For faster navigation, this Iframe is preloading the Wikiwand page for 降压变换器.

# 降压变换器

## 概念

### 连续模式（CCM）

• 当上述的开关导通（图2的上图），电感两侧的电压为${\displaystyle V_{L}=V_{i}-V_{o))$，流过电感的电流会线性增加，因为二极管被电压源V反向导通，理想上二极管不会有电流。
• 当上述的开关断路（图2的下图），二极管被正向导通，电感两侧的电压为${\displaystyle V_{L}=-V_{o))$（不考虑二极管压降），而电感电流${\displaystyle I_{L))$会线性下降。

${\displaystyle E={\frac {1}{2))L\cdot I_{L}^{2))$

${\displaystyle I_{L))$的变化率可以表示如下：

${\displaystyle V_{L}=L{\frac {dI_{L)){dt))}$

${\displaystyle \Delta I_{L_{\mathit {on))}=\int _{0}^{t_{\mathit {on))}{\frac {V_{L)){L))\,dt={\frac {\left(V_{i}-V_{o}\right)}{L))t_{\mathit {on)),\;t_{\mathit {on))=DT}$

${\displaystyle \Delta I_{L_{\mathit {off))}=\int _{t_{\mathit {on))}^{T=t_{\mathit {on))+t_{\mathit {off))}{\frac {V_{L)){L))\,dt=-{\frac {V_{o)){L))t_{\mathit {off)),\;t_{\mathit {off))=(1-D)T}$

{\displaystyle {\begin{aligned}&\Delta I_{L_{\mathit {on))}+\Delta I_{L_{\mathit {off))}=0\\&{\frac {V_{i}-V_{o)){L))t_{\mathit {on))-{\frac {V_{o)){L))t_{\mathit {off))=0\end{aligned))}

{\displaystyle {\begin{aligned}&(V_{i}-V_{o})DT-V_{o}(1-D)T=0\\&V_{o}-DV_{i}=0\\\Rightarrow \;&D={\frac {V_{o)){V_{i))}\end{aligned))}

### 不连续模式（DCM）

${\displaystyle \left(V_{i}-V_{o}\right)DT-V_{o}\delta T=0}$

${\displaystyle \delta ={\frac {V_{i}-V_{o)){V_{o))}D}$

${\displaystyle {\bar {I_{L))}=I_{o))$

{\displaystyle {\begin{aligned}{\bar {I_{L))}&=\left({\frac {1}{2))I_{L_{max))DT+{\frac {1}{2))I_{L_{max))\delta T\right){\frac {1}{T))\\&={\frac {I_{L_{max))\left(D+\delta \right)}{2))\\&=I_{o}\end{aligned))}

${\displaystyle I_{L_{Max))={\frac {V_{i}-V_{o)){L))DT}$

${\displaystyle I_{o}={\frac {\left(V_{i}-V_{o}\right)DT\left(D+\delta \right)}{2L))}$

${\displaystyle I_{o}={\frac {\left(V_{i}-V_{o}\right)DT\left(D+{\frac {V_{i}-V_{o)){V_{o))}D\right)}{2L))}$

${\displaystyle V_{o}=V_{i}{\frac {1}((\frac {2LI_{o)){D^{2}V_{i}T))+1))}$

### 连续模式和不连续模式的边界

{\displaystyle {\begin{aligned}&DT+\delta T=T\\\Rightarrow \;&D+\delta =1\end{aligned))}

${\displaystyle I_{o_{lim))={\frac {I_{L_{max))}{2))\left(D+\delta \right)={\frac {I_{L_{max))}{2))}$

${\displaystyle I_{o_{lim))={\frac {V_{i}-V_{o)){2L))DT}$

${\displaystyle V_{o}=DV_{i))$

${\displaystyle I_{o_{lim))={\frac {V_{i}\left(1-D\right)}{2L))DT}$

• 正规化电压，定义为${\displaystyle \left|V_{o}\right|={\frac {V_{o)){V_{i))))$。若输出电压${\displaystyle V_{o}=0}$，正规化电压也会是0，若输出电压等于输入电压，正规化电压也是1。
• 正规化电流，定义为${\displaystyle \left|I_{o}\right|={\frac {L}{TV_{i))}I_{o))$。其中的${\displaystyle {\frac {TV_{i)){L))}$等于电感器在一个周期可以增加的电流最大值，也就是在占空比D=1，电感电流的增加量。因此在变换器稳态运作下，若没有输出电流，${\displaystyle \left|I_{o}\right|}$等于0，若输出电流为最大输出电流，则${\displaystyle \left|I_{o}\right|}$会是1。

• 在连续模式下：
${\displaystyle \left|V_{o}\right|=D}$
• 在不连续模式下：
{\displaystyle {\begin{aligned}\left|V_{o}\right|&={\frac {1}((\frac {2LI_{o)){D^{2}V_{i}T))+1))\\&={\frac {1}((\frac {2\left|I_{o}\right|}{D^{2))}+1))\\&={\frac {D^{2)){2\left|I_{o}\right|+D^{2))}\end{aligned))}

{\displaystyle {\begin{aligned}I_{o_{lim))&={\frac {V_{i)){2L))D\left(1-D\right)T\\&={\frac {I_{o)){2\left|I_{o}\right|))D\left(1-D\right)\end{aligned))}

${\displaystyle {\frac {\left(1-D\right)D}{2\left|I_{o}\right|))=1}$

### 非理想电路下的情形

• 输出电容器够大，因此在驱动纯电阻负载时其电压没有显著的变化。
• 二极管的顺向压降为0。
• 开关及二极管都没有切换损失。

#### 输出电压涟波

${\displaystyle dV_{o}={\frac {idT}{C))}$

${\displaystyle dT_{on}=DT={\frac {D}{f))}$

${\displaystyle dT_{off}=(1-D)T={\frac {1-D}{f))}$

## 特殊结构

### 同步整流

${\displaystyle P_{D}=V_{D}(1-D)I_{o))$

• VD是负载电流为Io时，二极管的电压降
• D是占空比
• Io是负载电流

${\displaystyle P_{S2}=I_{o}^{2}R_{DSON}(1-D)}$

## 影响效率的因素

• 晶体管或是MOSFET在导通时的电阻。
• 二极管顺向电降（若是肖特基二极管，约为0.4 V0.7 V）。
• 电感绕组的电阻
• 电容器的等效串联电阻

• 电压-电流重叠的损失
• 切换频率*CV2的损失
• 反向延迟损失
• 因为驱动MOSFET闸及控制器本身耗能产生的损失。
• 晶体管漏电流损失，以及控制器待机功耗[5]

## 阻抗匹配

${\displaystyle \displaystyle V_{o}I_{o}=\eta V_{i}I_{i}TbH_{L}ads}$

• Vo为输出电压
• Io为输出电流
• η为效率（数值在0到1之间）
• Vi为输入电压
• Ii为输入电流

${\displaystyle \displaystyle I_{o}=V_{o}/Z_{o))$
${\displaystyle \displaystyle I_{i}=V_{i}/Z_{i))$

• Zo为输出阻抗
• Zi为输入阻抗

${\displaystyle V_{o}^{2}/Z_{o}=\eta V_{i}^{2}/Z_{i))$

${\displaystyle \displaystyle V_{o}=DV_{i))$

• D为占空比

${\displaystyle (DV_{i})^{2}/Z_{o}=\eta V_{i}^{2}/Z_{i))$

${\displaystyle \displaystyle D^{2}/Z_{o}=\eta /Z_{i))$

${\displaystyle D={\sqrt {\eta Z_{o}/Z_{i))))$

## 参考资料

1. ^ Mammano, Robert. "Switching power supply topology voltage mode vs. current mode." Elektron Journal-South African Institute of Electrical Engineers 18.6 (2001): 25-27.
2. ^ Keeping, Steven. Understanding the Advantages and Disadvantages of Linear Regulators. DigiKey. 2012-05-08 [2016-09-11]. （原始内容存档于2016-09-23）.
3. ^ Guy Séguier, Électronique de puissance, 7th edition, Dunod, Paris 1999 (in French)
4. ^ Tom's Hardware: "Idle/Peak Power Consumption Analysis". [2016-09-12]. （原始内容存档于2019-08-14）.
5. ^ iitb.ac.in - Buck converter (PDF). （原始内容 (PDF)存档于2011-07-16）. 090424 ee.iitb.ac.in
• P. Julián, A. Oliva, P. Mandolesi, and H. Chiacchiarini, "Output discrete feedback control of a DC-DC Buck converter," in Proceedings of the IEEE International Symposium on Industrial Electronics (ISIE’97), Guimaraes, Portugal, 7-11Julio 1997, pp. 925–930.
• H. Chiacchiarini, P. Mandolesi, A. Oliva, and P. Julián, "Nonlinear analog controller for a buck converter: Theory and experimental results", Proceedings of the IEEE International Symposium on Industrial Electronics (ISIE’99), Bled, Slovenia, 12–16 July 1999, pp. 601–606.
• M. B. D’Amico, A. Oliva, E. E. Paolini y N. Guerin, "Bifurcation control of a buck converter in discontinuous conduction mode", Proceedings of the 1st IFAC Conference on Analysis and Control of Chaotic Systems (CHAOS’06), pp. 399–404, Reims (Francia), 28 al 30 de junio de 2006.
• Oliva, A.R., H. Chiacchiarini y G. Bortolotto "Developing of a state feedback controller for the synchronous buck converter", Latin American Applied Research, Volumen 35, Nro 2, Abril 2005, pp. 83–88. ISSN 0327-0793.
• D’Amico, M. B., Guerin, N., Oliva, A.R., Paolini, E.E. Dinámica de un convertidor buck con controlador PI digital. Revista Iberoamericana de automática e informática industrial (RIAI), Vol 4, No 3, julio 2007, pp. 126–131. ISSN 1697-7912.
• Chierchie, F. Paolini, E.E. Discrete-time modeling and control of a synchronous buck converter .Argentine School of Micro-Nanoelectronics, Technology and Applications, 2009. EAMTA 2009.1–2 October 2009, pp. 5 – 10 . ISBN 978-1-4244-4835-7 .