电感器的作用就是试图保持固定不变的电流值，或者等效的说是限制流过电感器电流的变化率。
选择Buck-boost功率级的输出电感器电感值主要是限制流过它的纹波电流的峰峰值。选择以后，功率级的
工作模式，连续或非连续，就确定下来了。电感器纹波电流跟加载的电压和加载电压的时间成正比，跟电
感值成反比，这些在前面已经详细解释了。
很多设计者喜欢自己设计电感器，但是这不是我们这篇报告的主题。下面我们讨论在选择合适电感器必须
考虑的事项。
除了电感值，在选择电感器时需要考虑的其它重要因素有最大直流或峰值电流和最大工作频率。让电感器
在它的额定直流电流内工作对确保电感器不出现过热或饱和很重要。电感器工作在低于最大额定频率可以
保证不会超过最大内部损耗，从而避免出现过热或饱和。
磁器件制造商可以提供很多类型适用于直流-直流转换器的直接就可以买来用的电感器，其中有些是表面贴
装器件。电感器有很多种类，最流行的内部材料是铁氧体和铁精粉。筒管状或杆状核心电感器很容易买到
而且也很便宜，但是使用这些电感器的时候要非常小心，因为比起其它形状的电感器，它们更容易产生噪
声问题。考虑到体积空间足够大的话，用户自己设计也是可行的。
26
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
www.BDTIC.com/TI
Current flowing through an inductor causes power dissipation due to the inductor’s dc
SLVA059A
resistance; this power dissipation is easily calculated. Power is also dissipated in the
inductor’s core due to the flux swing caused by the ac voltage applied across it but this
www.ti.com.cn
Current flowing
through
angiven
inductor
causes power
dissipation
due to the the
inductor’s
dc
information
is rarely
directly
in manufacturer’s
data
sheets. Occasionally,
inductor’s
组件选择
resistance;
this
power
dissipation
is
easily
calculated.
Power
is
also
dissipated
in
the
maximum operating frequency and/or applied volt-seconds ratings give the designer some
inductor’s regarding
core due core
to the
fluxThe
swing
caused
by the causes
ac voltage
applied across
it but
guidance
loss.
power
dissipation
a temperature
increase
in this
the
由于电感器直流电阻
电流流过电感器时会有功率损耗
，这个损耗可以很容易计算得
。功率也会因为加载
information
is rarely，
directly
givencan
in manufacturer’s
data
sheets.
Occasionally,
inductor’s
inductor.
Excessive
temperature
cause degradation
in the insulation
of thethe
winding
and
maximum
operating
and/or
applied
volt-seconds
ratings
giveinductor’s
the designer
some
在电感器上的交流电压导致的流量振荡而损耗在电感器的内核上
不过这些信息很少会在制造商的数据说
cause
increased
corefrequency
loss. Care
should
be exercised
to insure
all the
maximum
，
guidance
regarding
core
loss.
The
power
dissipation
causes
a
temperature
increase
in the
ratings
are not exceeded.
明书中直接给出
。 一般 ， 电感器的最大工作频率和 （ 或 ） 加载的额定电压 - 秒曲线给了设计者关于内核损
inductor.
Excessive
temperature can cause degradation
in the insulation of the winding and
耗的指导。
功率的损耗会导致电感器内部温度升高
，过高的温度会降低线圈的绝缘性，导致更多的内核损
cause
increased
core loss.
Careby:
should be exercised to insure all the inductor’s maximum
The
loss
in the inductor
is given
耗。必须注意保证电感器所有的最大额定值都没有超过。
ratings
are not exceeded.
2
P inductor � �I Lrms� � R Cu � P Core
电感器的损耗由下式给出
: is given by:
The
loss in the inductor
where, RCu is the winding resistance.
2
P inductor � �I Lrms� � R Cu � P Core
5.3
5.3
5.3
where,
winding resistance.
Power
Switch
式中RCuR
为线圈电阻
Cu is the 。
In switching power supply power stages, the function of the power switch is to control the flow
of
energy
from the input power source to the output voltage. In a buck-boost power stage,
Power
Switch
功率开关
the
power switch (Q1 in Figure 1) connects the input to the inductor when the switch is turned
In
switching
power supply
power
stages,
theThe
function
the power
is to
on
and disconnects
when
the switch
is off.
powerofswitch
mustswitch
conduct
thecontrol
current
inflow
the 功率
在开关式功率源的功率级
，功率开关的功能是控制从输入功率源到输出电压的能量流动
。在the
buck-boost
of
energy
from
the
input
power
source
to
the
output
voltage.
In
a
buck-boost
power
stage,
output
inductor
while
on
and
block
the
difference
between
the
input
voltage
and
output
级，功率开关（图1中的Q1）当开关打开时连通输入到电感器，开关关上时断开连接。功率开关必须在开
the
power
switch
in the
Figure
1) connects
the input
to the
inductor
when
is turned
voltage
when
off.(Q1
Also,
power
switch must
change
from
one state
to the switch
other quickly
in
时在输出电感器传导电流
，关时阻止输入电压和输出电压的差值。而且功率开关必须很快的完成一个状态
on andtodisconnects
whenpower
the switch
is off. The
power
musttransition.
conduct the current in the
order
avoid excessive
dissipation
during
theswitch
switching
到另一个状态的转换
，从而避免在开关转换时间内的功率损耗
。 the input voltage and output
output
inductor while
on and block the difference between
voltage
off. Also,
the
power switch
must
change
from one
state toOther
the other
quickly
in
The
typewhen
of power
switch
considered
in this
report
is a power
MOSFET.
power
devices
这篇报告中考虑的功率开关类型是功率型金属氧化物半导体场效应管
（MOSFET）。
order
to avoidbut
excessive
dissipation
during the
switching
transition.
are
available
in mostpower
instances,
the MOSFET
is the
best choice
in terms 其它的功率器件也可
of cost and
performance
(when the drive
circuits are considered).
The two types
of MOSFET
available 。可以
以用，但是在大多数情况下
是最好的选择
，在考虑到费用和性能时
（考虑驱动电路时
），MOSFET
The
type
of
power
switch
considered
in
this
report
is
a
power
MOSFET.
Other
power
devices
for
use
are
the
n-channel
and
the
p-channel.
P-channel
MOSFETs
are
popular
for
use in
使用的MOSFET有两种类型：n通道型和p通道型。P通道型MOSFET在buck-boost功率级中的使用更流行
，
are available
but in
most because
instances,
the MOSFET
issimpler
the best
choice
in terms
of
cost and
buck-boost
power
stages
driving
the
gate
is
than
the
gate
drive
required
for
因为驱动p通道的门比驱动n通道MOSFET中的门要简单。
performance
the drive circuits are considered). The two types of MOSFET available
an
n-channel (when
MOSFET.
for use are the n-channel and the p-channel. P-channel MOSFETs are popular for use in
功率开关
消耗的功率由下式给出
Q1dissipated
: driving
buck-boost
power stages
because
the
gate
is simpler
The
power
by the
power
switch,
Q1,
is given
by: than the gate drive required for
an n-channel MOSFET.
P D(Q1) �
The power dissipated
by the power switch, Q1, is given
I O by:
2
�I Lrms� � RDS(on) � D � 1 � �V I � V O� �
� �t r � t f� � f S � Q Gate � V GS � f S
2
1�D
P D(Q1) �
其中: Where:
I
2
t are the 1MOSFET
turn-on
�
� andOturn-off �switching
� times
的打开和关闭的转换时间
t�rI和
tf是� MOSFET
r and
�tR
Lrms
DS(on)f � D � 2 � V I � V。
O � 1 � D � t r � t f � f S � Q Gate � V GS � f S
QGate总的门电荷
is the MOSFET
total gate charge
。
QGate是MOSFET
Where:
Other than selecting
or n-channel,
other
to consider
tr and p-channel
tf are the MOSFET
turn-on
andparameters
turn-off switching
timeswhile selecting
the appropriateQMOSFET
are
the
maximum
drain-to-source
breakdown
voltage, V(BR)DSS
is
the
MOSFET
total
gate
charge
Gate
,I
除了选择
时需要考虑的其它参数是漏极
，在选择合适的
p通道或n通道以外
MOSFET
-源极间击穿电压的最大
and
the maximum
drain current
.
D(Max)
Other
than
selecting
p-channel
or
n-channel,
other
parameters
to
consider
while
selecting
值V(BR)DSS
和最大漏极电流
，
ID(Max)。
the appropriate MOSFET are the maximum drain-to-source breakdown voltage, V(BR)DSS
and the maximum drain current, ID(Max).
�
�
ZHCA041–1999年3月–2002年11月修订
�
�
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
27
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
27
全面认识开关型电源中的BUCK-BOOST功率级
27
www.BDTIC.com/TI
The MOSFET selected should have a V(BR)DSS rating greater than the maximum difference
between the input voltage and output voltage, and some margin should be added for
The MOSFET
should
have aselected
V(BR)DSS
ratingalso
greater
than
maximum difference
transients
and selected
spikes. The
MOSFET
should
have
an Ithe
D(Max) rating of at least
SLVA059A
between
the
input
voltage
and
output
voltage,
and
some
margin
should
be this
added
for
two times the maximum power stage inductor current. However, many times
is not
transients
and
spikes.
The
MOSFET
selected
should
also
have
an
I
rating
of
at
least
D(Max)
sufficient margin and the MOSFET junction temperature should be calculated
to make
sure
www.ti.com.cn
The MOSFET
selected
should
have
a V(BR)DSS
greater
than the
maximum
difference
two
maximum
power
stage
inductor rating
current.
However,
many
times this
is not
组件选择
that ittimes
is notthe
exceeded.
The
junction
temperature
can be estimated
as
follows:
between margin
the input
and output
voltage,
and some
margin
should be
addedsure
for
sufficient
andvoltage
the MOSFET
junction
temperature
should
be calculated
to make
transients
and
spikes.
The
MOSFET
selected
should
also
have
an
I
rating
of
at
least
that it is not
exceeded.
temperature can be estimated D(Max)
as 而且要为瞬变量和尖峰信号预
follows:
TJ �
T The
� Pjunction
R �JA
，V
，
MOSFET
D �stage
(BR)DSSA的额定值要大于输入电压和输出电压的最大差值
two
times选取时
the maximum
power
inductor current. However, many
times this is not
留一点的余量
时还要求额定
至少是功率级电感器最大电流的两倍
然而有很多时候这
。选择
MOSFET
ID
sufficient
margin
and
the
MOSFET
junction
temperature
should
be
calculated
to。make
sure
(Max)
T J � T A � P D � R �JA
Where:
还不是足够的余量
还要考虑到
结的温度
that
it is not
The or
junction
temperature
can be estimated
as follows:
，保证没有超过范围
。结温度由下式估算
：
MOSFET
TA exceeded.
is the，ambient
heatsink
temperature
Where: R
ΘJA is the thermal resistance from the MOSFET chip to the ambient
TJ �
TA � P
� R �JA temperature
TAor
is heatsink.
the
ambient
orDheatsink
air
RΘJA is the thermal resistance from the MOSFET chip to the ambient
式中:
Where:
air or heatsink.
TA is the ambient or heatsink
temperature
；
TA是周围空气或热沉的温度
5.4 Output
Diode
R
is
the
thermal
resistance
from
。 the MOSFET chip to the ambient
ΘJA
RΘJA是
MOSFET片到周围空气或热沉的热阻抗
The
output
diode
conducts
when
the
power
switch
turns off and provides a path for the
or heatsink.
5.4 Output air
Diode
inductor current. Important criteria for selecting the rectifier include: fast switching,
输出二极管
5.4
The
output voltage,
diode conducts
when the
power switch
turns
provides
a path
for the
breakdown
current rating,
low-forward
voltage
dropofftoand
minimize
power
dissipation,
inductor
current.
Important
criteria
for
selecting
the
rectifier
include:
fast
switching,
5.4 and
Output
Diode packaging. Unless
appropriate
the application justifies
the expense and complexity of ：快速
输出二极管在功率开关关闭时导通
，为电感器电流提供通路
。在选择整流器时要考虑的主要要素为
breakdown
voltage,
current
rating,
low-forward
voltage outputs
drop to is
minimize
dissipation,
a开关
synchronous
rectifier,
the
best
solution
for
low-voltage
usually 。
apower
Schottky
rectifier.
击穿电压
除非应用场合确实需要用
、
、额定电流
、为降低功率损耗的低正向电压下降和合适的封装
The
output
diode
conducts
when
the
power
switch
turns
off
and
provides
a
path
for the
and
appropriate
packaging.
Unless
the
application
justifies
the
expense
and
complexity
of
The
breakdown voltage must
be greater than the maximum difference。between the input
到高费用和复杂的同步整流器
肖特基整流器通常是低压输出的最好解决方案
，
inductor
current.
Important
criteria
for
selecting
the
rectifier
include:
fast
switching,
a
synchronous
rectifier,
the
best
solution
for
low-voltage
outputs
is
usually
a
Schottky
rectifier.
voltage and output voltage, and some margin should be added for transients and spikes. The
breakdown
voltage,
current
rating,greater
low-forward
voltage
drop todifference
minimize between
power dissipation,
The
breakdown
voltage
than
the
maximum
input
current
rating should
be atmust
leastbe
two times the
maximum
power stage
output current. the
Normally
and
appropriate
packaging.
Unless
the
application
justifies
the
expense
and
complexity
of
击穿电压必须大于输入电压和输出电压的最大差值
而且必须为瞬时值和尖峰预留一定的余量
额定电流
voltage
and
output
voltage,
and
some
margin
should
be
added
for
transients
and
spikes.
The
，
。
the current rating will be much higher than the output current because power and junction
a
synchronous
rectifier,
the
best
solution
for
low-voltage
outputs
is
usually
a
Schottky
rectifier.
current
ratinglimitations
should be dominate
at least。two
times
the selection.
maximum power stage
output current. Normally
要至少是功率级最大电流的两倍
通常额定电流要远大于输出电流
，因为功率和结温度的限制决定了器件
temperature
the
device
The
breakdown
voltage
must
be
greater
than
the
maximum
difference
between
input
the
current
rating
will
be
much
higher
than
the
output
current
because
power
andthe
junction
的选择。
voltage
and
output
voltage,
and
some
margin
should
be
added
for
transients
and
spikes.
The
temperature
limitations
selection.
The voltage drop
acrossdominate
the diode the
in adevice
conducting
state is primarily responsible for the losses
current rating should be at least two times the maximum power stage output current. Normally
in
the diode. The power dissipated by the diode can
be calculated as the product of the
二极管上的损耗主要由导通态二极管上的电压降造成的
，二极管上的功率损耗可以由前向电压和输出负载
the
current
rating
will bethe
much
higher
than the output
current
because
power and
The
voltage
drop and
across
diode
in a conducting
state
is primarily
responsible
thejunction
losses
forward
voltage
the output
load
current. The
switching
losses
which for
occur
at the
temperature
limitations
dominate
the
device
selection.
电流的乘积来计算得
从导通态转化为非导通态时的转换损耗相比于传导损耗来说
非常小
通常忽略
。
，
，
in
the diode.
The
power dissipated
by the diode
can
calculated
as the product
of
the 。
transitions
from
conducting
to non-conducting
states
arebevery
small compared
to conduction
forward
voltage
and the
output load current. The switching losses which occur at the
losses and
are usually
ignored.
The
voltagefrom
dropconducting
across the to
diode
in a conducting
state
primarily
forconduction
the losses
transitions
non-conducting
states
areisvery
smallresponsible
compared to
整流器上的功率损耗为
:
in
the
diode.
The
power
dissipated
by
the
diode
can
be
calculated
as
the
product
of the
losses
and dissipated
are usuallyby
ignored.
The power
the catch rectifier is given by:
forward voltage and the output load current. The switching losses which occur at the
transitions
conducting
non-conducting
states are very small compared to conduction
The
power from
dissipated
by
theto�
catch
(1 � Dis
) given by:
P
�V
I O �rectifier
D
losses and are D(Diode)
usually ignored.
P D(Diode)
� voltage
V D � I Odrop
� (1of�the
D)catch rectifier.
forward
where VD is the
The power dissipated by the catch rectifier is given by:
式中VD为整流器的前向电压降。
forward voltage
of the as
catch
rectifier.
where
VD is the
The junction
temperature
can bedrop
estimated
follows:
P D(Diode) � V D � I O � (1 � D)
结温度估算公式为
The
junction temperature
as follows:
P Dbe
� estimated
R �JA
T:J � T A �can
voltage
drop
of the catch rectifier.
where VD is the forward
T J � T A � P D � R �JA
The junction temperature can be estimated as follows:
T J � T A � P D � R �JA
28
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
28
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
28
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
28
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
www.BDTIC.com/TI
www.ti.com.cn
总结
SLVA059A
6
66
6
6
SLVA059A
SLVA059A
SLVA059A
Summary
Summary
总结application report described and analyzed the operation of the buck-boost power stage.
This
Summary
Summary
The
two
modes report
of operation,
continuous
conduction
mode of
and
conduction
This
application
described
and
analyzed
the 。
operation
thediscontinuous
buck-boost power
stage.
这篇应用报告介绍分析了
功率级的工作过程
研究了连续导通模式和非连续导通模式两种工作模
buck-boost
This
application
report described
described
and
analyzed
the operation
operation
of the
the
buck-boost
power stage.
stage.
This
application
report
and
analyzed
the
of
buck-boost
power
mode,
were
examined.
Steady-state
and
small-signal
were
the
two
analyses
performed
on
The
two
modes
of
operation,
continuous
conduction
mode
and
discontinuous
conduction
式。two
分析了
功率级的稳态模型和小信号模型
。还介绍了作为基本
buck-boost
buck-boost功率级变型的反向功
The
modes
of
operation,
continuous
conduction
mode
and
discontinuous
conduction
The
two
modes
of operation,
continuous
conduction
andtwo
discontinuous
conduction
the buck-boost
power
stage.
The
flyback
power
stagemode
was the
presented
as a variation
of the
mode,
were
examined.
Steady-state
and small-signal
were
analyses
performed
on
率级。 were
mode,
examined.
Steady-state
and
small-signal
were
the
two
analyses
performed
on
mode,
were
examined.
Steady-state
and
small-signal
were
the
two
analyses
performed
on
basic
buck-boost
power
stage.
the buck-boost power stage. The flyback power stage was presented as a variation of the
the
buck-boost
power
stage.
The
flyback
power
stage
was
presented
as
a
variation
of
the
the
buck-boost
power
stage.
The
flyback
power
stage
was
presented
as
a
variation
of
the
basic buck-boost power stage.
basic
buck-boost
power
stage.
basic
buck-boost
power
stage.
稳态分析的主要结果总结如下
。
The
main
results of
the steady-state
analyses are summarized below.
The main results of the steady-state analyses are summarized below.
The
main
of
analyses
are
The
main results
results
of the
the steady-state
steady-state
analyses
are summarized
summarized below.
below.
voltage
conversion
relationship
for
CCM is:
连续导通模式下的电压转换关系为
:
The voltage conversion relationship for CCM is:
The
The voltage
voltage conversion
conversion relationship
relationship for
for CCM
CCM is:
is:
I �R
V O � � �V I � V DS� � D � V d � I L � R L
1�D
1�
� DL
V O � � ��V I � V DS�� � D
� V d � II L
�R
RL
L
D
L
D
V
�
�
V
�
V
�
�
V
�
1
�
D
1
DL
VO
d� 1�
O � � �V II � V DS
DS� � 1 � D � V d
�
or a slightly simpler version:
1�D
1�D
D
或者稍微简单些的关系式为
:
D
1
or
a slightly simpler version:
VO � � VI �
�
or
or a
a slightly
slightly simpler
simpler version:
version:
1�D
1 RL
VO � � VI � D
�1�
D
1
DD�
1R
VO �
��
�V
VI �
�1�
�
V
L �2
I
1
�
D
O
1�D
1 � D 1 � R��R
R
L
2
L
1
1�
� R��1�D
�22
which can be simplified to:
�
�
R�
1�D
R��1�D�
which
can :be simplified to:
还可化简为
D
which
can
be
simplified
to:
V Oto:� � V I �
which can be simplified
1�D
VO � � VI � D
D
DD
�
�
V
V
1�
I�
�
�
V
�
VO
I
The relationship between
the
average
current and the output current for the
1
�
D
O
1 � inductor
D
continuous
mode between
buck-boost
stageinductor
is givencurrent
by:
The
relationship
thepower
average
and the output current for the
The relationship
relationship between the
the average
average inductor
inductor current and
and the
the output
output current
current for
for the
the
The
continuous mode between
buck-boost power
stage is givencurrent
by:
连续导通模式
功率级的电感器平均电流和输出电流的关系为
continuous
mode
buck-boost
power
stage
is
given
by:
buck-boost
:
continuous mode buck-boost
stage is given by:
� power
I
I L(Avg) � � I O
(1 �I OD)
I L(Avg) � �
� IO
II L(Avg) �
(1 �OD)
�
(1 �
�mode
D) buck-boost voltage conversion relationship is given by:
L(Avg)
The discontinuous
conduction
(1
D)
��
�
��
�
The discontinuous conduction mode buck-boost voltage conversion relationship is given by:
The
discontinuous
conduction
mode
voltage
The
discontinuous
conduction
mode
buck-boost
voltage conversion
conversion relationship
relationship is
is given
given by:
by:
Dbuck-boost
非连续导通模式
电压转换关系为
：
buck-boost
VO �
�V
�
I
�DK
VO � � VI � D
V
� � V I � �DK
VO
O � � VI � �
where K is defined as:
�K
K
where K is defined as:
where
K
其中K定义为
:
where
K is
is defined
defined
as:2 � L
K �as:
R�
�TLs
K� 2
2
�
2
�TL
Ls
K�
�R�
K
R
�
T
The major results of the
small-signal
analyses are summarized below.
R�
T ss
The major results of the small-signal analyses are summarized below.
The
results
the
summarized
The major
major
results of
of
the small-signal
small-signal analyses
analyses
are
summarized
below.
small-signal
duty-cycle-to-output
transferare
function
for thebelow.
buck-boost power stage
operating
in CCM duty-cycle-to-output
is given by: 。
The
small-signal
transfer function for the buck-boost power stage
小信号分析的主要结果总结在下面
The
small-signal duty-cycle-to-output
duty-cycle-to-output
transfer function
function for
for the
the buck-boost
buck-boost power
power stage
stage
The
small-signal
transfer
operating
in CCM is given by:
operating
in
CCM
is
given
by:
operating in CCM is given by:
连续导通模式下buck-boost功率级的小信号占空比-输出电压传输函数有下式给出:
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
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
29
29
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
Understanding Buck-Boost
Buck-Boost Power
Power Stages
Stages in
in Switch
Switch Mode
Mode Power
Power Supplies
Supplies
Understanding
29
29
29
www.BDTIC.com/TI
www.ti.com.cn
总结
SLVA059A
SLVA059A
v^ O
^
d
(s) � G do �
式中: Where:
G do �
s z1 �
s z2 �
�1 � �sz1� � �1 � �sz2�
2
1 � � s�Q � s
o
�2
o
VI
2
(1 � D ) 2
1
RC � C
2
(1 � D ) 2 � R
D�L
�o � 1 � D
�L � C
Q�
(1 � D) � R
L
C
�
The small-signal duty-cycle-to-output transfer function for the buck-boost power stage
非连续导通模式下
功率级的小信号占空比-输出电压传输函数由下式给出:
operating
in DCMbuck-boost
is given by:
v^ O
^
d
� G do �
1
1 � �s
p
式中:
Where:
和:
and
V
V
G do � O � – I
D
�K
�p �
2
R�C
Also presented were requirements for the buck-boost power stage components based on
voltage and current stresses applied during the operation of the buck-boost power stage.
功率级工作过程中加载的电压和电流的压力，以及基于这些压力的buck-boost功率级组成部件的各种要求。
For further study, several references are given.
为了方便读者更深入的研究，这里给出了一些参考文献。
30
30
全面认识开关型电源中的BUCK-BOOST功率级
Understanding Buck-Boost Power Stages in Switch Mode Power Supplies
ZHCA041–1999年3月–2002年11月修订
www.BDTIC.com/TI
www.ti.com.cn
7
参考文献
参考文献
1. 应用报告TL5001脉冲宽度调制控制器设计, TI 文献号SLVA034A.
2. 应用报告 利用TPS5210设计快速响应的同步buck整流器, TI 文献号 SLVA044
3. V. Vorperian, R. Tymerski, and F. C. Lee,谐振腔和脉冲宽度调制开关的等效电路模型, IEEE功率电子学学
报, Vol. 4, No. 2, pp. 205-214, April 1989.
4. R. W. Erickson, 功率电子学基础 New York: Chapman and Hall, 1997.
5. V. Vorperian, 利用脉冲宽度调制开关模型来简单分析脉冲宽度调制转换器: Parts I and II, IEEE 航天和电
子系统学报, Vol. AES-26, pp. 490-505, May 1990.
6. E. van Dijk, et al., 直流-直流转换器的脉冲宽度调制开关模型, IEEE 功率电子学学报, Vol. 10, No. 6, pp.
659-665, November 1995.
7. G. W. Wester and R. D. Middlebrook, 开关式直流-直流转换器的低频特性, IEEE航天和电子系统学报,
Vol. AES-9, pp. 376-385, May 1973.
8. R. D. Middlebrook and S. Cuk,一种设计开关式转换器功率级模型的通用一体化方法, 电子学国际期刊,
Vol. 42, No. 6, pp. 521-550, June 1977.
9. E. Rogers, 开关式功率源的控制回路模型, Proceedings of EETimes模拟和混合信号应用会议, July
13-14, 1998, San Jose, CA.
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
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31
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by all associated warranties, conditions, limitations, and notices. Reproduction of this information with alteration is an unfair and deceptive
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restrictions.
Resale of TI products or services with statements different from or beyond the parameters stated by TI for that product or service voids all
express and any implied warranties for the associated TI product or service and is an unfair and deceptive business practice. TI is not responsible
or liable for any such statements.
TI products are not authorized for use in safety-critical applications (such as life support) where a failure of the TI product would reasonably
be expected to cause severe personal injury or death, unless officers of the parties have executed an agreement specifically governing such
use. Buyers represent that they have all necessary expertise in the safety and regulatory ramifications of their applications, and acknowledge
and agree that they are solely responsible for all legal, regulatory and safety-related requirements concerning their products and any use of
TI products in such safety-critical applications, notwithstanding any applications-related information or support that may be provided by TI.
Further, Buyers must fully indemnify TI and its representatives against any damages arising out of the use of TI products in such safety-critical
applications.
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Following are URLs where you can obtain information
on other Texas Instruments products and application
solutions:
相关产品链接:
•
DSP - 数字信号处理器 http://www.ti.com.cn/dsp
•
电源管理 http://www.ti.com.cn/power
•
放大器和线性器件 http://www.ti.com.cn/amplifiers
•
接口 http://www.ti.com.cn/interface
•
模拟开关和多路复用器 http://www.ti.com.cn/analogswitches
•
逻辑 http://www.ti.com.cn/logic
•
RF/IF 和 ZigBee® 解决方案 www.ti.com.cn/radiofre
•
RFID 系统 http://www.ti.com.cn/rfidsys
•
数据转换器 http://www.ti.com.cn/dataconverters
•
时钟和计时器 http://www.ti.com.cn/clockandtimers
•
标准线性器件 http://www.ti.com.cn/standardlinearde
•
温度传感器和监控器 http://www.ti.com.cn/temperaturesensors
•
微控制器 (MCU) http://www.ti.com.cn/microcontrollers
相关应用链接:
•
安防应用 http://www.ti.com.cn/security
•
工业应用 http://www.ti.com.cn/industrial
•
计算机及周边 http://www.ti.com.cn/computer
•
宽带网络 http://www.ti.com.cn/broadband
•
汽车电子 http://www.ti.com.cn/automotive
•
视频和影像 http://www.ti.com.cn/video
•
数字音频 http://www.ti.com.cn/audio
•
通信与电信 http://www.ti.com.cn/telecom
•
无线通信 http://www.ti.com.cn/wireless
•
消费电子 http://www.ti.com.cn/consumer
•
医疗电子 http://www.ti.com.cn/medical
www.BDTIC.com/TI
ZHCA041
重要声明
德州仪器 (TI) 及其下属子公司有权在不事先通知的情况下，随时对所提供的产品和服务进行更正、修改、增强、改进或其它更改，
并有权随时中止提供任何产品和服务。 客户在下订单前应获取最新的相关信息，并验证这些信息是否完整且是最新的。 所有产品的
销售都遵循在订单确认时所提供的 TI 销售条款与条件。
TI 保证其所销售的硬件产品的性能符合 TI 标准保修的适用规范。 仅在 TI 保修的范围内，且 TI 认为有必要时才会使用测试或其它质
量控制技术。 除非政府做出了硬性规定，否则没有必要对每种产品的所有参数进行测试。
TI 对应用帮助或客户产品设计不承担任何义务。 客户应对其使用 TI 组件的产品和应用自行负责。 为尽量减小与客户产品和应用相关
的风险，客户应提供充分的设计与操作安全措施。
TI 不对任何 TI 专利权、版权、屏蔽作品权或其它与使用了 TI 产品或服务的组合设备、机器、流程相关的 TI 知识产权中授予的直接
或隐含权限作出任何保证或解释。 TI 所发布的与第三方产品或服务有关的信息，不能构成从 TI 获得使用这些产品或服务的许可、授
权、或认可。 使用此类信息可能需要获得第三方的专利权或其它知识产权方面的许可，或是 TI 的专利权或其它知识产权方面的许
可。
对于 TI 的数据手册或数据表，仅在没有对内容进行任何篡改且带有相关授权、条件、限制和声明的情况下才允许进行复制。 在复制
信息的过程中对内容的篡改属于非法的、欺诈性商业行为。 TI 对此类篡改过的文件不承担任何责任。
在转售 TI 产品或服务时，如果存在对产品或服务参数的虚假陈述，则会失去相关 TI 产品或服务的明示或暗示授权，且这是非法的、
欺诈性商业行为。 TI 对此类虚假陈述不承担任何责任。
可访问以下 URL 地址以获取有关其它 TI 产品和应用解决方案的信息：
产品
放大器
http://www.ti.com.cn/amplifiers
数据转换器
http://www.ti.com.cn/dataconverters
DSP
http://www.ti.com.cn/dsp
接口
http://www.ti.com.cn/interface
逻辑
http://www.ti.com.cn/logic
电源管理
http://www.ti.com.cn/power
微控制器
http://www.ti.com.cn/microcontrollers
应用
音频
http://www.ti.com.cn/audio
汽车
http://www.ti.com.cn/automotive
宽带
http://www.ti.com.cn/broadband
数字控制
http://www.ti.com.cn/control
光纤网络
http://www.ti.com.cn/opticalnetwork
安全
http://www.ti.com.cn/security
电话
http://www.ti.com.cn/telecom
视频与成像
http://www.ti.com.cn/video
无线
http://www.ti.com.cn/wireless
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www.BDTIC.com/TI